Ans.2 Working Notes (1) For actual (standard) output of 85 kgs. Std. Input is 100 kgs.

For actual output of 1,700 kgs. the Std. input = 100kgs 1700kgs

85kgs =2,000 kgs.

(2) 2,000 kgs of standard input for an actual output of 1,700 kgs. Contains the Materials A and B in the proportion of (40:60) i.e., 800 kgs. of A and 1,200 kgs. of Material B.

(3) Actual Material consumption for 1,700 kgs. of actual output Particulars

A Stock on 1-9-2004 Add: Purchase during Sept. 2004

Less: Stock on 30-09-2004 Material consumed during Sept.2004

(4) Calculation actual purchase price per kg. of material

A =

(Kgs.) Materials

B 35

800 835

5 830

40 1,200 1,240

50 1,190

Rs.3400 Rs.4.25 800kgs

B = Rs.3000 Rs.2.50 1200kgs

Quantity Kg. 35

830 795 40

1190 1150

Statement shoeing Standard and Actual Cost of Actual output Material Standard

Quantity Rate Amount Kg. Rs. Rs.

A 800 4 3,200

B 1,200 3 3,600

Actual Rate Rs. 4.00

4.25 3.00

2.50

Amount Rs. 140.00 3,378.75

120.00 2,875.00

Loss Output

2,000 300 1,700 6,800

2,020 320 1,700 6,513.75

Calculation of Material Variances (a) Material price variance

Actual quantity (Std. price – Actual Price) A = [35 (4 – 4)] + [ 795 ( 4 – 4.25)] B = [40 ( 3 – 3)] +[1,150 ( 3 – 2.50 )]

(b) Material Usage variance Std. rate (Std. quantity – Actual Quantity) A = 4 (800 – 830) B = 3 (1,200 – 1,190)

=Rs.198.75 =Rs. 575

(A) (F) =Rs.376.25 (F)

=Rs.120 =Rs. 30

(A) (F) =Rs.90 (A)

(c) Material Yield Variance Std. rate of output (Actual yield – Std. Yield) =[Rs.6,800 x ( 1,700 kg. – 1,717 kg.)]

1,700

* Std. Yield = Actual std Output Actual input Std. Input

=Rs.68 (A)

85kgs 2020kgs 1717kgs 100kgs

=

(d) Material Mix Variance Actual Quantity ( Std. cost of Std. mix per kg. – Std. cost of actual mix per kg. )

Solutions of Standard Costing

Rs. 6800 Rs. 6890* = 2020 kgs 2000 kgs 2020 kgs

*[(830 kgs. x Rs.4)] + [(1,190 kgs x Rs.3 )]

=Rs.22(A)

=Rs.6,890

(e) Total Materials Cost Variance Std. Cost – Actual Cost =Rs.6,800 – Rs.6,513.75

Summary of Material variance Price variance Usage variance 1. Yield variance 2. Mix variance Total Material cost variance

=Rs.286.25 (F)

(Rs.) 376.25 (F)

68 (A) 22 (A) 90 (A)

286.25 (A)

Ans. 3: Working Note: Standard cost

Component

A

B

Total Input (-) Loss Total output

Solution

Qty. Kg. 48

112

160 16(10%) 144

Rate Rs. 10

30

Amount Rs.

480

224

704

Kg.

Actual cost Qty.

72 (B.F.)

108

180 36 144 5,360

Rate Amount Rs. 12

8

Rs. 864

864

1728

Revised std.quantity Oty. Kg. 54

126

180

—

(i) Mix variance

(ii) Yield variance

= Std. price (Revised Std. quantity – Actual quantity) A: 10 × (54-72) = 180 (A) B: 2 × (126-108) = 36 (F)

144 (A) = Std. price of yield (Actual yield – Std. yield for actual

mix)

= Rs. 880 × (144 –180×90%) = Rs. 88 (A) 180

(iii) Price variance =Actual qty. (Std. price – Actual price.) A: 72 × (10-12) = 144 (A) B: 108 × (2-8) = 648 (A)

792 (A)

A: 10 × (48-72) = 240 (A) B: 2 × (112-108) = 8 (F)

232 (A)

(iv) Total usage variance = Std. price (Std. qty. – Actual qty.)

Ans. 4: Take the good output of 182 kgs. The standard quantity of material required for 182 kg. of output

is

Statement showing the standard and actual costs and standard cost of actual mix Standard cost

Component

A (40% of 202.22 kg.) B (60% of 202.22 kg.) Total Input (-) Loss Total output

121.33

202.22 20.22 182.00

30 3,639.90

8,493.30

110

200 18 182 5,360 —

34 3,740

5,360

120

200

Qty. Kg. 80.89

Rate Rs. 60

Amount Rs.

4,853.40 Kg. 90

182 100 202.22 90

Actual cost Qty. Rate Amount

Rs. 18

Rs. 1,620

Revised std.quantity Oty. Kg. 80

Standard yield in actual input is 90 % of 200 kg. i.e. 180 kg. Variances :

(i) Price variance =Actual qty. (Std. price – Actual price.) A: 90 × (60-18) = 3780 (F) B: 110 × (30-34) = 440 (A)

3340 (F)

A: 60 × (80.89-90) = 546.60 (A) B: 30 × (121.33-110) = 339.90 (A)

206.70 (A) = Std. price (Revised Std. quantity – Actual quantity) A: 60 × (80-90) = 600 (A) B: 30 × (120-110) = 300 (F)

300 (A) = Std. price of yield (Actual yield – Std. yield for actual

mix)

= Rs.

(v) Total variance

8493.30 182 200 ) = Rs. 93.30 (F) × (182 –

202.22 182

(ii) Total usage variance = Std. price (Std. qty. – Actual qty.)

(iii) Mix variance

(iv) Yield variance

= Std. cost – Actual cost = Rs. 8,493.30 – Rs. 5,360 = Rs. 3133.30 (F)

Note : (iii) and (iv) above are subparts of total usage variance Proof : Price variance + Mix variance + Yield variance = Total variance

Rs. 3340 (F) + Rs.300 (A) + Rs. 93.30 (F) = Rs. 3133.30 (F)

Ans. 5: Working Notes : (i) Since the actual output is 1,000 units, the standard quantity of materials required for the actual

output is 1,000 units × 4 kgs. = 4,000 kgs. (ii) Statement showing computation of standard cost, standard cost of actual quantity and actual

cost.

Material Std. cost per Kg.

Actual cost per Kg.

Rs.

Std. qty in Kgs.

Actual qty in Kgs.

Rs.

Std. cost (Std. qty × Std. price) Rs.

Std. cost of actual qty. (Actual qty. × Std. price) Rs.

Actual cost (Actual qty. × Actual price) Rs.

a b c d e = a×c f = a×d g = b×d

A B C D

1.25 1.50 3.50 3.00

1.30 1.80 3.40 3.00

1,200 1,600

800 400

4,000

1,180 1,580

830 440

4,030

1,500 2,400 2,800 1,200 7,900

1,475 2,370 2,905 1,320 8,070

1,534 2,844 2,822 1,320 8,520

(iii) Standard cost per unit of the standard mix

=

(iv)

Rs. 7,900 4,000 Kgs. = Rs.1.975

Standard cost per unit of the actual mix = Rs.8070 Rs.2.002 4030kgs

Variances: (i) Price variance = Actual qty. (Std. price – Actual price)

= Rs.8,070 – Rs. 8,520 = Rs. 450 (A) = Total actual qty. (Std. cost per unit of (ii) Mix variance

std.mix – Std. cost per unit of actual mix) = 4,030 Kgs. (Rs. 1.975 – Rs. 2.002) = Rs. 110 (A) = Std. price per unit of std. mix (Total std. qty – (iii) Sub usage variance

Total actual qty.) = Rs. 1.975 (4,000 – 4,030) = Rs. 60.00 (A)

(iv) Total material cost variance = Std. cost – Actual cost = Rs. 7,900 – Rs.8,520 = Rs. 620 (A)

Price variance + Mix variance + Sub-usage variance Rs. 450 (A) + Rs. 110 (A) + Rs. 60 (A) = Rs. 620 (A)

= Total variance Proof :

Note : ‘Mix variance’ and sub usage variance are sub-part of total usage variance which may be calculated as below:

Usage variance = Std. price (Std. qty. – Actual qty.) = Standard cost – Standard cost of actual quantity = Rs. 7,900 – Rs. 8,070 = Rs. 170 (A)

Ans.6 Basic data for calculation of Labour variances Category of Workmen Standard

Weeks Rate Amount Rs. Rs.

1,80,000 60 3,000 Skilled 43,200 36 1,200 Semi – Skilled 43,200 24 1,800 Unskilled

Total 6,000 2,66,400

Weeks

2,560 1,600 2,240 6,400

Actual Rate Rs.

65 40 20

Amount Rs.

1,66,400 64,000 44,800

2,75,200

Calculation of Labour variances (1) Direct Labour Cost Variance

Std. cost for actual output – Actual Cost =2,75,200 – 2,66,400 =Rs.8,800 (A)

(2) Direct Labour Rate Variance Actual time (Std. rate – Actual rate) Skilled = 2,560 (60 – 65) Semi – Skilled =1,600 (36 – 40) Unskilled =2,240 (24 – 20)

=Rs.12,800 (A) =Rs. 6,400 (A) =Rs. 8,960 (F) =Rs.10,240(A)

(3) Direct Labour Efficiency Variance Std. rate ( Std. time for actual output – Actual time) Skilled =60(3,000 -2,560 ) =Rs.26,400 (F) Semi – Skilled =36 (1,200 -1,600) =Rs.14,400 (A) Unskilled =24 (1,800 – 2,240) =Rs.10,560(A) Direct Material efficiency Variance can be further analysed into:

Direct Labour Mix Variance Std. rate ( Revised Std. time – Actual time) Skilled =60(3,200 -2,560 ) Semi – Skilled =36 (1,280 -1,600) Unskilled =24 (1,920 – 2,240) * Revised Std. time

=Rs.1,440(F)

(a)

=Rs.38,400 (F) =Rs.11,520 (A) =Rs. 7,680 (A)

=3,200

=Rs.19,200 (F)

Skilled =6,400 x 3,000 6,000

=6,400 x 1,200 6,000

Semi- skilled =1,280

=6,400 x 1,800 =1,920 6,000

(b) Direct Labour Revised Efficiency variance Std. rate ( Std. time for actual output –Revised Std. time) Skilled =60(3,000 -3,200 ) =Rs.12,000 (A) Semi – Skilled =36 (1,200 -1,280) =Rs. 2,880 (A) Unskilled =24 (1,800 – 1,920) =Rs. 2,880 (A)

Summary of Labour variances Rate variance Efficiency variance (a) Mix variance 19,200 (F) (b) Revised efficiency variance 17,760 (A) Direct Material cost variance

Unskilled

=Rs.17,760(A) (Rs.)

10,240 (A)

1,440 (F) 8,800 (A)

Ans. 7: In a 40 hour week, the standard gang should have produced 1,000 std. hours as shown below: Gang: -

Skilled Semi - skilled Unskilled

16 No. of workers × 40 hrs. 6 No. of workers × 40 hrs. 3 No. of workers × 40 hrs.

640 240 120

1,000 hours

However, the actual output is 900 standard hours. Hence to find out the total labour cost variance, the standard cost (or cost charged to production) is to be computed with reference to 900 standard hours. This is done in the following statement:

Statement showing the Standard cost, Actual cost and Standard cost of Actual time for Actual output, i.e. 900

Standard hours. Gang Standard cost Actual cost Standard cost of

Actual time Rate Amount Hours Rate Amount

Rs Rs. Rs. Rs. Skilled

Hours Rate Rs.

600 900 1000 576

Amount Rs.

Hours

3 1,728 14×40 = 560 4 2,240 560 3 1,680 Semi-skilled

240 900 1000 216 2

Unskilled 120 900 1000 108 1

900 2.52

432 9 × 40 = 360

2 × 40 = 80 1,000

3

2 3.48

1,080

160 3,480

360

80 1,000

2

1 2.48

720

80 2,480

108 2,268

Variances: (i) Rate variance = Actual time (Std. rate – Actual rate)

= (Standard cost of actual time – Actual cost) = Rs. 2,480 – Rs.3,480 = Rs. 1,000 (A) = Total actual time ( Std. rate of std. gang–

Std. rate of actual gang) = 1,000 (Rs. 2.52 – Rs. 2.48) = Rs. 40(F) = Std. rate (Total std. time – Total actual time) = Rs. 2.52 (900 hours – 1,000) = Rs. 252 (A) = Std. labour cost – Actual labour cost = Rs. 2,268 – Rs. 3,480 = Rs. 1,212 (A)

(ii) Gang variance

(iii) Sub-efficiency variance

(iv) Total labour cost variance

The gang composition variance may also be known as labour mix variance and is part of efficiency variance which may be computed as under: Efficiency variance = Std. rate (Std. time – Actual time)

= Standard cost – Std. cost of actual time = Rs. 2,268 – Rs. 2,480 = Rs.212 (A)

Rs. 5,000

Rs. 4,500 Rs. 2.25 Rs. 2.00 500 hrs.

Ans. 8: Standard cost charged to production (1,000 units× 2.5 hours × Rs.2)

Actual wages paid Actual wage rate per hour (Rs. 4500÷2000) Std. wage rate per hour Abnormal idle time (25% of 2,000 hours) Variances :

(i) Wage rate variance = Actual time (Std.rate – Actual rate)

= 2,000 hours (Rs.2 – Rs.2.25) = Rs.500 (A) (ii) Efficiency variance

(iii) Idle time variance

(iv) Total variance

*Actual time less idle time.

Ans.9 Basic data for Standard and actual labour cost of producing 1,000 articles of ‘A’ and standard cost of actual labour hours

Standard Cost Actual Cost Labour Hours Rate Amount Hours Rate Amount Std. cost of

Rs. Rs. Rs. Rs. actual labour hours ( Actual hours x Std. rate)Rs 27,000 36,000 4.00 9,000 30,000 3.00 10,000 Skilled 12,600 12,600 1.50 8,400 12,000 1.50 8,000 Semi – Skilled 20,000 18,000 0.90 20,000 16,000 1.00 16,000 Unskilled

Total 34,000 58,000 37,400 66,600 59,600

Calculation of Labour variances (1) Labour Cost Variance

Std. cost – Actual Cost =Rs.58,000 – Rs.66,600

= Std. rate (Std.time – Actual time*) Rs.2 (2,500 hrs. –1500 hrs.) = Rs. 2,000 (F)

= Idle time × Std.rate = 500 hrs. × Rs. 2 = Rs. 1,000 (A) = Std.labour cost – Actual labour cost

Rs. 5,000 – Rs. 4,500 = Rs. 500 (F)

=Rs.8,600 (A)

(2) Labour Rate Variance Actual Hours (Standard rate – Actual rate)

OR

Std. cost of actual hours – Actual Cost =Rs.59,600 – Rs.66,600

(3) Labour Efficiency Variance Std. rate of Std. mix (Total Std. hours for actual output – Total Actual hours)

=Rs.7,000 (A)

=

(4)

Rs. 58000 34000 37400 34000

=Rs.5,800(A)

Labour Mix Variance Total actual hours ( Std. rate of standard mix – Std. rate of actual mix)

58000 59600 = 34000

34000 37400 Summary of Labour variances Rate variance Efficiency variance Mix variance

Labour Cost variance

=Rs.4,200(F)

(Rs.) 7,000 (A) 5,800 (A) 4,200 (F) 8,600 (A)

Ans. 10: (i) Variable overhead variance: = (Standard variable overhead – Actual variable overhead) = (Rs. 2,40,000 – Rs. 2,00,000) = Rs. 40,000 (Favourable) (Refer to Working note 1) (ii) Variable overhead budget variance: = (Budgeted variable overhead for actual hours – Actual variable overhead) = Rs. 2,24,000 – Rs. 2,00,000 = Rs. 24,000 (Favourable) (Refer to Working note 2) (iii) Variable overhead efficiency variance: = Standard variable overhead rate per hour [Std. hours for actual output – Actual hours] = Rs. 2 [1,20,000 hours – 1,12,000 hours] = Rs.2 × 8,000 hours = Rs. 16,000 (Favourable) Working notes: (1) Standard variable overhead = Standard cost of actual output = 20,000 units × 6 hours × Rs. 2

= Rs. 2,40,000 (2) Budgeted variable overhead (for actual hours)

= 1,12,000 hours × Rs.2 = Rs.2,24,000

Ans. 11: Actual output = 9,000 units Idle time = 5,000 hours Production time (Actual) = 1,05,000 hours Standard hours for actual production = 10 hours / unit 9,000 units = 90,000 hours.

Labour efficiency variance = 3,75,000 (A) i.e. Standard rate (Standard Production time – Actual production time) = 3,75,000(A). SR (90,000 – 1,05,000) = – 3,75,000

SR

(i) (ii)

3,75,000 Rs. 25

15,000 Idle time variance = 5,000 hours 25 Rs. / hour = 1,25,000. (A) Standard Variable Overhead = Rs. 150 / unit Standard hours = 10 hours / unit Standard Variable Overhead rate / hour = 150 / 10 = Rs. 15 / hour Total Variable Overhead variance = Standard Variable Overhead – Actual Variable Overhead

= Standard Rate Standard hours – Actual rate Actual hours = =

(15) (10 9,000) – 16,00,000 13,50,000 – 16,00,000

Total Variable Overhead Variance = 2,50,000 (A)

(iii) Variable Overhead Expenditure Variance = (Standard Rate Actual Hours) – (Actual Rate Actual Hours) = =

(15 1,05,000) – 16,00,000 15,75,000 – 16,00,000

= 25,000 (A) (iv) Variable Overhead Efficiency Variance = Standard Rate (Standard Hours for actual output – Actual hours for Actual output)

= = =

(b) Alternative Solution Actual Output = 9,000 Units Idle time = 5,000 hrs Direct Wages Paid = 1,10,000 hours @ Rs. 22 out of which 5,000 hours being idle, were not recorded in production. Standard hours

or Standard Rate (Standard Time – Actual Time) = – 3,75,000 Or Standard Rate = Rs 25/-

(i) Idle time variance = Standard Rate Idle time 25 5,000 = Rs 1,25,000 (A) (ii) Standard Variable Overhead / unit = 150

Standard Rate = 150 Rs.15/hour 10

= 16,00,000

= 16,00,000 = 2,50,000 (A) = Standard Variable Overhead for

actual hours – Actual Variable Overhead

= = =

(iv) Variable overhead efficiency variance

(150 1,05,000) – 16,00,000 15,75,000 – 16,00,000 25,000 (A)

=

=

= = =

15 (90,000 – 1,05,000) 15 (–15,000) 2,25,000 (A)

= 10 per unit. Labour efficiency variance = Rs. 3,75,000 (A)

Standard Quantity = 10 hours Actual Variable Overhead

Actual Variable Overhead Total Variable Overhead Variance (iii) Variable Overhead expenditure

Standard Variable Overhead = 150 9,000 = 13,50,000

Standard Variable Overhead for actual output Standard Variable Overhead for Actual hours) 15 (10 hours 90,000 units – 1,05,000) 15 (90,000 – 1,05,000) 15 (–15,000) 2,25,000 (A)

–

Ans.12: Computation of standard cost and actual cost Standard Cost

Direct Materials Direct Labour Variable Overheads Total standard Costs

Actual Costs Direct Materials

(6,000 x Rs.12) (6,000 x Rs.4.40) (6,000 x Rs.3)

(a)

(12,670meters x Rs.5.70)

72,000 26,400 18,000

1,16,400

Direct Wages Variable Overheads Total Actual Costs Total Variance

(b) (a)-(b)

72,219 27,950 20,475

1,20,644 4,244,(A)

Computation of Missing figures (1) Actual Labour hours Standard variable overhead rate hour (Standard hours – Actual hours) = Rs.1,500 (A) Rs.1,500 A =Rs.3 (6,000 x 1 hour – Actual hours) Rs.1,500 A =Rs.18,000 –(Rs.3 x actual hours) (Rs.3 x Actual hours) =Rs.18,000 + Rs.1,500 Actual hours =Rs.19,500 / 3 = 6,500 hours

= Actual wages paid =Rs.27,950 Total Actual hours 6,500 hours

Computation of Material Labour and Variable Overhead Variances 1. Material variances

(1) Material Cost Variance Standard Cost- Actual Cost =(Rs.72,000 – Rs.72,219)

(2) Material Price Variance Actual Quantity of Material consumed (Std, price- Actual Price) =12,670 meters (Rs.6- Rs.5.70)

(3) Material Usage Variance Standard price (Standard Quantity –Actual Quantity) =Rs.6 (12,000 metres -12,670 metres)

2. Labour Variances

(1) Labour Cost Variance Standard Cost- Actual Cost =(Rs.26,400 – Rs.27,950)

(3) Labour Rate Variance Actual hours (Std. wage rate per hour- Actual wage rate per hour) =6,500 hours (Rs.4.40- Rs.4.30)

(3) Labour Efficiency Variance Standard rate per hour (Standard hours –Actual hours) =Rs.4.40 (6,000 hours- 6,500 hours)

Variable Overhead Variances

(2) Actual Wage rate hour =Rs.4.3

=Rs.219 (A)

=Rs.3,801 (F)

=Rs.4,020 (A)

=Rs.1,550 (A)

=Rs.650 (F)

=Rs.2,200 (A) 3.

(1) Total Variable overhead Variance Standard Variable Overhead- Actual Variable Overhead =Rs.18,000 – Rs.20,475 =Rs.2,475 (A)

(4) Variable overhead Efficiency Variance Standard Variable overhead rate per hour (Std. hours for actual output-Actual hours) =Rs.3 ( 6,000 – 6,500) =Rs.1,500 (A)

(3) Variable overhead Budget Variance Budgeted variable overhead –Actual variable overhead) =(Actual hours worked x Std. variable overhead per hour) – Actual variable overhead =(6,500 x Rs.3 ) – Rs.20,475 =Rs.975 (A)

Note: (F) denoted Favourable Variance; (A) denoted Adverse Variance

Ans 13: Working Notes :

1. Standard cost of raw-material consumed : Total standard cost of ZED (1,000 units × Rs.21) Less: Standard cost : Labour 8,000

Rs. Rs. 21,000

Overheads Standard cost of raw materials used

2. Standard cost of raw–material per finished unit.

1,600 9,600 11,400

3. Standard quantity of raw - material per finished unit and total quantity of raw material required:

Total quantity – 3.8 kg. × 1,000 units = 3,800 kgs. 4. Total material cost variance :

Actual cost of raw material Rs.10,000 Standard cost of raw material Rs.11,400 Total material cost variance Rs. 1,400 (F)

5. Actual quantity (A Q) of raw–material (in kgs): Material usage variance = Standard rate (Standard quantity – Actual quantity). or, Rs. 600 (A) = Rs. 3 (3,800 Kgs. – AQ) or, 3AQ = 12,000 kgs. or, AQ = 4,000 kgs.

(Material usage variance is as given in the question and standard quantity is as per (3) above )

6. Actual rate of raw material per kg

7. Standard direct labour rate Standard direct labour hours = 1,600 (given) Standard direct labour cost = Rs. 8,000 (given)

8. Actual labour cost and actual labour rate per hour: Actual total cost of 1,000 units Rs. 21,070 1,000 units (Rs. 21 + Re. 0.07)

Rs. 10,000 Less : Actual cost of material Actual variable overheads Rs. 1,62 Rs. 11,620 Actual direct labour cost Rs. 9,450

9. Standard labour hours to produce one unit:

10.

11.

Standard labour cost per unit: Standard labour cost per unit = 1.6 hours × Rs. 5 = Rs.8

Actual hourly rate of variable overheads

: Standard qu antity of raw material per unit of ZED : 3.8 kg. (Refer to working note 3). Standard direct labour rate per hour Rs. 5 (Refer to working note 7).

(a) (b)

(c) (d) (e)

Standard direct material cost per unit of ZED : Rs. 11.40 (Refer to working note 2 ) . Standard direct labour cost per unit of ZED: Rs. 8 (Refer to working note 10). Standard total material cost for the output: Rs. 11,400 (Refer to working note 1). (f) Actual

Material price total direct labour cost for the output: Rs. 9,450 (Refer to working note 8). (g) variance = Total material cost variance – Material usage variance.

= Rs. 1,400 (favourable)* – Rs. 600 (Adverse) (*Refer to working note 4)

= Rs. 2000 (Favourable) Alternatively,

= Actual quantity (Standard rate – Actual rate) = 4,000 units (Rs. 3 – Rs. 2.50)* = Rs. 2,000 (Favourable)

(h) Labour rate variance: = Actual hours (Standard rate – Actual rate) = 1,800 hours (Rs. 5 – Rs. 5.25) = Rs. 450 (Adverse)

(i) Labour efficiency variance: Standard rate (Standard hours – Actual hours) = Rs. 5 per hour (1,600 hours – 1,800 hours) = Rs. 1,000 (Adverse) Variable overhead expenditure variance : = Actual hours (Standard rate – Actual rate)

(* Refer to working note 6)

(j)

= 1,800 hours (Re. 1 – Re. 0.90)* = Rs. 180 (Favourable) (*Refer to working note) (k) Variable overhead efficiency variance

= Standard rate (Standard hours – Actual hours) = Re. 1 per hour (1,600 hours – 1,800 hours) = Rs. 200 (Adverse)

Ans. 14: Budgeted daily hours per day of June =

Actual available hours for June Calendar Variance

12000hrs 500hrs / day 24days

= 500 hours × 25 days = 12,500 hours = Std. fixed overhead rate per hr

(No. of hrs. in actualperiod– No. of hrs. in budgeted period) = Re.0.50 (12,500 hours – 12,000 hours) = Rs. 250 (F)

Alternatively, this variance can be calculated by using number of days instead of hours. In that case, overhead rate will be on per day basis.

Ans. 15:Actual output : 8,400 hours × 22days × 1.2 units per hour = 2,21,760 units. Standard output per man hour: 1 Standard hours produced or std. hrs. for actual production :2,21,760 units×1 hr. = 2,21,760 hrs. Budgeted hrs. in budgeted days: 8,000 hours × 20 days = 1,60,000 hours Budgeted hours (capacity) in actual working days: 8,000 hrs. × 22 days = 1,76,000 hours Actual hours worked: 8,400 hours × 22 days = 1,84,800 hours Overheads as per budget: 8,000 hours × 20 days × Rs. 2 per hour = Rs.3,20,000

(a) Standard cost charged to production : 2,21,760 hours × Rs.2 (b) Actual hours worked × Standard rate : 1,84,800 hours × Rs.2 (c) Budgeted hours in actual days × Std. rate: 1,76,000 × Rs.2 (d) Overheads as per budget (e) Actual overheads

= Std.fixed overhead rate per hour (Std. hrs. for Efficiency variance production – Actual hrs.)

= Rs.2 (2,21,760 hours – 1,84,800 hours) = Rs.73,920 (F) = Standard fixed overhead rate per hour (Actual capacity – Capacity variance

Budgeted capacity) = Rs.2 (1,84,800 hours – 1,76,000 hours) = Rs.17,600 (F) = Standard fixed overhead rate per hour (Budgeted hrs. in Calendar variance

actual days – Budgeted hrs. in budgeted days) = Rs.2 (1,76,000 hours – 1,60,000 hours) = Rs.32,000 (F) = Standard fixed overhead rate per hour Volume variance

(Actual volume in hrs. – Budgeted volume in hrs.) = Rs.2 (2,21,760 hours – 1,60,000 hours) = Rs. 1,23,520(F) = Budgeted expenses – Actual expenses Expenses variance = Rs.3,20,000 – Rs.3,25,000 = Rs.5,000 (A) = Overheads charged to production – Actual overheads Total variance = Rs. 4,43,520 – Rs.3,25,000 = Rs. 1,18,520 (F)

OR Rs.

Efficiency variance : (a – b) 73,920 (F) Capacity variance : (b – c) 17,600 (F) Calendar variance : (c – d) 32,000 (F) Volume variance : (a – d) 1,23,520 (F) Expense variance : (d – e) 5,000 (A)

: (a – e) 1,18,520 (F) Total variance

Rs. 4,43,520 3,69,600 3,52,000 3,20,000 3,25,000

Ans. 16: (a)Total fixed overhead variance = Absorbed fixed overheads – Actual fixed overheads = (5,200units× Rs. 2) – Rs. 10,200 = Rs.200 (F)

(b) Expenditure variance

(c) Volume variance

= Budgeted overheads–Actual overheads = Rs. 10,000 – Rs. 10,200 = Rs. 200(A) = Standard rate of absorption per unit ×

(Actual production – Budgeted production = Rs.2 (5,200 units —5,000 units)=Rs. 400 (F)

This can be divided into capacity variance and efficiency variance as shown below : Capacity variance = Standard rate of absorption per hour (Actual hours capacity – Budgeted

hours capacity) = Re. 0.50 (20,100 hours – 20,000 hours) = Rs 50(F)

= Standard rate of absorption per hour (Standard hours required – Actual hours)

= Re.0.50 (20,800 hours – 20,100 hours) = Rs.350 (F)

Efficiency variance

Working Notes :

Std. fixed overhead rate of absorption per unit =

Std. fixed overhead rate of absorption per hour:

Rs.10000 Rs.2 5000units

Rs.10000 Re.0.50 5000units 4hrs.

Std. hours required for actual production: 5,200 units × 4 hours = 20,800 hours

Ans. 17:

Working Notes:

1) Budgeted output in units 40,000 man hours X 3.2 units per man hours

2) Standards variable overhead rate per unit Rs, 1,02,400/1,28,000 units

3) Standard variable overhead rate per man hour Rs. 1,02,400/40,000 man hours

4) Standard fixed overhead rate per unit Rs 32,000/1,28,000 units

5) Actual Production units 43,000 man hours X 3 units per man hour

Computation of variable Overhead variances:

i) Total Variable Overhead Variances = Variable overhead recovered on actual output – Actual variable overhead = (1,29,000 units X 0.80 P – Rs. 1,14,000) = Rs. 11,200 (A)

= 1,28,000 units.

= Rs. 0.80 per unit

= Rs. 2.56 per man hour

= Rs. 0.25 per unit

= 1,29,000 units

ii) Variable Overhead Expenditure Variance = Budgeted variable overhead for actual hours – Actual Variable overhead = (43,000 X 2.56 – Rs. 1,14,400) = Rs. 4,320 (A)

iii) Variable Overhead Efficiency Variance = Standard variable overhead rate per hour (Standard hours for actual output- Actual hours) = Rs. 2.56 (40,312.5 hours – 43,000 Hours) = Rs. 6,880 (A)

Computation on Fixed Overhead Variances: i) Total Fixed Overhead Cost Variance

= Fixed overhead recovered on actual output – Actual fixed overhead = (1,29,000 units – 0.25 P – Rs. 31,500) = Rs. 750 (F)

ii) Fixed Overhead Expenditure Variance = Budgeted fixed overhead – Actual fixed overhead = (Rs. 32,000 – Rs. 31,500) = Rs. 500 (F)

iii) Fixed Overhead Volume Variance = Standard fixed overhead per unit (Actual output units – Budgeted output units) = 0.25 P (1,29,000 – 1,28,000) = Rs. 250 (F)

iv) Fixed Overhead Efficiency Variance = Standard fixed overhead rate per unit (Actual Quantity – Standard Quantity)

= 0.25 P (43,000 hours X 3.2 units – 1,29,000 units) = Rs. 2,150 (A)

actual days) v) Fixed Overhead Capacity Variance

= Standard fixed overhead rate per hour (Actual capacity hours – Budgeted capacity hours in = (Rs. 32,000/40,000 hours) (43,000 – 21 days X 2,000 hours) = Rs. 800 (F)

vi) Calendar Variance = (Budgeted Days – Actual Days) Standard fixed overhead per day = (20 days – 21 days) (Rs. 32,000/20 days) = Rs. 1,600 (F)

Computation of Total Overhead Variances = Total variable overhead variances + Total fixed overhead variances = Rs. 11,200 (A) + Rs. 750 (F) = Rs. 10,450

Ans. 18: Basic calculation: Product Budgeted

price Actual Budgeted Actual Budgeted Actual Actual

price quantity quantity sales quantity at sales budgeted

sales Price

b c d (e)=a × c f=(a × d) g=(b × d) Rs. Rs. Rs. Rs.

2,000 2,400 5,000 6,000 7,200 3.00 1,500 1,400 7,500 7,000 6,300 4.50 1,000 1,200 7,500 9,000 8,400 7.00

500 400 5,000 4,000 4,200 10.50 5,000 5,400 25,000 26,000 26,100

A B C D

a Rs.

2.50 5.00 7.50

10.00

Computation of Variances : Sales price variance = Actual quantity (Actual price – Budgeted price)

= Actual sales – Standard sales = Rs.26,100 – Rs. 26,000 = Rs.100(F)

Sales volume variance = Budgeted price (Actual quantity – Budgeted quantity) = Std. sales – Budgeted sales = Rs.26,000 – Rs.25,000 = Rs.1,000 (F)

Total variance = Actual sales – Budgeted sales = Rs.26,100 – Rs.25,000 = Rs.1,100 (F)

Average budgeted price per unit of budgeted mix:

Average budgeted price per unit of actual mix: Hence, Sales mix variance = Actual total qty. (Budgeted price per unit of actual mix –

Budgeted price per unit of budgeted mix)

= 5,400 units (Rs.4.815—Rs.5.00) = Rs. 1,000 (A)

Sales quantity variance = Budgeted price per unit of budgeted mix = (Actual total qty. – Budgeted total qty.) = Rs.5 (5,400 – 5,000) = Rs. 2,000 (F)

Note: Instead of computing average price, one may use total figures to do away with the effect of rounding off.

For example, in case of sales mix variance figures may be as under:

= Rs. 26,000 – Rs 27,000 = Rs.1,000 (A)

Ans. 19: A. (a) Analysis of variances to show the effects on turnover : B. Working Notes : ( 1 ) Budgeted sales :

Budgeted sales units at budgeted (or standard) prices. Units

Bravo Champion Super

(2) Actual sales : Actual sales units at actual prices

Units Price

Bravo Champion Super

5,750 4,850 5,000

15,600

Rs. 120 180 165

Amount Rs.

6,90,000 8,73,000 8,25,000

23,88,000

5,000 4,000 6,000 15,000

Price Rs. 100 200 180

Amount Rs.

5,00,000 8,00,000

10,80,000 23,80,000

Standard sales: Actual sales units at Budgeted (or Standard) prices.

Units Price Amount Rs. Rs.

Bravo 5,750 100 5,75,000 Champion 4,850 200 9,70,000 Super 5,000 180 9,00,000

15,600 24,45,000 Computation of Variances : (i) Sales price variance = Actual quantity (Actual price – Budgeted price)

or Actual sales – Standard sales

(3)

= Rs.23,88,000 – Rs.24,45,000 = Rs.57,000 (A) (ii) Sales mix variance = Total actual quantity (Budgeted price of actual mix – Budgeted price of

budgeted mix

Rs.2445000 Rs.2380000 15600units 15600 15000

=Rs. 2475200 – Rs. 2380000 = Rs. 95200F

(iii) Sales quantity variance = Rs. 24,45,000 – Rs. 24,75,200 = Rs. 30,200 (A) = Budgeted price of budgeted mix ×

(Total actual quantity – Total budgeted quantity)

Rs. 23,80,000 = 15,000 units ( 15,600 units – 15,000 units)

= Rs. 24,75,200 – Rs. 23,80,000 = Rs. 95,200 (F) (iv) Total sales value variance = Actual sales – Budgeted sales

= Rs.23,88,000 – Rs.23,80,000 = Rs. 8,000 (F) (b) Analysis of variances to show the effects on profit : Working Notes : (1) Budgeted margin per unit

Bravo Champion Super

(2) Actual margin per unit

Sales price Rs. 100 200 180

Cost Rs.

90 170 130

Margin Rs.

10 30 50

Computation of variances: (i) Sale margin price variance Actual quantity (Actual margin – Budgeted margin)

or Actual profit – Standard profit

Rs. 3,96,000 – Rs. 4,53,000 = Rs. 57,000 (A) (ii) Sales margin mix variance = Total actual quantity (Budgeted margin on actual mix – Budgeted Margin on budgeted mix

= Rs. 4,53,000 – Rs. 4,88,800 = Rs. 35,800 (A) (iii) Sales quantity variance

= Budgeted margin on budgeted mix (Total actual qty. – Total budgeted qty.)

= Rs. 4,88,800 – Rs. 4,70,000 = Rs. 18,800 (F) (iv) Total sales margin variance = Actual profit – Budgeted profit

= Rs. 3,96,000 – Rs. 4,70,000 = Rs. 74,000 (A)

Ans. 20:Working Notes: 1. Statement of budgeted average contribution margin per unit for the year 1995:

Product different PC models

Budgeted contribution margin per unit of each

product (Rs.)

PC Portable PC Super PC

10,000 6,000

40,000

=

Budgeted sales volume

(Units) 7,000 1,000 2,000

Total budgeted contribution

margin (Rs.)

7,00,00,000 60,00,000

8,00,00,000

Budgeted average contribution margin per unit

10,000 15,60,00,000 Rs.15,60,00,000

10,000 units = Rs.15,600

2. Actual market share percentage = Actual sales of - 3 PC models Actual industry sales

11,000 units 68,750 units

× 100

= × 100

= 16

3. Actual sales mix percentage of product = Actual sales of Product Total Actual sale of 3 PC models

= 8,250 units 11,000 units

1,650 units 11,000 units

× 100

Actual sales mix percentage of product PC × 100 = 75

× 100 = 15

× 100 = 10

Actual sales mix %age of product Portable PC =

Actual sales mix %age of product Super PC

(i)

= 1,100 units 11,000 units

Computation of individual product and total sales volume variance

Actual Budgeted Budgeted contribution Sales Sales Sales =

Volume Volume margin per

in units in units unit

Individual product sales volume variance: PC = (8,250 units – 7,000 units) × Rs.10,000 = Rs.1,25,00,000 (Fav.) Portable PC = (1,650 units – 1,000 units) × Rs.6,000 = Rs.39,00,000 (Fav.) Super PC = (1,100 units – 2,000 units) × Rs.40,000 = Rs.2,60,00,000 (Adv.) Total Sales Volume Variance = Rs.1,96,00,000 (Adv.)

(ii) Computation of total sales quantity variance:

Total sales quantity variance = Total actual sales Unit

Budgeted average Total Budgeted contribution margin Sales units per unit

= (11,000 units – 10,000 units) × Rs.15,600 = Rs.1,56,00,000 (Fav.) (iii) Computation of the market size and market share variance

1. Market size variance:

Budgeted market Share %age = Actual Industry Budgeted Industry Sales in units Sales in units contribution margin

per unit

Budgeted average

= 0.20 (68,750 units – 50,000 units) × Rs.15,600 = Rs.5,85,00,000 (Fav.) 2. Market share variance:

= Actual Total Budgeted average

Actual market Budgeted market Sales Volume Contribution margin share percentage share percentage in units per unit

= (0.16 – 0.20) × 68,750 units × Rs.15,600 = Rs.4,29,00,000 (Adv.) (iv) Computation of individual product and total sales mix variances

1. Individual product and total sales mix variance: Sales mix variance:

Budgeted Actual sales Budgetedsales ActualTotal Individual mix %ageof mix %ageof SalesVolume

on Contributi in units product product margin

Budgetedaverage contributi on margin

PC*** = (0.75 – 0.70) × 11,000 units × (Rs.10,000 – Rs.15,600) = Rs.30,80,000 (Adv.)

Super PC****= (0.10 – 0.20) × 11,000 units × (Rs.40,000 – Rs.15,600) = Rs.2,68,40,000 (Adv.)

2. Total sales mix variance * Refer to working note 1. **Refer to working note 2. ***Refer to working note 3.

Note: Sales variances can also be calculated by using sales value approach. (v) Comment on above results:

= rs.3,52,00,000 (Adv.)

1. Favourable sales quantity variance of Rs.1.56 crores was because of growth in industry as a whole. However the firm could not retain the budgeted market share of 20%. As a result the benefit of increased market size i.e. Rs.5.85 crores is partly offset by loss due to fall in market share i.e. Rs.4.29 crores. Increase in the percentage sale of computers below-average budgeted margins and a decrease in the percentage sale of computers above-average budgeted margins had resulted in the reduction of operating profit by Rs.3.52 crores. As a result of above, the operating profit of ‘Super Computers’ had been adversely affected by Rs.1.96 crores due to sales variances.

2.

3.

Ans 21:Working Notes 1. Material data

Standard data for actual output Quantity

Kgs. 32,000

2. Labour data

Standard data for actual output Labour Rate/hour Amount Labour

Price Per Kg.

8

Amount Rs.

2,56,000

Quantity Kgs.

36,000

Actual output 6,400 units Actual data for actual output

Price Amount Per Kg. Rs.

7.50 2,70,000

Actual output 6,400 units Actual data for actual output Rate/hour Amount

hours 32,000

3.

Rs. 8

Rs. 2,56,000

hours 36,000

Rs. 7.50

Rs. 2,70,000

Variable overheads data

6,50,000 Actual (Rs.) Actual Units Actual Hours

Actual data variable overheads 6,48,000

6,400 65,000

Standard/Budgeted data Budgeted variable overheads for actual hours

Standard variable overhead Rate/hour Standard variable overhead rate/ unit

4. Sales data

Budgeted data Budgeted

Margin p.u. Rs. 50

(Rs. 250 – Rs. 200)

Rs. 10

Rs. 100

Sales Units

6,000

1.

Amount Rs.

3,00,000

Sales Units

6,400

Actual data Actual

Margin p.u. Rs. 65

(Rs. 265 – Rs. 200)

Amount Rs.

4,16,000

Market Size Variance = Budgeted market share percentage [Actual industry sales in units – Budgeted industry sales

in units] Budgeted contribution margin per unit

= 0.12 [60,000 units – 6,000 units/12%] Rs. 50 = 0.12 [60,000 units – 50,000 units] Rs. 50 = Rs. 60,000 (F)

2. Market Share Variance =[

=[0.106666 – 0.12] 60,000 units X 50 = (6,400 units – 7,200 units) Rs. 50 = Rs. 40,000 (A)

3. Gross Margin Sales Volume Variance = (Actual quantity – Budgeted quantity) Budgeted margin per unit = (6,400 units – 6,000 units) Rs. 50 = Rs. 20,000 (F)

4. Gross Margin Sales Price Variance = (Actual margin per unit – Budgeted margin per unit) Actual quantity of units sold = [(Rs. 65 – Rs. 50) 6,400] 6,400 units = Rs. 96,000 (F)

Direct Material Usage Variance = (Standard quantity – Actual Quantity) Standard Price per kg. = (32,000 kgs – 36,000 kgs.) Rs. 8

5.

= Rs. 32,000 (A)

Direct Material Price Variance = (Standard price/kg. – Actual price/kg.) Actual quantity of material used = (Rs. 8 – Rs. 7.50) 3,600 kgs. = Rs. 18,000 (F)

6. Direct Labour Efficiency Variance = (Standard labour hours – Actual labour hours) Standard rate per hour = (64,000 hours – 65,000 hours) Rs. 6 = Rs. 6,000 (A)

Direct Labour Rate Variance = (Standard labour rate per hour – Actual labour rate per hour) Actual time taken in hours

= (Rs. 6 – Rs. 6.40) 65,000 hours

7.

= Rs. 26,000 (A)

Variable Overhead Efficiency Variance = (Standard hours for actual output – Actual Hours) Standard variable overhead per hour = (64,000 hours – 65,000 hours) Rs. 10 = Rs. 10,000 (A)

Variable Overhead Expense Variance = Budgeted Variable Overhead – Actual Variable Overhead = Rs. 6,50,000 – Rs. 6,48,000 = Rs. 2,000 (F)

Operating Statement (Reconciling the budgeted contribution with actual contribution

Rs. Budgeted Contribution Gross margin sales volume variance Gross margin sales price variance

Cost Variances Material usage Material price Labour efficiency Labour rate Variable overhead efficiency Variable overhead expense

Total Actual Contribution

20,000 96,000

- 18,000

- - -

2,000 20,000

Rs.

- -

32,000 -

6,000 26,000 10,000

- 74,000

Rs. 3,00,000

1,16,000 4,16,000

54,000 3,62,000

Verification: Actual Contribution = Actual sales revenue – Actual variable costs = Rs. 16,96,000 – [ RS. 2,70,000 (actual material cost) + Rs. 4,16,000 (actual labour cost) + Rs. 6,48,000 (actual variable

overheads)] = Rs. 16,96,000 – Rs. 13,34,000 = Rs. 3,62,000

Ans.22:Working (i) Normal / Budgeted hours (ii) Budgeted output (iii) Budgeted fixed overhead rate

(iv) standard cost and profit per unit Direct materials Direct labour Variable overheads Fixed Overheads Total Selling price Standard profit

=60,000 Direct Labour hours. =60,000/ 12 =5,000 units =9,00,000 / 60,000 =Rs.15 per hour or 9,00,000 / 5,000 =Rs.180 per unit

(Rs.) (20kg X 10) (12 hrs. X 5.50) (12 hrs. X 10) (12 hrs. X 15)

200 66

120 180 566 600

34

(v) Actual profit Sales Less: cost of sales; Direct Material Direct wages Overheads Actual profit Direct Material variances

(Rs.) 28,32,000

10,50,000 3,10,000

15,26,000 28,86,000 (54,000)

DMCV

DMPV

DMUV

= Standard Cost for actual output – Actual cost =(4,800 X 200 )-10,50,000 =9,60,000-10,50,000 =Rs.90,000 (A) = Actual qty. X ( standard rate – Actual rate) =1,00,000 X (10-10.5) =Rs.50,000 (A) = Std. rate X (std. qty. for actual output- actual qty.) =10 x ( 4,800 X 20)-1,00,000 ) =10 X (96,000-1,00,000) =Rs.40,000 (A)

Direct Labour variances DLCV = Standard Cost of actual output – Actual cost

=(4,800 X 12 X 5.50 )-3,10,000 =3,16,800-3,10,000 =Rs.6,800 (F) DLRV = Actual Time X ( Standard rate – Actual rate)

=62,000 X (5.50-5) =Rs.31,000 (F) DLEV = Std. Rate X (Std. Time. for actual output- actual Time)

=5.50 x ( 4,800 X 12)-62,000 ) =5.50 x (57,600-62,000) =Rs.24,200 (A)

Overhead variances VOCV = Recovered variable Overheads – Actual variable Overheads

=(4,800 X 120 ) – 5,86,000 = 5,76,000 – 5,86,000 =Rs.10,000 (A) FOCV = Recovered fixed overheads – Actual fixed overheads

=(4,800 X 180 ) – 9,40,000 =8,64,000 – 9,40,000 =Rs.76,000 (A) FOEXPV = Budgeted fixed overheads – Actual fixed overheads

=9,00,000 – 9,40,000 =Rs.40,000 (A) FOVV = Recovered fixed overheads – Budgeted fixed overheads

=8,64,000 – 9,00,000 =Rs.36,000 (A) FOCAPV = Std. rate per hour (Actual time – budgeted time)

=15 X (62,000 – 60,000 ) =Rs.30,000 (F) FOEFEV =Std. Rate per hour X (Std. time for actual output – Actual time)

=15 X (4,800 X 12) – 62,0000 =15 X (57,600 – 62,0000=15 X 4400 =Rs.66,000(A)

Sales Variances Sales Value = Budgeted Sales – Actual Sales Variance =( 5,000 X 600 ) -28,32,000 = Rs.30,00,000 – Rs.28,32,000 =1,68,000(A) Sales Price = Actual qty. (Std. Price – Actual price) Variance = 4,800 X ( 600 – 590) =Rs.48,000 (A) Sales Volume = Std. Price X (Budgeted qty. – Actual qty.) Variance =600 X ( 5,000 – 4,800) =Rs.1,20,000(A) Loss of profit due to loss of sales volume = 200 X 34 =Rs.6,800 (A)

Ans. 23:Working Notes :

( a ) Actual sales Less : Price variance (Favourable) Standard sales Units sold

Rs. 2,22,750

6,750 2,16,000

4,800

( d ) Standard direct wage rate is Rs.4.50 per hour. Hence standard time per unit: Rs. 9 ÷ 4.50 hour = 2 hours

(e) Variable overheads : Standard rate Rs.7.50 per hour Variable overhead per unit: 2 hrs. × Rs.7.50 = Rs. 15

(Note : Alternatively, this may be calculated by adjusting variances as in other cases).

(f) Fixed overhead spent Less : Fixed overhead expense

variance (Adverse) Rs.1,500

Rs.39,000

Budgeted overheads Rs. 37,500

(g) Fixed overhead recovered: 4,800 units × Rs.7.50 = Rs.36,000 (h) Fixed overhead volume variance

Rs.36,000 – Rs.37,500 (i) Budgeted sales: 5,000 units × Rs.45 (j) Standard sales: 4,800 units × Rs.45 (k) Actual sales (1) Sales volume variance:

Rs. 2,16,000 – Rs.2,25,000 (m) Sales price variance:

Rs.2,22,750 – Rs.2,16,000 (i) Original budget: Budgeted sales : (A)

= Rs.1,500 (Adverse) = Rs.2,25,000 = Rs.2,16,000 = Rs.2,22,750 = Rs.9,000 (Adverse)

= Rs. 6,750 (Favourable)

(5,000 units × Rs.45) Rs.

2,25,000

Budgeted costs Direct material Direct wages Variable overheads Fixed overheads Total budgeted costs : (B) Profit : (A) – (B)

(ii) Standard product cost sheet per unit

Direct materials Direct wages Prime cost Variable overheads Fixed overheads Total cost Profit Selling price

(5,000 units × Rs.6) (5,000 units × Rs.9)

(5,000 units × Rs.15) (5,000 units × Rs.7.50)

30,000 45,000 75,000 37,500

1,87,500 37,500

Rs. 6.00 9.00

15.00 15.00

7.50 37.50

7.50 45.00

(iii) Statement showing Reconciliation of the original Budgeted Profit and the Actual Profit.

Rs. Rs. Budgeted profit 37,500 Less: Sales margin volume variance (Adverse)*

or loss of profit on sales volume variance

= Rs. 9000 × 16 2 % **

3 1500

36,000 Standard profit *Sales margin volume variance (Adverse) (200 units × Rs.7.50 = Rs.1,500)

**Profit as % of selling price : Rs. 7.50 ×

Add: Sales price variance (Favourable)

Add: Favourable cost variances: Wage rate Variable overhead expenses

Less : Adverse cost variances Material price Material usage Labour efficiency Variable overhead efficiency Fixed overhead expense

Less: Fixed overhead volume variance (Adverse) [See working note (h)]

%

6,750 42,750

750 3,000

300 600

2,250 3,750 1,500

3,750 46,500

8,400 38,100

1,500

36,600

Ans. 24:Details of original and revised standards and actual achieved

Original standards Fruit Glucose Pectin Citric acid

Revised standards Rs6,400 Rs7,000

Rs 3286.8 Rs 200

Rs16,886.8 Rs 585.0

1,200 kgs Loss 36 kgs

1,164kgs Rs 17,471.8

17,471.8 1,200 kgs 36kgs

1,164kgs Rs 20,071.8

Actual Rs7,600 Rs 8,400

Rs 3286.8 Rs 200

Rs19,486.8 Rs 585.0 20,071.8 1,296 kgs

132 1,164 Kgs Rs 21,403

428 Kgs Rs 18 742 Kgs

Rs7,704 Rs 8,904 Rs 4,100

Rs 95 Rs20,803

Rs 600 21,403

Rs16 700 Kgs Rs10

99 Kgs Rs 33.2 1 Kg Rs 200

400 Kgs

1,200 kgs

Rs 19 700 Kgs Rs12

99 Kgs Rs 33.2 1 Kg Rs 200

400 Kgs

1,200 kgs

Rs 12 125Kgs Rs 32.8

1 Kg Rs 95 1,296 kgs

Labour

(i) Planning variances * Fruit extract (6,400 less 7,600) Rs 1,200(Adverse)

Rs1,400(Adverse) Rs 2,600(Adverse)

Glucose syrup (7,000 less 8,400) Total * (Std qty Std price less Std qty Revised Std price)

(ii) Ingredients operating variances Total (19,486.8 less 20,803) = Rs 1,316.2(Adverse)

Ingredients Price variance (Revised Material Price – Actual Material Price) ( Actual Qty Consumed)

Variance in Rs Fruit extract Glucose syrup Pectin Citric acid

(19 – 18) 428

(33.2 – 32.8) 125 (200 – 95) 1

428(F) Nil

50(F) 105(F) 583(F)

Usage variance (Std Qty on Actual Production less Actual Qty on Actual Production) Revised Std Price/Unit

Variance in Rs Rs Fruit extract Glucose syrup Pectin Citric acid

(iii) Mix Variance

(400 – 428) 19 (700 – 742) 12

(99 – 125) 33.2

532(A) 504(A)

863.2(A) Nil

1,899.2(A)

(Actual usage in std mix less Actual usage in actual mix ) std price

Variance in Rs Fruit extract (432 – 428) 19 76(F)

Glucose syrup Pectin Citric acid

(756 – 742) 12 (106.92 – 125) 33.2 (1.08 – 1) 200

168 (F) 600.3(A) 16(F) 340.3 (A)

Yield variance (Actual yield – Std yield from actual output) Std cost per unit of output

= (1,164 – 1,296 0.97) 19486.8 = 1,558.9(A)

1164

Labour operating variance 585 – 600 = 15(A)

(iv) Total variance = Planning variance + Usage Variance + Price Variance + labour operating Variance. Or Total Variance = (2,600) + ( 1,899.2 ) + 583 + (15) = 3931.2 (A).

Ans.26: Standard hours produced

Out put (units) Hours per unit Standard hours Actual hours worked

Product X 1,200

8 9,600

Product Y 800 12

9,600

Total

19,200

17,600

15,500

100 workers 8 hours 22 days =

Budgeted hours per month

1,86,000/12 =

actual hours 17,600 100 = Budgeted hours 15,500

Capacity Ratio = 113.55 %

Efficiency Ratio = Standard Hours Produced 19,200 100 100 Actual hours 17,600

109.09%

Activity Ratio = Standard Hours Produced 19,200 100 100 Budget hours 15,500

123.87%

Relationship : Activity Ratio = Efficiency Ratio Capacity Ratio

109.09 113.55 100

or 123.87 =

Ans: 27: (1) Capacity Ratio

= Actual working Hours Budgeted working hours x 100

= 25 days x 8 hours x 50 workers 8,500 hours (i.e.,1,02,000/12)

(2) Activity Ratio

x 100 =117.65%

=Actual production in standard hours x 100 Budgeted hours

=(1,000 units x 5 hours) + (600 units x 10 hours) 8,5000 hours

(3) Efficiency Ratio =Standard hours for actual production

Actual hours x 100

x 100 =129.41%

=(1,000 units x 5 hours ) + (600 units x 10 hours) x 100 =110% 10,000 hours

Inter – relationship Capacity Ratio x Efficiency Ratio =Activity Ratio 117.65% x 110% =129.41%

Ans. 28: Report to the Departmental Manager showing the cost ratios: (a) Efficiency Ratio = Standard hours produced 2112 100 110%

Actual hours worked 1920 Standard hours produced 2112 (b) Activity Ratio = 100 82.50%

Budgeted Std. Hours 2560 Budgeted Std. Hours 2560 100 80%

Maximum Possible Hours 3200 Actual hours worked 1920 (d) Actual Capacity utilisation Ratio = 100 75%

Budgeted hours 2560

(c) Standard Capacity usage Ratio =

(e) Calendar Ratio = 24 100 96% 25

(ii) Report to the Departmental Manager Setting out the analysis of variances

Standard fixed overhead rate per hour =

A. Fixed Overheads (a) Charged to production (2112 × 6)

15360 Rs.6 2560

Rs. 12672

(b) Actual hours × Std. rate (1920 × 6)

(c) Revised budgeted hours × Std. rate (24×8×16×

(d) Original budgeted overheads (e) Actual overheads

Variances: Efficiency variance (a-b) Capacity variance (b-c)

80 100

11520

×6) 14746

15360 16500

1152(F) 3226(A)

Calendar variance (c-d) Volume variance (a-d) Expenditure variance (d-e) Total variance

B. Variable overheads:

614(A) 2688(A) 1140(A) 3828(A)

Standard variable overhead rate per hour =

(a) Charged to production (2112 × 8) (b) Actual hours × Std. rate (1920 × 8) (c) Actual overheads

Variances: Efficiency variance (a-b) Expenditure variance (b-c)

20840 2560

=Rs.8

16896 15360 14500

1536(F) 860(F)

2396(F) Total variance (a-c)

Working note: Maximum possible hours (25×8×16) Budgeted hours: 3200 less 20% downtime Actual hours Budgeted standard hours Standard hours produced Budgeted working days Actual working days

3200 2560 1920 2560 5112 25 24

Ans. 29: Maximum capacity in a budget period = 50 employees × 8 hrs.×5 days×4 weeks = 8,000 hrs. Budgeted hours 40 employees ×8 hrs.×5 days×4 weeks = 6,400 hrs. Actual hrs. = 6,000 hrs. (from the sum) Standard hrs. for actual output = 7,000 hrs. Budget no. of days = 20 days = 20 days (4 weeks ´5 days) Actual no. of days = 20-1 = 19 days

1. Efficiency ratio = Standard Hrs 100 {(7000 6000) 100} 116.67% Actual Hrs

2. 3.

Activity ratio = {(7,000÷6,400)×100} = 109.375%

Calendar Ratio = (Available working days ÷ budgeted working days) × 100

4.

5.

6.

= {(19÷20)×100} = 95% Standard Capacity Usage Ratio = (Budgeted hours ÷ Max. possible hours in the budgeted period) × 100 = {(6,400÷8,000)×100} = 80% Actual Capacity Usage Ratio = (Actual hours worked ÷ Maximum possible working hours in a period) × 100 = {(6,000÷8,000)×100} = 75% Actual Usage of Budgeted Capacity Ratio = (Actual working hours ÷ Budgeted hours) × 100 = {(6,000÷6,400)×100} = 93.75%

Ans.30: (i)

(ii)

(iii)

Dr. Material Control A/c Dr. or Cr. Material Price Variance A/c Cr. Creditors A/c (Being price variance during purchase of

materials) Dr. WIP Control A/c Dr. or Cr. Material Usage Variance A/c Cr. Material Control A/c (Being recording of usage variance at

Standard cost of excess/under utilized quantity)

Dr. Wages Control A/c Dr. or Cr. Labour Rate Variance A/c Cr. Cash (Being entry to record wages at standard rate)

Ans. 31:(A) The cost sheet for 900 units will appear as under :

Cost

Direct material Direct labour Overheads

(B) Calculation of variances: Material price variance Material usage variance Labour rate variance

Labour efficiency variance Overhead variances : (a) Charged to production as per cost sheet Rs. 13,500 (b) Actual

= 9,500 Pcs. (Re. 1.00 – Rs.1.10) = Rs. 950 (A) = Re. 1.00 (9,000 pcs. – 9,500 pcs.) = Rs. 500 (A) = 2,475 hrs. (Rs. 3.00 – Rs. 3.50)

= Rs. 1,237.50 (A) = Rs. 3.00 (2,250 hrs. – 2,475 hrs.) = Rs. 675(A)

Std. qty.

9,000 2,250 2,250

Std. rate

1.00 3.00 6.00

Std.cost Rs.

9,000 6,750

13,500 29,250

hours × Std. rate: 2,475 hrs. × Rs. 6 Overheads as per budget (d) Actual overheads

Efficiency variance : Capacity variance : Expense variance :

(a – b) Rs. 1,350 (A) (b – c) Rs.1,650 (A) (idle time) (c – d) Rs. 500 (A)

Rs. 14,850 (c) Rs. 16,500 Rs. 17,000

(a – d) Rs. 3,500 (A) Total variance : (C) The. journal entries for recording these transactions are as under

Dr. Rs.

(i) Material Control A/c To General Ledger Adjustment A/c

(Being the purchase value of 10,000 pieces of materials at Rs. 1.10 each)

(ii) Work-in-Progress A/c To Material Control A/c (Being the cost of 9,500 pieces of materials actually issued to production at the actual price of Rs. 1.10 each)

(iii) Work-in-Progress A/c To Wages Control A/c

(Being the actual amount of direct wages paid for 2,475 hours at Rs. 3.50 per hour

(iv) Work-in-Progress A/c To Overhead Expense Control A/c

(Being the actual overhead expenses incurred) (v) Finished Stock Control A/c

To Work-in-Progess A/c (Being the standard cost of production transferred to finished goods account)

(vi) Cost of Sales A/c To Finished Stock Control A/c

(Being the standard cost of goods sold transferred to Cost of Sales A/c)

Dr. 29,250

Dr. 29,250

Dr. 17,000

Dr. 8,662.50

Dr. 10,450

Dr. 11,000

Cr. Rs.

11,000

10,450

8,662.50

17,000

29,250

29,250

After the basic transactions are posted, the materials control account will show the actual value of stock of material in hand and the work-in-progress account will show a balance representing the cumulative variances on all the accounts and closing balance of work-in- progress at standard cost. The variances have already been analysed in Para (B) above and they will be carried to the respective accounts pending investigation before being finally disposed off. In this problem we have assumed that there is no closing balance of work-in- progress. (D) The journal entries for transferring the variances to their respective

accounts are as under

price variance A/c Material usage variance A/c Labour rate variance A/c Labour efficiency variance A/c Overhead efficiency variance A/c Overhead capacity variance A/c Overhead expense variance A/c

Dr. Dr. Dr. Dr. Dr. Dr. Dr.

Rs. 950.00 500.00

1,237.50 675.00

1,350.00 1,650.00

500.00

Rs. Material

To work-in-progress A/c (E) The ledger accounts will appear as under: Dr.

To Opening balance To General Ledger Adjustment A/c 11,000

11,000 Work-in-Progress Control A/c

To To To To

Rs. Opening balance – Material control A/c 10,450.00 Wages control A/c 8,662.50 Overheads control A/c 17,000.00

Material Control A/c Rs.

- By Work-in-Progress A/c By Balance c/d

6,862.5

Cr. Rs.

10,450 550

11,000

36,112.50

Ans. 32:(A)Computation of variance:

Rs. By Finished stock control A/c 29,250.00 By material price variance A/c 950.00 By material usage variance A/c 500.00 By labour rate variance A/c 1,237.50 By labour efficiency variance A/c 675.00 By overhead efficiency A/c Variance A/c 1,350.00 By overhead capacity Variance A/c . 1,650.00 By overhead expense Variance A/c 500.00

36,112.50

(i) Material price variance: 8,600 pcs. (Rs. 2.15 – Rs. 2.50) = Rs. 3,010 (A) (ii) Material usage variance: Rs. 2.15 (8,400 Pcs. – 8,600 Pcs.) = Rs. 430 (A)

[Standard requirement of materials = 2,800 units produced × 3 pcs. per unit = 8,400 pcs.] (iii) Labour efficiency variance: Dept. A: Standard time required = 2,800 pcs. × 2 hrs. = 5,600 hours. Dept. B: Standard time required = 2,800 pcs. × 4 hrs. = 11,200 hours.

Variances : Dept. A: 1.75 (5,600 – 5,200) = Rs. 700 (F) Dept. B: 1.50 (11,200 – 12,000) = Rs. 1,200 (A) (iv) Overheads variances:

(i) Material Control A/c Material price variance A/c To Creditors A/c

(ii) Work-in-Progress Dept. A. A/c Material usage variance A/c To Material Control A/c

(iii) Work-in-progress Dept. A. A/c To wages control A/c

(iv) Wages Control A/c To Labour Efficiency Variance Dept A A/c

(v) Work-in-Progress Dept. B A/c. Labour Efficiency Variance Dept. B A/c To Wages Control A/c

(vi) Work-in-Progress Dept. A A/c Overhead Capacity Variance Dept. A. A/c To Overhead Efficiency Variance Dept. A. A/c To Overhead Expense Control Dept. A A/c

(vii) Work-in-Progress Dept. B A/c Overhead Efficiency Variance A/c Overhead Expenses Variance A/c To Overhead Control Dept. B A/c

(viii) Work-in-Progress Dept. B A/c To Work-in-Progress Dept. A A/c (Being the transfer at standard cost of finished Production of Department A to Department B for processing in Department B)

(ix) Finished Stock control A/c

Dr. Dr.

Dr. Dr.

Dr.

Dr.

Dr. Dr.

Dr. Dr.

18,490 3,010

21,500 18,060

430 18,490

9,800 9,800

700 700

16,800 1,200

18,000 2,800

400 200

3,000 Dr. Dr. Dr.

Dr.

11,200 800 500

12,500 30,660

30,660

Dr. 58,660

To Work-in-Progress Dept. B A/c 58,660

Ans.33:All figures of Ans. 31are 5 times of Ans. 32

Ans. 34: Material – 1 Rate Variance = Standard cost of material purchased – Actual cost = Rs24, 000 – Rs21, 600 = Rs2, 400 (F)

Material – 2 Quantity Variance = SR × SQ – SR × AQ = Rs900 × 80 units – Rs75, 600 = Rs3, 600 (A)

Labour Spending Variance = SR × AH – AR × AH = Rs24/per hour × 2300 hours – Rs51, 750 = Rs3, 450 (A)

Labour Efficiency Variance = SR × (SH – AH) – 7200 SH

Total Cost of material purchased Less Purchase Value of Material – 2 Cost of material –1

Working Notes:

Standard cost of Material – 2 per unit: 5 litres × Rs180 No of units produced

Total material – 1 used in production Add Closing Inventory Less Opening Inventory Hence Standard Cost of Material – 1 purchased

= 24 (SH – 2300) = 2000 Hrs.

Rs 1,27,200 1,05,600

21,600

(1) Standard Cost of Material – 2 actually consumed in production = Rs72, 000 (Given) = Rs900

= Rs72, 000 / Rs900 = 80 units = Rs18, 000 (Given) = Rs6, 000 (Given)

=0 = Rs24, 000

(2) Standard Rate of Material -1

Standard Cost of Material – 1 Add favourable Quantity Variance Material – 1 allowed Standard quantity of Material – 1 allowed Standard quantity per unit Standard purchase price for Material – 2 Add unfavourable Rate Variance Actual cost Price of Material – 2

(3) Opening balance of Material – 2 Add Standard Cost of Purchase (550 litres × Rs180) Less Closing Balance Material-2 Consumed at Standard cost

Ans. 35: (i) Budgeted Machine Hours:

= Rs24, 000 / 1,000kg = Rs24 per kg

= Rs18, 000 = Rs1, 200

= Rs19, 200 = Rs19, 200/Rs24= 800 Kg.

= 800kg/80units = 10 kg = (550liters × Rs180)= Rs99, 000

= Rs6, 600 = Rs1, 05, 600

= Rs18, 000 = Rs99, 000 = Rs41, 400 = Rs75, 600

We know that:

Volume variance = Std. fixed overhead Std. machine hours rate per hour

= 11,300 – Y

for actual output

Budgeted machined hours for actual output

or Rs.80,000 (Fav.) = Rs.100 (11,300 – Y) or 800 or Y = (11,300 – 800) hours or Y = 10,500 hours Hence budgeted machine hours for actual output are 10,500 hours.

(ii) Actual machine Hours: We know that:

Efficiency variance =

or Rs.36,000 (Fav.) or 600 or X

Std. variable overhead Std. hours for rate per hour

Actual hours actual output for actual output

= Rs.60 (11,300 hours – X) = 11,300 hours – X = 10,700 hours.

Hence Actual machine hours are 10,700 hours. (iii) Applied Manufacturing Overhead:

Applied Manufacturing overhead Actual overhead incurred + Total Variance = Rs.16,50,000 + Rs.30,000 (Refer to working note) = Rs.16,80,000 Hence total applied manufacturing overhead are Rs.16,80,000.

(iv) Total Amount of Fixed Overhead Cost: We know that: Spending variance = (Flexible budget for actual hours – Actual factory overhead incurred) Rs.86,000 (Adv.) = 10,700 hours × Rs.60 + total amount of fixed overhead) – Rs.16,50,000) Rs.86,000 (Adv.) = (Rs.6,42,000 + Total amount of fixed overhead cost (budgeted) – Rs.16,50,000)

Total amount of fixed overhead cost = Rs.10,08,000 – Rs.86,000 = Rs.9,22,000 Total amount of fixed overhead cost = Rs.9,22,000 Working note: Given that: Spending variance (Rs.) Efficiency variance (Rs.) Volume variance (Rs.) Therefore, Total variance = Spending variance + Efficiency variance + Volume variance = Rs.86,000 (Adv.) + Rs.36,000 (Fav.) + Rs.80,000 (Fav.) = Rs.30,000 (Fav.) Alternative approach: Total factory overhead variance = {factory overhead applied - actual factory overhead incurred} = (Std. hours for actual output × Budget rate per hour – Actual cost incurred) = (11,300 hours × Rs.160 – Rs.16,50,000) = Rs.1,58,000 (Fav.)

Under alternative approach, Applied Manufacturing Overhead and Total Amount of Fixed Overhead Cost would come to Rs.18,08,000 and Rs.10,50,000. Budgeted and actual machine hours would come to 10,500 and 10,700. Spending, Efficiency and Volume Variances would come to Rs.42,000 (Fav.), Rs.36,000 (Fav.) and Rs.80,000 (Fav.) respectively.

86,000 (Adv.) 36,000 (Fav.) 80,000 (Fav.)

Ans. 36: (1) Actual material cost incurred

Standard variable of material Material cost variance of actual output

Material cost variance = Standard cost of material of actual output – Actual material cost incurred

Or Actual material cost incurred =

= (10,000 units × 2 units× Rs.15 + Rs.50,000) = Rs.3,00,000 + Rs.50,000

(2) Standard cost of materials actually consumed Material price variance = (Standard cost – Actual cost) Actual quantity consumed

Or Standard cost of materials actually consumed =

= Rs.3,50,000 – Rs.70,000 = Rs.2,80,000 (3) Labour efficiency variance (Refer to working note 1)

Actual material Material price variance cost incurred

Standard hours for Actual hours Standard rate = per hour actual output worked

= (10,000 units × 3 hours – 35,000 hours) Rs.20 = (Rs.6,00,000 – Rs.7,00,000) = Rs.1,00,000 (Adv.)

(4) Variable OH efficiency variance (Refer to working note 2)

= Standard variable overhead Standard rate per hour

hours hours

Actual

= Rs.5 (30,000 hours – 35,000 hours) – Rs.25,000 (Adv.) (5) Variable OH expenditure variance (Refer to working note 1)

= Budgeted variable overhead Actual variable for actual hours overhead

= (Rs.5 × 35,000 hours – Rs.2,00,000) – Rs.25,000 (Adv.) (6) Fixed OH efficiency variance (Refer to working notes 1 & 2)

Standard fixed overhead Standard hour for Actual = actual ouput rate per hour hours = Rs.5 (30,000 hours – 35,000 hours) = Rs.25,000 (Adv.)

Fixed OH capacity variance (Refer to working notes 1 & 2) Standard variable overhead Actual capacity Budgeted

= hours capacity hours rate per hour

= Rs.5 (35,000 hours – 50,000 hours) = Rs.75,000 (Adv.) (7) Fixed OH volume variance (Refer to working note 3)

= Standard variable overhead Actual rate per hour

output output

Budgeted

= Rs.15 10,000 units

50,000 hours 3 hours

= Rs.1,50,000 – Rs.2,50,000 = Rs.1,00,000 (Adv.) Working notes: 1. Labour rate variance:

= (Standard rate per hour – Actual rate per hour) Actual hours (x) Or Rs.50,000 = 20x – Rs.6,50,000 Or x = 35,000 hours

2. Standard hours = 10,000 units × 2 hours = 30,000 hours

Budgeted hours = 30,000 hours 100 = 50,000 hours

60

= Actual fixed overhead + Expenditure variance = Rs.3,00,000 – Rs.50,000 = Rs.2,50,000

Budgeted fixed overhead

Standard fixed overhead recovery rate per hour

Total overhead rate per hour

3.

= Rs.2,50,000 50,000 hours

= Rs.5 per hour

= Rs.10 Variable overhead rate per hour = Rs.5 (Rs.10 – Rs.5) Standard fixed overhead per unit = Rs.15 (3 hours × Rs.5/-)

Ans. 37: Working notes: 1. (a) Budgeted fixed overhead per unit:

= (Budgeted fixed overheads p.a / Budgeted output for the year) = Rs.4,80,000 p.a. / 1,20,000 units = Rs.4 per unit.

(b) Budgeted fixed overhead hour: = Budgeted fixed overhead per unit / Standard labour hours per unit = Rs.4 / 2 hours = Rs.2 per hour

2. (a) Standard cost per unit: Rs.

Direct material (5 kg × Rs.4/- per kg) Direct labour (2 hours × Rs.3/- per hour) Fixed overhead (2 hours × Rs.2) Total standard cost (per unit)

(b) Budgeted selling price per unit Standard cost per unit Standard profit per unit (25% on slaes or 33 – 1/3% of standard cost) Budgeted selling price per unit 40

30 10

30

4

6

20

3 (a) Actual output units for April, 2001: Fixed overhead volume Variance = Efficiency variance + Capacity variance or (Budgeted output units – Actual output units) Budgeted fixed overhead p.u. Rs.2,400 (Favourable) + Rs.4,000 (Adverse) = Rs.1,600 (Adverse) or (10,000 units – x units) Rs.4 – Rs.1,600 (Adverse) or (10,000 units – 400 units) = x (Actual output units) or Actual output units = 9,600 units

(b) Actual fixed overhead expenses: (budgeted fixed overhead – Actual fixed overhead) = Fixed overhead expenses variance or (Rs.40,000 – x) = Rs.1,400 (Favourable)

or x = Rs.40,000 – Rs.1,400 = Rs.38,600

4. (a) Actual sales quantity units: Sales volume variance Actual sales Budgeted

= Budgeted margin per unit quantity units quantity units = Rs.4,000 (Adverse) = Rs.10 (x – 10,000 units) or 400 units = x – 10,000 units or x (Actual sales quantity) = 9,600 units

(b) Actual selling price per units

Sales price variance = Actual Selling Budgeted selling Actual Sales units

price per unit price per unit

or Rs.9,600 (Fav.) = (x – Rs.40) × 9,600 units or Actual selling price per unit = Rs.41/-

5. (a) Actual quantity of material consumed:

Material usage variance = Standard Actual Standard price quantity quantity per unit

or 6,400 (Adv.) = (9,600 units × 5 kgs.) Rs.4 or x kgs. = 49,600 kgs. (actual quantity of material consumed)

(b) Actual price per kg: Actual price per kg.: Material price variance = (Standard price per kg – Actual price per kg) Actual quantity of material consumed -Rs.4,960 -0.1 or y

6.

= = =

(Rs.4 –Rs. y per kg.) 49,600 kg. (Rs.4 – Rs. y per kg) Rs.4.10 per kg.

(a) Actual direct labour hour used: Labour efficiency variance = (Standard hours – Actual hours) Standard rate per hour Rs.3,600 (Favourable) Rs.3,600 (Favourable) P hours

= (9,600 units × 2 hours – p hours) Rs.3 = (19,200 hours – p hours) Rs.3 = (19,200 hours – 1,200 hours) – 18,000 hours (Actual direct labour hours)

(b) Actual direct labour hour rate:

Labour rate variance = Standard rate per hour per hour

Actual rate Actual Direct labour hours

Rs.3,600 (Adverse) = (Rs.3 per hour – t per hour) 18,000 hours or t = Rs.3 + Rs.0.20 – Rs.3.20 per hour

(actual direct labour hour rate) 7. Actual fixed overheads:

Fixed overhead expense variance or Rs.1,400 (Favourable) or Actual fixed overhead or Actual fixed overhead

= Budgeted fixed overhead – Actual fixed overhead = 10,000 units × Rs.4 p.u. – Actual fixed overhead = Rs.40,000 – Rs.1,400 = Rs.38,600

Annual financial Profit /Loss Statement (for April, 2001)

Account (a)

Qty./ Hours (b)

Rate/Price (c)

Actual/ Value (d)=(b)×(c)

Sales: (A) (Refer to working note 4) Direct Materials (Refer to working note 5) Direct labour (Refer to working note 6) Fixed Overheads (Refer to working note 6 (a) and 7) (Rs.38,600/18,000 hours) (absorbed on direct labour hour basis) Total costs: (B) Profit : [(A) – (B)]

9,600 units

49,600 kgs.

18,000 hours

18,000 hours

41

4.10 per kg.

3,20 per hour

2.14444 per hour

3,93,600

2,03,360

57,600

38,600

2,99,560 94,040

Ans: 38. Working notes: 1. Direct material units in actual output Output of units produced Add: Closing WIP units (200 units x 50% complete) Less: Opening WIP units (300 units x 100% complete) Total direct material units in actual output (work done)(i.e. units introduced)

2. Basic data of direct materials

(Units) 7,620

100 (300) 7,420

7,420

A.P./KG. Rs.

23.75

Amount Rs.

2,66,570

(Units)

Standard Data Standard quantity of material

11.130 (7,420 units x 1.5 kgs.)

S.P./ KG. Rs.

24

Amount Rs.

2,67,120

Actual output units Actual Data Actual qty. of material kgs.

11,224

3. Direct wages and overhead units in actual output Output of units produced Add: Closing WIP units (200 units x 40% complete) Less: Opening WIP units (300 units x 60% complete) Total direct wages and overhead units in actual output (work done)(i.e. units introduced) 4. Basic data of direct wages

Actual output units Standard Data Actual Data

7,620 80

(180) 7,520

7,520

Standard Labour hours

22,560 (7,520 units x 3 hours)

5.

S.W./ hour Rs.

400

Amount Rs.

90,240

Actual Labour hours

22,400

A.W./ hour Rs.

4.30

Amount Rs.

96,320

Budgeted variable overhead per unit = Difference in factory overhead Difference in output

= Rs.92,400 – Rs.81,600 (7,500 units – 6,000 units)

=Rs.7.20 per unit

6 Budgeted fixed overheads Total overhead on 8,000 units Less: Variable overhead of Budgeted fixed overheads

7. Basic data for variable overhead Budgeted data Budgeted variable overhead For actual hours (22,400 hours x Rs.2.40 Standard hours required per unit Standard variable overhead rate p.u

(8,000 units x 12 0 8,000 units @ Rs.7.20 per unit

(Rs.) 96,000

(57,600) 38,400

Rs.53,760

3 Rs.7.20

Rs.240

Actual data Actual variable overhead Actual output units Actual hours Actual variable overhead Recovery rate per hour

Rs.58,240 7,520

22,400 Rs.2.60

Standard variable overhead rate p.u.

8. Basic data for fixed overhead Standard / Budgeted data Budgeted fixed overhead Rs.38,400

8,000 units 24,000

Rs.1.60 Rs.4.80

3

Budgeted output Budgeted hours Standard fixed overhead rate per hour Standard fixed overhead p.u Standard hours required p.u.

Computation of Variances: Material variances 1. Material usage variance

Actual data Actual fixed overhead (Rs.96,440 – Rs.58,240) Actual output Actual hours

Rs.38,200

7,520 units 22,400

= =

= =

= =

= =

= =

= =

(S.Q.-A.Q.) S.P. (11,130 kgs.-11,224 kgs.) Rs.24

(S.P.-A.P.) A.Q (Rs.24-Rs.23.75) 11,224 kgs.

(S.C.-A.C.) (Rs.2,67,120-Rs.2,66,570)

(S.H.-A.H.) S.R. (22,500 hours- 22,400 hours) Rs.4

(S.R.-A.R.) A.H (Rs.4-Rs.4.3) 22,400 hours

(S.C.-A.C.) (Rs.90,240 - Rs.96,320)

=Rs.2,256 (A)

=Rs.2,806 (F)

=Rs.550 (F)

2. Material price variance

3. Material cost variance

Labour variances 1. Labour efficiency variance

=Rs.640 (F)

=Rs.6,720 (A)

=Rs.6,080 (A)

2. Labour rate variance

3. Labour cost variance

Variable Overhead variances

1. Variable overhead Expenditure variance

2. Variable overhead Efficiency variance

={ Budgeted variable overhead – Actual variable overhead}

= (Rs.53,760 – Rs.58,240) =Rs.4,480 (A) =Standard variable {Standard hrs. – Actual hrs}

overhead rate per hour =Rs.2,40 (22,560 hrs – 22,400 hrs) =Rs.384 (F)

3. Total variable overhead cost variance = { Standard variable overhead –Actual variable overhead}

= (7,520 units x Rs.7.20 – Rs.58,240)

Fixed Overhead variances 1. Expenditure variance

2. Volume variance

=Rs.4,096 (A)

={ Budgeted fixed overhead – Actual fixed overhead}

= (Rs.38,400 – Rs.38,200) =Rs.200 (F) = { Budgeted volume – Actual volume} Standard fixed overhead rare per unit

=(8,000 units – 7,520 units) Rs.4.80 =Rs.2,304 (A)

3. Efficiency variance = { Standard hours for actual production –Actual hours} Standard fixed overhead rate per hour

= 22,560 hours – 22,400 hours) Rs.1.60 =Rs.256 (F) ={Budgeted hours – Actual Hours } standard fixed overhead rate per hour = (24,000 hours – 22,400 hours ) Rs.1.60 =Rs.2,560 (A)

4.Capacity variance

5.Total fixed overhead cost variance ={Fixed overhead recovered – Actual overhead} ={7,520 units x Rs.4.80 – Rs.38,200} =Rs.2,104 (A)

Ans. 39: Statement of Equivalent Production in Units

Particulars % age

Materials Wages & Overhead Units %age Units

Units Completed Closing W.I.P. Equivalent Units

100% 100%

9000 100% 900 50% 9900

9000 900 9900

Material Variances Standard qty for actual output **

x std price Actual qty

X actual price Material A Material B

19,800 @ 3 9,900 @ 4

29,700

= 59,400

99,000

22,275@2.8*

33,165

= 62,370 = 44,649 1,07,019

= 39,600 10,889 @4.1*

*Actual Cost / Actual Quantity ** Standard Quantity for actual output = ( std qty/ budgeted prod) x actual output MCV = TSC – TAC

= 99,000 – 1,07,019 = 8,019 (A) MPV = AQ (SP – AP) A B

= 22,275 (3 – 2.80) = = 10,890 (4 – 4.10) =

4,455 (F) 1,089 (A)

3,366 (F) MUV = SP (SQ – AQ) A B

= 3 (19,800 – 22,275) = = 4 (9,900 – 10,890) =

7,425 (A) 3,960 (A)

11,385 (A) MMV = SP (RSQ – AQ) A B

MYV

= 3 {19,800 ÷ 29,700 × 33,165 – 22,275} = = 4 {9,900 ÷ 29,700 × 3,165 – 10,890} =

495 (A) 660 (F) 165 (F)

= S. C Per Unit (S. O. For Actual Mix – A. O.) = 99,000 ÷ 9,900 {9,900 ÷ 29,700 × 33,165 – 9,900} = 10 (11.055 – 9,900) = 11,550 (A)

Labour Variances: LCV

LRV

LITV

LEV

(ii)

= TSC – TAC = 2,40,000 ÷ 12,000 × 9,450 – 1,91,250 = 2,250 (A) = AH (SR – AR) = 48,000 {4 – (1,91,250 ÷ 48,000)} = 750 (F) = No. of Idle hours × SR = 48,000 – (47,500 ÷ 4) = 1,200 (A) = SR (SH – AH) = 4 {(60,000 ÷ 12,000) × 9,450 – 47,700} = 1,800 (A)

Variable Overhead Variances = Recovered Overheads – Actual Overheads = 9,450 × 5 – 45,000 = 2,250 (F)

= Standard V.O. – Actual V.O. = 47,700 × 1 – 45,000 = 2,700 (F) = Recovered Overheads – Standard Overheads = 9,450 × 5 – 47,700 = 450 (A)

VOC

V.O (Exp.) V

V.O. (Eff.) V

Fixed Overheads Variances FOCV = Recovered Overheads – Actual Overheads

= (1,20,000 ÷ 12,000) × 9,450 – 1,20,900 = 94,500 – 1,20,900 = 26,400 (A)

F.O.(Exp.) V

FOVV

= Budgeted Overheads – Actual Overheads = 1,20,000 – 1,20,900 = 900 (A)

= Recovered Overheads – Budgeted Overheads = 95,500 – 1,20,000 = 25,500 (A)

Sales Variances Sales Price Variance = Actual Unit Sold (SP – AP)

= 9,000 {50 – (4,57,500 ÷ 9,000)} = 7,500 (F) Sales Volume Variance (Contribution Loss)

= S. R. of Profit (Budgeted Qty. – Actual Qty.) = (60,000 ÷ 12,000) (12,000 – 9,000) = 15,000 (A)

Ans 40:. (a) sales Variance Present Market size =60,000 units.

16 100 =9,600 units.

At 16% the share should have been = 60,000 x

Standard Gross Margin : SP Rs.53 – ( DM Rs.9 + DL Rs.24 + VO Rs.4 + FO Rs.12) = Rs.4 Budgeted Qty. Revised Budgeted Actual Qty. Booked Actual Qty. Std. Gross Margin

Qty Supplied (Rs.) 8,000 9,600 8,200 7,500 4

Budgeted Qty. x Std. G.M.

32,000

Revised Budgeted Qty x Std. G.M. 38,400

Actual Qty. Booked x Std. G.M. 32,800

Actual Qty. Supplied x Std.G.M. 30,000

Actual G.M.

5

(Rs.) Actual Qty. supplied x Actual G.M. 37,500

Market size variance 32,000 - 38,400 Market share variance 38,400 – 32,800 Sales volume variance 32,800 – 30,000 Sales price variance 30,000 – 37,500 Sales Margin Production Quantity Variance = (7500-8200)X4

=6,400 F =5,600 A =2,800 A =7,500 F = 2800 A

[Note: Since actual order received ≠ actual sales quantity, Market share variance will be on the basis of actual order received and we will also calculate one further variance regarding inefficiency of production department about fulfilling order quantity, Sales Margin Production Quantity Variance = (Actual sales quantity – Sales order quantity) × Std. margin p.u. While calculating all other variance sales order quantity shall be ignored.]

(b) Direct Material Variances (Units) 7,500 Production

600 - Op. Stock + Cl. Stock 300 Introduced 7200

Std. requirement 7,200 units @ 1.5 kg. =10,800 kg.

Std. Qty.

10,800

Usage Variance Price Variance Total Variance

Actual Qty.

12,000

S.P.

Rs. 6

Std. Qty. x SP Rs. 64,800

Actual Qty. x SP Rs. 72,000

AP

Rs. 6/50

Actual Qty. x AP Rs. 78,000

=Rs.7,200 A =Rs.6,000 A =Rs.13,200 A

Rs.64,800 – Rs.72,000 Rs.72,000 – Rs.78,000 Rs.64,800 – Rs.78,000

7,500

450

180 7,230

Std. hours produced 7,230 x 4

(c ) Direct Labour Variance Production

Less: Op. Stock

Add: Cl. Stock

75 600 x 100

60 300 x 100

= 28,920

Std. Hours

28,920

Actual Hours

29,000

S.R.

Rs. 6

Std. Hrs. x SR Rs. 1,73,520

Actual Hrs. x SR Rs. 1,74,000

AR

Rs. 6 / 25

=480 A =7,250 A =7,730 A

Actual Hrs. x AR Rs. 1,81,250

Efficiency Variance Rate Variance Total variance

(d) Variable Overheads Variance

A

B

C

=Charged to Production 28,920 x 1

(1,73,520 – 1,74,000) (1,74,000 – 1,81,250)

Rs. 28,920

29,000

36,000

A – C Total V

Efficiency variance

Expenditure variance

=Rs.80A

=Rs.7,000 A =Std. Cost of Actual Hours 29,000 x 1

=Actual Overheads

=Rs.7,080 A

(e) Fixed Overhead Variance

(Rs.) A = Charged to Production 28,920 x 3 B = Std. Cost of Act. Hrs. 29,000 x 3 C = Budget D = Actual Efficiency Variance (86,760 – 87,000) Volume Variance (86,760 – 94,000)

86,760 87,000 96,000 94,000

=Rs.240 (A) =Rs.9,240 (A)

Ans. 41:

(1)

(2) (3)

(4)

Budgeted contribution = Budgeted Profit + Budgeted Fixed Cost

Plus Contribution quantity variance Total Standard contribution Standard Contribution per unit Actual Sales Volume Actual Sales Volume 10,600 17 Actual quantity of Raw Materials used Standard consumption 10,600 5

400 Add: Material Usage Variance

.2 Actual consumption Labour Efficiency variance Standard labour cost for Standard hours (63,000 + 600) Standard labour cost for actual hours

Rs. 15,000 + 15,000 = 30,000

1,800 31,800

3 10,600 units

1,80,200

2,000 Kgs. 2,000 kgs.

55,000 Kgs.

63,600 61,950

(5)

(6)

Labour efficiency variance Actual variable overhead Selling Overhead variance – Variable overhead

1,650 F

Rs. 84,800 Rs. 1,800 = Rs. 83,000

61,950 1.5

Variable Overhead efficiency variance Actual hours (AH)

Standard hours (SH) Standard rate per hour (SR)

41,300 hours

42,400 hours Rs. 1.5

60,600 4 63,600

10,600 4

(7)

(8)

Efficiency variance SR (SH – AH) = 2 (42,400 – 41,300) = 2,200F Actual fixed overheads: Budgeted Overhead + Fixed Overhead

variance = 15,000 + 600 = Rs. 15,600. Operating profit variance If budgeted profit is considered (15,000 – 7,000) = Rs. 8,000 adverse If standard profit is considered (16,800 – 7,000) = Rs. 9,800 adverse

Ans. 42:

Where RSQ B = Revised Standard Quantity of ‘B’ = (Actual total qty of all DM used) × Standard Mix %age of ‘B’ and SQ B = Standard quantity of DM ‘B’ for Actual Production = Standard quantity of all DM allowed for actual output × Standard Mix %age of ‘B’ Since Standard Mix %age is the same for both ‘A’ and ‘B’ (1: 1) we have, Total Yield variance for ‘A’ and ‘B’= T × (Std price of ‘A’ + Std price of ‘B’) Where T = (Std qty of all DM allowed for actual output - Actual total qty of all DM used)× 0.5 As Total Yield variance for ‘A’ and ‘B’ is given as – Rs 270, we have - Rs 270 = T × Rs 24 + T × Rs 30 Or T = - 5 Hence Yield Variance for ‘A’ = - 5 × 24 = - Rs 120 and

Yield variance for ‘B’ = - 5 × 30 = - Rs 150. Also

Similarly (SQ B - RSQ B ) × 30 = - 150 or SQ B - RSQ B = - 5

Alternative 1 Let total actual quantity consumed; X kg. Then, Quantity of A = X – 70

X X RSQ = of A & of B. (Since the Mix ratio is 1:1) 2 2

The Standard input for both ‘A’ and ‘B’ will be 0.5X – 5 Since Cost Variance for ‘A’ is given to be nil, we have, (SP A SQ A) (AQ A AP A) = 0 i.e. 24 × (0.5 X – 5) – (X 70) 30 = 0 or X = 110 Kgs Therefore Actual Input for ‘A’ = 110 – 70 = 40 Kgs

Alternative 2 Let the standard input of ‘A’ = X kg. Therefore, the total standard input for ‘A’ + ‘B’= 2X Actual input = (2X + 10) Kgs. Actual input for ‘A’ = (2X +10 – 70)= (2X – 60)Kgs Forming the equation for nil cost variance of ‘A’. Rs. 24 X – Rs. 30 (2X – 60) = 0 Or X = 50 Kgs. Using this quantity in the Cost Variance of ‘B’, the actual price per kg. of ‘B’ (AP B) will be , 50 30 – 70 AP B = 1,300 Or AP B = Rs. 40. Alternative 3 Let the actual input of ‘A’ =X

Then the total actual input = (X + 70). Therefore, RSQ of ‘A’ and ‘B’ each = 0.5X + 35 and Standard Input of ‘A’ and ‘B’ each = 0.5X +30. Forming the equation for nil cost variance of ‘A’, we have, 24 × (0.5X + 30) – 30 × X = 0

Or X = 40 Kgs. Standard Input will be 50 Kgs. Using this, quantity in the Cost Variance of ‘B’, the actual price per kg.

of ‘B’ (AP B) will be, 50 30 – 70 AP B = 1,300 Or AP B = Rs. 40. Substituting various values for quantity and price, we get the following table.

(1) (2) (3) (4)

Std. Price SQ

A

B

24 50 = 1200

30 50 = 1500 2700

Std. Price RSQ

24 55 = 1320

30 55 = 1650

2970

Std. Price Actual Qty.

24 40 = 960

30 70 = 2100

3060

Actual Price Actual Qty.

30 40 = 1200

40 70 = 2800

4000

(1) – (2) Yld variance

A

B

1200 1320 = 120(A)

1500 1650 = 150(A) 270A)

(2) – (3) Mix variance 1320 960 =

360(F) 1650 2100 =

450(A) 90A)

(1) – (3) Usage variance 1200 960 =

240(F) 1500 2100 =

600(A) 360A)

(3) – (4) Price variance 960 1200 =

240(A) 2100 2800 =

700(A) 940A)

(1) – (4) Cost variance 1200 1200 =

0 1500 2800 =

1300(A) 1300A)

Actual Output = 90 Kgs. (Actual output and standard o utput are always equal numerically in any material variance analysis) Standard output = Standard input – Standard loss or 100 – 10 = 90 Kgs.

Ans. 43: Working Notes

a) Computation of Standard Price per kg of Material Let ‘x’ be the standard price per kg

Direct material price variance = Rs. 15,750 (A) (given) A.Q. (S.P. – A.P.) = DMVP 63,000 kgs (x – 3.25) = -15,750 63,000 x – 2,04,750 = -15,750 63,000x = 1,89,000 x = 1,89,000 / 63,000 = 3

∴ Standard price per kg of material is Rs. 3

b) Computation of Standard Quantity of material for actual output Let ‘x’ be the standard quantity

Direct material usage variance = Rs. 27,000 (A) (given) S.P. (S.Q. – A.Q.) = DMUV 3(x – 63,000) = -27,000 3x – 1,89,000 = -27,000 3x = 1,62,000 x = 1,62,000/ 3 = 54,000

∴ Standard Quantity for actual output is 54,000 kgs.

c) Computation of Standard Labours hours per unit Let ‘x’ be the Standard labour hours per unit D.L. rate variance + D.L. efficiency variance =D.L. Cost Variance Rs. 6,840 (A) + Rs. 10,800 (F) = Rs. 3,960 (F) Direct labour cost variance = Rs. 3,960 (F) (given) Standard cost of Standard hours – Actual cost of actual hours = Rs. 3,960 (F) (x X Rs.6) – (Rs. 2,12,040 = Rs. 3,960 (F) 6x = Rs. 2,16,000 x = 2,16,000 / 6 = 36,000

∴ Standard hours for actual output is 36,000 hours Standard hours per unit = 36,000 hours/ 18,000 units = 2 hrs.

d) Computation of Actual Hours per unit Let ‘x’ be actual hours Direct labour efficiency variance (Standard hours – Actual hours) Std. rate [(18,000 units X 2) – x] Rs. 6 2,16,000 – 6x 6x x

= Rs. 10,800 (F) (given) = DLEV = Rs. 10,800 (F) = 10,800 = 2,16,000 – 10,800 = 34,200

∴ Actual labour hours are 34,200 for actual output Actual labour hours per unit = 34,200 hrs / 18,000 units = 1.9 hrs.

e) Computation of Standard variable overhead per hour Budgeted fixed overheads – Actual fixed overheads = Fixed overhead expense variance Let Budgeted fixed overheads be ‘x’ FOEV = Rs. 25,000 (A) (given) x – Rs. 3,25,000 = Rs. 25,000 (A) x = 3,25,000 – 25,000 = 3,00,000

∴ Budgeted fixed overheads is Rs. 3,00,000 Standard fixed overhead rate per unit = Rs. 3,00,000/ 20,000 units = Rs. 15 per unit

fixed overhead rate per hour = Rs. 15 / 2 hours = Rs. 7.50 per hour Standard

f) Computation of Budgeted selling price per unit Let ‘x’ be the budgeted selling price per unit Sales price variance = Rs. 45,000 (F) (given) Actual quantity (Actual selling price – Budgeted selling price) = Sales price variance

18,000 units (Rs. 67.50 – y) = Rs. 45,000 (F) 12,15,000 – 18,000y = 45,000 18,000y = 12,15,000 – 45,000

y = 11,70,000 / 18,000 = 65

∴ Budgeted selling price is Rs. 65 per unit. Budgeted Sales

Quantity Price Amount (Units) (Rs. p.u.) Rs.

20,000 65 13,00,000

Quantity (Units)

18,000

Actual Sales Price

(Rs. p.u.) 67.50

Amount Rs.

12,15,000

Statement showing Standard Cost per unit and Budgeted Profit for 20,000 units. Particulars Per Unit Sales (a) 65 Costs:

Direct Material 9 Direct Labour 12 Variable Overhead 16 Fixed Overhead 15

Total Cost (b) 52 Standard Gross Margin 13

For 20,000 Units 13,00,000

1,80,000 2,40,000 3,20,000 3,00,000 10,40,000 2,60,000

(ii) Computation of sales gross margin volume and fixed overheads volume variances Sales Gross Margin Volume Variance

= Standard Margin per unit (Actual Quantity – Budgeted Quantity) = Rs. 13 (18,000 units – 20,000 units) = Rs. 26,000 (A)

Fixed Overhead Volume Variance = Standard fixed overhead rate per unit (Actual output – Budgeted output)

= Rs. 15 (18,000 units – 20,000 units) = Rs. 30,000 (A)

(Rs.) 2,60,000

26,000 (A) 2,34,000

45,000 (F) 2,79,000

Adverse 15,750 27,000

6,840 -

3,420 -

25,000 30,000

1,08,010

Operating Statement Reconciling the Budgeted Profit with Actual Profit Budgeted Profit (20,000 units X Rs. 13 p.u.) Sales Margin Volume Variance Standard Profit Sales Price Variance

Cost Variances: Direct Material Price Variance Direct Material Usage Variance Direct Labour Rate Variance Direct Labour Efficiency Variance Variable Overheads Expense Variance Variable Overheads Efficiency Variance Fixed Overheads Expense Variance Fixed Overheads Volume Variance

Actual Profit

Ans: 44: Reconciliation Statement of Actual profit and Standard profit.

Favourable - - -

10,800 -

14,400 - -

25,200 82,810 (A) 1,96,190

(Rs)

3,20,000 64,000

2,56,000

Budgeted Profit Less: Sales volume variance (Adverse) Standard profit

(10,000 @ Rs.32) (Rs.32 (8,000-10,000) (8,000 units @ Rs.32)

Adverse

66,000 10,000

6,800 12,000

8,000 4,000

16,000 6,000

34,000 1,42,800

Favourable Cost Variances: 1. Direct Materials

(i) Price variance 16,500(Rs.20-Rs.24) (ii) Usage Variance Rs.20 (16,000-16,500)

2. Direct labour (i) Labour rate variance 1,70,000(Rs.2.00-Rs.2.04) (ii) Labour efficiency variance Rs.2 (1,60,000-1,66,000) (iii) Idle time variance (Rs.2.00 x 4,0000

3. Variable Overheads (Rs.8 x 8,000) – Rs.60,000 4. Fixed Overheads

(i) Expenses variance (Rs.20 x 10,000) –Rs.1,84,000 (ii) Efficiency variance Rs.20 (8,000 – 8,300) (iii) Capacity variance Rs.20 (8,300 – 10,000) Total

Less: Net Adverse variance Actual profit for the period

20,000 1,22,800 1,33,200

Ans. 45: (b) Working notes:

(i)

(ii)

(iii)

(iv)

Standard sales units : Sales quota Rs. 400

Ravi 1,875

Richard 2,250

110

2,500

Rs. 14,000

Rahim Roop Singh 2,875 1,500

100

2,625

Rs. 18,000

150

1,300

Rs. 20,000

Standard selling expenses per unit (Rs.) 120 (Std. selling expenses/Std. sales units) Actual sales units : 2,000 Actual sales÷Rs. 400

Rs. Actual selling costs Daily allowance 16,000

Conveyance allowances 30,000 27,000 27,000 45,000 Salaries 80,000 80,000 80,000 80,000 Free samples 9,000 7,500 5,375 8,000 Postage & stationery 8,000 9,000 10,000 6,000 Other expenses 9,000 5,000 4,000 10,000 Commission on sales 48,000 50,000 52,500 26,000 Corporate sales office expenses 60,000 75,000 1,05,000 52,000

2,60,000 2,67,500 3,01,875 2,47,000 Total actual selling cost (v) Standard selling cost 2,40,000 2,75,000 2,62,500 1,95,000

(Actual units sold × Std. selling expenses per unit)

Since all the selling expenses have been related to sales units, only one variance can be calculated by comparing the standard and actual selling costs as is shown in the schedule below:

Schedule showing the selling cost variances by salesman Rs.

Standard Selling expenses (Refer to Working Note (v))

Rs. Rs. Rs. Total (Rs.)

2,40,000 2,75,000 2,62,500

3,01,875 (39,375)

(A)

1,95,000 9,72,500 Actual selling expenses (Refer to Working Note (iv)) 2,60,000 2,67,500 Selling cost variance (20,000) 7,500

(F) (A) A = Adverse F = Favourable

2,47,000 10,76,375 (52,000) (1,03,875) (A) (A)

Ans 46: Statement showing the computation of standard cost of production of shirts

Lot no.

45(UK) 46(US) 47(CAN) Total

Cost per Dozen of 46 (US) lot.

Units (Dozen) 1,700 1,200 1,000

Cost per Dozen 531.00 477.60 531.00

Total standard cost( Rs.)

9,02,700 5,73,120 5,31,000 20,06,820

(Rs.)

264.00 213.60

477.60

Material cost 100% Conversion cost 80%(80%of Rs.267)

Total

Statement of material used and its variance

Lot no.

45(UK) 46(US) 47(CAN) Total

Output Dozen

1,700 1,200 1,000

Std. Qty per Dozen ( Mtrs.)

24 24 24

Total Total Std. qty. ( Mtrs.) 40,800 28,800 24,000 93,600

Variation Actual Qty. ( Mtrs.) 40,440 28,825 24,100 93,365

360(F) 25(A)

100(A) 235(F)

Statement of labour hour worked and its variance

Lot no. Output Dozen

Std.labour hour per Dozen

Total labour hours

Total actual labour hours

Variation (Hours)

45(UK) 46(US)

47(CAN) Total

1,700 960

(1200×0.8) 1,000

3 3

3

5,100 2,880

3,000 10,980

5,130 2,980

2,890 11,000

30(A) 10(A)

20(F) 20(A)

Calculation of variances

(1) Material price variance actual quantity (standard rate –actual rate) = (95,000 metres *Rs. 11)-Rs.10,64,000 = Rs.10,45,000-Rs. 10,64,000 (2) Labour rate variance actual hour (Std. rate per hour – actual rate per hour ) = 11,000 (Rs. 49-Rs.50) (3) Variable overhead efficiency variance Std. variable overhead rate per hour (Std.hour –actual hour)

= Rs. 24(10980-11,000) (4) Fixed overhead volume variance Std. fixed overhead rate per hour (Std.hour for actual output–Budgeted hour)

= Rs. 16(10980-48000×3/12)

Working Notes : (1) standard variance overhead rate per hour

= 40*60/100 = Rs.24 (2) standard fixed overhead rate per hour

= Rs. 40*40/100= Rs. 16

Ans: 47.

1. Sales variances (5) Sales Volume Margin Variance

(Std. Margin on actual Sales – Budgeted Margin) =(Rs.25,000 units x Rs.6) – (36,000 units x Rs.6) =(Rs.1,50,000 – Rs.2,16,000)

=Rs. 19,000(A)

= Rs.11,000(A)

= Rs. 480 (A)

= Rs. 16,320(A)

=Rs.66,000 (A)

(6) Sales Price Variance (Actual Sales at actual price – Actual Sales at Std. Price) =(25,000 Units x Rs.51.50)-(25,000 units x Rs.50) =(Rs.12,87,500 – Rs.12,50,000)

2. Material variances (1) Material Price Variance

(Std Cost of Material Used- Actual Material Cost =(96,000 kgs x Rs.2) – (96,000 kg. x Rs.2.25) =(Rs.1,92,000 – Rs.2,16,000)

=Rs.37,500 (F)

=Rs.24,000(A)

(3) Material Usage Variance Std Material cost of Actual production- Std. Cost of Material used) =(1,00,000 kgs. x Rs.2) – (96,000 Kgs. x Rs.2) =(Rs.2,00,000 – Rs.1,92,000)

3. Labour Variances (1) Labour Wages Rate Variance

(Actual Labour hrs. at Std. rate- Actual Labour Wages) =(1,60,000 hrs x Rs.4) – (1,60,000 hrs. x Rs.4.10) =(Rs.6,40,00 – Rs.6,56,000)

=Rs.8,000 (F)

=Rs.16,000 (A)

(2) Labour Efficiency Variance Std. Labour Wages for actual production –Actual Labour hours worked at Std. rate) =(1,50,000 hrs. x Rs.4) –(1,54,000 hrs. xRs.4) =(Rs.6,00,000 – Rs.6,16,000) =Rs.16,000 (A)

(3) Idle Time variance (6,000 hrs. x Rs.4 variance)

4.

=Rs.24,000 (A)

Variable Overhead Variances (1) Total Variable overhead Variance

(Allowed Expenditure for actual hours-Actual variable overheads) =Rs.(1,84,000 – Rs.1,82,000) =Rs.2,800 (F)

(2) Variable overhead Efficiency Variance ( Allowed Expenditure for Std. hours- Allowed Expenditure for actual hours) =(Rs.1,50,000 hrs. x Rs.1.20)- 1,54,000 hrs. x Rs.1.20) =(Rs.1,80,000 – Rs.1,84,800) =Rs.4,800 (A)

5. Fixed Overhead Variances (1) Fixed Overhead Expenditure variance

(Budgeted Expenditure – Actual Expenditure) =(Rs.1,44,000 – Rs.1,50,000) =Rs.6,000 (A)

(2) Fixed Overheads Efficiency variance (Std. hours of production x Std. fixed overhead recovery rate per hour)-(Actual hours worked x

Fixed overhead recovery rate per hour) =(Rs.1,50,000 hrs. x Re.0.80)-(1,54,000 hrs. x Re.0.80) =(Rs.1,20,000 – Rs.1,23,200) =Rs.3,200(A)

(3) Fixed Overhead Capacity variance (Actual hours worked x Fixed overhead recovery rate per hour)-(Std. Fixed overhead recovery r

rate per hour x Budgeted capacity hours) =(1,54,000 hrs. x 0.80)-(Re.0.80 x 1,80,000 hrs.) =(Rs.1,23,200 – Rs.1,44,000) =Rs.20,800(A)

A. Std. Variable Overhead Rate per hour. = Std. Variable Overheads

Total Std. hours

=(30,000 units x Rs.12)-Rs.1,44,000 1,80,000 units

B. Std Fixed Overheads rate per hour =Budgeted Overheads

Budgeted hours =Rs.1,44,000 / 1,80,000 hrs.

=Rs.1.20

=Rs.0.80

(Rs.) 2,16,000 6,56,000 3,32,000

12,04,000 12,87,500

83,500

Statement of actual profit / loss for the second quarter of the year Direct Material (96,000 kgs.@Rs.2.25) Direct Wages (1,60,000 hrs. ‘ Rs.4.10) Overhead

Total Cost Sales Revenue (25,000 units @ 51.50) Actual Profit

Operating Statement reconciling the budgeted profit with actual profit Particulars Reference to

working note

Budgeted profit (36,000 units x Rs.6) 1. Sales – Volume Margin Variance

Price Variance Profit before adjustment of Cost Variances

- (1) (2)

Variance

Favourable - -

37,500

Adverse -

66,000 -

(Rs.) Actual

2,16,000 - -

1,87,500

II Material - Price - Usage

III. Labour - Rate -Efficiency -Idle time

IV. V. Overheads -Expenditure -Efficiency

V. F. Overheads -Expenditure - Efficiency -Capacity

Actual Profit

(1) (2) (1) (2) (3) (1) (2) (1) (2) (3)

- 8,000

- - -

2,800 - - - -

10,800

24,000 -

16,000 16,000 24,000

- 4,800 6,000 3,200

20,800 1,14,800

1,04,000 83,500

Ans. 48:

Overhead Expenses Schedule Budget: 120 Std. Hours Actual: 156 Hours

Rate per hour Expenses Rate per hour Expenses Rs. Rs. Rs. Rs.

0.40 48 0.50 78 0.60 72 0.60 94 0.40 48 0.45 70 0.30 36 0.32 50 0.30 36 0.29 45 2.00

2.00

240

240 480

2.16 337

250 587

Expenses

Indirect material Indirect labour Maintenance Power Sundries Total variable overheads Fixed overheads Total overheads

Actual output = 12,160 units. Hence standard hours produced or std. hours for actual production

= Computation of variances:

A. Fixed expenses (a) Charged to production (152 hours × Rs. 2 per hours) (b) Fixed expenses as per budget (c) Actual fixed overheads

Rs. 304 Rs. 240 Rs. 250

Volume variance = Fixed overhead recovery rate (Actual volume in std. hrs. – Budgeted volume in standard hrs.)

= Rs.2 (152 – 120) = Rs.64 (F) Expenses variance =

Total variance

Volume variance: (a – b) Expenses variance: (b – c) Total variance : (a – c)

(Budgeted expenses – Actual expenses) = Rs.240 – Rs.250 = Rs. 10 (A)

= (Fixed overheads absorbed – Actual fixed overheads) = Rs.304 – Rs.250 = Rs.54 (F) Or

Rs.64 (F) Rs. 10 (A) Rs.54 (F)

Rs.304 B. Variable expenses

(a) Charged to production: (152 hours × Rs.2)

(b) Actual expenses Variable overhead cost variance (a – b)

Ans. 49: Basic Data:

Rs.337 Rs.33 (A)

(1) Statement showing standard and actual costs of material for 1,000 units of output and standard cost of actual input

Standard Cost Actual cost Standard cost of actual input = (Actual quantity × Standard

price)

Amount Actual Qty.

Kg.

11,000

5,200

Standard Price/kg

Rs.

10

6

Amount Ma Qty. Price Amount Qty. Price

Kg.

A

B

12,000

5,000

Rs.

10

6

Rs.

1,20,000

30,000

1,50,000

Kg.

11,000

5,200

Rs.

11

5.50

Rs.

1,21,000

28,600

1,49,600

Rs.

1,10,000

31,200

1,41,200

Standard yield (units) = 1,000 units 17,000 Kg.

× 16,200 kg. = 952.941764 units approx.

(2) Statement showing standard and actual labour cost of 1,000 units produced and standard cost of actual labour hrs.

Hours Rate p.h. Rs.

5,000 3

Amount

Rs. 15,000 5,500

Hours Rate p.h. Rs.

3.1818

Amount

Rs. 17,500 5,500

Hours Rate p.h. Rs. 3

Amount

Rs. 17,500

(3) Overheads Fixed overheads (Rs.) Budgeted Actual Hours Output Standard time p.u. (hrs.) Standard fixed overheads p.u. (Rs.) Standard fixed overhead rate p.h. (Rs.) Computation of material variances (Refer to Basic data 1): Computation of material variances (Refer to Basic data (1): Material cost variance

Material price variance

= Standard cost – Actual cost

38,500 5,500 1,100

5 35 7

39,000 5,500 1,000

= Rs.1,50,000 – Rs.1,59,500 = Rs.9,500 (Adv.) = Actual quantity (Std. price – Actual price)

= 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.)

Material usage variance = Standard price (Standard quantity – Actual quantity)

= Rs.10 (12,000 kg – 11,000 kg) + Rs.6(5,000 kg–5,200 kg) = Rs.10,000 (Fav.) + Rs.1,200 (Adv.) = Rs.8,800 (Fav.)

Material mix variance Std. price of Std. price of

= Total actual quantity Std. mix per kg 16,200 kg

= 16,200 kg Rs.1,50,000 Rs.1,41,200

17,000 kg 16,200 kg

= Rs.1,741.18 (Fav.) Material yield variance = Std. Rate (Actual yield – Std. Yield

= Rs.150 (1,000 units – 952.9411764 units) = Rs.7058.82

Material purchase price variance: = Actual quantity of material purchased (Std. Price per kg. – Actual price per kg) = 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.) Computation of labour variances (Refer to basic data 2): Labour cost variance

Labour rate variance

= (Standard cost – Actual cost) = Rs.15,000 – Rs.17,500 = Rs.2,500 (Adv.)

= Actual hrs. (Std. Rate – Actual rate) = 5,500 (Rs.3 – Rs.3.1818) = Rs.1,000 (Adv.)

Labour efficiency variance = Std. rate p.h. (Std. Hours – Actual hours) = Rs.3 (5,000 hrs. – 5,500 hrs.) = Rs.1,500 (Adv.)

Computation of fixed overhead variance: Total fixed overhead variance: = Fixed overhead absorbed – Actual fixed overhead = 1,000 units × Rs.35 – Rs.39,000 = Rs.35,000 – Rs.39,000 = Rs.4,000 (Adv.) Fixed overhead expenditure variance: = Budgeted fixed overhead – Actual fixed overhead = Rs.38,500 – Rs.39,000 = Rs.500 (Adv.) Fixed overhead volume variance: = Std. Fixed overhead rate per unit (Actual output – Budgeted output) = Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.) Efficiency variance: = Std. fixed overhead rate per unit (Actual output – Budgeted output)

= Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.)

Ans. 50: (i) Working Notes: 1. Standard quantity and cost of raw material required for actual output

Actual output of EXE (units) Standard output per kg. of raw material (units) Standard quantity of raw material required for actual output (kgs.) (4,680 units / 12 units) Standard cost of 390 kgs. of raw material at Rs.60 per kg. (Rs.)

2. Basic data for the computation of labour variances: Standard labour data for actual

output Actual data

Actual cost

hours

Rate p.h.

Amount Std. Time hours Rate p.h.

Amount Standard cost of actual hours

2,340 (4,680 units ×½ hr.)

5 11,700 12,000 240 320

1,840

4.80 5.20 5.00

1,152 1,664 9,200

12,016 2,340 11,700 12,000 2,400 3. Basic data for the computation of fixed overhead variances:

Budgeted / Std. data Actual data

Budgeted fixed overhead (Rs.) (for 1 week)

Budgeted hours

(60 workers×40 hrs. per week)

Budgeted output (units)

Std. rate p.h. (Rs.)

Std. rate p.u. (Rs.) (i)

24,400 Actual fixed overhead (Rs.)

2,400 Actual labour hours

Actual output (units)

4,800

8.50

4.25

19,800

2,400

4,680

Computation of labour and overhead (variances): Labour cost variance: (Refer to working Note 2) = (Std. cost of labour – Actual cost of labour) = Rs.11,700 – Rs.12,016 = Rs.316 (Adverse) Labour rate variance: = Actual hours (Std. rate – Actual rate) = Rs.12,000 – Rs.12,016 = Rs.16 (Adv.) Labour efficiency variance:

= Standard rate per hr. (Std. hours – Actual hours paid) = (Rs.11,700 – Rs.12,000) = Rs.300 (Adv.) = Total fixed overhead cost variance: = (Fixed overhead absorbed – Actual fixed overhead) = [(4,680 units × Rs.4.25) – Rs.19,800] = Rs.19,890 – Rs.19,800 = Rs.90 (Fav.) Fixed overhead volume variance: = Std. fixed overhead rate per unit [Actual output – Budgeted output] = Rs.4.25 (4,680 units – 4,800units) = Rs.510 (Adv.) Fixed overhead expenditure variance: = [Budgeted fixed overhead – Actual fixed overhead] = [Rs.20,400 – Rs.19,800] – Rs.600 (Fav.)

(ii) Statement showing total standard cost, standard profit and actual profit for the week. Sales 4,680 units × Rs.15 Less: Standard cost of :

Rs. Rs. 70,200

23,400 11,700 19,890 54,990

Direct material Direct labour Overheads (4,680 × Rs.4.25) (Refer to working notes 1 to 3)

Standard Profit Less: Adjustment for variance:

15,210

Raw Material: Price variance : 800 (A) Usage variance : 600 (A)

Labour: Rate Variance : 16 (A) Efficiency variance : 300 (A)

Overhead: Expenditure variance: 600 (F) Volume variance: 510 (F)

Actual Profit

Ans.51: Sales variances (Sales Value Method)

Budgeted Calculations: Budgeted Sales Actual Sales

1,400 (A)

316 (A)

90 (F) 1,626 13,584

Product Qty. Rate Amount Qty. Rate Amount Units

A B C

Rs. Rs. Units Rs. Rs. Actual

quantity× Budgeted price

10,000 12 1,20,000 11,000 11.50 1,26,500 6,000 15 90,000 5,000 15.10 75,500 8,000 9 72,000 9,000 8.55 76,950

24,000 2,82,000 25,000 2,78,950 Computation of sales variances : (1) Sales value variance = Actual sales – Budgeted sales

= Rs. 2,78,950 – Rs. 2,82,000 = Rs. 3,050 (A)

(2) Sales price variance = Actual quantity (Actual price – Budgeted price) = Rs. 2,78,950 – Rs. 2,88,000

= Rs. 9,050 (A) = Budgeted price (Actual Qty. –Budgeted Qty.) = Rs. 2,88,000 – Rs. 2,82,000 = Rs. 6,000 (F)

Rs. 1,32,000

75,000 81,000

2,88,000

(3) Sales volume variance

(4) Sales mix variance = Total actual qty. (Budgeted price of actual mix – Budgeted price of budgeted mix)

= = 25,000 units (Rs. 11.52 – Rs. 11.75)

Rs. 5,750 (A) (5) Sales quantity variance = Budgeted price of budgeted mix (Total actual

quantity – Total budgeted qty.) = Rs. 11.75 (25,000 – 24,000) = Rs. 11,750 (F)

Check Sales value variance Rs. 3,050 (A) Sales volume variance Rs. 6,000 (F)

= Sales price variance + Sales volume variance = Rs. 9,050 (A) + Rs. 6,000 (F) = Sales mix variance + Sales quantity variance = Rs. 5,750 (A) + Rs. 11,750 (F)

Alternative solution (sales margin method)

Basic calculations : Budgeted margin

Product

A B

Qty. Units

10,000 6,000

Rate Amount Rs. 5 6

Rs. 50,000 36,000

Actual margin

Qty. Units

11,000 5,000

Rate Rs.

4.50 6.10

Rs. 49,500 30,500

Actual quantity × Budgeted margin

Amount Rs.

55,000 30,000

C 8,000 24,000

3 24,000 1,10,000

9,000 25,000

2.55 22,950 1,02,950

27,000 1,12,000

Computation of variances: Sales margin variance = Actual margin – Budgeted margin

= Rs. 1,02,950 – Rs. 1,10,000 = Rs. 7,050 (A) = Actual quantity (Actual margin – Budgeted margin) = Rs. 1,02,950 – Rs. 1,12,000 = Rs. 9,050 (A) = Total actual quantity (Budgeted margin of actual mix –Budgeted margin of budgeted mix

Sales price margin variance

Sales margin mix variance

Material Variances: Basic Calculations

Standard and actual costs of material for actual output i.e. 11,000 units of A, 5,000 units of B and 9,000 units of C and standard cost of actual input material. Material

Qty Units

X Y

51,000* 74,000** 1,25,000

Standard cost

Rate Rs.

2 1

Amount Rs.

1,02,000 74,000

1,76,000

Qty. Units

54,000 72,000

1,26,000

Actual cost

Rs. 1,09,620

73,000 1,82,620

Actual quantity × standard price

Rate Amount Rs.

1,08,000 72,000

1,80,000 * 11,000 × 2 + 5,000 × 4 + 9,000 × 1 = 51,000 **11,000 × 3 + 5,000 × 1 + 9,000 × 4 = 74,000. Computation of variances : Material cost variance = Standard cost – Actual cost

= Rs. 1,76,000 – 1,82,620 = Rs. 6,620 (A) Material price variance = Actual quantity (Standard price – Actual price)

= Rs. 1,80,000 – Rs. 1,82,620 = Rs. 2,620 (A) Material mix variance = Total quantity (Standard price of standard mix – Standard price of actual mix

Check: Material cost variance

Rs. 6,620(A)

Ans. 52

= Material price variance + Material mix variance + Material yield variance

= Rs. 2,620(A) + Rs. 2,592(A) + Rs. 1,408(A)

(i) Reconciliation statement showing which factor has contributed change in profit (Rs. in lacs)

Favourable Increase in contribution due to increase in volume (Rs.280 lacs – Rs.240 lacs) (Refer to working note 3) Sales price variance (Refer to working note 3) Material usage variance (Refer to working note 4) Material price variance (Refer to working note 4) Direct labour rate variance (Refer to working note 4)

Direct labour efficiency variance (Refer to working note 4) Fixed overhead expenditure variance (Refer to working note 3)

Total change in profit

Adverse

40

140

52

—

—

36

—

0

28

—

— 268 100

140 168

= 160 lakhs = Rs. 800 lakhs

Rs. 240 lakhs 100 Rs. 1200 lakhs

Break-even sales (Year 2)

(Refer to working note 3) = 300 lakhs = Rs. 962.50 lakhs

Rs. 480 lakhs 100 Rs. 1540 lakhs

(iii) Percentage increase in selling price needed over the sales value of year 2 to earn a margin of safety of 45% in year 2 P/V ratio = (Rs. 480 lacs/Rs. 1,540 lacs) × 100 = 31.169%

If Margin of safety to be earned is 45% then Break-even point should be 55% Revised contribution = 1,540 lacs × 35.4193% = 545.45 lacs Present contribution Increase in selling price required

= Rs. 480 lacs = Rs. 65.45 lacs (Rs. 545.45 lacs – Rs. 480 lacs)

Working notes: 1. Budgeted sales in year 2 If actual sales in year 2 is Rs. 110 then budgeted sales is Rs. 100.

3. Statement of figures extracted from working results of a company (Figure in lacs of Rs.)

Year 1 Actual

(a)

Sales : (A) 1,200

Year 2 (Budgeted)

(b)

1,400

Year 2 Actual

(c)

1,540

Total Variance

d = (c) – (b)

140 (Fav.)

(Refer to working note 1) Variable costs : Direct material (Refer to working note 2) Direct wages and variable overhead (Refer to working note 2)

Total variable costs : (B) Contribution (C) = {(A) – (B)} Less : Fixed cost

Profit

Total variable costs : (B) Contribution (C) = {(A) – (B)} Less : Fixed cost Total variable costs : (B) Contribution (C) = {(A) – (B)} Less : Fixed cost

Profit

(4) (i) Data for Material variances : Standard data for actual output

Quantity of material

m/t Rs.

5,83,333 120 Rs.

700 lacs 5,40,000

Rate per m/t

Amount Quantity of material

m/t Rs. 120

Rs. 648 lacs

Actual data Rate per

m/t Amount

600 700 648 52 (Fav.)

360

960 240 160

80

960 240 160

960 240 160 80

420

1,120 280 160 120

1,120 280 160

1,120 280 160 120

412

1,060 480 300 180

1,060 480 300

1,060 480 300 180

8 (Fav.)

60(Fav.) 200 (Fav.) 140 (Adv.)

60(Fav)

60(Fav.) 200 (Fav.) 140 (Adv.) 60(Fav.) 200 (Fav.) 140 (Adv.) 60(Fav)

Material price variance = (Standard rate – Actual rate ) Actual quantity = Nil Material usage variance = (Standard quantity - Actual quantity) Standard rate per m/t

= (5,83,333 – 5,40,000) Rs.120 = Rs. 52 lacs (Fav.) (ii) Data for labour variances overhead variances

Standard data for actual output Labour hours

87,50,000

Rate per hour Rs. 4.80

Amount

Rs. 4.20 lacs 80,00,000

Actual data Labour hours

Rate per hour Rs. 5.15

Amount

Rs. 412 lacs

Labour rate variance = (Standard rate – Actual rate) Actual labour hours = (Rs.4.80 – Rs.5.15) 80,00,000 = Rs. 28 lacs (Adv.)

Labour and variable overhead efficiency variance : = {Standard labour hours – Actual labour hours} × Standard rate per hour

= {87,50,000 – 80,00,000} Rs. 4.80 = Rs. 36 lacs (Adv.)

Ans. 53: Basic Calculations Equivalent Production in Units Particulars Direct Material Units completed 100 % Work-in-progress 100 % Total Equivalent Units

6,000 600

6,600

Labour & Overhead 100 % 50 %

6,000 300

6,300

(a) Direct Material Variances

Standard output 6,600 units

Qty. 13,200

6,600 19,800

Rate (Rs.) 3 4

Amount (Rs.) 39,600 26,400 66,000

Qty. (kg) 14,850

7,260 22,110

Actual output 6,600

units Rate (Rs.)

2.90* 4.098*

Material

A B

Amount (Rs.) 43,065 29,750 72,815

*(Actual Cost/ Actual Quantity)

DMCV

DMPV A B

DMUV A B

DMMV A

B

= = = = =

= = =

= = = = =

= = =

Standard Cost for actual output – Actual Cost 66,000 – 72, 815 = Rs. 6,815 (A) Actual Qty. (Std, Rate – Actual Rate) 14,850 (3 – 2.90) = 1,485 (F) 7,260 (4 - 4.098) = 710 (A)

775 (F) Std. Rate (Std. Qty. for actual output – Actual Qty.) 3 (13,200 – 14,850) = 4,950 (A) 4 (6,600 – 7,260) = 2,640 (A)

7,590 (A) Std. Rate (Revised Std. Qty. – Actual Qty.) 3 3 (14,740 – 14,850) = 330 (A) 4 4 (7,370 – 7,260) = 440 (F)

110 (F)

Std. Cost per Unit (Std. output for actual mix – Actual output) 66,000 10 (7,370 -6,600) = Rs. 7,700 (A)

DMYV

(b) Direct Labour Variances

DLCV

DLRV

ITV

DLEV

= =

= =

= =

= = =

Std. Cost for Actual Output – Actual Cost (6,300 X 20) – 1,27,500

Actual Time (Std. Rate – Actual Rate) 32,000 [

Std. Rate X Idle Hours 4 X 200 = Rs. 800 (A)

Std. Rate (Std. Time for actual production – Actual time worked) 4 [(6,300 X5) – 31,800] 4 (31,500 – 31,800) = Rs. 1,200 (A)

= Rs. 1,500 (A)

= Rs. 500 (F)

(c) Variable Overhead Variances

VOC = Recovered Overheads – Actual Overheads

= =

VOEXPV

VOEEFV

= = = = =

6,300 X 5 – 30,000 31,500 – 30,000 = Rs. 1,500 (A)

Std. Variable Overheads – Actual Variable Overheads. (31,800 X 1) – 30,000 31,800 – 30,000 = Rs. 1,800 (F) Recovered Overheads – Standard Overheads 1 X (31,500 -31,800) = Rs. 300 (A)

(d) Fixed Overhead Variances

FOCV = = =

= =

= =

Recovered Fixed Overheads – Actual Fixed Overheads (6,300 X 10) – 80,600 63,000 – 80,600 = Rs. 17,600 (A)

Budgeted Fixed Overheads – Actual Fixed Overheads (8,000 X 10) – 80,600 = Rs. 600 (A)

Recovered Fixed Overhead – Budgeted Fixed Overhead 63,000 – 80,000 = Rs. 17,000 (A)

FOEXPV

FOVV

Fixed Overhead Volume Variances may be segregated into the following:

FOEFFV

FOITV

FOCAPV

= =

= = = =

Std. Rate (Std. time for actual production – Actual time booked) 2 (31,500 – 31,800) = Rs. 600 (A)

Std. Rate per hour X Idle hours 2 X 200 = Rs. 400 (A) Std. Rate per hour (Actual time – Budgeted time) 2 (32,000 – 40,000) = Rs. 16,000 (A)

(e) Sales Variances

SPV = =

Actual Qty. (Std. Price – Actual Price) 6,000 = Rs. 5,000 (F)

Sales Volume Variance (Contribution loss) : = Std. Rate of profit (Budgeted Qty. – Actual Qty.) = 5 (8,000 – 6,000) = Rs. 10,000 (A)

Operating Statement showing the Reconciliation between Budgeted and Actual Profit for the Month (Rs.)

Budgeted Profit (8,000 X Rs. 5) Sales Variances

Volume Total

Cost Variances: Direct Materials

Price Yield Mix

Direct Wages Rate Efficiency Idle Time

Rs. Price 5,000 (F)

10,000 (A) 5,000 (A)

40,000

5,000 (A)

775 (F) 7,700 (A)

110 (F)

500 (F) 1,200 (A)

800 (A)

Variable Overheads Expense Efficiency

Fixed Overheads Expense Efficiency Idle Time Capacity

Total Cost Variances Actual Profit

Ans:54:Computation of Variances (a) Material Price variance

Material Qty. Purchase Std. Price Rs. (1) Kg. (2) (3) A 9,000 10.00 B 5,000 3.00

1,800 (F) 300 (A)

600 (A) 600 (A) 400 (A)

16,000 (A) 24,415 (A) 24,415 (A)

10,585

Actual Price Rs.(4)

10.25 2.75

Std. cost Rs. (2x3)=5

90,000 15,000

1,05,000

Std. Cost of Std. Qty. (2x4)=5

80,000 12,000 92,000

Actual Cost Rs. (2x4)=(6)

92,250 13,750

1,06,000

Std. Cost of Actual (4x5)=6

78,000 12,900 90,900

Price Variance Rs. (5-6)=(7)

2,250 (A) 1,250 (F) 1,000 (A)

Usage Variance (5-6)=(7)

2,000 (F) 900 (A)

1,100 (F)

(b) Material Usage Variance Actual Qty. Material Std. Qty. for (3) (1) actual output

(2) A 8,000 7,800 B 4,000 4,300

Std. Price (4)

10 3

(C ) Labour Rate Variance Actual Hours Std. Rate (1) (2)

Rs.

4200 3

Actual Rate (3) Rs.

2,875

Std. Rate (3) Rs.

3

Std. Wage (4)=(1x2) Rs.

12,600

Std. Cost of Std. Hours (4)=(1x3) Rs.

12,000

Actual Wages (5)=(1x3) Rs.

12,075

Std. Cost. Of Actual Hours (5)=(2x3) Rs. 12,600

Rate Variance (6)=(4-5) Rs.

525 (F)

Efficiency Variance (6)=(5-6) Rs. 600 (A)

(d) Labour Efficiency Variance Actual Hours Std. Hours (2) for actual

output (1) 4,000 4,200

Overhead Variances Basic calculations

(a)

(b) (c ) (d) (e) (f)

Budgeted overheads for November

Std. hours produced for November Fixed production overheads per hour Recovered overhead Actual overheads Standard overheads

= 10,800 X 25 =Rs.22,500 12

= 800 units X 5 hrs per unit=4,000 = 25/5=5 = 4,000 X 5 =Rs.20,000 = Rs.23,500 = 4,200 X 5 =Rs.21,000

Variances Overhead Cost variance

=Recovered Overheads- Actual Overheads =20,000-23,5000 =Rs.3,500 (A)

Overhead Expenditure Variance =Budgeted Overheads-Actual overheads =22,500-23,500 =Rs.1,000 (A)

Overheads Volume variance =Recovered Overheads-Budgeted Overheads =20,000-22,500 =Rs.2,500 (A)

Overhead Volume Variance may be segregated into: (a) Overhead Capacity Variance

=( Std. Overhead rate per hour) X (Actual hours-Budgeted hours) = Standard Overheads-Budgeted Overheads =21,000-22,500 =Rs.1,500 (A)

(b) Overhead Revised Capacity variance = ( Std. rate per hour ) X (Std. hrs. produced – Actual hours)

Or

= Recovered overheads- Std. overheads =20,000-21,000

(ii) Operating Statement (a) Sales

Less: std. Cost of Sales Standard profit

(b) Variances Materials Price Usage Direct Labour Rate Efficiency Fixed Overheads Expenditure Capacity 1,500 (A)

Efficiency 1,000 (A)

=Rs.1,000 (A)

(Rs.) 1,60,000 1,24,000

36,000 Adverse

1,000 -

- 600

1,000

2,500 5,100 3,475 (A)

32,525

(800 X Rs.200) (800 X Rs.155)

Favourable

- 1,100

525 -

-

- 1,625

( c) Actual Profit

(iii) In the solution given the price variance has been calculated at the point of purchase. In case it is calculated at the point of issue the variance will be as follows: (Rs.)

1,950 (A) A 7,800 X (10-10.25) B 4,300 X ( 3-2.75) 1,075 (F)

875 (A) Present variance 1,000 (A) Hence difference 125 Actual profit as in (ii) above 32,525 Price variance difference 125 Actual profit as per question

32,650

Ans: 55: Statement showing the computation of standard cost per unit Particulars Actual 960 units

(Rs.) Standard 960 units

768 1,152 1,920 1,000 4,840 920

5,760

Standard cost per unit

0.80 1.20 2.00 1.04 5.04 0.96 6.00

Direct Material Direct Wages Variable overhead Fixed overhead Total Cost Profit

Balancing figure

792 1,192 1,940 1,040 4,964 976

5,940

Variance (-) Adv. (+) Fav.

(-)24 (-) 40 (-) 20 (-) 40 (-)124 (+)56

(+)180

Original Budget and Flexible budget for sales achieved Particulars

(Rs.) Original budget (1,000 units)

800 1,200 2,000 1,040 5,040 960

6,000

Flexible budget (960 units)

768 1,152 1,920 1,040 4,880 880

5,760

Direct Material Direct Wages Variable overhead Fixed overhead Cost of Sales Profit Sales

Standard Cost (per unit)

0.80 1.20 2.00 1.04 5.04 0.96 6.00

Ans: 56: (i)

Units Flexible budget for May 2004

Original Budget 20,000

2 24,00,000

6,00,000 8,00,000 2,00,000 3,00,000

19,00,000 5,00,000

1,00,000 2,00,000 3,00,000 2,00,000 2,00,000

-1,50,000

Flexible Budget for May 2004

18,000 3

21,60,000 5,40,000 7,20,000 1,80,000 2,70,000

17,10,000 4,50,000

1,00,000 2,00,000 3,00,000 1,50,000

-

Actuals may 2004

18,000 4

22,00,000 5,20,000 7,56,000 1,84,000 2,88,000

17,48,000 4,52,000

1,16,000 1,84,000 3,00,000 1,52,000

Variance

5 40,000 F 20,000 F 36,000 A

4,000 A 18,000 A 38,000 A

2,000 F

16,000 A 16,000 F

- 2,000 F

50,000 A (48,000)

1 Sales Variable costs Direct Materials Direct Labour Factory Overheads Selling overheads Total Contribution (A) Fixed Cost Factory overheads Selling overheads Total (B) Profit (A-B) Volume variance Net Loss

(ii)

(1)

Variance Analysis

Sales Std. Price Std. profit Actual quantity Turnover on Std. Price Actual turnover is given at Rs.22 lakhs. : Price Variance Std. Qty X Std. Profit Actual Qty .X Std. Profit Quantity Variance Direct Materials Std. Cost Actual Qty.=18,000 AQ X SC Total Actual Cost Material Price Variance Direct Wages Std. Time per unit Std. hourly rate Std. Hours produced Std. Hours=90,000 (a) Std. Hrs. X Std. rate (b) Actual Hrs. X Actual Rate © Actual Hrs. X Std. Rate Efficiency variance

=Rs.24 lakhs /20,000 =Rs.2 lakhs / 20,000 =18,000 and standard price =18,000 X 120

=40,000 (F) =20,000 X 10 =18000 X 10 =Rs.20,000 A

=Rs.6,00,000/20,000 =18,000 X 30

=Rs.120 =Rs.10 =Rs.120 =Rs.21,60,000

=Rs.2 lakhs =Rs.180 lakhs

=Rs.30 =Rs.5,40,000 =Rs.5,20,000 =Rs.20,000 (F)

=5 hours =Rs.8/hr. =90,000 hrs. Std. Rate Rs.8 =Rs.7,20,000

=Rs.7,60,000

(2)

(3) =1,00,000/20,000 =8,00,000/1,00,000 =18,000 units X 5 hrs. Actual Hours=95,000 =90,000 X 8. =Rs.7,56,000 =95,000 X 8 =(a)-( c)=Rs.40,000 (A)

(4)

(5)

(6)

(7)

Rate Variance =( c) –(b)=Rs.4,000 (F) Factory Variable overheads: Std. Rate =Rs.2,00,000/1,00,000 (a) Charged to production =90,000 X2 (b) Std. cost of actual hours =95,000 X 2 (c ) Actual overheads

(a) – (b) =Rs.10,000 (A) (b) – (c ) =Rs.6,000 (F)

Selling variable overheads: Std. Rate =Rs.3,00,000/20,000 (a) Std. cost of output =18,000 X 15 (b) Actual overheads

Adverse Variance Factory overheads- Fixed: Std. Rate = Rs.1,00,000/1,00,000 (a) Std. cost of output of 90,000 (b) Std. cost of actual hours. (95,000) (c ) Budgeted (d) actual

Efficiency variance : (a) – ( b) =Rs.5,000 (A) Capacity variance : (b) – ( c) =Rs.5,000 (A) Expenses variance : (c )- (d) =Rs.16,000 (A)

Selling overheads : Fixed: Standard =Rs.2 lakhs / 20,000 (a) Std. cost of output =18,000 x 10 (b) Budget (c )Actual Volume variance = (a) – (b) Expense variance = (b)-( c)

=Rs.2/hr. =Rs.1,80,000 =Rs.1,90,000 =Rs.1,84,000

Being efficiency variance Being expense variance

=Rs.15 / unit =Rs.2,70,00 =2,88,000 =18,000

=Re.1/hr. =Rs.90,000 =Rs.95,000 =Rs.1,00,000

=Rs.10 per unit =Rs.1,80,000 =Rs.2,00,000 =Rs.1,84,000 =Rs.20,000 (A) =Rs.16,000 (F)

Ans: 57:Working Notes: 1. Sales Variances (1) Sales Volume Margin Variance

(Actual Sales Volume – Budgeted Volume ) x Standard Margin =(22,000 units – 20,000 units) x Re.1

(2) Sales Margin Price Variance Actual Sales Volume x (Actual Selling Price – Budgeted Selling Price) =(14,000 units (Rs.5 – Rs.5) + ( 8,000 units x (Rs.4.75 – Rs.5)

2. Material Variances (1) Material Price Variance

(Std. Price – Actual Price) x Actual Quantity A : (0.30 – 0.20) x 16,000 kg. B : (0.70 – 0.80) x 10,000 kg.

=Rs.2,000 (F)

=Rs.2,000 (A)

=Rs.1,600 (F) =Rs.1,000 (A) =Rs.600 (F)

(2) Material Mix Variance Total Actual Quantity (S.C. of Std. mix per kg. – S.C. of actual mix per kg.)

= 26000kg Rs.10000 Rs.11800

20000kg 26000kg

=Rs.1,200 (F) (3) Material Yield Variance

Std. rate per kg. of output (Actual Yield – Std. Yield ) = 0.50 ( 24,000 kg. – 26,000 kg.)

(3) Labour Variance (1) Labour Rate Variance

(Std. rate p.h. – Actual rate p.h. ) x Actual hours Skilled Labour : (Rs.3 – Rs.2.95 ) x 13,000 hrs.

=Rs.1,000 (A)

=Rs.650(F)

(2)

(3)

(4) (1)

(5) (1)

(2)

Unskilled Labour : (Rs.2.50 – Rs.2.60 ) x 6,300 hrs. =Rs.630(A) Labour Efficiency Variance (Std. hrs. for Actual output – Actual hours ) x Std. rate p.h. Skilled Labour : (Rs.10,800 hrs-12,000 hrs.) x Rs.3 =Rs.3,600 (A) Unskilled Labour : (6,240 hrs. – 6,300 hrs.) x Rs.2.50 =Rs.150 (A) Idle Time Variance (Idle hours x Standard Wage rate p.h) Skilled Labour : 1,000 hours x Rs.3 Variable Overhead Variance Variable Overhead Expenditure Variance (Variable Overhead recovered on actual output – Actual Variable Overhead) = (24,000 units x Re.0.50) – Rs.15,000 Fixed Overhead Variances Fixed Overhead Expenditure Variance (Budgeted Expenditure – Actual Expenditure) = (Rs.20,000 – Rs.18,020) Fixed Overhead Volume Variance (Budgeted Volume – Actual Volume ) x Std. rate per unit = (20,000 units – 24,000 units ) x Re.1

Variance

Favourable

=Rs.20(F)

=Rs.3,750 (A)

=Rs.3,000 (A)

=Rs.3,000 (A)

=Rs.1,980 (F)

=Rs.4,000 (F)

Actual

Adverse 20,000

Statement reconciling Actual Profit and Budgeted Profit Particulars Reference to

working note

Budgeted profit (as per Budgeted income statement) 1.Sales Variances Sales Volume Margin Variance Sales Volume Margin Variance

Profit before adjustment of Cost Variances II Material - Price

- Mix - Yield

III. Labour Variance - Rate -Efficiency -Idle time

IV. V. Overheads -Expenditure

V. F. Overheads

Actual Profit

-Expenditure -Volume

-

(1) (2)

(1) (2) (3)

(1) (2) (3) (1)

(1) (2)

2,000 -

600 1,200

-

20 - - -

1,980 4,000 7,800

2,000

- -

1,000

- 3,750 3,000 3,000

- -

10,750

20,000

2,950 17,050

Ans. 58: (1) Statement showing the amount of sales target fixed and the actual amount of contribution earned.

(Rs.’000)

Zonal Sales Officers A B C D Commission earned Actual sales: (Commission earned / 5%) Sales price variance Sales volume variance

29.9

598 4 (F) 6 (A)

23.5

470 6 (A) 26 (F)

24.5

490 5 (A) 15 (F)

25.8

516 2 (A) 8 (F)

Sales target / Budgeted sales Standard cost of sales target Standard margin/ Budgeted margin Sales margin mix variance Sales price variance Actual margin

600 500 100

14 (A) 4 (F) 90

450 375 75

8 (F) 6 (A) 77

480 400 80

17 (F) 5 (A) 92

510 425 85

3 (A) 2 (A) 80

Note: As there is no information about sales margin quantity variances, therefore for calculating actual contribution the same has been assumed to be zero.

(2) Statement to evaluate the performance of zonal sales officers

Zonal Sales Officers S. No. Base factor to

evaluate performance A B C D

Efficiency towards the target sales:

1. (a) Whether target achieved (b) Actual sales to Target sales ratio (Actual / target) (%)

(c) Ranking 2. (a) Contribution

earned (in Rs.’000) (b) Ranking

3.. (a) Standard margin/ sales target ratio (b) Actual margin / Actual sales ratio (%) (c) Ranking

Recommendation:

No

99.67 598 100

Yes

104.44 470 100

Yes

102.98 490 100

Yes

101.18 516 100

600 IV 90

II 16.67

15.05

IV

450

I 77

IV 16.67

16.38

II

480

II 92

I 16.67

18.78

I

510

III 80

III 16.67

15.50

III

A review of performance of four officers based on three based factors, shows that the performance of officer C is the best.

Ans. 69:Kitchen King’s Score card should describe its product differentiation strategy. The key points that should be included in its balance score card are

Financial Prospective – Increase in operating income by charging higher margins on Maharaja. Customer Prospective – Market share in high-end kitchen range market and customer satisfaction. Internal business perspectives: Manufacturing quality, order delivery time, on time delivery and new

product feature added. Learning and Growth prospective: Development time for designing new end product and improvement

in manufacturing process. Operative Income:

(Amount in 000 Rs.)

2003 2004 Revenue (40000×1000: 42000×1100) 40000 46200

Direct Material 12000 13530 Conversion cost 10000 11000 Selling and Customer service 7200 7250 Total cost 29200 31780 Operative Income 10800 14420

Change in operating Income 36, 20,000 (F) A. Growth Component

(a) Revenue effect = Output Price in 2003{Actual units sold in 04 – Actual units sold in 03} = Rs.1, 000 (42,000 units – 40,000 units) = Rs.20, 00,000 (F) (b) The cost effect = Input price in 2003{Actual units of input to produce 2003 output less Actual units of input which would have been used to produce year 2004 output on the basis of 2003}

(i) Direct Material = Rs.100 [1, 20,000sqft – 1, 20,000sqft × 42000 units] 40000 units

= Rs.6, 00,000 (A) (ii) Conversion cost and selling and customer service will not change since adequate capacity exists in 2003 to support 2004 output and customers. Hence variance Conversion cost = 200(50000 – 50000) = 0 S & Customer Service = 25000(300 – 300) = 0 Increase in operating effect of Growth component is Rs14, 00,000 (F)

B. Price recovery Component: (i) Revenue effect = Actual output in 2004 [Selling price per unit in 2004 less Selling price per unit in 2003]

= 42,000units (Rs.1, 100 – Rs1, 000) = Rs.42, 00,000 (F) (ii) Cost effect = Unit of input based on 2003 actual that would have been used to produce 2004 output {Input prices per unit in 2003 less Input prices per unit in 2004}

(a) Direct material = 1, 26,000sqft (Rs.100/sqft – Rs.110/sqft) = Rs.12, 60,000 (A)

(b) Conversion Cost = 50,000 units (Rs.200/unit –Rs.220/unit) = Rs.10, 00,000 (A)

(c) S & Custr Service = 300 customers (Rs.24, 000 –Rs.25,000) = Rs.3,00,000 (A) = Rs.25, 60,000 (A)

Increase in Operating income due to Price Recovery is Rs.16, 40,000 (F) {Rs.42, 00,000 – Rs.25, 60,000} (C) Productivity Component

Productivity component = Input Prices in 04 {Actual units of input which would have been used to produce year 2004 output on the basis of 2003 actual less Actual Input} (i) Direct Material: Rs.110/sqft (1, 26,000 units – 1, 23,000 units) = Rs.3, 30,000(F) (ii) Conversion Cost: Rs.200/unit (50,000 units – 50,000 units) = 0 (iii) Selling & Customer = Rs.25, 000 (300 customers – 290 customers)

= Rs.2,50,000 (F) = Rs. 5,80,000 (F)

The change in operating income from 2003 to 2004 is analyzed as follows: (Amount in 000 Rs.)

2003 Growth component Price recovery Cost effect of productivity component 2004 Revenue 40000 2000 (F) 4200 (F) ------------ 46200 Cost 29200 600 (A) 2560 (A) 580 (F) 31780 Operating Income 10800 1400(F) 1640 (F) 580 (F) 14420

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Ans. 7: Maximum capacity 80,000 units Presented sales 20,000 units @ `100 p.u.

Selling price/unit 100

90 80

∴Target cost/unit

(b) At present Variable cost/unit = 40% of cost i.e. 75 = `30 ∴Fixed cost/unit = 100 –25% = 75

COS Less: Variable cost/unit

Fixed cost cost 45×80,000 = 36 lakhs ∴Add full capacity target cost

Total estimate cost Fixed cost Variable cost (80,000 ×40)

= `60/unit ×80,000 units = `48 lakhs

36 lakhs 24 lakhs

60 lakhs ∴Required. Cost reduction following value engineering is `12 lakhs.

(e) Rate of return 15%

ROCE = (PBI/Investment) ∴Investment = (PBI/ROCE) = 16 lakhs/15% = `10666667.

Ans. 8: Target profit Add: Fixed cost Add: Additional Advertisement (a) Total contribution (b) Required. Sales volume contribution/unit (a¸b) Target Selling price/unit Less: Contribution/unit Target variable cost p.u.

Less: material cost p.u. Labour + Variable overhead Labour: x hr. @ 4

CA. Parag Gupta Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in

Demand 20,000 40,000

80,000 = Full capacity = 80 –25% of sales = 80- 20 = 60 p.u.

75 30

45 p.u. Total fixed

Profit p.u. 25% of 80 = 20/unit Profit before tax = 20×80,000 = 16 lakhs

25,000 1,40,000

28,500 1,93,500

12,000 16.125

32 16.125 15.875

8.000 7.875

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Solutions of Target Costing, Value Chain Analysis

-2-

Variable overhead x hr. @ 0.5 ∴4.5x = x (hr.) Time/unit Present Time reduced

Ans. 9 (i) Cost of product as per Target Costing

Selling Price per unit Less: Markup (25% of cost or 20% of selling Price) Target Cost per unit (`)

(ii) Cost of product as per Traditional Costing

Maximum Volume (units)

Material Labour Prime Cost Store Support (30% of Prime Cost) Total Cost per unit Total Cost

Coco 60,500

Stawberry 24,200

Vanilla 72,600

Coco 23.00 4.60

18.40

Stawberry 18.00 3.60

14.40

Vanilla 13.00 2.60

10.40

7.875 1.75 1.75

_ 2.00 0.25 hr.

` 8.00 5.00

13.00 3.90

16.90 10,22,450

` 6.00 4.00

10.00 3.00

13.00 3,14,600

Stawberry 24,200

` 5.00 3.00 8.00 2.40

10.40 7,55,040

Vanilla 72,600

(iii) Cost of product as per Activity Based Costing Coco

Maximum Volume (units) 60,500 `

Material Labour Prime Cost Overheads (Working Note-2) Total Cost per unit Total Cost

8.00 5.00

13.00 3.29

16.29 9,85,320

` 6.00 4.00

10.00 5.23

15.23 3,68,670

` 5.00 3.00 8.00 2.17

10.17 7,38,100

Vanilla 10.40 10.40 10.17

(iv) Comparision in Cost of each product under each method Coco Stawberry

As per Target Costing 18.40 14.40 As per Traditional Costing 16.90 13.00 As per Activity based Costing 16.29 15.23

Comment: Since cost of Strawberry is high in ABC costing in comparison to target costing and traditional methods, it is indicating that actual profit under target costing is less than targeted.

Working Note-1 :

Current Selling Price per unit (`) Current Sales (units) Selling Price (`) Revised Sales (units) Selling Price (`) Revised Sales (units) (upto production capacity)

Coco 25.00

50,000 24.00

55,000 23.00

60,500

Stawberry 20.00

20,000 19.00

22,000 18.00

24,200

Vanilla 15.00

60,000 14.00

66,000 13.00

72,600

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-3-

Working Note-2 :

Ordering Cost (35/30/15 @ 800) Delivery Cost (112/66/48 @ 700) Shelf Stocking (130/150/160 @ 199) Customer Support (60,500/24,200/72,600 @ 1.1) TOTAL COST No. of units Cost per unit

Coco 28,000 78,400 25,870 66,550

1,98,820 60,500

3.29

Stawberry 24,000 46,200 29,850 26,620

1,26,670 24,200

5.23

Vanilla 12,000 33,600 31,840 79,860

1,57,300 72,600

2.17 Note: On calculation of total overhead costs under traditional & ABC system, costs are same i.e. `4,82,790, hence we will ignore the line “In ABC these costs are coming under customer support and assistance.” written in question.

Ans. 10: (a) (i) The target cost of each product after reduction is computed as follows:

Product

A B C D

Present Price (`) 180 175 130 180

Proposed Price (`) 175 170 125 175

Target Cost (`) (with 25% Margin)

140 136 100 140

(ii) Statement showing cost/unit of Driver as per ABC

Cost

Set-ups Stores receiving Inspection/Quality Handling/Dispatch Machine Department

Amount

26,250 18,000 10,500 23,100 52,130

Driver

Production runs Requisition Production runs Orders Machine Hrs.

No.

105* 400** 105 210

6,500

Cost/unit of Driver

`250.00 `45.00 `100.00 `110.00 `8.02

* Production runs = (600/20) + (500/20) + (400/20) + (600/20) = 105 ** Requisitions = 100 for each product or 400 total Machine hours = 2,400 + 1,500 + 800 + 1,800 = 6,500 hours.

Statement showing Total Cost and Cost Per Unit as per ABC

Item

Direct Material Direct Labour Set-up Stores receiving Inspection/Quality Handling/Dispatch Machine Dept. Cost

CA. Parag Gupta

A `

24,000 16,800 7,500 4,500 3,000 6,600 19,248

B `

25,000 10,500 6,250 4,500 2,500 5,500 12,030

C `

12,000 5,600 5,000 4,500 2,000 4,400 6,416

D `

36,000 12,600 7,500 4,500 3,000 6,600 14,436

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-4-

Total Cost Output (Units)

81,648 600

66,280 500

39,916 400

99.79

C `

99.79 100.00 (-) 0.21

84,636 600

141.06

D `

141.06 140.00 (+) 1.06

Cost per unit 136.08 132.56 (iii) Comparison of Actual Cost and Target Cost

Cost

Actual Target Difference

Comment:

A `

136.08 140.00 (-) 3.92

B `

132.56 136.00 (-) 3.44

The total actual cost of A, B and C product is less than the target cost so there is no problem in reducing the cost of these product by `5 from the present price. It will increase the profitability of the company but the cost of D is slightly more than the target cost, it is therefore, suggested that the company should either control it or redesign it.

Ans. 11: Working Notes: Particulars

(a) (b) (c) (d) (e) (f) (g)

Production/Sales Quantity (units) Batch Size (units) No. of batches Set up time per batch (hours) Total set up hours (c d) (hours) Machine set up cost (`) Cost driver per machine set up hour 4,62,000

= `70 6,600

(h) (i) (j)

(k)

Testing time per unit Total testing time (a h) (hours) Testing cost

5 hours 5,00,000

9 hours 4,50,000

P 1,00,000

1000 100

30 3,000

Q 50,000

500 100

36 3,600

4,62,000

`23,75,000 Cost driver per testing hour 23,75,000

= `2.50 9,50,000

(a) Computation of full cost per unit using Activity Based Costing: Particulars Direct material Direct labour Direct machine cost Machine set up cost

Testing cost

CA. Parag Gupta

Basis Direct Direct Direct

3,000 hours @ `70 3,600 hours @ `70

5,00,000 hours @ `2.50

P 42,00,000 15,00,000 7,00,000 2,10,000

Q 30,00,000 10,00,000 5,50,000

2,52,000 12,50,000

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-5-

Engineering cost Total cost (`) Cost per unit (`)

4,50,000 hours @ `2.50 Allocated

11,25,000 8,40,000

87,00,000 87.00

14,10,000 73,37,000

146.74

Per unit 100.05

87.00 13.05

(b) Mark up on full cost basis for Product P: Particulars Selling price Less: Full cost Mark up Percentage of mark up on full cost = 13.05 /87 = 15 %

(c) Target cost of Product P after new design is implemented

Target price (given)

Mark-up 86.25 ×15 115

75.00

86.25 11.25

Target cost per unit (`)

(d) Statement of cost for new design of P Particulars

Direct Material Direct Labour Direct Machining cost

Machine set up cost Testing cost Engineering cost Total cost

Basis Decreased by `5 p.u. Decreased by `2 p.u. No change as machine is dedicated 100 set up 28 hours 1,00,000 units `2.5 No change

Cost P.U. 37.00 13.00 7.00

1.96 10.00 8.40 77.36

Total Cost 37,00,000 13,00,000 7,00,000

1,96,000 10,00,000 8,40,000

77,36,000

`70 4 hours

The target cost is `75 p.u. and estimated cost of new design is `77.36 p.u. The new design does not achieve the target cost set by Computo Ltd. Hence the target mark up shall not be achieved.

(e) Possible Management Action: Value engineering and value analysis to reduce the direct material costs. Time and motion study in order to redefine the direct labour time and related costs. Exploring possibility of cost reduction in direct machining cost by using appropriate techniques. Identification of non-value added activities and eliminating them in order to reduce overheads. The expected selling price based on estimated cost of `77.36 per unit is (`77.36 + 15%) `88.96. Introduce sensitivity analysis after implementation of new design to study the sales quantity changes in the price range of ` 86.25 to `88.96.

Ans. 12:

P1

CA. Parag Gupta Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in

P2

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-6-

`/unit Material Overhead-Material handling Assembly Management Machine insertion Manual insertion Quality testing Present cost Target cost

407.5 85×1.2 = 102 40×3.2 = 128

48×0.7 = 33.6 36×2.1 = 75.6

1.4×25 = 35 781.70 680.00

Revised P1 `/unit

Direct material Overhead: Material handling Assembly hour Machine inspection Manual inspection Electronics Estimated cost Target cost

381.20

(71×1.2) = 85.2 (21×40) = 84.0 (59×0.7) = 41.3 (12×2.10) = 25.2 (1.2×25) = 30.00 646.90 680.00 Achieved

Ans. 24: Machine X-Life 12 years Year

Purchase price Overhead cost Trade-in-value Annual repair cost

Annualized equivalent

Machine W-Life 6 years Year

Purchase price Overhead cost Trade-in –value Annual repair cost

0 4 6

1-6

Cost

0 8

12 1-12

Cost

`/unit 292.1

46×1.2 = 55.2 40×1.9 = 76

31×0.7 = 21.7 25×2.1= 31.5

1.1×25 = 27.5 504.00 390.00

Revised P2 `/unit 263.10

(39×1.2) = 46.8 (1.6×40) = 64.0 (29×0.7) = 20.30 (10×2.10) = 21.00 (0.9×25) = 22.50 437.70 390.00 not achieved

` 19,000

4,000 (3,000)

2,000

Discount Factor

1.00 0.47 0.32 6.81

=`33,540 / 6.81=`4,925

Discount Factor

1.00 0.68 0.56 4.36

Discounted Cost ` 19,000

1,880 (960)

13,620 33,540

` 13,000

2,000 (3,000)

2,600

Discounted Cost ` 13,000

1,360 (1,680) 11,336 24,016

Annualized equivalent `24,601 / 4.36=`5,508 Recommendation : Purchase machine ‘X’ Assumptions:

a. Same performance, capacity and speed. b. No. inflation. c. 12 year-estimates are as accurate as 6 – year estimates. d. Cash flow at the year end.

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-7-

Ans. 25: The cost driver rates are as follows: Product design = `250 per design hour (`2m/8000 hours) Purchasing = `50 per purchase order (`200000/4000 orders) Production (excluding depreciation) = `100 per machine hour ((`1 500000-`300000)/ 12000 hours) Packing =`20 per cubic meter (`400000/ 20000) Distribution =`5 per kg (`600000/ 120000) The activity –based overhead cost per unit is as follows:

(`) Product design

Purchasing

Production Depreciation

(400 design hours at `250 per hour=`100000 Divided by life –cycle output of 5000 units) (5 purchase orders at 50 units per order costing A total of `250 per output of 250 units) (0.75 machine hours at `100 per machine hour) (Asset cost over life cycle of 4 years= 16 quarters Depreciation at `8000 per quarter divided by life cycle Output of 5000 units) (0.4 cubic meters at `20) (3 kg at `5)

20.00

1.00 75.00

25.60 8.00

15.00 144.60

Packing Distribution Total costs Ans. 26: The total cost consists of the installation cost plus electrical charges for 5 years.

(i) So total cost for Electric immersion heater =`160 + 200X5 =`1160 (ii) Total cost for a gas boiler =`760 + `80X5 =`1160

Hence, on the total cost basis, both the equipments have equal preference, and the housewife can choose any one. Let us now calculate the present value of money for each of the two possibilities. Year PV factor @ Electric Immersion heater Gas Boiler

9% p.a Operating Cost Discounted Operating Cost ` Discounted Cost `

` Cost ` 0 1.0000 160 160.00 760 760.00 1 0.9174 200 183.48 80 73.39 2 0.8417 200 168.34 80 67.33 3 0.7722 200 154.44 80 61.78 4 0.7084 200 141.68 80 56.67 5 0.6499 200 129.98 80 51.99

Total Cost=937.92 Total Cost =1071.16 (`938,say)

(`1071 say) On the basis of present value @ 9% p.a over a period of five years, the total cost of Electric immersion heater is `938 and that of a Gas boiler is `1071. Hence, the housewife is advised to purchase an electric immersion heater. If the equipment are to be considered for a period of 8 years, then Total cost for electrical immersion heater =`160+200X8 =`1760 Total cost for gas boiler =`760+`80X8 =`1400 Hence, the housewife will be advised to purchase a gas boiler. Year PV factor @ Electric Immersion heater Gas Boiler

9% p.a Operating Cost Discounted Operating Cost ` Discounted Cost `

` Cost ` 6 0.5963 200 119.26 80 47.70 7 0.5470 200 109.40 80 43.76 8 0.5019 200 100.38 80 40.15

329.04 (329,say) 131.61 (`132 say)

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-8-

= P.V. over five years + P.V. over next three years =`938+`329 =`1267 Present value in case of gas boiler =`1071+`132 =`1203 Hence, over a 8 years period, the present value of a gas boiler is less. On the basis of total cost as well as present value of money, gas boiler is cheaper over 8 years period, hence the housewife is advised to purchase a gas boiler. Ans. 27: Relevant Operating Cash outflow p.a. if part X 248 is outsourced Purchase Cost (Cash outflow) (a) 50000 Relevant Cash inflow from outsourcing: Direct materials 22000 Direct Labour 11000 Variable Overhead 7000 Product and Process engineering 4000 Rent 1000 Total Cash Savings (b) 45000 Net Cash Outflow (a) - (b) (5000) Net Present Value of cash inflow if part is outsourced Particulars Year P.V. factor @ 12% Amount ` P.V ` Disposal value of machine 0 15000 1000 15000 Cash Outflow due to outsourcing 1 5000 0.893 (4465)

2 5000 0.797 (3985) 3 5000 0.712 (3560) 4 5000 0.636 (3180) 5 5000 0.567 (2835)

NPV (3025) Analysis : Since the NPV is negative , it is desirable to manufacture the part internally. Notes:

(1) Equipment depreciation is a non- cash cost item. Therefore, it is not relevant. (2) Product and process engineering cost being avoidable hence relevant for the entire period of

outsourcing i.e. for 5 years. (3) Allocated rent is irrelevant but rent saved (i.e, `1000) is relevant. (4) Allocated general plant overhead is irrelevant.

(ii) Sensitivity analysis with respect to quantity is desirable: � If demand for the part decreases vendor is willing to supply a lower quantity at the same price (`

50/-). � If the part is continued to be made internally, the costs would not decrease quite fast with lower

quantities because of fixed costs. � Net cash outflows of outsourcing will be smaller if lower quantities of the part are demanded. But if

the demand increase, it would be preferable to make the part – in – house.

Non – financial factors: � Will the units of part required be delivered on schedule? � Will quality be maintained? � Can suggested modifications be really accommodated? � Will the subcontractor remain in business for next five years?

(iii) As the outsourcing of part X – 248 will start from July ‘1998, the bonus of Gemini enterprises based on the accounting income, which Mr. Sen wishes to maximise will remain unchanged for the year 1997 - 98

Ans. 28: Evaluation of Alternative proposals Alternative I :Repairs to existing machine: Cost of Repairs Equivalent annual cost for 5 years Add: Running and Maintenance cost p.a net of tax Present value of cash outflows p.a

Alternative II : Replace the old machine

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(`) 19000 X 50 / 100 (9500 / 3.791) (20000 X 50 / 100)

=`9500 2506

10000 12506

-9-

49000 5000

44000 (44000 / 6.145) 7160 (14000 X 50 / 100) 7000

14160 Less : Tax Saving on depreciation (49000 / 10 ) X 50 / 100 2450 Present value of cash outflow p.a. 11710 Analysis : From the above analysis it is observed that alternative II i.e., replacement of old machine with a new machine is more profitable, since the cash outflow p.a. will decrease by `796 (i.e. `12506 – `11710 ) if old machine is replaced with new machine.

Purchase cost of new machine Less: sale proceeds of old machine Net: Cash Outflow Equivalent annual cost for 10 years Add: Running and maintenance cost p.a. net of tax

CA. Parag Gupta Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in Costing & O.R. World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

TRANSFER PRICING U

Ans 9 (i) In this case there are two options available –

(a) Sell at the sub assembly stage (after completion of Div. A) @ Rs. 2000/- Incremental cost in Div. A Contribution

(b) Sell at the final product stage Cost at Div. A and Div. B Rs(1200+1500)

Rs 1,200/- Rs 800/- Rs. 3,000 Rs 2,700

Contribution Rs 300 Therefore it is profitable to sell at the subassembly stage because of higher contribution, provided there is a market. Hence, if there is market at intermediate stage, first priority is to sell assembly).Therefore, 800 units should be sold as sale of intermediary.

intermediary (sub

The balance capacity available of (1000 – 800) = 200 units should be transferred to B and B should complete the assembly and sell as final product, since the company can earn Rs. 300 per unit for each unit of such sale.

(ii) If B Div. receives the subassembly at market price of Rs. 2,000, plus its own incremental cost of Rs. 1,500 will give total cost of Rs. 3,500, thereby yielding a loss of Rs. 3500 – Rs. 3000 = Rs. 500 per unit, whereas the company makes a profit of Rs. 300 per unit. In order to keep the manager of Div. B motivated, the profit earned of Rs. 300 per unit should be shared between A and B. Hence transfer price will be variable cost of Div. A + 50% of profit earned in the final product = 1200 + 150 = Rs. 1,350

(iii) Both Div. A and the Company make higher contribution by selling to intermediate market. If the market demand increases to 1,000 units, the full quantity should be sold outside as intermediary and nothing should be transferred to Div. B

Ans.10: Transfer Price is Rs. 4,500 for each consulting day. Profit mark-up = 150% Let cost = x

Profit = x × 150 = 1.5x

100 Cost + profit = Transfer price x + 1.5x = 4,500 2.5x = 4,500 x = 1,800 ∴Cost = Rs. 1,800 and profit = 1.5x = 1.5×1,800 = Rs. 2,700

Variable cost (80%) = Rs. 1,800× 80% = Rs. 1,440 Fixed cost (20%) = Rs. 1,800 ×20% = Rs. 360.

Scenario (i): Every consultancy team is fully engaged. There is no idle time or spare capacity. Hence, transfer price = Marginal cost plus opportunity cost Marginal cost = Rs. 1,440 Saving for internal work = Rs. 200 Net Marginal Cost = Rs. 1,240

Opportunity cost is the lost contribution. Lost contribution = Contribution from external client

= Fee charged from external client – Variable cost = Rs. (4,500 – 1,440) = Rs. 3,060.

∴Transfer price = Rs. 1,240 + 3,060 = Rs. 4,300 per consulting day per team.

Scenario (ii): One team is idle. Idle time has no opportunity cost. Variable cost for internal work is Rs. 1,240 per consulting day. Second team is busy. Hence opportunity cost is relevant in case of second team. Hence charge of second team is Rs. 4,300 per consulting day per team. Average of charge of two teams = Rs. (1,240 + 4,300) / 2

= Rs. 2,770 per consulting day per team.

Scenario (iii): New client offers a fee of Rs. 15,84,000 Duration: 5 days of 48 weeks ×2 teams Fee per day 15,84,000 / 480 Variable cost = Rs. 1,440 Contribution Rs. (3,300 – 1,440)

Fee for consulting day for internal work: Variable cost Contribution lost Fee to be charged

= 480 days = Rs. 3,300

= Rs. 1,860

= Rs. 1,240 = Rs. 1,860 = Rs. 3,100 per consulting day per team.

Ans.11:

100% capacity 4,000 tones (Maximum) Distribution market Processing unit

80% capacity 3,200 tones Market Processing unit

2,000 Tones 2,000 Tones

2,000 Tones 12,00 Tones

(a) 80% capacity – price Rs. 400 per ton (Rs.) Particulars Basic unit Particulars Processing unit Sales (3,200 * 400) 12,80,000 (24,000 * 40) 9,60,000 Raw materials (3,200 * 70) 2,24,000 Tr. Price (1,200 * 4,80,000 Variable cost (3,200 * 140) 4,48,000 400) 2,04,000

(1,200 * 170) Fixed overhead 3,00,000 1,20,000 9,72,000 8,04,000

Profit 3,08000 1,56,000 Total profit of the company = Rs. 4, 64,000

(b) 100% capacity – price Rs. 400 per ton Particulars Basic unit

Sales (4,000 X 400) Raw materials (4,000 X 70) Variable cost (4,000 X 140) Fixed overheads

Profit

(Rs.) Processing unit

12,80,000 8,00,000 3,40,000 1,20,000

12,60,000 20,000

Particulars

16,00,000 (4000 X 320) 2,80,000 Tr. Price (2,000 X 400) 5,60,000 (2,000 X 170) 3,00,000

14,00,000 4,60,000

Total Profit of the Company = Rs. 4,80,000

(c ) 80% capacity- Market price @ Rs.360 & Transfer price to processing @ Rs. 400 per tonne

Particulars Sales (2,000 X 360) + (1,200 X 400) Raw materials (3,200 X 70) Variable Cost (3,200 X 140) Fixed overheads

Basic unit

12,00,000 2,24,000 4,48,000 3,00,000 9,72,000

Particulars

(24,000 X 40) Tr. Price (1,200 X 400) (1,200 X 170)

(Rs) Processing unit

9,60,000 4,80,000 2,04,000

1,20,000 8,04,000 1,56,000 Profit 2,28,000

Total Profit of the Company = Rs. 3,84,000

(d) 100% capacity- Price Rs. 360 per tonne Particulars Basic unit Sales (4,000 X 360) 14,40,000

2,80,000 Raw material (4,0000 X 70) 5,60,000 Variable overheads (4,000 X 140) 3,00,000 Fixed overheads

11,40,000

Particulars

Tr Price (2,000 X 360) (2,000 X 170)

(Rs.) Processing units

12,80,000 7,20,000 3,40,000

1,20,000 11,80,000

1,00,000 Profit 3,00,000 Total profit o the Company = 4,00,000

Comments : At Rs. 400 per tonne, the processing unit will not be interested in buying more than 1,200 tonnes because the profitability of the processing unit will be reduce from Rs. 1,56,000 to Rs. 2,000. When the market price reduce to Rs. 360 per tonne the processing unit will not be interested in purchasing more than 1,200 tonnes because at this level it can maintain the same level of profit. Even if the price is reduced to Rs.360 for the processing unit, it may not be interested in buying more than 1,200 tonnes as its profitability will be reduced from Rs.1,56,000 to Rs.1,00,000. When the market price reduced to Rs.360 per tonne and the transfer price is maintained at Rs.400, the processing unit may get its suppliers of 1,200 tonnes via open market at the price less than Rs.400 per tonne. This will increase the profitability of the processing unit but reduced the profitability of the basic unit. Thus the present policy market price for transfer pricing does not offer incentive to the processing unit. Hence cost plus method should be restored to.

Ans. 12 (i) (a) At 80% level (in Rs)

24,00,000 -Process house Sales(1,50,000/100) × 825 Less Transfer Price (1,50,000 × 6) Variable cost (1,500 Fixed cost Profit

12,37,500

9,00,000 1,20,000 1,00,000 1,17,500

-Textile unit Sales (4,00,000 × 6) Less Raw material (4,00,000 Variable cost (4,00,000 Fixed cost Profit

× 3) × 1.2)

12,00,000 4,80,000 4,12,000 3,08,000

× 80)

Overall profit = 3,08,000 + 1,17,500 = Rs 4,25,500 At 100% level Sales (5,00,000 Less Raw material (5,00,000

Variable 1.2) Fixed cost Profit

cost

× 6) 30,00,000 Sales (2,50,000/100) Less Transfer × 6) Price

× 725

(2,50,000

18,12,500

× 3) 15,00,000

6,00,000

4,12,000 4,88,000

15,00,000 2,00,000

1,00,000 12,500

(5,00,000 × Variable cost

Fixed cost Profit

Overall profit = 4,88,000+12,500 = Rs 5,00,500

(b) At 80% level (market price 5.60 and transfer price 6/-) Textile unit Sale (2,50,000

Process house 1400000

900000 23,00,000

Less Raw material (4,00,000 Variable cost (4,00,000 Fixed cost Profit

(in Rs)

× 5.6) (1,50,000 × 6.0)

× 3) × 1.2)

12,00,000 4,80,000 4,12,000 2,08,000 Profit 1,17,500

Overall profit = 2,08,000+1,17,500 =Rs 3,25,500 (c) Sales 100% level at (5.60) (in Rs)

Sale (5,00,000 Less

× 5.6) 28,00,000 Sales(2,50,000 Less

× 725) 18,12,500

Raw material (5,00,000

Variable cost (5,00,000

Fixed cost Profit

× 3)

× 1.20)

15,00,000

6,00,000

4,12,000 2,88,000

Transfer Profit (2,50,000 × 5.6) Variable cost (2,500 80) Fixed cost Profit

14,00,000 2,00,000

1,00,000 1,12,500

×

Overall profit = 2,88,000 + 1,12,500 =4,00,500 (ii) Comments on the profitability of processing units:-

Transfer price (Rs) (a)

(b) (c)

80% capacity 100% capacity 80% capacity 100% capacity

6.00 6.00 6.00 5.60

Profit (Rs) 1,17,500

12,500 1,17,500 1,12,500

Processing house will not be interested to buy more than 1,50,000 meters from textile units.

Ans.: 13 Particulars Selling Price Variable costs Contribution Alternative I Division AD

Contribution (15,000 units of BRITE X Rs.150) (40,000 units of LITE X Rs.20) Total Contribution Fixed Expenses Profit

Division CD (Rs)

Contribution (5,000 units of TITE X Rs.110) Fixed Expenses Profit Overall profit of the company

BRITE 300 150 150

LITE 60 40 20

(Rs.) TITE 700 590 110

(Rs)

22,50,000 8,00,000

30,50,000 20,00,000 10,50,000 (a)

(b) (a + b)

5,50,000 4,00,000 1,50,000

Rs.12,00,000

Alternative II Division AD

(Rs) Contribution (15,000 units BRITE outside customer @ Rs.150) (5,000 units of BRITE Division CD @ 150) (20,000 units of LITE (limited capacity) @ Rs.20) Total contribution Fixed expenses Profit

Division CD Extra cost of labour Rs.50 and variable cost Rs.640 Hence contribution Rs.700 - Rs.640 = Rs.60

(Rs) Contribution (5,000 units @ Rs.60) Fixed Expenses Loss Overall profit of the company

Alternative III Division AD Price of BRITE to CD reduced by Rs.50 Hence Contribution/unit Rs.250 – Rs.150 = Rs.100

(Rs) Contribution (15,000 units of BRITE outside party @ Rs150) (5,000 units of BRITE to CD @ Rs100) (20,000 units of LITE to capacity @ Rs20) Total contribution Fixed expenses Profit Division CD BRITE from AD Rs.250 contribution Rs.700-Rs.590 = Rs.110 per unit Lobour and overhead Rs.340, Variable costs Rs.590 Contribution (5,000 units @ Rs.110) Fixed expenses Loss Overall profit of the company

22,50,000 5,00,000 4,00,000

31,50,000 20,00,000 11,50,000

300,000 400,000 100,000

13,00,000

22,50,000 7,50,000 4,00,000

34,00,000 20,00,000 14,00,000 (a)

(b) (a-b)

(a)

(Rs.) 5,50,000 4,00,000 1,50,000

Rs.13,00,000 (b)

(a+b)

Alternative 1V Division AD Contribution

(15,000 units BRITE outside customer @ Rs.150) (10,000 units of BRITE to CD @ Rs.250 i.e., contribution @ Rs.100)

Total contribution Fixed expenses Profit (a)

(Rs.)

22,50,000 10,00,000 32,50,000 20,00,000 12,50,000

Division CD (Rs.) Contribution

(10,000 units with BRITE of AD @ Rs.110) 11,00,000 (2,000 units with imported component @ Rs.110) 2,20,000

Total contribution 13,20,000 Fixed expenses 11,70,000 Profit (b) 1,50,000 Overall profit of the company (a+b) Rs.14,00,000 Recommendation on best alternative Alternative (iv) seems to be the best because it leads to the maximum profit of Rs. 1400000 for the company. But management should consider whether stopping the production of Lite altogether will, in any way, be detrimental to company’s interests. Negotiated price of Rs. 240 per unit.

The price of Rs. 240 per unit will be acceptable to AD because it will lead to a contribution of Rs. 22.50 per hour i.e. (Rs. 240-Rs.150)÷4 hours. If this proposal is not accepted AD will have to produce Lite which will yield a contribution of only Rs. 20 per hour, i.e. (Rs. 60-Rs.40)÷1 hour.

Ans.: 14: Alternative I AJ

Sales : outside (18,000x15) DJ (2,000x10) Total Less V. Costs( 20,000x8.50) Net Contribution

U Rs. DJ

2,70,000 Sales (2,000 x 105) 20,000 Variable Costs (2,000 x 99)

2,90,000 Contribution 1,70,000 Interest 1,20,000 Net Contribution

Total Group contribution =Rs.1,31,000

3,00,000 Sales (2,000 x 105) 1,70,000 Variable Costs (2,000 x104) 1,30,000 Contribution

Interest Net Contribution

Total Group contribution = Rs.1,31,000

Rs. 2,10,000 1,98,000

12,000 1,000

11,000

Alternative II Sales : (20,000x15) Variable costs(20,000x8.50) Contribution

2,10,000 2,08,000

2,000 1,000 1,000

Alternative III Sales : (20,000x15) Variable costs(20,000x8.50) Contribution

3,00,000 Sales (2,000 x 105) 1,70,000 Variable Costs (2,000x 104) 1,30,000 Contribution

Interest Net Contribution

Total Group contribution = Rs.1,31,000

2,10,000 2,08,000

2,000 1,000 1,000

Alternative IV Sales : (22,000x15) Variable costs 1,87,000 Over time 4,000 Contribution

3,30,000 Sales (2,000 x 105) Variable Costs(2,000 x 104)

1,91,000 Contribution 1,39,000 Interest

Net Contribution Total Group contribution = Rs.1,40,000

2,10,000 2,08,000

2,000 1,000 1,000

Comments: Alternative 1: AJ can supply part 35 to DJ at Rs.10 because the variable cost is Rs.8.50 only and by this transaction a contribution of Rs.1.50 is available. But the overall contribution which would have been Rs.13,000 if the part has been sold to outside buyers, would come down to Rs.1,20,000. DJ however, will earn a net contribution of Rs.11,000. Thus the divisional performance of AJ will go down and that of DJ will boost up at the cost of AJ. Alternative 2: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. Alternative 3: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. In these three cases the group income will not change but the performance of the individual divisions will vary. Alternative 4: AJ’s performance will boost up but DJ’s performance will remain at the low level .DJ cannot show better performance except at the cost of AJ. Hence AJ should not reduce the price particularly when it has an assured market for part 35 at Rs.15 each.

Ans.: 15:

Statement showing profitability of two divisions at two different levels of output using different transfer prices

No. of bottles 8,00,000 Rs.

91,20,000

12,00,000 Rs.

1,27,80,000 Sales value (Packed Product) : (A) Less : Costs Product Manufacturing Division 64,80,000 96,80,000 Bottle Manufacturing Division 10,40,000 14,40,000

75,20,000 1,11,20,000 Total costs : (B) Profit :{(A) – (B)} 16,00,000 16,60,000 Profit pro-rated to Bottle Mfg. Division and Product Mfg. Division. Share of Bottle Manufacturing Division: 16,00,000 × 10,40,000/75,20,000 2,21,276 16,60,000 × 14,40,000/1,11,20,000 2,14,964 Balance profit relates to Product Mfg. Division 13,78,724 14,45,036

16,00,000 16,60,000 Rs. Rs.

Transfer prices of bottles Costs 10,40,000 14,40,000 Profit as computed above 2,21,276 2,14,964

12,61,276 16,54,964 Total price Rs. 1.577 Rs. 1.379 Transfer price per bottle

From the above computations, it is observed that shared profit relative to the cost involved is Rs. 2,21,276 (Re. 0.2766 per bottle) at 8,00,000 production level and Rs. 2,14,964 (Re. 0.179 per bottle) at 12,00,000 production level. The profit of Product Mfg. Division is Rs.13,78,724

(Rs.1.723 per bottle) at 8,00,000 production level and Rs. 14,45,036 (Rs. 1.2042 per bottle) at 12,00,000 production level.

Profitability based on market price No. of bottles Bottle Mfg. Division Market price Less: Cost Profit (i) Product Mfg. Division Sales Less: Bottle cost

Product cost Profit (ii) Total profit : (i) + (ii)

Profit based on cost (Rs.Lakhs)

Product Bottle Mfg. Div. Mfg. Div.

2.21 13.79 2.15 14.45

8,00,000 Rs.

14,00,000 10,40,000

3,60,000

91,20,000 14,00,000 64,80,000 12,40,000 16,00,000

12,00,000 Rs.

20,00,000 14,40,000

5,60,000

1,27,80,000 20,00,000 96,80,000 11,00,000 16,60,000

Production level

8,00,000 bottles 12,00,000 bottles

Observations:

Profit based on Market price (Rs.Lakhs)

Product Bottle Mfg. Div. Mfg. Div.

3.60 12.40 5.60 11.00

1.

2.

3.

Market price methods gives a better profitability to Bottle Mfg. Division at both the production levels. Market price method gives a lower profitability to Product Mfg. Division as compared to Bottle Mfg. Division. Under Cost-based method, there is a better profit at lower level of production in Bottle Mfg. Division. However in Product Mfg. Division 12,00,000 production level gives a higher profit. But in Market price method, the position is quite reverse.

Ans. 16 (i) Statement of contribution (a) When component is purchased by Division B from outside Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) 300000 Company’s total contribution

(Rs.) Nil

8,00,000

3,80,000 1,00,000 1,00,000

(Rs.) (b) When component is purchased from Division A by Division B Division A Sales (2000x 220) 4,40,000 Less: Variable costs (2000x 190) 7,00,000 Division B Sales (2000x 400) 8,00,000 Less: Variable Costs: Purchase cost in Division A (2000x 220) 440000 Variable cost in Division B (2000x 150) 300000 7,40,000 Company’s total contribution

60,000

60,000 1,20,000

Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: 30,000 Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) 300000 7,00,000 1,00,000 Company’s total contribution 1,30,000

Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside.

(iii) Statement of total contribution when component is available from outside at Rs. 185 Division A: Nil Division B: Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) 300000 6,70,000 1,30,000 Company’s total contribution 1,30,000

If the component is purchased by Division B from Division A, the contribution is Rs.1,20,000 as calculated under above. Hence it will be beneficial to buy the component outside. (iv) Fixations of transfer price

(a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged.

(b) If facilities of Division A can be put to alternative uses: (Rs.)

Variable cost Opportunity cost Transfer price

only from

190 15

205

(c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of A. the variable cost of Rs.190 per component should be charged.

U

Division

Ans.17U For the budgeted level of activities and expenses of LD the various costs and prices can be worked out as follows:

(Rs.) Total overheads 7,56,000 Less: Variable overheads 4,20,000 Fixed overheads per year 3,36,000

LXU 4,20,000 x 90,000U

2,10,000 1,80,000

U U Variable overheads

LY 4,20,000 x 1,20,000

2,10,000 2,40,000

U U

Fixed overheads per year At the budgeted level of activities

3,36,000 x 90,000U 2,10,000

1,44,000

U 3,36,000 x 1,20,000U 2,10,000

1,92,000

U

The costs and selling prices of the products of LD for normal sale to outside parties will be as under: (Rs.per kg.) Particulars LX LY Direct material 36 28 Direct wages 30 20 Variable overheads 60 40 Total Variable cost: 126 88 Fixed costs 48 32 Total costs 174 120 Add: Mark-up 50% 87 60 Selling price 261 180

Labour hours calculated as under: Particulars Direct wages Wages rate (Rs./hr.) Direct labour hr.

LX 30

5 6

LY 20

5 4

Committed production of LY of 6,000 kg. would involve labour of 6000 x 4 = 24,000 Balance labour available for:

Production of LX Production of LY

= 42,000-24,000 = 18,000 hrs. / 6 DLH

= 18,000 Hrs. = 3,000 Kg.

Cost estimate of KX it KD purchase Lx from LD at normal prices (Rs.)

Cost of LX Processing materials & Wage costs Variable Overheads Total Variable Cost

Profit Statement of LD & KD (1) Transfer price based on total cost

LD Rs. KD Sales LX (3000 x 261) 7,83,000 Sales KX (2000 x 300)

LY (6000 x 180) 10,80,000 Total Sales 18,63,000 Variable cost Variable cost (2000 x 295)

LX (2000 x 122) 2,44,000 (1000 x 126) 1,26,000

LY (6000 x 88) 5,28,000 Total variable cost 8,98,000 Fixed costs Fixed cost 3,36,000 Total costs Total cost

12,34,000 Profit Loss 6,29,000

Total profit for the company = 6,29,000 – 90,000

261 30

4 295

Rs. 6,00,000

5,90,000

1,00,000 6,90,000 (-)90,000

=Rs.5,39,000

(ii) Transfer price based on total Cost after adjustment for selling expenses LD Rs. KD

Sales LX (2000 x 257) 5,14,000 Sales (2000 x 300) (1000 x 261) 2,61,000

LY (6000 x 180) 10,80,000 Total Sales 18,55,000 Less: Costs as above 12,34,000 Total costs (690000-4 x 2000) Profit 6,21,000 Less

Rs. 6,00,000

6,82,000 (-)82,000

(iii) Total profit to the company =6,21,000-82,000 =Rs.5,39,000 LD Rs. KD

Sales LX (2000 x 122) 2,44,000 Sales KX (2000 x 300) (1000 x 261) 2,61,000

LY (6000 x 180) 10,80,000 Variable cost (2000 x 156) Fixed costs

Total Sales 15,85,000 Total costs Less: Total Costs as above 12,34,000 Profit 3,51,000 Profit

Rs. 6,00,000

3,12,000 1,00,000 4,12,000

1,88,000

Total profit for the Company =3,51,000 + 1,88,000 =Rs.5,39,000 LD Rs. KD Rs.

Sales LX (3000 x 152) (a) 3,04,000 Sales KX (2000 x 300)(a) 6,00,000 (Including Rs.30 oT)

(iv)

3,04,000 3,78,000 5,28,000

12,10,000 Total variable cost 3,36,000 Fixed costs

15,46,000 Total costs Total costs (b) 6,21,000 Profit Profit (a-b)

Total profit for the company =6,21,000 + 1,28,000

(3000 x261) LY (6000 x 180)

Total Sales Variable cost

LX (2000 x 152) (3000 x 126)

LY (6000 x 88)

7,83,000 10,80,000 21,67,000

Variable cost (2000 x 186) 3,72,000 1,00,000

(b) (a-b)

Rs.7,49,000

4,72,000 1,28,000

Ans.18 (i) Department ‘A’ By product BYEA Sales Income

Production 3000 Tonnes (30% of 3000 Tonnes @ Rs.200) (70% of 3000 Tonnes @ Rs.1200)

Total

(Rs.) 1,80,000

25,20,000 27,00,000

(ii) Department ‘B’ Production of RESP (3000 x 200,i.e.,600000 litres) Sales (600000 litres @ Rs.15) Costs: Opportunity Cost of BYEA Variable Costs (600000 @ Rs.4) Fixed Costs Total Profit

(iii) Department ‘C’ Production of POTS 5% wastage

(a)

(b) (a-b)

(Rs.) 90,00,000 27,00,000 24,00,000 12,00,000 63,00,000 27,00,000

(ltrs.) (600000 x 1.6) 9,60,000

48,000 9,12,000

(a) Sales Pack (ML)

200 300 Total

(b) Costs

%

75 25

Litres

6,84,000 2,28,000 9,12,000

No.of packs Price/Pack Rs.

34,20,000 2.50 7,60,000 3.50

Sales Value Rs

85,50,000 26,60,000

1,12,10,000

(Rs.) RESP Mfg. Cost Total

(600000 x 15) (912000 x 1.50)

90,00,000 13,68,000

1,03,68,000

8,42,000

=Rs.62,42,000

Profit (a-b) (iv) Total Profit under the existing arrangement A-27,00,000 + B-27,00,000 + C-8,42,000

Under the new proposal

Total quantity of RESP purchased Production of POTs Amount of Saleable POTs

(3000 x 120) (360000 x 1.60) (576000 x 95/100)

(Ltrs.) 3,60,000 5,76,000 5,47,200

(a) Sales Pack (ML)

200 300 Total

%

75 25

Litres

4,10,400 1,36,800 5,47,200

No.of packs Price/Pack Rs.

2,05,200 2.50 4,56,000 3.50

Sales Value Rs

51,30,000 15,96,000 67,26,000

(Rs.) (b) Costs RESP Mfg. Cost Fixed Overhead of Dept. B

(360000 x 6.25) (547200 x 1.50)

22,50,000 8,20,000

12,00,000 42,70,800

Profit (a)- (b) 24,55,200 Analysis : Since under the new proposal profit gets lowered from Rs.62,42,000 to Rs.24,55,200 the proposal is not acceptable.

Ans.19. The transfer price will be notional revenue to S and notional cost to T. (a) S will continue to produce more output until the costs of further production exceed the

transfer price revenue. (b) T will continue to want to receive more output from S until its net revenue from further

processing is not sufficient to cover the incremental transfer price costs.

Output Units

600 700 800 900

1000 1100 1200

Division S Incremental Cost Rs.

- 100 140 160 200 250 350

Division T Incremental Costs Rs.

- 300 280 250 220 200 150

Since S will continue to produce more output if the transfer price exceeds the incremental costs of production, a price of at least Rs.200 per 100 units (Rs. 2 per unit ) is required to ‘persuade’ the manager of S of produce as many as 1,000 units, but a price in excess of Rs.250 per 100 units would motivate the manager of S to produce 1,100 units (or more). By a similar argument, T will continue to want more output from S if the incremental revenue exceed the transfer costs from S. If T wants 1,000 units the transfer price must be less than Rs.220 per 100 units. How ever, if the transfer price is lower than Rs.200 per 100 units, T will ask for 1100 units from S in order to improve its divisional profit further.

In summary (a) The total company profit I maximised at 1,000 units of output. (b) Division S will, want to produce 1,000 units, no more and no less, if the transfer price is

between Rs.2 and Rs.2.50(Rs.200 to Rs.250 per 100 units).

(c) Division T will want to receive and process 1,000 units, no more and no less, if the transfer price is between Rs.2 and Rs.2.20

(d) A transfer price must therefore be selected in the range Rs.2.00 to Rs.2.20 per unit(exclusive).

Thus, if a price of Rs.2.10 per unit is selected, profits at 1,000 units of output would be; (Rs.)

Particulars Division S Division T Total Sales/Net revenue 2,100 4,000 4,000 Costs 1,200 2,100 1,200 Profit 900 1,900 2,800

At a transfer price of Rs.2.10 any increase in output above 1,000 units, or shortfall in output below this amount, would reduce the profits of company as a whole, but also the divisional profits of S and T.

Ans.20. (a)The problem The overall company interest is obviously to produce 1,400 units which will given the maximum profit. The problem is to fix the transfer price (TP) with which both X and Y will find 1,400 units to be the optimum output for them severally. Let us analyse and examine the incremental costs at X and the incremental revenue at Y Level of output Incremental Cost for Incremental Net Company profit

X revenue for Y Rs. 1,000 - - 3,100 1,100 100 300 3,300 1,200 120 240 3,420 1,300 130 190 3,480 1,400 150 170 3,500 1,500 180 130 3,450 1,600 220 80 3,310

A price of at least Rs. 150 per 100 units (Rs.1.50 per unit) is required to induce the manager of X to produce as many as 1,400 units; but the price must not exceed Rs.180 per 100 units, for in that event X would like to produce 1,500 units (or more) Similarly, Y will keep producing so long as the incremental revenues exceed the transfer cost from X. in order that Y wants 1,400 units, the TP must be lower than Rs.170 per 100units; but it shall not be lower than Rs.130,for Y will then ask for 1,500 units from X to increase his (Y’s) divisional profit further. If the TP is selected at Rs.1.60 per unit, profits at 1,400 units of output would be

(Rs.) Particulars X Y Company Sales / Net revenue 2,240 4,900 4,900 Costs 1,400 2,240 1,400 Profit 840 2,660 3,500

At a TP of Rs.1.60 any increase in output above 1,400 units or shortfall in output below this level would reduce the profits of the company as a whole and also the divisional profits of X and y. With Rs.1.60 as TP, neither X or Y will like to deviate from 1,400 units, which incidentally is also wanted y the corporate Management.

Ans. 21. (i) Calculation of transfer price to be quoted by Alfa to Beta based on residual income

(Rs.) Fixed Costs 80

Return on capital employed (Rs.750 lakhs x 12/100) 90 Residual income desired 100 Total 270 Desired contribution per unit =Selling price p.u.-Variable cost p.u. =Rs.180- Rs.60 =Rs.20 p.u. Total desired contribution =12,00,000 units x Rs.20 p.u =Rs.240 lakhs Minimum contribution to be earned from sale of additional 3 lakh units.

Rs.270 lakhs-Rs.240 lakhs =Rs30 lakhs.

Contribution p.u. on additional 3,00,000 units =Rs.30,00,000/3,00,000 units = 10 p.u.

Variable cost of modification per unit =Rs.5

Hence, the minimum transfer price per unit to be quoted will be =Rs.160 + 10 + 5 =Rs.175

(ii) If Beta can buy from outside at less than the variable cost of manufacture, Rs.165, than only the decision to transfer at the price of Rs.175 will become sub-optimal for the group as a whole.

Ans.22. Working Notes: (i) Computation of Sales revenue from Foam Division

(Rs.) Sales of Foam Division to outside customers Less: Variable Mfg. Costs

(Rs.1,600-Rs.200) (Rs.1,200-Rs.200)

1,400 1,000

400

280 1,400 1,680

Mark-up on outside Sale (Rs.400/Rs.1000)x 100=40% Transfer Price of Foam to Upholstery Division Sales of Foam Division to outside Customers Total (ii) Variable Mfg. Cost of Upholstery Division =(Rs.680-Rs.200 + Rs.280)

(Rs.’000) =Rs.760

(iii) Computation of Traceable Administration Expenses Divisions Foam Carpets Given Administration expenses 134 116 Less: Common expenses (10% of Gross Profit) 40 40 Traceable Administration Expenses 94 76

(iv) Computation of Traceable Selling Expenses Divisions Foam Given Selling expenses 202 Less: Common expenses (2.5% of Sales) 40 Traceable Selling Expenses 162

( Rs.’000) Upholstery Total

172 422

50

122

130

292

Carpets 210

30 180

( Rs.’000) Upholstery Total

232 644

30 202

(Rs.000)

Upholstery 1,200 760

Total 4,080 2,660

100 544

(a) Revised operating statement (using Contribution approach)

Divisions Sales Revenue Less: Variable Mfg. Costs Contribution (i)

Foam 1,680 1,200

Carpets 1,200 700

Traceable Costs: Fixed Mfg. Costs Admn. Expenses Selling Expenses Total (ii) Operating Income (i)-(ii) Less: Common expenses Net Income of the Company

480

- 94

162 256 224

500

100 76

180 356 144

440

20 122 202 344 96

1,420

120 292 544 956 464 230 234

(b) (i) Computation of contribution Margin (Rs.’000) Contribution X 100

Contribution Margin Ratio % = Sales U

Foam Carpets Upholstery

(Rs.480/Rs.1680) x100 (Rs.500/Rs.1200) x 100 (Rs.440/Rs.1200) x 100

(Ranks) 28.57% 41.67% 36.67%

III I II

(ii) Computation of Net Contribution Ratio (Rs.’000)

Net Contribution Ratio (%) = Net Contribution X 100 Sales

U

Foam Carpets Upholstery

(Rs.224/Rs.1680) x100 (Rs.144/Rs.1200) x 100 (Rs.96/Rs.1200) x 100

13.33% 12% 8%

III I II

It is observed from the above analysis that foam Division’s Manager argument I correct when we look at the calculation given above which shows that even though contribution margin ratio of Foam Division is lower, the divisions ranking is higher based on the Net Contribution Ration.

The use of contribution approach for reporting is more realistic for assessing the performance of various divisions as it considers variable and traceable costs only and avoids common costs while finding out profitability. This approach enables the management to rightly interpret the information. Further, pricing of internal transfers at market price will give due credit to specific profits centre i.e. transferor.

Ans. 23 U The desired rate of return is 28% on investments. Investments include: (i)

Fixed assets after depreciation (ii) Net working capital. In the question, current assets and debtors are given but current liabilities and creditors are not indicated. Therefore, these are assumed to have nil value. Investments

Fixed assets 5,00,000 Net working capital Rs. Current assets 3,00,000

Debtors 2,00,000 5,00,000 Total investments

The desired rate of return is 28% The profit margin will be Budgeted volume

10,00,000

Rs. 280000 400000unit

Profit margin per unit (Rs. 280000 ÷ 400000 units) Fixed cost per unit Variable cost per unit

Rs. 0.70 2.00 10.00

Transfer price per unit 12.70

Ans.24 (i) Profit Average assets Sundry Debtors Inventories Plant & equipment

=20% return on average assets employed (Rs.Lakhs)

2 5 5

12 Total

Profit =Rs.12,00,000 x 20 /100 =Rs.2,40,000 (2) Budgeted sales revenue (2,00,000 units of component X) Fixed cost Variable cost (2,00,000 units @ Rs.1) Profit Total Sales

(Rs.Lakhs) 5.00 2.00 2.40 9.40

Selling price per unit of component X =Rs.9,40,000/2,00,000 units =Rs.4.70 per unit Options in hand with Division A Option 1 -Sell 1,50,000 units in market and transfer 50,000 units to Division B Option 11 -Sell only 1,50,000 units in market. Statement of profitability of Division A under two options (Rs.) Particulars Option-I Option-II Sales (1,50,000 units @ Rs.4.70) 7,05,000 7,05,000 Transfer to Division-B (50,000 units @ Rs.2) - 1,00,000 Total Sales revenue 8,05,000 7,05,000 Less: variable overhead 2,00,000 1,50,000 Contribution 6,05,000 5,55,000 Less: Fixed Cost 5,00,000 4,75,000 Profit (a) 1,05,000 80,000 Capital employed (b) 12,00,000 10,00,000 Return on capital employed (a)/(b)X100 8.75% 8%

Analysis : From the analysis of the above it is observed that under Option-I, Division A’s, Profit and ROCE is increased by Rs.25,000 and 0.75% respectively. Hence Option-I is suggested for Division-A.

Ans. 25 (i) The company as a whole will not benefit if Division C bought the component from an outside supplier at

Rs.135/- per unit. Rs.

Purchase cost from outside supplier (1,000 units × Rs.135 per unit) Less: Saving in variable cost of division A by reducing Division’s output (1,000 units × Rs.120 per unit)

1,20,000

1,35,000

Net cost (benefit) to the company as a whole 15,000 The company as a while will not benefit, as it will be required to incur an additional cost of Rs.15,000 if Division C bought the component from outside supplier.

(ii) The company will be benefited if C purchased the component from an outside supplier and Division A uses the facilities for other activities.

Rs. Purchase cost from outside supplier (1,000 units × Rs.135) Less: Saving in variable cost of Division A for the units purchased by Division C from outside (1,000 units × Rs.120 per unit) Cash operating saving of Division A for the use of facilities for other activities

U

Rs. 1,35,000

1,20,000

18,000 U 1,38,000

(3,000) U Net cost (benefit) to the company as a whole

It is advisable that Division C should purchase the component from outside sources as this decision will benefit the company by Rs.3,000.

(iii) The company will be benefited if C purchase the component from an outside supplier and there is no alternative use of Division A’s facilities.

Rs. Purchase cost from outside supplier (1,000 units × Rs.115) Less: Saving in variable cost of Division A by reducing division’s output (1,000 units × Rs.120)

U

1,15,000

1,20,000

. Net cost (benefit) to the company

U (5,000) It is advisable that the Division C should buy the component from outside as this decision will benefit the company by Rs.5,000.

Ans 26 (i) 1.

Working notes: Contribution per hour of Super-chips and Okay-chips:

Super-chips Selling price per unit (Rs.) Less: Variable cost per unit (Rs.) Contribution per unit (Rs.) Hours required per unit Contribution per hour

2.

600 300 300

2 150

(Rs.300/2 hrs)

Okay-chips 120 80 40 0.5 80

(Rs.40/0.5 hrs) Details of hours utilized in meting the demand of 15,000 units of Super-chips and utilizing the remaining hours for Okay-chips out of available hours of 50,000 per annum:

Rs. Hours utilized for manufacturing 15,000 units of Super-chips (15,000 units × 2 hours) Hours utilized for manufacturing 40,000 units of Okay-chips

U

30,000

20,000 (40,000 units × 0.5 hours)

50,000 U

3. Contribution of a process control unit (using an imported complex circuit board):

Rs. Selling price per unit: (A) Variable costs Circuit board (Imported) Other parts Labour cost (5 hours × Rs.100) Total variable costs: (B) Contribution per unit (Rs.) : [(A) – (B)] Contribution of process control unit (using a Super-chips):

Selling price per unit: (A) Variable costs Super-chip (Material + Labour costs) Other parts Labour (6 hours × Rs.100) Total variable costs: (B) Contribution per unit (Rs.) : [(A) – (B)]

80 600 980 420

300

600 80

500 1,180

220

Rs. 1,400

1,400

4.

5. Incremental contribution per unit of a process control unit, when instead of using imported complex circuit board Super-chip is used:

Rs. Incremental contribution per unit (Rs.420 – Rs.220) (Refer to W. N. 3&4) 200

(ii) Super-chips to be transferred to Mini Computer Division to replace Circuit Boards: Out of 50,000 available hours 30,000 hours are utilized for meeting the demand of 15,000 unit of Super-chips, the rest 20,000 hours may be used for manufacturing 40,000 Okay-chips, which yields a contribution of Rs.40 per unit or Rs.80/- per hour (Refer to working note 1) or a contribution of Rs.160 per two equivalent hours. In case the company decides to forego the manufacturing of 20,000 units of Okay-chips in favour of 5,000 additional units of Super-chips to be used by Mini-Computer division (instead of complex imported Circuit Board) for manufacturing process control units. This decision would increase the existing contribution of Mini-computer Division by Rs.200/- per two-equivalent hours (Refer to working note 5). Hence the entire requirement of 5,000 units of Super-chips be produced and transferred to Mini- Computer Division.

(ii) Minimum transfer price of Super-chip to Mini Computer Division: Variable cost of a Super-chip + Opportunity cost of foregoing the production

of an Okay-chip and using craftsmen time for Super-chip

= =

Rs.300 + 2 hours × Rs.80 Rs.460

(iii) Super –chips to be produced for the production of 12,000 units of process control units: After meeting out the order of 15,000 Super-chips per year, the concern is left out with 20,000 hours. Use of Super-chips for control units production would increase the existing contribution of Mini-

Computer Division by Rs.200/- per unit. Out of the remaining 20,000 craftsmen hours, 10,000 units of Super-chips can be made, which may be used for the production of 10,000 process control units.

Ans 27 (i) Statement of the overall profit of the company

(By harvesting 2,000 kgs of oil seeds, processing it into edible oil & selling the same in 2 kg cans) Harvesting

Division Output of department Total costs Variable cost (Rs.) : (A) 5,000

(2,000 kgs × Rs.2.50)

Fixed cost (Rs.): (B) 10,000 (2,000 kgs ×

Rs.5) Total cost (Rs.): (C) = [(A)+(B)] Sales revenue (Rs.): (D) (500 cans × Rs.150) Profit (Rs.) [(D) – (C)]

(ii) Working note: (a) Total Contribution =

= (Sales revenue – total variable cost) Rs.75,000 – Rs.16,875 = Rs.58,125

36,250

15,000

10,000 (1,000 kgs ×

Rs.10) 7,500

(1,000 kgs × Rs.7.50) 17,500

1,875 (500 ×

Rs.3.75) 4,375 (500 ×

Rs.8.75) 6,250 38,750

75,000

21,875

16,875

each 2,000 kgs of oil seed

Oil Mill Division

1,000 kgs. of oil produced

Marketing Division

500 cans of 2 kg each

Total Rs.

(b) Amount of shared contribution in relation to variable costs:

Harvesting Division

Oil Mill Division

Marketing Division

=

=

=

Rs.58,125 ×

Rs.58,125 ×

Rs.58,125 ×

Rs.5,000 Rs.16,875

Rs.10,000 Rs.16,875

Rs.1,875 Rs.16,875

= Rs.17,222

= Rs.34,445

= Rs.6,458

Computation of Transfer Price (for internal transfers) under the following pricing methods: (1) Shared contribution in relation to variable costs:

Transfer price from harvesting Division to Oil Mill Division =

=

=

Variable cost of Harvesting Division + Shared contribution of Harvesting Division in relation to variable costs Rs.5,000 + Rs.17,222 (Refer to working note 2) = Rs.22,222 Transfer price from Oil Mill Division to Marketing Division Transfer price from Harvesting Division to Oil Mill Division + Variable cost of Oil Mill Division + Shared contribution of Oil Mill Division in relation to variable costs (Refer to working note 2)

= Rs.22,222 + Rs.10,000 + 34,445

= Rs.66,667 (2) Market price:

Transfer price from Harvesting Division to Oil Mill Division = =

= =

Market price of 2,000 kgs of Oil seeds transferred to Oil Mill Division 2,000 kgs. × Rs.12.50 = Rs.25,000

Market price of 1,000 kgs of edible oil 1,000 of kgs × Rs.62.50 – Rs.62,500

From Harvesting Division to Oil Mill Division

Rs. Shared contribution method Transfer price: (Refer to (1) above) Less: Transfer price (Refer to (ii) above) Less: Variable cost Less: Fixed cost (Refer to (i) above) Profit Market price method Transfer price (Refer to (2) above) Less: Transfer in price (Refer to (ii) above) Less: Variable cost (Refer to (ii) above) Less: Fixed cost (Refer to (i) above) Profit 10,000 20,000 6,250 Decision: Divisional Manager of Harvesting Division would prefer the use of market price method for transferring 2,000 kgs of oil seeds to Oil Mill Division because its usage increases the profit by Rs.2,778 (Rs.7,222) over the shared contribution method. Whereas Oil Mill Division manager would prefer the use of shared contribution method over the market price method because its use would increase its profit by Rs.6,945 (Rs.26,945 – Rs.20,000). Similarly Marketing Divisional Manager would be benefited to the extent of Rs.4,167 (Rs.6,250 – Rs.2,083) by using market price method.

Ans 28 (i) Statement of profitability of Division X

No. of components Transfer price for the component to

Department Y@

Total cost of components (Rs.)

Profit / (Loss) (Rs.)

10,000 7,500 4,375

5,000 10,000 1,875

__ 25,000 62,500

25,000 62,500 75,000

7.222 26,945 2,083

5,000 10,000

10,000 7,500

1,875 4,375

__ 22,222 66,667

22,222 66,667 75,000

From Oil Mil to Marketing Division

Rs.

From Marketing Division to market (500 cans of 2 Kgs.)

Rs.

Transfer price from Oil Mill Division to Marketing Division

(iii) Statement of profitability (under different transfer prices method)

Rs.90 per unit (a) 5,000 10,000 15,000 20,000 25,000 30,000

No. of Components

Sale revenue on

average price basis

Rs. (a) 5,000 10,000 15,000 20,000 25,000 30,000

(b) 19,68,750 29,85,000 37,12,500 41,70,000 45,00,000 45,00,000

(b) 4,50,000

9,000 13,50,000 18,00,000 22,50,000 27,00,000

Component cost

(Transfer price) to Dept. Y

Rs. (c)

4,50,000 9,00,000

13,50,000 18,00,000 22,50,000 27,00,000

Manufacturing cost in

division Y

(c) 5,62,500 9,00,000

12,37,500 15,75,000 19,12,500 22,50,000

Total cost

(d) = {(b) – (c)} (1,12,500)

__ 1,12,500 1,25,000 3,37,500 4,50,000

Profit/(Loss) Statement of profitability of Division Y

Rs. (d)

14,06,250 16,87,500 19,68,750 22,50,000 25,31,250 28,12,500

Rs. (e)={(c)+(d)}

18,56,250 25,87,500 33,18,750 40,50,000 47,81,250 55,12,500

Rs. (f)={(b)-(e)}

1,12,500 3,97,500 3,93,750 1,20,000

(2,81,250) (9,90,000)

Rs. 4,50,000

(9,00,000) U

(ii) Profitability of the company as a whole (a) At 30,000 units level, at which Division X’s net profit is maximum

Profit of Division X Profit of division Y Operating profitability / (Loss) of the company

U (5,40,000) Rs. NIL

3,97,500 U

(b) At 10,000 units level, at which Division Y’s net profit is maximum Profit of division X Profit of division Y Operating profitability of the company

U 3,97,500

Manufacturing cost in

division Y

(Rs.) (d)

14,06,250 16,87,500 19,68,750 22,50,000 25,31,250

Total cost Profit/ (Loss)

(Rs.) (f)={(b)–(e)}

- 3,97,500 5,06,250 3,45,000

56,250

(iii) Profitability of the company, if it is not organised on profit centre basis

No. of components

Sales revenue on

average basis (Rs.)

(a)

5,000 10,000 15,000

20,000 25,000

(b)

19,68,750 29,85,000 37,12,500 4170,000

45,00,000

Cost of component

to division X

(Rs.) (c)

5,62,500 9,00,000

12,37,500 15,75,000 19,12,500

(Rs.) (e)={(c) +

(d)} 19,68,750 25,87,500 32,06,250 38,25,000 44,43,750

30,000 45,22,500 22,50,000 28,12,500 50,62,500 (5,40,000)

The level of output, the company will earn maximum profit, if the company is not organized on profit centre basis is 15,000 components.

Ans.29. Statement showing contribution P.U. of ranking Particulars

A Market Price P.U. 150 Less: Variable Production Cost P.U 130 Contribution P.U. 20 Labour hours P.U. 3 Contribution per labour hour (i)/(ii) 6.67 Ranking IV

(i) Allocation of 20,000 labour hours C D B A (Balance)

(Rs.) Product

B 146 100 46 4

11.5 III

C 140 90 50 2 25 I

D 130 85 45 3 15 II

(2,300 units x 2 L.H.) (1,600 units x 3 L.H.) (2,500 units x 4 L.H.) (200 units x 3 L.H.0

4,600 4,800

10,000 600

20,000

Product D can be transferred to Division Y, but the maximum Quantity that might be required for transfer is 2,500 units of D. Time required for 2,500 units of D =2,500 units x 3 L.H =7,500 L.H 2,500 units of Product D for Division Y can be met by sacrificing as follows:

(Labour hours) Product A (200 units x 3 L.H.) 600 Product B (Balance) (1,725 units x 4 L.H.) 6,900

7,500

Transfer price to be charged by Division Z to Division y on supply of 2,500 units of product D.

(Rs.) Variable cost (2,500 units x Rs.85) 2,12,500 Add: opportunity cost of contribution foregone Product A (200 units x Rs.20) 4,000 Product B (1,725 units x Rs.46) 79,350 Transfer Price 2,95,850 Transfer Price P.U. (Rs.2,95,850 / 2,500 units) 118.34

(ii) Allocation of 30,000 Labour Hours

C D B A Idle Labour (Balance) Total

(2,300 units x 2 L.H.) (1,600 units x 3 L.H.) (2,500 units x 4 L.H.)

(2,800 units x 3 L.H.)

4,600 4,800

10,000 8,400 2,200

30,000

2,500 units of Product D for Division Y can be met by sacrificing as follows:

Idle labour hour Product A Total

(1,725 units x 3 L.H.) 2,200 5,300 7,500

(Rs.) 2,12,500

35,340 2,47,840

99.14

Calculation of transfer price Variable cost (2,500 units x Rs.85) Opportunity cost of Contribution foregone of Product A (1,767 units x Rs.20)

Transfer price P.U.

Ans. 30 Working Notes: (i) Hours required to meet maximum demand:

External sales (i)

X 800 units Y 500 units Z 300 units

(ii) Contribution per unit: Product

Selling price Less : Variable cost U

(Rs.2,47,840 / 2,500 units)

Hours reqd. (ii)

3 4 2

Total

Total Hrs. per unit (iii) = (i) × (ii)

2,400 2,000

U U

600 5,000

Y Rs.

46 24 U U

X Rs.

48 33

15

3

5

III

Z Rs.

40 28

12

2

6

I

Contribution per unit : (A)

Labour hours required per unit : (B)

Contribution per hour (Rs) : (A) / (B)

Ranking

(a)

22

4

5.5

II

If only 3,800 hours are available in Division A.

600 hrs. 2,000 hrs. 1,200 hrs.

U

300 units of Z (maximum), which will take* 500 units of Y (maximum), which will take 400 units of X to use remaining hrs.

3,800 hrsU.

*Note: Labour hours required per unit are given in the question. If 300 units of Y are to be transferred to ‘B’ division, then 1,200 hours will have to be used for production of Y instead of X. It means Division A will sacrifice production of 400 units of X, which are yielding Rs. 5 per hr. Given above is the optimum mix for Division A for 3,800 hrs. If 300 units of Y are to be transferred to ‘B’ division with time constraint of 3,800 hours, then additional 300 units of Y will have to be produced sacrificing the production of 400 units of X which is yielding contribution.

Rs. 24.00

Transfer price (i) Variable cost of Y Opportunity cost

(ii) Contribution relating to ‘X’ forgone for producing additional units of Y

(4 hrs × Rs. 5*) U 20.00 44.00

*Y takes 4 hours and in each hour production of X would have generated contribution of Rs. 5. (b) If 5,600 hours are available

Maximum time required to meet external sales (Refer to Working note 1) 5,000 hrs. Hours now available 5,600 hrs.

(i) It means 600 hrs can be easily used for the production of Y and transfer price will be variable cost only

i.e. (600 hrs. 4 hrs) × Rs. 24 Rs. 3,600 Note: Y takes 4 hours per unit (ii) For producing additional 150 units, production of X will be disturbed. Variable costs (i) 150 units of X @ Rs. 24 Rs. 3,600 Opportunity cost (ii) Contribution of ‘X’ units

forgone (600 hrs. × Rs. 5) Rs. 3,000* 6,600 10,200 Total price for 300 units

Average transfer price should be Rs. 34 per unit *Contribution per hr. of X forgone.

Ans.31. (1) Maximum hours required to meet the present outside market requirement Maximum sales units Hours required per Total hours

unit Vx 900 3 X1 300 2 Xt 600 4 Maximum total hours required to meet the outside market requirement 5,700

(2) Contribution per unit, per hour and ranking Product Selling price per units Less: Variable cost per unit Contribution per unit Labour hours required per unit Contribution per hour Ranking

(Rs.) V

24 17

7 3

2.33 II

X 23 12 11

2 5.5

I

2,700 600

2,400

X 20 14

6 4

1.5 III

(hours) 600

2,700 1,500 4,800

(3) Utilisation of 4,800 available hours according to ranking 300 units of products X1 (300 units x 2 hours) 900 units of products Vx (300 units x 3 hours) 375 units of products Xt (300 units x 4 hours) Total hours

(a) computation of transfer price for each unit of Vx if total labour hours available in Department x are 4,800

According to the ranking 4,800 available hours are utilized to produce 300 units of X 900 units of Vx and 375 units of X. The aforesaid product mix would give rise to optimum mix for optimum profit.

In case 400 units of Vx are to be supplied to Department y in addition to existing outside sale then the production of product X is to be curtailed partially and the hours thus obtained will be utilized for the production of 400 additional units of Vx. The new product mix will be as follows:

(Hours) 300 units of products X1 (300 units x 2 hours) 600 1,300 units of products Vx (1,300 units x 3 hours) 3,900 75 units of products Xt (75 units x 4 hours) 300 Total hours 4,800

Computation of transfer price per unit Variable cost of one unit of Vx Contribution foregone (opportunity cost) per unit due to the curtailment of Xt(3 hours x Rs.1.5) Transfer price per unit

(Rs.) 17.00

4.50 21.50

(b) Computation of transfer price for each unit of Vx, if total labour hours available in Department x are 6,200

Hours required to meet the present outside market requirement 5,700 Remaining hours available for producing 400 additional units of Vx 500 After meeting the present outside market requirement (6,200 hours -5,700 hours) Computation of transfer price per unit: (Rs.) Total variable cost on the production of 166.67 units of Vx 2,833 (500 hours / 3 hours) @ Rs.17 per unit by utilizing 500 remaining available hours Total variable cost of 233.33.units of Vx @ Rs.17 per unit 3,967 (400 units – 166.67 units) produced by curtailing the production of Xt product to the tune of 700 hours. Contribution foregone (opportunity cost ) on the diversion of 700 hours of 1,050 Production of Xt for producing 233.33 units of Vx (700 hours x Rs.1.50) Total cost for producing 400 additional units of Vx 7,850 Transfer price for one unit of Vx (Rs.7,850 / 400 units) 19,625

Ans. 32U (i) Statement of contribution (a) When component is purchased by Division B from outside Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) 300000 Company’s total contribution

U

U

(Rs.) Nil

8,00,000

3,80,000 1,00,000 1,00,000

(Rs.) (b) When component is purchased from Division A by Division B Division A Sales (2000x 220) 4,40,000 Less: Variable costs (2000x 190) 7,00,000 60,000

Division B Sales (2000x 400) Less: Variable Costs: Purchase cost in Division A (2000x 220) Variable cost in Division B (2000x 150) Company’s total contribution

8,00,000

440000 300000 U 7,40,000 60,000

1,20,000

Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: 30,000 Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) 300000 7,00,000 1,00,000 Company’s total contribution 1,30,000

U

Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside.

(iii) Statement of total contribution when component is available from outside at Rs.185. Division A: Nil Division B: Sales (2000x 400) 8,00,000 Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) 300000 6,70,000 1,30,000 Company’s total contribution 1,30,000

U

If the component is purchased by Division B from Division A, the contribution is only Rs.1,20,000 as calculated under

(2) above. Hence it will be beneficial to buy the component from outside. (v) Fixations of transfer price

(a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged.

(b) If facilities of Division A can be put to alternative uses: Variable cost Opportunity cost Transfer price

(Rs.) 190

15 205

(c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of Division A. the variable cost of Rs.190 per component should be charged.

Ans. 33 U Fastners Limited

(a) Present profitability of individual shops and overall profitability Particulars Welding shop

Qty. Rate Painting shop

Value Qty

Less: Variable cost : (B) (12,000 units × 9.50)

Contribution : {(A) – (B)} Less: Fixed cost

1,14,000 (9600 units × Rs.20)

30,000 25,000

1,92,000

48,000 30,000

5,000 18,000 Profit Overall profit for the company (Rs. 5,000 + Rs. 18,000) = Rs. 23,000

(b) (i) When painting shop purchases all its requirement from open market at a price of Rs. 10 per unit

Welding shop Rate Qty. Unit

Rs. Sale

Less: Variable cost Contribution Less: Fixed cost Profit/(Loss) Overall profit for the company

2,400 2,400

12.00 9.50

Val ue

R 28,800 22,800 6,000 25,000 (19,000)

Rs. 37,200 – Rs. 19,000 = Rs. 18,200

Painting shop Rate Qty

Rs. Unit 9,600 9,600

25.00 18.00*

Value Rs.

2,40,000 1,72,800 67,200 30,000 37,200

*It is given in the question that cost of painting including transfer price from welding shop is Rs. 20 per unit. The transfer price from welding shop is Rs. 12 per unit. Therefore, the variable cost of Rs. 8 (Rs. 20 – Rs. 12) is incurred by painting shop exclusively. The painting shop will be purchasing its requirement from open market at Rs. 10 per unit. Therefore, the variable cost per unit in painting shop will be Rs. 18 (Rs. 10 + Rs. 8). This point should be noted carefully. (b) (ii) When all the requirements of painting shop is met by transfer from welding shop at a transfer price of Rs. 10 per unit

Welding shop Qty. Unit

Sale in the open market Transfer to painting shop Total sales

Contribution Less: Fixed cost Profit/(Loss)

9,600 12,000

10.00 96,000 1,24,800 1,14,000 (9,600 units×Rs.18)

10,800 25,000

(14,200)

1,72,800 67,200 30,000 37,200

2,400 12.00 28,800 9,600 25.00 2,40,000

Rate Rs.

Value Rs.

Qty Unit

Painting shop Rate

Rs. Value

Rs.

Less:Variable cost (12,000 units×Rs.9.50)

Overall profit of the company = Rs. 37,200 – Rs. 14,200 = Rs. 23,000 For the purpose of comparison, the results of the three alternatives are summarised below:

Welding shop Painting shop Rs. Rs.

Profit under (i) Profit/(Loss) under (b)(i) Profit/(Loss) under (b)(ii)

The overall profit under (a) b(i)

b(ii)

(a)

(b) (c)

U

5,000 (19,000) (14,200)

Rs. 23,000 18,200 23,000

18,000 37,200 37,200

Alternative (b)(ii) should be accepted due to the following reasons: It gives a maximum overall profit of Rs. 23,000. The discussion is confined to either b(i) or b(ii). Each shop is treated as a separate cost centre and not a profit centre. The policy of overall goal congruence of the company is followed.

Ans. 34 Neither selling price nor total sales is given. Division A of Better Margins Ltd. expects a return of 25% on average assets employed i.e., Rs. 12,00,000.

Total sales will be: Rs. (a) Profit (25% of 12,00,000) (b) Fixed overhead (c) Variable cost (2,00,000 × Re. 1) Total sales Sales per unit (Rs. 9,00,000 ÷ 2,00,000 units)

Transfer to Division B sale to outside parties

Sales (units)

Sales value (1,40,000 units @ Rs. 4.50) (60,000 units @ Rs. 2.25)

Less: Variable cost (Re. 1 per unit) Contribution Less: Fixed overhead Net profit Average assets employed Return on investment

2,00,000 Rs.

6,30,000 1,35,000 7,65,000

2,00,000 5,65,000 4,00,000 1,65,000

12,00,000 13.75%

U

9,00,000 Rs. 4.50

Sale to outside and parties only

1,40,000 Rs.

6,30,000 Nil

6,30,000

1,40,000 4,90,000 3,60,000 * 1,30,000

10,00,000 13.00%

If the component is transferred to Division B as well as sold to outside parties, it is more profitable as the contribution, net profit and return on investment is more than the existing proposal. Therefore selling the components to Division B at Rs. 2.25 per unit is in the overall interest of the company. *Reduction in selling and administration expenses (fixed in nature) by Rs. 40,000.

Ans. 35 U Statement showing the contribution to profit for each assuming that all estimates and budgets materialised as expected

Sales Centre (S) New Board Sold

– Selling price – Purchase price

Gross margin Less: Second hand boat

Part-exchange of old boat Broker’s Price

Less: Repairs Contribution

Brokerage Centre (B) Second-hand boat sold Less: Paid to Centre S

Paid to Centre R Contribution

Repair Centre (R) Sales to Centre B Less: Materials

Direct labour variable cost Contribution

Rs. Rs. Rs.

35,000 29,000

6,000

16,000 15,000 1,200 (13,800) 2,200

3,800

19,000 13,800

1,200 15,000 4,000

1,200

U 300 360 660

540

(ii) Assuming Additional Costs It is noticed that all estimates and budgets are materialised except that repairs undertaken by R took an extra 10 hours and Rs. 100 of materials due to a problem not noticed by B or R. R is responsible for giving correct repair costs and, therefore, he has to bear the additional cost:

Rs. Rs. Repair Centre (R)’s contribution 540 Less: Extra cost of materials 100 Extra D.L. variable cost (10 hrs × Rs. 6) 60 160

380 Revised contribution However, full details are not given in the question. ‘B’ is a middleman passing on R’s costs to S and as such should not bear additional costs. Had the item been noticed originally then S would have paid the cost and perhaps it should be passed back. This would be particularly so if R had insufficient opportunity for a complete inspection. In that case extra cost should be:

Rs.

U

Material Labour (10 hrs. × Rs. 15)

Reduced contribution of S = Rs. 3,800 – Rs. 250 = Rs. 3,550 Rs. Original

contribution of R Add.: Saving in variable cost [10 hrs × (Rs. 15 – Rs. 6)] Increased contribution of R

90 630

540

100 150 250

Note: Other solutions are equally acceptable if well argued and logically justified.

Ans. 36: U (a) (i) AB sells product at external market

Selling price (Rs.) 30 Less Variable cost 18

45 18

60 18

Contribution (per unit) Demands (units) Total contribution

12 60,000

7,20,000

27 40,000

10,80,000

42 20,000

8,40,000

Optimal output is 40,000 units at a selling price of Rs.45

AB transfer at Rs.42 to XY division then contribution of XY Selling price (Rs.) 120 135 150 Less Variable cost V+TP (42+60) 102 102 102 Contribution (per unit) 18 33 48 Demands (units) 15,000 10,000 5,000 Total contribution 2,70,000 3,30,000 2,40,000

Manager will choose out put level 10,000 units at a selling price of Rs.135.

Overall profit when transfer made at Rs.42 Division AB contribution on 10,000 units [42 – (18 -3)] Division XY contribution 10,000 (135 – 102) Total contribution Division AB contribution from external market sale Total profit

(ii) AB transfer at variable cost Selling price (Rs.) 120 Less Variable cost (15+60) 75 Contribution (per unit) 45 Demands (units) 15,000 Total contribution 6,75,000

= 2,70,000 = 3,30,000 = 6,00,000 10,80,000 16,80,000

135 75 60

10,000 6,00,000

150 75 75

5,000 3,75,000

Optimal is 15,000 units at the rate of 120 per unit. If AB transfer at Variable cost (Rs.15) then no contribution will be generated by AB division

XY division choose 15,000 units level gives contribution 15,000 × 45 = 6,75,000 Division AB contribution from external market sale = 10,80,000 Total contribution = 17,55,000

(iii) Contribution AB division by selling 10,000 units to new external market at Rs.32 and XY division purchasing at Rs.31.

Contribution (32 – 18) × 10,000 XY contribution [135 – (31 + 60)] Division AB contribution from external market sale Total contribution

U

= 1,40,000 = 4,40,000

= 10,80,000 = 16,60,000

Ans. 37 (a) The variable costs per unit of output of sale outside the company are Rs.11 for the intermediate product and rs.49(Rs.10 for A+Rs.39 for B) for the final product. Note that selling and packing expenses are not incurred by the supplying division for the transfer of the intermediate product. It is assumed that the company has sufficient capacity to meet the demand at the various selling prices.

Optional output of intermediate product for sale on external market. Selling Price (Rs.) 20 30 Unit contribution (Rs.) 9 19 Demand (units) 15,000 10,000

Total contribution (Rs.) 1,35,000 1,90,000

40 29

5,000

1,45,000

Optimal output is 10,000 units at a selling price of Rs.30. Optimal output for final product Selling Price (Rs.) 80 Unit contribution (Rs.) 31 Demand (units) 7,200

90 41

5,000

100 51

2,800

Total contribution (Rs.) 2,23,200 2,05,000 1,42,800 Optimal output is 7200 unit at a selling price of Rs.80.

Optimal output of Division B based on a transfer price of Rs.29. Division B will regard the transfer price as a variable cost. Therefore, total variable cost per unit will be Rs.68(i.e.,29+39) and Division B’s contribution will be as follows: Selling Price (Rs.) 80 90 100 Unit contribution (Rs.) 12 22 32 Demand (units) 7,200 5,000 2,800

Total contribution (Rs.) 86,400 1,10,000 89,600

The manager of Division B will choose an output level of 5,000 units at a selling price of Rs.90. This is sub-optimal for the company as a whole. Profit for the company as a whole from the sale of the final product are reduced from Rs.2,23,200 (72,00 units) to Rs.2,05,000 (5000 units). Rs.2,05,000 profits would be allocated as follows:

Division A Rs.95,000 (5000 units at Rs.19 i.e.,Rs.29-Rs.10) Division b Rs.1,10,000

(b) At a transfer price of Rs.12 the variable cost per unit produced in Division B contribution will be as follows:

Selling Price Unit contribution Demand

Total contribution

(Rs.) (Rs.) (units)

(Rs.)

80 29

7,200

2,08,800

90 39

5,000

1,95,000

100 49

2,800

1,37,200

The manager of Division B will choose an output level of 7200 units and a selling price of Rs.80.This is the optimum output level for the company as a whole. Division A would obtain a contribution of Rs.14,400 (7200 units @ Rs.2 (I.e.,Rs.12-Rs.10) from internal transfers of the intermediate product whereas Division B would obtain a contribution of Rs.2,08,800 from converting the intermediate product and selling as a final product. Total contribution for the company as a whole would be Rs.2,23,200. Note that Division A would also earn a contribution of Rs.1,90,000 from the sale of the intermediate product to the external market.

Ans. 38:

Opticals Ltd manufactures P( lenses) and Q ( swimming goggles ). Division P has option to supply to Division Q or sell to outside market. Division Q has option to buy from Division P or purchase from outside market. However, both divisions have to work within their individual capacity. Variable Cost for product P in Division P = Rs 60. Variable cost for product Q in Division Q ( excluding 2 Nos P's) = Rs 80. Division P has better market price of its product P than the market price offered to Q division.

For maximizing profit of the organization : P division should optimise its profit by selling maximum units to outside market. Contribution per unit for sale to outside for division P Contribution per unit for Div Q as follows : Sale price - Variable cost ( excluding lenses) Max Contribution per unit ( if procured from P div at its variable cost i.e Rs 60) Min Contribution per unit ( if procured at Rs 90 per unit from outside) Contribution per unit at transfer price of Rs 70 i.e minimum market price

Rs

40

330 210 150 190

Option 1 : Division Q buys 5001 units from market @ Rs 70 and meets its capacity. Division P sells 3000 units to outside market @ Rs 100

Sale / Transfer Contrib. /unit

Contribution in thousand rupees

Rs P Div DivP :Sale of 3000 units to outside market @ Rs 100 DivQ: Sale of 2500 units with P from market @ Rs 70 Less : cost of rejection of one unit of product P Total 120

40 190

120 Q Div

475 -0.07

474.93

Total 120 475

-0.07 594.93

Option 2 : Division P sells 3000 units to outside market, transfer 4000 units to div Q and Division Q buys 1000 units from outside market to work within the capacity P Division agrees to a transfer price so that profitability of Q is not affected. To maintain the same profitability of Q, contribution required from 2000 units for Div Q is Rs 400,000 i.e contribution per unit Rs 200 i.e transfer price per unit of P is Rs 65 per unit to make cost of lences Rs 130

Contrib Contribution in Sale / Transfer

/unit thousand rupees

- 11 -

Rs P Div

Div P : Sale of 3000 units to outside market Div P : Transfer of 4000 units to div Q at Rs 65 Div Q :Sale of 2000 units with P from P div @ Rs 65 Div Q : Sale of 500 units with P from market @ Rs 90 Total

40 5

200 150

140

120 20

Q Div Total

120 20

400 75

475

400 75

615 Under Option 1, both divisions worked dis-jointly without caring for capacity utilization resulting lower profitability of the organization. Under Option 2, both divisions worked with mutual advantages for optimizing their individual profits and overall profit for the organization has gone up by effective utilization of capacity. Product P from Division P fetches higher price from open market indicating good quality of product. Moreover, supply from P division is well assured in the long run which is the justification of establishment of two parallel divisions. Hence, Option 2 is suggested. (ii) Division functioning as profit centers strive to achieve maximum divisional

profits, either by internal transfers or from outside purchase. This may not match with the organisation’s objective of maximum overall profits. Divisions may be commercial to advice overall objects objectives, where divisional decisions are in line with the overall best for the company, and this is goal congruence. Div isions at a disadvantage may be given due weightage while appraising their performance. Goal incongruence defeats the purpose of divisional profit centre system.

(b) In an assignment minimization problem, if one task cannot be assigned to one person, introduce a prohibitively large cost for that allocation, say M, where M has a high the value. Then, while doing the row minimum and column minimum operations, automatically this allocation will get eliminated.

Ans. 39 U (a)

Direct Material (Other than A) Direct Labour Variable Overhead (Production) Variable Production Cost (excl. A) From A From Outside Variable production Cost / unit Selling Price From outside Less: Selling Overhead

Div A Rs. / unit

50 25 20 95

B Rs. / unit

24 14

2 40

144 ____ 184

B Rs. / unit

40

160 200

160 13

300 26

- 12 -

Net Selling Price (outside) Net Selling Price to B Net Selling Price to S

Net Selling Price (outside) Variable Production Cost Contribution / unit (outside)

(Sale to B & S respectively) Variable Production Cost Contribution / unit

147 144

274

250

147 − 95

52

144 − 95

49

274 − 184

90

250 − 184

66

274 − 200

74

250 − 200

50

Best strategy A = Maximise Production; Sell maximum no. of units @

52 / unit (outside)

(To B) remaining units Total Contribution for A

Best strategy for B:

18,000 × 52 = 9,36,000

2,000 × 49 = 98,000 10,34,000

Maximise contribution / unit by selling outside and procuring from A 90 / unit Contribution × 2,000 units Balance units can yield contribution of either 74/ unit for outside or Rs. 50 / unit to S Ltd. Production Capacity = 28,000.

Option I Outside Sales

20,000 × 74 = 14,80,000 2,000 × 90 = 1,80,000

16,60,000 Total Contribution

3,00,000 (16,60,000 + 3,00 ,000)19,60,000 19,56,000

Sales to S

6,000 × 50 = 3,00,000

Option II Outside Sales × contribution /

unit 24,000 × 74 = 17,76,000

2,000 × 90 = 1,80,000

(B) Choose Option I i.e. get 2,000 units from A, sell 6,000 units to S and 20,000 to outside. Make 28,000 units @ full capacity. Total Contribution Rs19,60,000. If A and B are allowed to act independent of the group synergy,

Rs. A – 10,34,000

B – 19,60,000 Total contribution for X Ltd. 29,94,000

Cost from X Ltd.’s Perspective

Variable Cost of production

Variable cost of production other than A A supplied by Division A – Variable Cost

Div A Div B

40 95

40

Rs. 95

Total contribution

- 13 -

A purchased

Option I Outside 20,000 × (274 – 135)

2,000 × (274 – 200) 22,000

S Ltd. 6,000 units (250 – 200)

Choose Option I Contribution = Rs. 32,28,000 for X Ltd. as a whole Transfer (2,000 units)

Outside 26,000 units 27,80,000 1,48,000

3,00,000 32,28,000

Option II

____ 135

160 200

20,000 (274 – 135) 6,000 (274 – 200)

27,80,000 4,44,000

_________ 32,24,000

Make A transfer all output to B. Sell 6,000 units of B to S and 22,000 units to out side market. This will make X Ltd. better off by 32,28,000 – 29,94,000 = Rs 2,34,000 (i.e. 18,000 units of A sold to outside increases contribution to A by 3 Rs. / unit and decreases contribution to B by 16 Rs. / unit Net negative effect = 13 × 18,000 = Rs.2,34,000).

Ans. 40: (i) Division A’s best strategy – 2011 Maximum Manufacturing capacity = 50,000 units

Per unit

Demand (units) Selling price Variable Prod cost Variable Selling cost Total Variable cost Contribution Rs.

External Spl order Market

30,000 65 35 10 45 20

15,000 55 35 -

35 20

Transfer to B partially < 45,000

55 35 -

35 20

Transfer to B full

45,000 60 35 -

35 25

Transfer to B in full gives maximum contribution. Hence, 45,000 units to be transferred. Balance 5000 will be sold to the external market. Partial fulfilment of Special order will not be possible.

Statement of profitability for best strategy in 2011 : Rs

Transfer 45000 units to B @ Rs 60 Per Unit : Contribution : 25 x 45000 Supply to external market : Contribution : 20 x 5000 units Total Contribution Annual fixed cost Step fixed cost Fixed selling costs Profit in 2011

(ii) Company’s best strategy for 2010

Rs 4,30,000 Rs 2,00,000 Rs 50,000

11,25,000 100000

12,25,000

6,80,000 5,45,000

- 14 -

For Division A

Variable cost Price Contribution to Division A Margin for Division B

External Market

45 65 20

Special Order

35 55 20

B – Partial

35 45 10 5

B - Full

35 50 15 0

It is clear from the above table that the Company will have more profitability if A first satisfies external market demand and special order and then supply to B. As quantity for special order and transfer is more than 10,000 units, Div A will always opt for fixed cost of 50,000 instead of variable selling cost of Rs 5 / unit. The company’s strategy for Division A’s production, sales/ Transfer will be :

External Market 25,000

5.00

Special Order 10,000

2.00

B– Partial 5,000 0.75

Total

40,000 7.75 5.80

1.95 50,000

9.25 6.80

2.45

Strategy I : A’s sale/ transfer (units) Contribution of A & B ( Rs laks) Fixed Cost Rs Lakhs( 4.30 + 1.00 +0.5) Net for company – Rs lakhs Strategy II : from A ( units) Contribution of A & B : RS Lakhs Fixed Cost Rs Lakhs ( 4.30 + 2.00 +0.5) Net for company Rs. Lakhs

25000 5.0

10000 2.00

15000 2.25

Thus, the strategy II will be the one for the Company for the year 2010.

(iii) B’s negotiating range in 2011 : Upper limit: The effective price of Rs. 60 for procurement from outside source. Lower Limit : Minimum price A will look for i.e Variable cost + Maximum possible contribution from other source + additional fixed cost = Rs ( 35 + 20 + ( 50000/45,000) = Rs 56.11 Thus, Price range for negotiation without changing A’s strategy is Rs 56.11 to Rs 60 per unit.

Ans.: 41 U (a) (i) Contribution per unit against sale to outside = Rs ( 200-120-20) = Rs 60

In case of transfer, good units and rejected units are in proportion of 9:1 In case of transfer, contribution per good unit = Rs (190 – 120) = Rs 70 In case of transfer, contribution per rejected unit = Rs (150 – 120-100) = Rs -70 Thus, effective contribution per unit of transfer = Rs (70 x 0.9 – 70x 0.1) = Rs 56

As contribution per unit against outside sale is higher, the best strategy should be to sell maximum number of unit to outside marker.

Contribution from outside market from sale of 900 units = Rs 54,000 {Rs.(900 x 60)}

- 15 -

Contribution from transfer of 300 units to B {Rs (300 x 56)} Total Contribution from best strategy

(ii) If B’s demand is 540 units, total production required (540 /0.9)

= =

=

Rs 16,800 Rs 70,800

600 units.

Taking outside market demand of 600, it is within production capacity of 1200 units. Now contribution from 600 units of outside sale Rs (600 x 60 ) = Rs 36,000 Contribution from rejected 60 units Rs (60 x – 70) = Rs (4,200)

= Rs 31,800

To keep same level of contribution as in (i), the contribution required from transfer of 540 unit to B (Rs 70,800 – 31,800) = Rs 39,000

Thus, contribution required per unit Rs 39,000 /540 Hence price to be charged p. u. against transfer to B Rs (120 + 72.22)

=

=

Rs 72.22

Rs 192.2

Alternative Solution: Let x be the number of units sold outside and y be the number of units sold to B, before B returns 10% as defectives.

Then, x + y = 1,200, is the limitation on production capacity of A.

Department A Outside

Rs. 200 120

___20 140

60

to B Rs. 190 120

___-- 120

70

Selling Prices Variable Cost – Production Variable Cost – Sale Total Variable Cost Contribution Contribution on x units sold outside = 60x

1 Out of y units to B, 10% = 10 y. 1 = .1y is returned to A. If A scraps, amount got = 30 per unit.

If A reworks and sells, it gets 150 – 100 ∴Decision to reworks all defectives. i.e. (.1) (y) Contribution on good units of B = 0.9y × 70 Contribution on reworked units of B = (.1) (y) × 50 Amount of material lost on manufacture of defectives to B ∴Contribution on y gross units transferred to B 63y + 5Y – 12y Total contribution earned by A 56y Where x + y

To maximize contribution, maximize units sold outside. ∴900 units – sell outside.

Balance 300÷1,200 units (gross transfer to B, of which B gives back defectives)

Contribution: Rs.60 (900) + Rs.56 (300) = Rs.54,000 + Rs.16,800

= 50/unit.

= 63y = 5y =12y(.1)(y)×120 = 56y

=

=

60x

1200

+

- 16 -

Contribution Fixed Cost (i) Profit

= Rs.70,800 = Rs.36,000 = Rs.34,800

(ii) Outside demand = 600 units Contribution = 600 × Rs.60 Balance to be got

= Rs.36,000 = Rs.34,800 = Rs.70,800

Out of Rs.34,800, defectives of B will give Rs. 3,000 60 × 50 Rs. 31,800 charge to B for 540 units

Contribution to be obtained from 540 units of B Add: Production cost of 600 units @ 120/- Amount changed for 540 units

∴Price to be charged to B = 1,03,800÷540 = 192.22

Per good unit transferred, to maintain the same level of profit as in (a).

Ans 42: B will not pay A anything more than 13, because at 13, it will incur additional cost of Rs.2/- to modify it, 13 + 2 = 15, the outside cost.

= Rs. 31,800 = Rs. 72,000 = Rs.1,03,800

A Outside

sale Divisional variable production

Transfer from A Modification

Total Variable Cost of production Selling Price Contribution

7 15 8

7 13 6

cost of 7

Transfer to B & C

7

B C

19

13 2 34 40 6

25

13

38 50 12

Option for C, Purchase all units from A @ 13: Any other option is costlier.

A B C

- 17 -

Maximum external demand Exiting capacity Maximum capacity that can be added Total maximum that can be produced Additional fixed expansion

cost on

be this

3,750 5,000 5,000

10,000

24,000

24,000÷6 = 4,000

5,000 2,500 1,250

3,750

6,000

6,000÷6 = 1,000

4,000 2,500 2,250

4,750

18,700

18,700÷6 = 1,558.33

Units that must sold/transfer to get amount as contribution External demand not covered by existing capacity Decision

-

Expand make Expand make Do not expand 10,000 units 2,500 + 1,250 make only 2,500 3,750 – outside = 3,750 units units. 3,750 –B 2,500 – C

A Outside

sale Transfer to B & C 3,750 + 2,500 = 6,250

6 37,500

67,500

3,750

6 22,500 22,500 6,000 16,500

2,500

12 30,000 30,000

- 30,000

B C

Units

Contribution / unit Contribution (Rs.)

Additional Fixed Cost Net revenue addition

3,750

8 30,000

24,000 43,500

Individual strategy is the company’s best strategy.

- 18 -

Ans. 43

- 19 -

Manager of division X will sell 14,000 units outside at 110 Rs. per unit and earn contribution of Rs. 3.50 lakhs.

Excess capacity of 6,000 units can be offered to Y at a price between 70 (the variable manufacturing cost at X) and Rs. 95 (the maximum amount to equa l outside contribution). But Y can get the material outside @ 85. So, y will not pay to X anything above (Rs.85 – 6) = Rs. 79 to match external available price. X will be attracted to sell to Y only in the range of 71 – 79 Rs. per unit at a volume of 6,000 units. At Rs. 70, X will be indifferent, but may offer to sell to Y to use idle capacity. Z will not buy from Y at anything above 135. If X sells to Y at 70 per unit, Y can sell to Z at 134 and earn no contribution, only for surplus capacity and if units transferred by X to Y at Rs. 70 per unit.

Y

Provided X sells to Y at Rs. 70 per unit

Sell 4,000 units to Z at 134 (Indifferent) Sell 4,000 units to Z at 135 (willingly for a contribution of Re. 1)

Z Buy 4,000 units from y at 134 (attracted) Indifferent, since market price is also 135

For buying from X at 71 – 79 price range, Y will be interested in selling to Z only at prices 136 – 143, which will not interest Z. Thus Y will sell to Z only if X sells to Y at Rs. 70 per unit and Y will supply to Z maximum 4,000 units.

Ans. 44: Capacity of X division = 7000 units X has the following option to sell following number of units:

Option I II III

Domestic Market 6000 5000 5000

Export 800 800

Transfer 200

l200 2000

800

Hiring out (equivalent unit)

IV 5000 800 400 According to the condition given in (iii) for procurement policy of Y,

= 7000 x Rs 900 = Rs 63,00,000 For 7000 units, maximum amount Y is agreeable to pay at market rate i.e Rs 900 per unit

If X transfers l200 units to Y, It has to incur expenses for 5800 units from market = = 5800 x Rs 920 = Rs 53,36,000

It means for l200 units from X, Y will pay = Rs ( 63,00,000 – 53,36, 000)

- 20 -

= Rs 9,64,000 = Rs 803.33 per unit If X transfers 2000 units to Y and Y buys 5000 units,, Y can pay to X only

= Rs ( 63,00,000 – 5000 X 920) = Rs l7,00,000 = Rs 850.00 per unit If transfer of less than l000 units to Y, X can claim transfer price of Rs 900 per unit

Realization ( Rs) Option I Option II Option III Option IV

6000 x l000 + 800 x 900 + 200 x 900 5000 x ll20 + 800 x 900 + l200 X 803.33 5000 x ll20 + 2000 x 850

Rs 69,00,000 Rs 72,84,000 Rs 73,00,000

5000 x ll20+ 800 x 900 + 400 x 900 plus Rs 66,80,000 plus contribution from hiring out

Above table shows that Option III is preferable in comparison to Option I and II . If Option III for X, transfer price will br Rs 850.00 per unit. For taking a decision on option IV, contribution from equivalent unit from hiring out has to be compared with contribution from minimum sales realization of Rs 775 because sales realization of Rs 775 per unit from equivalent 800 units gives the amount of Rs 6,20,000 which makes up the gap between option III and option IV. In that case, transfer price will be Rs 900 per unit.

Ans. 6 (a)

3

4

8

40

(ii)

20

20

---

-- 9

4

3

50

6 ----

--- 6

5

30

20

40

60

120

20

30 30

Initial allocation under NW corner rule is as above. Initial cost: 20×3 = 60

20×4 = 80 20×4 = 80 30×3 = 90 30×5 = 150

460

3

4

8

40

1

4

(a) 20

20

---

-- 9

4

3

50

1

1

1

6 ----

--- 6

5

30

1

1

1

20

40

60

3

0

2

0

2

2

2

20

30 30

Initial solution 20×3 20×4 50×3 20×6 10×5

= = = = =

60 80

150 120

__100 __460

Checking for optimality 3

4

3

V1 =3 v2 = 3

6

5

v3 = 5

U1 = 0

U2 = 1

U3 = 0

Solutions of transportation

Ui+ vj 3

4

3

3 3 5

5 0

1

0

ij = Cij- (ui-vj)

6 0

5 ij > 0

1

Solution is optimal

Conclusion: The solution under VAM is optimal with a zero in R2C2 which means that the cell C2R2 which means that the cell C2R2 can come into solution, which will be another optimal solution. Under NWC rule the initial allocation had C2R2 and the total cost was the same Rs. 460 as the total cost under optimal VAM solution. Thus, in this problem, both methods have yielded the optimal solution under the 1st allocation. If we do an optimality test for the solution, we will get a zero for ij in C3R2 indicating the other optimal solution which was obtained under VAM.

Ans. 8 The new transportation costs table, which consists of both production and transportation costs, is given in following table. Store

P A B

Factories C D

Demand

2+2=4 10+3=13 13+1=14 4+5=9

25

Q 4+2=6 8+3=11 3+1=4 6+5=11

35

R 6+2=8 7+3=10 9+1=10 8+5=13

105

S 11+2=13 5+3=8

12+1=13 3+5=8

20

Supply 50 70 30 50

200 185

Since the total supply of 200 units exceeds the total demand of 185 units by 200-185 =15 units of product, there fore a dummy destination (store) is added to absorb the excess supply. The associated cost coefficients in dummy store are taken as zero as the surplus quantity remains lying in the respective factories and is, in fact, not shipped at all. The modified table is given below. The problem now becomes a balanced transportation one and it is a minimization problem. We shall now apply Vogel’s Approximation method to fine an initial solution.

P A

B

C

D

Demand Difference

25 4

13

14

9

25/0 5 5 5 - -

11

30

5 Q

20 6

70

R 13

8 8

10 10

4 15

13

13

20

S Dummy 0

0

0

15 8

15/0 0 - - - -

0

Supply 50/25/20/0

70/0

30/0

50/35/15/0

200

Difference 42225

822222

46____

811335 11

35/5/0 2 2 5 5 -

105/85/15/0 20/0 2 2 2 2 2

0 0 0 0 0

The initial solution is shown in above table. It can be seen that 15 units are allocated to dummy store from factory D. This means that the company may cut down the production by 15 units at the factory where it is uneconomical. We will now test the optimality of the solution. The total number of allocations is 8 which is equal to the required m+n-1 (=8) allocation. Introduce ui’s, vj’ s, i= (1,2,- - - - -4) and j =(1,2,- - - -5) ∆ij=cij-(ui+vj) for allocated cells. We assume that u4 =0 and remaining uj’s, vj’s and ∆ij’s are calculated below”

P A

B

C

D

Demand Vj

25 4

13 +7

14 +1

9 0

25 V1=9

35 2

11 0

105 2

30 4

15 13

20 0

11 +3

10 +4

20 8

15 0

5 6

70 10

13 +12

15 0

Q 20

8 8

+3 0

+7 50 U4 = 0

R 13

+10 0

+3 30 U3 = -7

S Dummy 0

+5 70 U2 =

50 Supply Ui

U1= -5

Please not that figures in top left hand corners of the cell represent the cost and the one in the bottom right hand corner of the non basic cell are the values of ∆ij=cij-[(ui+vj)] Since opportunity cost in all the unoccupied cells is positive, therefore initial solution is an optimal solution also. The total cost (transportation and production together) associated with this solution is Total cost = 4×25+6×5+8×20+10×70+4×30+13×15+8×20+0×15

= 100+30+160+700+120+195+160 = Rs.1,465/-

Ans.9:

The given problem is an unbalanced transportation problem since the availability of trailers (= 10+4+6+5=25) is less than the requirement (=13+10+6+6=35). Therefore, it is first converted into a balanced problem by adding a dummy terminal with an availability of 10 trailers and cost elements for various plants as zero. The problem becomes as given below.

Plants Terminals

U V W X

Dummy Requirement

A 20 40 75 30 0 13

B 36 20 35 45 0 10

C 10 45 45 40 0 6

D 28 20 50 25 0 6

Availability 10 4 6 5 10

The objective of the company is to minimize transportation cost. To achieve this objective, let us find an initial feasible solution by applying Vogel’s Approximation Method to the above matrix.

Plants Terminals

U

V 40

W 75

X 30

Dummy

Requirement Difference

10 0

13/3/0 20 10 10 10

20 15 15 0

0 10/6/0 6/0

10 30 0 -

0 6/1/0 20 5 5 5

0 10/0 0/-/-/-

35 40

6 35 45

5 25 5/0 5/5/5/5

50 6/0 10/10/15/15

3 20

4 20 45 20 4/0 0/0/0/-

36

A B 6

10

C 1

28 10/4/1/0 10/10/8/8

D Availability Difference

The initial solution is as given below which is tested for optimality.

Plants Terminals

U

V 40

W 75

X 30

Dummy

Requirement

10 0

13 10 0

6 0

6 0 10

35 40

6 35 45

5 25 5

50 6

3 20

4 20 45 20 4

36

A B 6

10

C 1

28 10

D Availability

The number of allocation is 7 which is one less than the required m+n-1 (=8) allocations. Introduce a very small quality e in the least cost independent cell (Dummy, B0. Let us also introduce uj, vj; I- (1,2 – 5) j = (1,2,3,4) such that ∆ij =

cij-(u1+vj) for allocation cells. We assume that u1=0 and remaining ui’s, vj’s and ∆ij’’s are calculated as below:

Terminals U

V

W

X

Dummy

vj’s

3

20 40

40 75

13 30

10

20

-θ 0

20

e

18 35 +θ 0

10

10 0

28

6 35

33 40

-8 0 -20

A +θ 20

4

16 36 -θ 20

20 45

5 25 -3

35 45

7 50 15

B 6

10 -8

C 1

D -θ 28 +θ 20 0

0

ui’s

Since some of the ∆ij’’s are negative, the above solution is not optimal. Introduce in the cell (V,D) with the most negative ∆ij an assignment θ. And the reallocated solution as obtained from above is given below. The values of ui’s and vj’’s and ∆ij’’s also calculated.

Terminals U

V

W

X

Dummy

vj’s

4 A

16 20

20 40

40 75

5 30

9 0

20

1

10

6

3

B 6

36 35

20 20

35 25

35 10

0 20

C 8

10 1

45 15

45 5

40 0

0 10

D

28

20

50

25

0 20

ui’s

0

0

15

5

-20 -20

Since all Ij’s for non basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of terminals to plants and their cost is given below.

Terminal Plant Cost

U U V V W X

A C B D B D

4 × Rs.20 6 × Rs.10 3 × Rs.20 1 × Rs.20 6 × Rs.35 5 × Rs.25

= Rs.80 = Rs.60 = Rs.60 = Rs.20 = Rs.210 = Rs.125 = Rs.555

Ans. 10: Answer (a) The problem may be treated as an assignment problem. The solution will be the same even if prices

are halved. Only at the last stage, calculate the minimum cost and divide it by 2 to account for fall in oil prices.

A X Y Z

15 21 6

B 9 12 18

C 6 6 9

Subtracting Row minimum, we get

A X Y Z

9 15 0

B 3 6 12

C 0 0 3

Subtracting Column minimum,

A B C

No of lines required to cut Zeros = 3 Cost / u

Allocation: X Y Z

B C A

9 6 6

Units

10 10 10

Cost

90 60 60 210

Minimum cost = 105 Rs.

Alternative Solution I Least Cost Method

Revised Cost

45 30 30

105

X–BY–CZ–A

Test for optimality No. of allocation = 3 No. of rows m =3, no. of column = 3

m+n–1=3+3–1=5 2 very small allocation are done to 2 cells of minimum costs, so that , the following table is got :

A

X

Y

Z

m +n–1=5 Now testing for optimality

ui 9 e

0

6 0

6

vj 6 ui + vj for unoccupied cells

A X Y Z

Diff = Cij – (ui + vj) A

X

Y Z

9

15 -

B -

3 9

C -

- -

6 6 -

9

B - 9 9

6

C - - -

e 0

15

21

6

10

B

9

12

18

e

C

6

6

9

10

10 e

All Δij > 0, Hence this is the optimal solution.

Original Costs

X–B Y–C Z–A

9 6 6

Reduced Costs due to Oil Price

4.5 3 3

Qty.

10 10 10

Cost

45 30 30 105

Total cost of transportation is minimum at Rs.105

Alternative Solution II

No. of rows + no. of column – 1 m+n–1=5 No. of allocation = 3

Hence add ‘e’ to 2 least cost cells so that

Now m + n – 1 = 5 Testing for optimality, ui, vj table

A X

Y

Z 3

4.5 3

B 4.5

C e

0

3 0

e 0

vj 3 ui + vj for unoccupied cells

3 3 -

Cij

7.5 11.5

- 6

- - -

- -

ui

- 4.5 4.5

- - -

u i+vj

3 3 -

- 4.5 4.5

- - - - 9

Δij = Cij – (ui + vj)

4.5 11.5

- 1.5

8.5 4.5 - All Δij > 0. Hence the solution is optimal.

Qty. X–B Y–C Z–A

10 10 10

Cost/u 4.5 3 3

Total Cost 45 30 30

105 Total minimum cost at revised oil prices

Ans.11: The concept tested in this problem is Degeneracy with respect to the transportation problem. Total of rows and columns = (4 + 5) = 9. Hence, the number of allocations = 9

– 1 = 8. As the actual number of allocation is 7, a ‘zero’ allocation is called for. To resolve this, an independent cell with least cost should be chosen. R4C2 has the least cost (cost = 3), but this is not independent. The next least cost cell R4C3 (cost = 5) is independent.

9 C1

0R1

2 C2

8 11

10 0R2

9 9 12 8

7 2

0R4

Total 9

12 3 8

5 8

6 3 0

6 8

7 2

11 4

4

40

7 8

9 6 10

2 8 6

5 C3

6 C4

6 2

2 C5

4 18

Total

2R3

Forming Equations through allocated cells Basic equation

R1 + C2 = 2 R1 + C4 = 6 R1 + C5 = 2 R2 + C1 = 9 R3 + C3 = 3 R4 + C1 = 9 R4 + C3 = 5 R4 + C4 = 6

Setting R1 = 0 other values Setting R1 = 0, C2 = 2

C4 = 6 C5 = 2 R2 = 0 R3 = 2 C1 = 9 C3 = 5 R4 = 0

Evaluate unallocated cells R1C1 = 11 0 9 = 2 R1C3 = 8 0 5 = 3 R2C2 = 9 0 2 = 7 R2C3 = 12 0 5 = 7 R2C4 = 9 0 6 = 3 R2C5 = 6 0 2 = 4

R3C1 = 7 + 2 9 = 0 R3C2 = 6 + 2 2 = 6 R3C4 = 7 + 2 6 = 7 R3C5 = 7 + 2 2 = 7 R4C2 = 3 0 2 = 1

R4C5 = 11 0 2 = 9 Since all the evaluation is 0 or +ve, the optimal solution is obtained.

Optimal cost = (8 2) + (6 6) + (4 2) + (10 9) + (8 3) + (2 9) + (0 5) + (2 6) = 16 + 36 + 8 + 90 + 24 + 18 + 10 + 12 = Rs. 204. Note: As regards allocation of the zero values, the solution to the above problem is also obtained by allocating the zero value in other independent cells such as R1C3, R2C2, R2C3, R3C1, R3C2, R3C4,

R3C5. In such situation there will be one more iteration.

Ans. 12 The optimum distribution for this company to minimize shipping costs

Availabilities Requirements Availabilities –Requirement

= 160 +150 +190 = 500 = 80 +90 +110 +160 = 440 = 500 – 440 = 60

Therefore, a dummy warehouse H is introduced, and initial solution is obtained below by VAM in just one table.

D

A

B

C Reg. Diff.

42 80

40

39 80/0 0 1

49 90

38 90/0 0 10*

52 100 40 110/10/0 0 2

43 160/0 0 6*

0 60/0 0 0

190/100/0 38/1/1/3

48

E

38 10

51 0

F

37

G 160

0 60

150/90/10/0 48*/9/11*/1

H e

160/0 37/1/1/1

Available Diff.

since there are only 6 (one less than m+n –1) allocations, an infinitesimally small allocation e is placed in the least cost and independent cell (1, 5). This solution is tested for optimality below. (N.B.: if allocations were m +n –2 we would place two e’s, e ,

which are virtually zero in the 2 least cost independent cells). This device enables us to e2 apply to optimality test on (m +n –1) allocations.

Vj 37

40 38

Vj 40 50 52

52 40

37 0

0 0

0 0

–12

40

28

2

11

–2 –1

50 50

52 37 25

–14 14 18 12

(ui + vj) matrix

–12

Δ ij m atrix

Since there are –ve Äij ‘s the initial solution is not optimal. Reallocation is done below by ticking the most -ve Äij cell (1, 3) and involving it in the loop.

θ mx

√ 160 e−θ =0

min 10 − θ = 0 =e

80 90

10 100

e 60

Note that the maximum that can be tansferred to the ticked cell is e. Since e is infinitestimally small it leaves other corner allocations unaffected. (Intermediate i.e. non corner allocations are never altered in the process of reallocations).

160 60

80 90

This solution is tested for optimally below :

e 10 100

Reallocation

38 40

38 -12

26

28

16 12 –1

11

-2

36 50

0

52 40

-1

37 0

-52

–14 51 39 –12

14 0 4 12

38 52 40

(ui+vj) matrix)

Δ j matrix

Since there are –ve ΔØ, this solution too is not optimal. Reallocation is done below : 10 − θ = 0

θmax = min 80 √ 10–θ 90 − θ = 0

90–θ

e 80 10

80 110

160 60

100+θ

160 60

Reallocation

Since there are –ve Δij this solution too is not optimal. Reallocation is done below. This solution is tested for optimality below:

u 38

40 0

Vi 40 49

49 -3 8

51 40

50 0

37 0 0

–11

i –13

27

29

15

10

26 51 50

39

12 1 1

4

–13 ( v i + v j)

–11

13 Δ ij m a t rix

11

Since all Δij’s are +ve, this solution is optimal. j

Ans. 15:

The initial solution is found by VAM below: Factory Godown

1 2 3 4 1 7 20 5 7 7

2

3

4

Demand

Diff.

10 9

11

50 9

60 50 0 2

11

10

10

20 0

5

10 6

30 6

9

40 10 0

0/1

11

20 2

6

20 0

4

Availability Diff. 5 5

∞

40 2

9

40 0

3

6 40 3

5

8

12

40 0

2

60/40/0

20/10/0

2/4/0

1/3

90/70/30/0 0/4/2/5

50/0 3/0

The above initial solution is tested for optimality. Since there are only 8 allocations and we require 9(m+n-1 =9) allocations, we put a small quantity in the least cost independent cell (2, 6) and apply the optimality test. Let u= 0 and then we calculate remaining ui and v 3

vj ui Factory Godowns

1 2 3 4 5 6 1 7 20 40

-2 5 7 7 5 3 2 10 10 e

0 9 11 6 11 ∞ 5 3 30 20 40

0 11 10 6 2 2 8 4 50

9 10 9 6 9 12 0 Vj 9 7 6 2 2 5

Now we calculate Δij = cij – (ui +vj) for non basic cells which are given in the table below:

0 4

2 3 3 3 4

Δ ij matrix 7

3 7 9

5 ∞

3 7

Since all Δij are positive, the initial solution found by VAM is an optimal solution. The final allocations are given below: Factory

1 1 2 2 3 3 3 4

to Godown 2 6 1 3 3 4 5 1

Unit 20 40 10 10 30 20 40 50

Cost 5 3 9 6 6 2 2 9

Total cost Rs. =

Value 100 120

90 60

180 40 80

450 1,120

The above solution is not unique because the opportunity cost of cell (1,2) is zero. Hence alternative solution exists. Students may find that the alternative solution is as given below: Factory

1 1 1 2 2 3 3 3 4

to Godown 1 2 6 3 6 3 5 4 1

Unit 10 20 30 10 10 30 40 20 50

Cost 7 5 3 6 5 6 2 2 9

Total cost (Rs.)

Value 70

100 90 60 50

180 80 40

450 1,120

Ans. 16 The given problem is a balanced minimization transportation problem. The objective of the company is to minimize the cost. Let us find the initial feasible solution using Vogel’s Approximation method (VAM) Outlets Plants X

4 Y

3 Z 400

3 Requirement 400/0 Difference 0

0 -

1 1 1

9 450/400/0 350/0

4 - -

6 500/300/0 0 0 0

50 5

A 400

6 350

2 200

5 600/200/0 2240

8

B C 300

6 400/50/0 1200

D Capacity 700/300/0

Difference 2200

The initial feasible solution obtained by VAM is given below:

Outlets Plants X

4 Y

3 Z

Requirement

400 3

400 450 9

350 6

500

50 5

A 400

6 350

2 200

5

5 600

8

B C 300

6 400

D Capacity 700

Since the number of allocations = 6= (m+n-1), let us test the above solution for optimality. Introduce ui (i=1,2,3) and vj (1,2,3,4) such that ∆ij= Cij –(ui+vj) for allocated cells. We assume u1=0, and rest of the ui’s, vj’s and ∆ij’s are calculated as below:

Outlets Plants X

Y

Z

Vj

0 4

0 3

400 3

4 6

4 9

3

50 5

4 6

6

A 400

6 350

2 200

5

B 5

8 0

5 -1

C 300

6 -1

D Ui 0

On calculating ∆ij’s for non-allocated cells, we found that all the ∆ij≥0, hence the initial solution obtained above is optimal. The optimal allocations are given below.

Plants X X Y Y Z Z

Outlet →B →D →B →C →A →D

Units 400 300 50

350 400 200

× × × × × ×

Cost 6 6 5 2 3 5

= = = = = =

Total Cost 2,400 1,800 250 700

1,200 1,000 7,350

The minimum cost = 7,350 thousand rupees. Since some of the ∆ij’s = 0, the above solution is not unique. Alternative solutions exist.

Ans.17: The given problem is a transportation problem. The profit matrix for various factories and sales counters is calculated below:

Factory 1

A B C D

3 0 4 2

Sales Centres 2 2 -1 3 1

3 4 1 5 3

Capacity (kgms)

100 20 60 80

Demand (kgms) 120 140 60 Since this is an unbalanced transportation problem (demand > capacity), let us introduce a dummy factory with profit as Rs.0 per unit for various sales centres and capacity equal to sixty units. The resulting matrix would be as below:

Factory 1

A B C D

Dummy Demand (kgms)

3 0 4 2 0

120

Sales Centres 2 2 -1 3 1 0

140

3 4 1 5 3 0 60

100 20 60 80 60

Capacity (kgms)

The above profit matrix can be converted into a loss matrix by subtracting all its elements from the highest payoff of the matrix i.e. 5. The loss matrix so obtained is given below:

Factory 1

A B C D

Dummy Demand (kgms)

2 5 1 3 5

120

Sales Centres 2 3 6 2 4 5

140

3 1 4 0 2 5 60

100 20 60 80 60

Capacity (kgms)

The initial solution is obtained by applying Vogel’s approximation method. Factory

1 A

B 5

C 1

D 20 2 60

100 2 3

20 6 4

60 0 60/0 1--

20/0 111

1 100/0 11-

Sales Centres 2 3

Capacity Difference

3 Dummy

5 Demand

Difference 120/20/0

1 1 2

4 60 5 140/120/60/0

1 1 1

2

5 60/0

1 - -

80/60/0

60/0

111

000

The solution obtained by VAM is as given below: Factory

1 A

B

C

D

Dummy

Vj

100 2 0 5 0 1 20 3 1 5 -1

Sales Centres 2 0 3 20 6 0 2 60 4 60 5 0

3 E 1 0 4 60 0 0 2 2 5 2

5

4

2

6

3

Ui

Since all ∆ij ≥ 0 for the non allocated cells, hence the solution given by above matrix is optimal. The optional solution for the given problem is given below:

From Factory

A B C D D

Dummy

To Sales Centre

1 2 3 1 2 2

Quantity

100 20 60 20 60 60

Profit per unit (Rs.)

3 -1 5 2 1 0

Total Profit = (Note: since some of the ∆ij’s are equal to zero, alternative solutions also exist.)

Ans.18: The given problem is an unbalanced transportation problem which is converted into a balanced on by adding a dummy investment as given below:

Total Profit (Rs.)

300 -20 300 40 60 0

660

Year P

1 2 3 4

Maximum Investment

95 75 70 90 40

Net Return data (in paise) of Investment Q 80 65 45 40 50

R 70 60 50 40 60

S 60 50 40 30 60

Dummy

0 0 0 0 20

Amount Payable

70 40 90 30

The values in the table represent net return on investment of one rupee till the end of the fourth year. The objective of the company is to maximize the net return. For achieving this objective, let us convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. 95, and apply Vogel’s approximation method for finding the initial feasible solution.

Year

P

1 40 0

2 20

3 25

4 35

Maximum Investment

Difference

40/0

20

-

-

-

55

50/20/0

15

15

20

-

55

60/40/0

10

10

10

10

50

20 30

40 45

10 6 5

60/10/0

10

10

10

10

20/0

0

0

0

0

30 15

20 35

50 5 5

20 9 5

30/20/0 10/3/0

9 5

90/50/0

4 5

9 5

40/20/0 10/5/5/10

10/40/20 /0/0

25 3 5

9 5

70/30/0 15/10 _ _

Loss Matrix – Investment type

Q R S

Dummy Amount Available

Difference

solution obtained by VAM is as given below

Year

P

1 40 0

2

Loss Matrix – Investment type

Q

30 15

20 20 30

40 25 50 45

10 35 55

50/20/0

55

60/40/0

65

60/10/0

20 35

50 55

45

25 35

R S

Dummy Amount Available

95 70

95 40

3 95

20 95

20/0

90

4 30

Maximum Investment

40/0

This initial solution is tested for optimality. There are 8 (=m+n-1) independent allocations. Let us introduce ui, vj,

i=(1,2,3,4); = (1,2,3,4,5 such that Dij = cij = (ui+vj) for allocation cell. We assume u1 = 0 and remaining u1’s vj’s and Dij’s are calculated.

Year

P

1 40 0

2 5 20

3 0 25

4 0 35

vj’s 0 15

5 55

20

55

30

10 50

20 30

40 45

10 65

60

30 15

20 35

50 55

20 95 35

Loss Matrix – Investment type

Q

5 25

0 45

10 95 25

R

5 35

20 95 15

S

35 95 0

Dummy Amount Available

On calculating Aijs for non-allocated cells, we found that their values are positive, hence the initial solution obtained above is optimal. The optimal allocations are given below: Year 1

Invest in Invest Rs 40 lacs in investment P

Net Return 0.95xRs.40 lacs = Rs. 38,00,000

Rs 30 lacs in investment Q 2 Invest Rs 20 lacs in investment Q

Rs 20 lacs in investment R

3

4

Invest Rs 40 lacs in investment R Rs 50 lacs in investment S Invest Rs.10 lacs in investment S Total Rs.130,00,000

0.80xRs.30 lacs = Rs. 24,00,000 0.65xRs.20 lacs = 13,00,000 0.60xRs.20 lacs = 12,00,000

0.50xRs.40 lacs = Rs. 20,00,000 0.40xRs.50 lacs = Rs. 20,00,000 0.30xRs.10 lacs = Rs.3,00,000

Ans. 19: The given information can be tabulated in following transportation problem:

Profit Sales offices

Plant 1 2 3 4 5 5 5 6 11 9 1 1 9 1 3 -1 2 4 14 10 9 8 3

125 45 75 100 80 Demand

Capacity in units

150 200 125

Where entries in the cells of the above table indicate profit per unit received by selling one unit of item from plant i (1 =1,2,3) to the sales office (i=1,2,3,4,5). The profit per unit is calculated using the following formula.

Profit = sales price –(production cost +Shipping cost)

The objective of the company is to maximize the profit. For achieving this objective, let us convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 14.

Loss matrix Sales offices Capacity in

units Plant 1 2 3 4 5

1 5 3 8 9 9 150 2 15 11 13 5 13 200 3 6 5 4 0 10 125

Demand 80 100 75 45 125 The problem is an unbalanced transportation problem since capacity (=475 units) is 50 units more than the demand. Hence a dummy sales office is added with cost equal to zero for all plants and demand equal to 50 units. Now, let us apply Vogel’s Approximation method to the resultant balanced matrix for finding the initial feasible solution.

Plant 1

2

1 50

5 25

15 5

2 100

3

11

5

80/30 /25/0

1 1 1 1 1

3

8

Sales offices 4 5

9 125

9

Dummy

0

50 0

13

Capacity

150/50/0

Difference

3/3/2/2/4

200/150/125/0 5/11/2/2/2/2

13 5 75 45

4

100/0

2 2 2 2 --

0

75/0

4 4 4 -- --

3

Demand

differ

6 10

45/0

5 -- -- -- --

0 125/80/5/0

125/0

1 1 1 1 1

50/0

0 0 -- -- --

0/4/1/1/4/4

The initial solution obtained by VAM is given below which is tested for optimality.

Plant

1

2

3

Demand in units

50 5

25 11

15 5

6

80

6

100 75

75 4

13

45 0

45

10

125

6

50

125

5

1

100 3 8 9

125 13

9 50

0 200

0 150

2 3 4 5 Dummy Capacity in units

These are m +n –1 =8 independent allocations. Let us now introduce ui, vj, I = (1,2,3); j = (1,2-----6) such that ∆ ij = Cij –(ui +vj) for allocation cells. We assume u2 = 0 and remaining ui’s vj’s and ∆ij’s are calculated as below:

Sales offices 3 4

10 8 9

13

3

Vj’s

15 5

15

11 +θ 1

6

13

75 5

13

4 0

9 13 0

-4 θ

45

Plant 1

2

1 50

5

25 -θ 3 -2

100 2

5

10

5 6

Dummy 10

0

50 13 0

9 10 0

Ui’s

-10

0

-9

9 + 125

5 -6 θ

Since some of the Δij’s are negative, therefore, the above solution is not optimal. Introduce in the cell (2,4) with the most negative Δij, an assignment. The value of θ and reallocated solution as obtained from above is given below. The reallocated solution is again tested for optimally. Hence, the values ui’s vj’s and Δij’s are again calculated.

Sales offices 3 4

5 10 8

4 11

1 6

Vj’s

Plant 1

2

3

1 50

5

4 15

30

11

3 2

100 2 5

2 9

125 5 13

2 0 10

13

9

Dummy 6

0

50 0

5 0

0

Ui’s

-6

0

-5

25 13

20 4

9 5

75 5

9

Since all Δij’s for non-basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of plants to sales officers and their profit amount is given below:

Plant

1 1 2 2 2 3 3 3

Ans.20:

Convert the given profit matrix into a loss matrix by subtracting each element of the matrix from the highest value viz.44.The resulting loss matrix is as follows:

Loss Matrix

Customer ------------------------------------------------

A B C

4 0 6

40

19 9 6

20

22 14 16 60

Sales Office

1 2 4 5 Dummy 1 3 4

units

50 100

25 125

50 30 75 20

profit per unit

9 11

9 1 0 8

10 14

Total

profit

450 1,100

225 125

0 240 750 280

3,170

Factory

P Q R Demand

D

11 14 14 30

supply

100 30 70

150/200

The loss matrix, obtained as above is an unbalanced one, We introduce a dummy column to make it a balanced one.

Loss Matrix

Customers ______________________________________

A B C D

4 0 6

40

19 9 6

20

22 14 16 60

11 14 14 30

Factory

P Q R Demand

Dummy

0 0 0

50

Supply

100 30 70

200/200

By using Vogal’s approximation method, the following initial feasible solution is found

Customers C Factory A B D Dummy Supply

P 10 60 30 e 100

4 19 22 11 0 -------------------------------------------------------------------------------------------------------------- Q 30 30

0 9 14 14 0 ---------------------------------------------------------------------------------------------------------------- R 20 50 70

6 6 16 14 0 ----------------------------------------------------------------------------------------------------------------- Demand 40 20 60 30 50 200/200

Since the number of allocation’s in the initial feasible solution are 6 and for applying optimality test they should be equal to (m+n-1)=7, therefore we enter a very small assignment equal to e in the minimum cost so that no loop is formed.

Let us introduce the variables Ui and Vj such that Ui + Vj = Cij for allocated cells. We thus have the following relations:

U1 + V1 = 4 U2 + V1 = 0 U1 + V3 = 22 U3 + V2 = 6 U1 + V4 = 11 U3 + V5 = 0 U1 + V5 + 0 Put U1 = 0,we get V1 = 4;V3 = 22; V4 = 11; V5 = 0; U3 = 0;V2 = 6 and U2 = (-4)

Compute: Cij – (Ui + Vj) for non-allocated cells. U1V2 =19 - (0 + 6) = 13 U2V2 = 9 - (- 4 + 6) =7

U2V3 = 14 - ( - 4 + 22) = (-4) U2V4 = 14 - (- 4 + 11) = 7 U2V5 = 0 - (- 4 + 0) = 4 U3V1 = 6 - (0 + 4) = 2 U3V3 = 16 - (0 + 22) = (-6) U3V4 = 14 - (0 + 11) = 3

Since the value of Cij - (Ui + Vj)is negative in two cells therefore the initial solution is not optimal, Introduce an assignment 0 in the cell U3V3 and construct a loop shown as below, after adjusting.

Customers

Factory A B C D Dummy Supply Ui --------------------------------------------------------------------------------------------------------------------------- ----- P 10 60-0 30 e+0 100 U1 = 0

4 30

Q (-4)

0 20

R 6

Demand

Vj

40

V1= 4

6

20

V2 = 6

16

60

V3 = 22

14

30

V4 =11

50

V5 = 0

0

200/200

9 0

14 14 50-0

70 U3 = 0

0

30 U2 =

19 22 11 0

Maximum value of 0 = 50

Apply optimality test once again. Introduce Ui and Vj’s and determine their values

Compute Cij - (Ui + Vj) for non-allocated cells, since it comes out to be negative for U2V3 cell, therefore we repeat the aforesaid process by introducing 0 in U2V3 cell, the minimum value 0f 0 is 10.

Customers

Factory

P

A

10+

4

B C

10-

19 0

22

D

30

11

Dummy

50

0

Supply

100

Ui

U1=0

Q 30-

0 9

20

6 6

20

V2=12

50

16

60

V3=22

14

30

V4=11

50

V5=0

0

14 14 0

30 U2=(-4)

R 6)

70 U3 = ( -

Demand

V1

40

V1=4

200/ 200

The second improved solution obtained is as under: Apply optimality test to the solution once again after determining the values of Ui and Vj. Since Cij - (Ui + Vj) for non-allocated cell is positive, therefore the following solution is optimal one.

Customers

Factory A B C D Dummy Supply Ui --------------------------------------------------------------------------------------------------------------------------- --- P 20 30 50 100 U1=0

4

Q 20

0

R

6

Demand 40

9

20

6

20

14

50

16

60

14

30

0

50 200/200

14 0

70 U3=(-2)

19 10

30 U2=(-4)

22 11 0

Vj V1=4 V2=8 V3=18 V4+11 V5=0

Transferring the solution to the original profit matrix, we get;

Customers

Factory A B C D Dummy ------------------------------------------------------------------------------------------------- P 20 30 50

40

Q 20

44

R

38

Demand 40

20

38

20

35

50

28

60

30

30

0

50

25 22

10

30 30 0

70

33 0

30

Supply

100

Maximum profit =20 Rs.40+30Rs.33+20*Rs.44+10*Rs.30+20*Rs.38+50*Rs.28+50*Rs.0 =Rs.800+Rs.990+Rs.880+Rs.300+Rs.760+Rs.1,400 =Rs.5,130

Ans. 21 The given information can be tabulated in following transportation problem:

Project Auditor 1 2 3 Time available

(Hours)

1 2 3

Time Required (Hours)

(Rs.) 1,200 1,400 1,600

130

(Rs.) 1,500 1,300 1,400

140

(Rs.) 1,900 1,200 1,500

160

160 160 160

The given problem is an unbalanced transportation problem. Introducing a dummy project to balance it, we get

Project Auditor

1 2 3

Time Required

(hrs.)

1

1,200 1,400 1,600 130

2

1,500 1,300 1,400 140

3

1,900 1,200 1,500 160

Dummy

0 0 0

50

Time available (Hours)

160 160 160 480

The objective here is to maximize total billing amount of the auditors. For achieving this objective, let us convert this maximization problem into a minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 1900.

Project Auditor

1 2 3

Time required

(Hrs)

1 700 500 300 130

2 400 600 500 140

3 0

700 400 160

Dummy 1900 1900 1900

50

Time available 160 160 160 480

Now, let us apply Volgel’s Approximation Method to the above matrix for finding the initial feasible solution.

Project (Figure of payoff’s in Rs. 00’s) 2 3 Dummy

160 1

2 130

3 Time Required

Difference

3 130/0

2/2/-/-

7 110

5 30

5 140/110/0

1/1/1/1

4 160/0

4/-/-

19 50/0

0/0/0

160/30/0 1/2/14/-

6 7

4 0 50

19 160/50/0 1/1/13/13

19 160/0 4/-/-/-

Auditor 1 Time Available

Difference

The initial solution is given below. It can be seen that it is a degenerate solution since the number of allocation is 5. In order to apply optimality test, the total number of allocations should be 6 (= m + n -1). To make the initial solution a non-degenerate, we introduce a very small quantity in the least cost independent cell which is cell of Auditor 3, Project 3.

Project Auditor

1

2 130

1

7 110

5 30

6 e

7

2 160

4 0 50

19 160

19 160

3 Dummy Time Available

3 3 5 4 19 160 Time 130 140 160 50

Required Introduce ui’s and vj’s such that ∆ij = Cij– (ui+vj) (for I, = 1 to 3; j = 1,2,3, dummy). To determine the values of ui’s and vj’s we assume that u3 = 0, values of other variables i.e. ui’s, vj’s and … are calculated as follows:

Project Auditor

1

2

3

1 8

7 1

5 130

3 30

5

110 6

e 4

2 3

4 2

7 1

19 U3=0

3 160

0 50

19 U2=1

Dummy 5

19 U1=-4

Uj’s

Vj’s v1=3 v2= 5 v3=4 v4=18 Since all for non basic cells are positive, therefore the initial solution obtained above is optimal. The allocation of projects to auditors and their billing amount is given below: Here an auditor may be involved in more one project as apparent from the following solutions.

Auditor 1 2 3 3

Project 3 2 1 2

Total billing

Billing amount (Rs.) 160xRs. 1900 = 3,04,000 110xRs. 1300 = 1,43,000 130xRs. 1600 = 2,08,000 30xRs. 1400 = 42,000

= 6,97,000

Hence, the maximum total billing during the next month will be Rs. 6,97,000

-1-

Ans. 1:

1 2 3 4

Step 1:

I 16 26 76 38

II 52 56 38 52

III 34 8 36 48

IV 22 52 30 20

Subtract the smallest element of each row from every element of the corresponding row I II III IV

1 0 36 18 6 2 18 48 0 44 3 46 8 6 0 4 18 32 28 0

Step 2: Subtract the smallest element of each column from every element in that column

I

1

2

3

4

I

1

2

3

4

0

18

46

18

0

18

46

18

II

28

40

0

24

II

28

40

0

24

III

18

0

6

28

III

18

0

6

28

IV

6

44

0

0

IV

6

44

0

0 Step 3: Drew minimum number of horizontal and vertical lines to cover all the zeros

The optimal assignment is 1 2 3 4

─ ─ ─ ─

I III II IV

= = = =

=

16 8

38 20 82 hours

Minimum time taken 82 hours

Ans. 2:

(a) Consider the following assignment problem: Division

N

A 14

E

20

W

11

S

19

Some solutions of Assignment

-2-

B Marketing Executives

C

D

12

16

17

10

19

13

15

18

15

9

15

14

Step 1 Select the minimum element of first row and subtract it from all the elements of the row. On repeating the step with all the rows of the above matrix, we get the following

N

A

B Marketing Executives

C

D Step 2

Select the minimum element of first column and subtract it from all the elements of the column. On repeating this step with all the columns of the above matrix; we get the following

Division

N

A B

Marketing Executives C D

0 3

4 0

3 2

0 1

Step 3 On drawing the minimum number of lines in the above matrix, so as to cover at the zeros, we get the following matrix. Division

N

A B

Marketing Executives C 0 Ā 3 0

D 3 0 2 1 Since the minimum number of lines drawn under the step is equal to number of marketing executives or number of divisions, therefore we go over to the final step for determining the required optimal solution.

Step 4 For determining the optimal solution scan each row in turn for a single uncovered zero in it, encircle it and pass a line in its column.

Division

2 2

E

9 1

W

0 6

S

8 0

2 2

E

9 1

W

0 6

S

8 0

1

4

4

0

3

2

0

1

3

3

Division E

9

1

W

0

6

S

8

0

-3-

N

A B

Marketing Executives C

D

0

3

2 2

E

9 1

4

0

W

0 6

3

2

S

8 0

0

1

The optimal assignment obtained in this case is as under:

Marketing Executive

A B C D Total minimum cost

Division

W S

N E

Cost Rs. 11 09 16 13 49

Ans. 5: Using the information that the factory works effectively 7 hours (=420 minutes) a day and the time required by each operator for producing each of the products, we obtain the following production and profit matrices:

Production Matrix (units) Operator

A P Q R S

70 60 70 21

Product B 42 84 60 42

C 30 140 42 28

D 35 105 42 28

P Q R S

Operator A

210 180 210 63

Profit Matrix (in Rs.) Product

B 84 168 120 84

C 120 560 168 112

D 35

105 42 28

In order to apply the assignment algorithm for minimizing losses, let us first convert this profit matrix to a loss matrix by subtracting all the elements of the given matrix from its highest element which is equal to Rs.560. The matrix so obtained is given below:

Operator A

P Q R S

350 380 350 497

B 476 392 440 476

Product C

440 0

392 448

D 525 455 518 532

Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each row from all elements of that row, we get the following matrix:

Operator Product

-4-

P Q R S

A 0

380 0 49

B 126 392 90 28

C 90 0 42 0

D 175 455 168 84

Now subtract the minimum element of each column from the elements of that column to get the following matrix:

Operator A

P Q R S

0 380 0 49

B 98 364 62 0

Product C 90 0 42 0

D 91 371 84 0

Draw the minimum number of lines to cover all zeros. The minimum number of lines to cover all zeros is three which is less than the order of the square matrix (i.e.4) thus the above matrix will not give the optimal solution. Subtract the minimum uncovered element (=62) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix:

Operator A

P Q R S

0 380 0

111

B 36 302 0 0

Product C 90 0 42 62

D 29 309 22 0

The minimum number of lines which cover all zeros is 4 which is equal to the order of the matrix, hence, the above matrix will give the optimal solution. Specific assignments in this case are as below:

Operator A

P Q R S

0 380 0

111

B 36 302 0 0

Product C 90 0 42 62

D 29 309 22 0

Operator P Q R S

Total

Product A C B D

Profit (Rs.)

Profit (Rs.) 210 560 120 28 918

Ans. 8: (i)

-5-

4 20 36 52

12 28 44 60

16 32 48 64

8 24 40 56

Subtracting minimum element – each row. 0 0 0 0

8 8 8 8

12 12 12 12

4 4 4 4

Subtracting minimum element – each column, 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Minimum no. of lines to cover all zeros = 4 = order of matrix. Hence optional assignment is possible. Minimum cost = 4 + 28 + 48 + 56 = 136.

= AR1 + BR2 + CR3 + DR4 Since all are zeros, there are 24 solutions to this assignment problem. Viz. A

R1 R2 R3 R4 R1

(ii) SP – VC = 100 Rs. A

R1 R2 R3 R4

0 16 32 48

0

96 80 64 48

8 24 40 56

8

B 88 72 56 40

12 28 44 60

12

C 84 68 52 36

4 20 36 52

4

D 92 76 60 44

B R2 R3 R4 R1 R3

C R3 R4 R1 R2 R4

D R4 R1 R2 R3 R2 etc.

A can be assigned in 4 ways, B in 3 ways for each of A’s 4 ways.

Subtracting the highest term

Subtracting minimum term of each row.

-6-

0 0 0

8 8 8

12 12 12

4 4 4

Which is the same as the earlier matrix Maximum contribution = Rs. (96 + 72 + 52 + 44) = Rs. 264.

Alternative Solution: Maximisation of contribution is same as minimizing cost. Hence, same assignments as in (i) will be the optional solution. Maximum Contribution Rs. (400 – 136) = Rs. 264

(iii) (a)

(b)

(c)

The relative cost of assigning person i to region r does not change by addition or subtraction of a constant from either a row, or column or all elements of the matrix. Minimising cost is the same as maximizing contribution. Hence, the assignment solution will be the same, applying point (i) above.

Many zero’s represent many feasible least cost assignment. Here, all zeros mean maximum permutation of a 4 4 matrix, viz. 4 3 2 1 = 24 solutions are possible.

Ans. 9: Reducing minimum from each column element (figure in ’000s)

Step 1 R1

C1 C2 C3 C4

1 0

R2 1 0

R3 0 2

R4

0

1

C1 C2 C3 C4

R1 0 0

Step 2 R2 0 0

R3 0 1

R4

0

0 Number of lines to connect all zeros nos. is 4 which is optional. Alternatively you may also reduce the minimum from each row.

Step 1 R1

C1 C2 C3 C4

0

1

R2 1 0

R3

0 0

R4

0

1

C1 C2 C3 C4

R1 0

0

Step 2 R2 1 0

R3

0 0

R4

0

0

Number of lines to connect all zeros nos. is 4 which is optional. All diagonal elements are zeros and are chosen. The minimum cost is Rs.15,000 C1 – R1 4,000; C2 – R2 4,000; C3 – R3 2,000; C4 – R4 5,000; (Total) = 15,000.

Ans.10: Let us first formulate the preference ranking assignment problem.

MANAGERS Room No. M1 M2 M3 M4 M5

-7-

301 – 4 2 – 1 302 1 1 5 1 2 303 2 – 1 4 – 304 3 2 3 3 3 305 – 3 4 2 –

We have to find an assignment so that total preference ranking is minimum. In a cell (-) indicates that no assignment is to be made in that particular cell. Let us assign a very large ranking value M to all such cells. Step 1 : From each row, subtract the minimum element of that row, from all the elements of that row to get the following matrix.

MANAGERS

Room No 301 302 303

M1 M 0 1

M2 3 0 M

M3 1 4 0

M4 M 0 3

M5 0 1 M

304 1 0 1 1 1 305 M 1 2 0 M

Draw the minimum number of lines in the above table to cover all zeros. In this case the number of such lines is five, so the above matrix will give the optimal solution. The assignment is made as below:

Rooms No. 301 302 303 304 305

M1 M 0 1 1

M

M2 3 0 M 0 1

MANAGERS M3 M4 1 4 0 1 2

M 0 3 1 0

M5 0 1 M l M

Thus, the assignment is M1 → 302, M2 → 304, M3 → 303, M4 → 305, M5 → 301 and the total minimum ranking = 1 + 2 + 1 + 2 + 1 = 7

Ans. 11: Dummy machine (M5) is inserted to make it a balanced cost matrix and assume i ts installation cost to be

zero. Cost of install at cell M3 (J) and M2 (L) is very high marked as é. J

M1 M2 M3 M4

M5 (Dummy) Step 1 Subtract the minimum element of each row from each element of that row

J K L M N

18 24 é 28 0

K

22 18 22 16 0

L

30 é 28 24 0

M

20 20 22 14 0

N

22 18 14 16 0

-8-

M1 M2 M3

M4 M5 (Dummy)

Step 2

0 6 é

14 0

4 0 8

2 0

12 é 14

10 0

2 2 8

0 0

4 0 0

2 0

Subtract the minimum element of each column from each element of that column

J M1 M2 M3 M4

M5 (Dummy)

Step 3 Draw lines to connect the zeros as under:

J M1 M2 M3 M4

M5 (Dummy)

0 6 é 14 0

K 4 0 8 2 0

L 12 é 14 10 0

M 2 2 8 0 0

N 4 0 0 2 0

0 6 é 14 0

K 4 0 8 2 0

L 12 é 14 10 0

M 2 2 8 0 0

N 4 0 0 2 0

There are five lines which are equal to the order of the matrix. Hence the solution is optimal. We may proceed to make the assignment as under:

J M1

M2

M3

M4

M5 (Dummy)

0

6

e

14

0

K 4

0

8

2

0

L 12

e

14

10

0

M 2

2

8

0

0

N 4

0

0

2

0

The following is the assignment which keeps the total cost at minimum:

Machines M1 M2

Location J K

Costs Rs. 18 18

-9-

M3 M4

M5 (Dummy) Total

N M L

14 14 0

64

Ans. 12: Since the Executive Director of the 5 star hotel is interested in maximizing the revenue of the hotel, therefore, the objective of the given problem is to identify the preferences of marriage parties about halls so that hotel management could maximize its profit. To solve this problem first convert it to a minimization problem by subtracting all the elements of the given matrix from its highest element which is equal to Rs. 10,000. The matrix so obtained which is known as loss matrix is given below:

Marriage party

A B C D

1

0 2000 3000

0

2

1000 0 0

2000

Loss matrix/Hall 3

M 2000 4000 M

4

M 5000 2000

M

Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each column from all elements of that column, we get the following matrix.

Marriage party

A B C D

1

0 2000 3000 0

Loss matrix/Hall 2

1000 0 0

2000

3

M 0 2000

M

4

M 3000

0 M

The minimum number of lines to cover all zeros is 3 which is less than the order of the square matrix (i.e. 4), the above matrix will not give the optimal solution. Subtracting the minimum uncovered element (= 1000) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix

Marriage party

A B C D

1

0 3000 4000 0

2

0 0 0

1000

3

M 0 2000 M

4

M 3000 0 M

Since the minimum number of lines to cover all zeros is 4 which is equal to the order of the matrix, the above matrix will give the optimal solution which is given below:

Marriage party

A B C D

1

0 3000 4000 0

2

0 0 0

1000

3

M 0 2000 M

4

M 3000 0

M

- 10 -

and the optimal schedule is :

Marriage party A B C D

→ → → →

Revenue (Rs.) Hall 2 9,000

Hall 3 8,000 Hall 4 8,000 Hall 1 10,000

Total 35,000

Ans. 14: The following matrix gives the cost incurred if the typist (i = A, B, C, D, E) executes the job (j = P, Q, R, S, T). Job

Typist A B C D E

P 85 90 75 80 76

Q 75 78 66 72 64

R 65 66 57 60 56

S 125 132 114 120 112

T 75 78 69 72 68

Subtracting the minimum element of each row from all its elements in turn, the above matrix reduces to

Job Typist P Q R S T

A 20 10 0 60 10 B 24 12 0 66 12 C 18 9 0 57 12 D 20 12 0 60 12 E 20 8 0 56 12

Now subtract the minimum element of each from all its elements in turn, and draw minimum number of lines horizontal or vertical so as to cover all zeros . All zeros can be covered by four lines as given below:

2 6 0 2 2

2 4 1 4 0

0 0 0 0 0

4 10 1 4 0

0 2 2 2 2

Since there are only 4 lines (<5) to cover all zeros, optimal assignments cannot be made. The minimum uncovered element is 2. We subtract the value 2 from all uncovered elements. Add this value to al junction values and leave the other elements undisturbed. The revised matrix to obtained is given below:

2 4 0 0 2

2 2 1 2 0

2 0 2 0 2

4 8 1 2 0

0 0 2 0 2

- 11 -

Since the minimum no. of lines required to cover al the zeros is only 4(<5), optimal assignment cannot be made at this stage also. The minimum uncovered element is 1, repeating the usual process again, we get the following matrix.

2 4 0 0 3

1 1 0 1 0

2 0 2 0 3

8 7 0 1 0

0 0 2 0 3

Since the minimum number of lines to cover all zeros is equal to 5, is this matrix will give optimal solution? The optimal assignment is made in the matrix below:

Typist A B C D E

Cost ( Rs.) Thus typist A is given job 75 Thus typist B is given job 66 Thus typist C is given job 66 Thus typist D is given job 80 Thus typist E is given job

T R Q P S Total

Ans. 17: (a) Sum of the proportion = (8 + 7 + 5 + 4) = 24

Assuming Rs. 1,000 as one unit, the effective matrix is as follows: Effective Matrix

Z N O P

East (8/24) 240 = 80 (7/24) 240 = 70 (5/24) 240 = 50 (4/24) 240 = 40

Managers West North South

(8/24) 192 = 64 (8/24) 144 = 48 (8/24) 20 = 40 (7/24) 192 = 56 (5/24) 192 = 40 (4/24) 192 = 32

(7/24) 144 = 42 (5/24) 144 = 30 (4/24) 144 = 24

(7/24) 120 = 35 (5/24) 120 = 25 (4/24) 120 = 20

P 2 4 0 0 3

Q 1 1 0 1 0

R 2 0 2 0 0

S 3 7 0 1 0

T 0 0 2 0 3

: : : : 112 Rs.399

Note: In case the above solution is not unique. Alternate solution also exists.

Convert the maximization problem to minimization problem The resultant loss matrix is as follows: Loss Matrix Managers

M East

0 West

16 North

32 South

40

- 12 -

N O P

Row operation Managers

M N O P

Column operation Managers

M N O P

Managers M N O P

Managers M N O P

Managers M N O P

Assignment

M – East N – West O – North P – South

10 30 40

24 40 48

38 50 56

45 55 60

East 0 0 0 0

West 16 14 10 8

North 32 28 20 16

South 40 35 25 20

East 0 0 0 0

East 0 0 0 2

East 0

0 4 6

East 0 0 4 8

West 8 6 2 0

West 6 4 0 0

West 2 0 0 0

West 2 0 0 2

North 16 12 4 0

North 14 10 2 0

North 10 6 2 0

North 8 4 0 0

Sales Rs.

South 20 15 5 0

South 18 13 3 0

South 14 9 3 0

South 12 7 1 0

- 13 -

1,86,000

Ans. 20 The initial matrix relating to nurse-patient combination is as under:

Nurse

K L M

W 10 30 20

Patients X 10 10 30

Y 30 20 20

Deducting the lowest element of each row from the other elements of the same row, we get the following matrix:

0 0 20 20 0

0 10

10 0

We deduct the lowest element of each column from the other elements of the same column. Since there is zero in each column, the same matrix will be returned. Draw lines to connect zeros as under:

0 20

0 0

20 10

0 10 0 There are three lines as required by the order of matrix of three. Hence the solution is optimal. Allocation of patients to nurses as under to minimize the cost

0 20 0

K L

M

W X Y

0 0

10 10 10 20

400 400 800

1600

400 400 800

Total minimum cost (iii) With the introduction of a new patient and a new nurse, the original matrix of nurse-patient

combinations will stand revised as under:

Nurse W

K L

M N

10 30 20 50

X 10 10 30 50

Patients Y 30 20 20 50

Z 40 40 40 50

- 14 -

9

Deducting the lowest element of each row from the other element of the same row, we get the following matrix:

0 20 0 0

0 0 10 0

20 10 0 0

30 30 20 0

Deduct the lowest element of each column from the other elements of the same column. Since there is zero in each column, the same matrix will be returned. Draw lines to connect zeros as under:

0 20 0 0

0 0 10 0

20 10 0 0

30 30 20 0

There are four lines as required by the order of matrix of four Hence the solution is optimal.

Proceed to allocate the patients to nurses as under to minimize the cost. 0 20 0 0

K L M N

W X Y Z

0 0 10 0

20 10 0 0

10 10 20 50

400 400 800

2000 3600

400 400 800

2000 Total minimum cost

(iv) The cost of new nurse per hour is Rs. 50 in respect of any patient and the cost of the existing nurses for attending to the new patient is Rs. 40 per hour. Both these rates are greater than the values of other elements of existing nurse-

patient combination matrix. Thus the new nurse row and new patient column will have a higher value than the element of the existing matrix. Hence the new nurse can be allocated to the new patient without having to redo the assignment exercise. Hence we need not to a fresh assignment. N will be assigned to patient Z at 50/ hr is Rs. 2000/ week. This will be the extra minimum cost to the hospital i.e. 2000 + 1600 = 3600.

Ans. 6 (i) Actual learning curve rate is 80%. Time taken to produce the first machine

Average time taken to produce two machines

Cumulative time taken to produce two machines

Time taken to produce the second machine

(ii) Actual learning curve rate is 90%. Time taken to produce the first machine Average time taken to produce two machines

Cumulative time taken to produce two machines

Time taken to produce the second machine

= 600 hours = 600 90% hours = 540 hours. = 540 2 hours

= 1080 hours. = (1080 600) hours

= 480 hours. The time taken to produce the second machine is lower at 80% learning rate and hence 80% learning rate shows faster learning rate.

= 480 hours. = 480 2 hours

= 960 hours. = (960 600)hours

= 360 hours.

= 600 hours = 600 80% hours

Ans. 10: (i) 1st unit

Variable Cost Labour Target Contribution

2000 1000

Rs/u Avg/u after 4 th at

2000 810 1500

4310 (Rs./u) Price to be quoted (ii) No, the company cannot quote this price for varying products because the learning

curve Ratio does not apply to non-repeated jobs. Each product will carry a different price according to its direct labour hours.

Ans. 13: 5,000 units

Material Direct Labour

Variable Overhead Total Variable Cost Fixed Cost Total Cost Total cost / unit Sales 100 5,000 15,000 x(assumed selling price) (Total Sales less Total Cost) = Profit 50,000

1,50,000 1,00,000

50,000 3,00,000 1,50,000 4,50,000

90 5,00,000

20,000 units 6,00,000 2,56,000

Refer to W Note i 2,00,000 10,56,000 1,50,000 12,06,000

60.3 5,00,000 15,000 x

15,000 x – 7,06,000

Or minimum selling price = 50.4(refer to Working Note ii) Working Note: I Units Hours

Some solutions of Learning Curve

5,000 10,000 20,000 Working Note: II 15,000 x – 7,06,000 > 50,000 15,000 x > 7,56,000 or x > 50.4

Alternative Solution: Total cost / unit of capacity 20,000 = 60.3 Weighted average selling price > 80.4

i.e. 5,000 100 15,000 x > 60.3

20,000

5,000 10,000 1 .8 = 8,000 hours

20,000 1 .8 .8 = 12,800 hours

= 5,00,000 + 15,000 x > 60.3 20,000 = 15,000 x > 12,06,000 – 5,00,000

Or 15,000 x > 7,06,000 x > 47.06 Minimum price to cover production Cost = 47.06 Minimum price to cover same amount of profit = 50.40 (refer to W orking Note 1) Working Note 1 ( 47.06 + 50.04) 15,000 units = Rs. 50,000

Ans. 14: Units 1 2 4 8 Material Cost / u Variable cost Variable Cost Option I

Average/ hrs/u. 2,000 1,600 1,280 1,024 = 10,000 = 2,000 = 12,000

If both the orders came together, learning rate 80% applies and 8 units can be made, with average time of 1,024 hours per unit. Cost to PQ: Variable cost excl. labour Labour cost 1,024 hrs × 4 Rs./hr

= Rs.12,000 = Rs. 4,096 = Rs.16,096

In this case,

Y Selling Price p. u. Variable Cost p. u. Contribution p. u. No. of units Contribution (Rs.) Option II

Hence: hrs/ u = 1280 Y

Selling Price Variable Cost (excl. labour) Labour cost:

1280 × 4

1280 × 1 Total Variable Cost Contribution Units

Rs.5,120

. Rs.17,120

Rs.80 4

Rs.1280 Rs.13,280

Rs.720 4

3,200

Rs.17,200 Rs.12,000

X Rs.14,000 Rs.12,000

Rs.17,200 Rs.16,096 Rs.1,104

4 4416

X Rs.16,500 Rs.16,096

Rs.404 4

1616 6032

→ (under option I)

If X Ltd supplies its labour. 80% learning curve will apply to 4 units each of PQ & X.

Contribution (Rs.) 320 2,880 PQ should not take labour from X Ltd. It should choose option I.

Ans. 16: Working notes :

(1) By the theory of learning curve YX = KX5 ……………………… (i) Here X is the cumulative number of units or lots produced, Y is the cumulative average unit time of those X units. K is the average time of the first unit or lot, s is the improvement exponent or the learning coefficient or the index of learning.

Taking log on both sides of relation (i) we have Log YX = log K + s log X ……………(ii)

(2) Time required for 30 units order (when the time required for the first unit is 40 hours)

Log 40 + (-0.322) log 30 0.4756

Anti log of 1.1264 Hence hours required Per unit

= 1.6021 + (- 0.322) (1.4771) = 1.6021 –

= 1.1264 = 13.38

= 13.38

Total time required for 30 units = 30 units x 13.38 hours = 401.40

(3) Time required for 50 units order (When the time required for first unit is 40 hours)

log 40 + (-0.322) log 50 = 1.6021 + (-0.322) 1.6990 = 1.055 Anti log of 1.055 = 11.35 Hence hours required per unit 11.35 hours Total time required for 50 units = 11.35 x 50 units = 567.5 hours

(4) Fixed overhead recovery rate per labour hour

Total labour hours 10 men x 25 days x 8 hours Less : 25% downtime (in hours)

Total effective hours Total fixed overheads per month (Rs.) Fixed overhead recovery rate per labour hour (Rs) (Rs. 7,500/1,500 hours)

(i) Computation of cost per unit of the first order of 30 units

Direct material cost (30 units x Rs. 60) Direct labour cost (401.4 hours x Rs. 6) Variable overheads (401.40 hours x Re 1) Fixed overheads (401.4 hours x Rs. 5) Total cost of 30 units Cost per unit (Rs. 6,616.80/30 units)

(ii)

Rs. 1,800.00

2,408.40

401.40

2,007.00

6,616.80 220.56

2,000

500 _____ 1,500 7,500

5

Cost per unit, when a repeat order for 20 units is also placed.

Direct material cost (20 units x Rs. 60) Direct labour (567.5 hours – 401.40 hours) x Rs. 6 Variable overheads (1.66.1 hours x Re 1) Fixed overheads (166.1 hours x Rs. 5)

Total cost of 20 additional units

Cost per unit (Rs. 3,193.20/20 units)

Price to be quoted to yield a profit of 25% on selling price

If selling price is Rs. 100 then profit is Rs. 25 and cost is Rs. 75

Rs. 1,200.00

996.60

166.10

830.50

________ 3,193.20

159.66

Hence selling price per unit = 100 x 159.66 75

= Rs. 212.88

Ans. 18 (i) Rs

Direct material Direct labour

Variable Overhead Fixed Overhead

Total cost Profit 25% Selling price per unit

(ii) Price per unit for second order of 60 units Learning will be applicable only in department B. Cumulative output becomes 100 units + 60 units = 160 units i.e 1.6 times for which learning is 86.1 % from the tables. Therefore Total Hrs for 160 units = 160 units 40 .861 = 5,510.4 Hrs Therefore Hrs for 60 units = Hrs for 160 units less Hrs for 100 units Or 5510.4 less 40 100 = 1510.4 Hrs

Therefore Hrs per unit =

Dept A 20 Hrs @ 10 = 200 Dept B 40 Hrs @ 15 = 600 20% of Rs 800 Dept A 20 Hrs @ 8 = 160 Dept B 40 Hrs @ 5 = 200

1,820.00 455.00

2,275.00

160.00 360.00

Price per unit for first order of 100 units Rs

500.00 800.00

1510.4 = 25.17

60

Rs 500.00 577.55

115.51 285.85

1,478.91 369.73

1,848.64

Calculation of selling price per unit

Direct materials Direct labour

Variable Overhead Fixed Overhead

Dept A 20 Hrs @ 10 = 200 Dept B 25.17 Hrs @ 15 = 377.55 20% of 577.55 Dept A 20 Hrs @8= 160 Dept B 25.17 Hrs @5=125.85

Total cost Profit 25% Selling price per unit

(iii) Price per unit for third order of 40 units Cumulative output becomes 100 + 60 + 40 = 200 units i.e. 2 times for which learning is 80% from the table Total Hrs for 200 units = 200 40 .80 = 6,400 Hrs Hrs for 40 units = Hrs for 200 units less Hrs for 160 units

Or 6,400 less 5510.4 = 889.6 Hrs

Therefore Hrs per unit = 889.6

= 22.24 40

Rs 500.00 533.60

106.72 271.20

1,411.52 352.88

1,764.40

Calculation of selling price per unit

Direct materials Direct labour

Variable Overhead Fixed Overhead

Total cost Profit 25% Selling price per unit

Dept A 20 Hrs @ 10 = 200.00 Dept B 22.24 @ 15 = 333.60 20% of 533.60 Dept A 20 Hrs @ 8 = 160 Dept B 22.24 Hrs @ 5 = 111.20

-1-

Ans. 12 (i) The required network is given below:

(ii) Critical path : B,E,F =7+7+6 = 20 days

Ans. 13 The network is constructed as given in figure below:

(i) The TE’s and TL’s for various events computed on the network are as follows: Event No.: TE TL

1 0 0

2 4 12

3 1 1

4 5 13

5 7 7

6 11 17

7 15 15

8 17 17

9 18 18

10 25 25

(ii) Activity floats are computed using the following formula: Float = TL (Head event) – TE (Tail event) – Duration

Activity 1-2 1-3 2-4 3-4 3-5

Duration 4 1 1 1 6

TE (Tail Event) 0 0 4 1 1

TL(Head Event) 12 1

13 13 7

Float 8 0 8 11 0

Sol of PERT CPM

-2-

4-9 5-6 5-7 6-8 7-8 8-9

8-10 9-10

5 4 8 1 2 1 8 7

5 7 7 11 15 17 17 18

18 16 15 17 17 18 25 25

8 5 0 5 0 0 0 0

Critical path is given by all those activities which have zero floats. Along the zero float activities, there are two such critical paths: (i) (ii)

1 → 3 → 5 → 7 → 8 → 9 → 10 1 → 3 → 5 → 7 → 8 → 10

The project duration is 25 weeks.

Ans. 16(i)

(ii)

(iii)

(iii)

A� D� F = 16+ 10+12 = 38 B� E� F = 20+ 6+ 12= 38 A-C –E- F = 16+8 +6 +12 = 42

Total float and free float for each activity

Total float and free float for each activity

Activity

A B C D E F

Normal Time Days

16 20

8 10

6 12

Earliest start

0 0

16 16 24 30

Time finish

16 20 24 26 30 42

Critical Path

Latest start

0 4

16 20 24 30

Time finish

16 24 24 30 30 42

Float total

0 4 0 4 0 0

Free

0 4 0 4 0 0

Ans. 18

(a) Z 20 20 = 0; Probability = 0.50

4

-3-

(b) Z

(c) Z

18 20 = –0.50; Probability = 0.31

4 24 20

= 1; Probability = 0.84 4

Ans. 19

Tcp = 60 S.D. = 9 = 3.

60 + 3 × 2.3 = 67 weeks (Answer)

Ans. 21 The required network is drawn below:

(i) From the above network, it can be noted that the critical path is 1 – 2 – 4 – 6 – 8. (ii) Expected cost of construction of the plant = (5 + 3 + 4 + 9 + 2 + 12 + 20 + 7 + 14 + 4) millions of Rs.

= Rs.80 million (iii) Expected time required to build the plant = 4 + 6 + 9 + 1 = 20 months. (iv) It is given that the time required for one activity is independent of the time and cost of any other activity and variations

are expected to follow normal distribution, the S.D. Hence, the variance of the expected time is determined by summing the variance of critical activities and is = 1 + 2 + 5 + 1 = 9. Standard Deviation of the expected time = √9 = 3 months.

Ans. 24 The earliest expected completion time, latest allowable completion time and slack time for each event is:- Event (I – j) 1–2 1–3 2–4 2–5 3–4 3–6 4–5 4–6 5 –7 6–7

2 te

4 5

20 20

3 8

10 6 8

10

2 3

01 10

2 4 4 2 1 8

Earliest start

0 0 4 4 5 5

24 24 34 30

Earliest finish

04 5

24 24 08 13 34 30 42 40

Latest start

0 16

4 14 21 24 24 26 34 32

Latest finish

4 21 24 34 24 32 34 32 42 42

Slack

0 16

0 10 16 19

0 2 0 2

-4-

- The critical path is 1 2 4 5 7 = 42 Variance of project time 2 =2+1+4+1=8

2 Therefore, = 8 and scheduled time T5 = 38

Z= 38 42

8 =

4 8

= - 1.41

From table on normal curve, the area of Z = 1.41 is given as 0.4207 Therefore the probability of completion of the project by the scheduled time = (0.5 – 0.4207) = 7.93%

Ans. 25

Calculation of expected time and variance of each activity: Activity

1 2 1 3 1 4 2 5 3 5 4 6 5 6

Optimistic Days

4 3 4 5 8 4 2

Most likely Days

10 6 7 5

11 10 5

Pessimistic Days

16 9

16 5

32 16 8

Expected Duration

10 6 8 5

14 10 5

Variance

4 1 4 0 16 4 1

The network diagram is as under:

According to probability values given in the question probability is 11.9% To obtain 95% confidence level:

Critical Path: Duration (days)

1-3 6

3-5 14

5-6 5 = 25 days

-5-

Standard deviation: 1 + 16 + 1 = 18 18 = 4.24

Probability that the project will be completed five days earlier:

Z= 20 25

= 1.18 4.24

According to probability values given in the question probability is 11.9% To obtain 95% confidence level:

1.65= X 25 4.24

X – 25 = 6.996 X = 32 days

Ans. 26:

i. Activity to tm tp Expected 2 t p t0 Variance σ 6

2

----------------------------------------------- duration (in weeks) te = (t0 + 4tm + tp) / 6

1-2 1-3 1-4 2-5 2-6 3-6 4-7

3 2 6 2 5 3 3

6 5

12 5

11 6 9

15 14 30

8 17 15 27

7 6

14 5

11 7

11

4 4

16 1 4 4

16

Critical Path 1-2-6-7 Expected project duration = (7+11+18)=36 week (iv) Probability of project completion in 38 weeks o = 4 + 4 +16 = 24 o = 24 = 4.90 o

-6-

38 - 36 2s Z = -------- = --------- = 0.41

4.9 4.9 Value of Z = 0.41 in Z tables is 0.1591

P(Z) = 0.5+ 0.1591 Probability of project completion in 38 weeks is 66%

(v) Project duration (say x weeks) with 95% chances of completion: x - 36

1.65 = --------- 4.9

or 8.085 = x - 36 or x = 44 weeks

Ans. 27: The earliest and latest expected time for each event is calculated by considering the expected time of each activity as shown in the table below:

Activity (i – j)

1-2 1-3 1-4 2-5 3-5 4-6 5-6

t0 tm tp te = (t0 + 4tm + tp) / 6 t p t0 σ2 6

4 4 4 0 16 4 16

2

2 2 4 2 4 4 6

2 8 4 2 10 10 12

14 14 16 2

28 16 30

4 8 6 2

12 10 14

(a) The project network is drawn below:

(i) (ii)

Critical Path is : 1 – 3- 5 – 6 The expected duration and variance of each activity is shown in the table above. The expected project length is the sum of the duration of critical activities. Hence, Expected project Length = 8 + 12 + 14 = 34 months

-7-

(iii) Variance of the project length is the sum of the variances of critical activities. Variance of project length = σ² = 4 + 16 + 16 = 36 months Therefore, Standard Deviation = σ = √36 = 6

(iv) Probability that the project will be completed at lest 8 months earlier than the expected time of 34 months is given by

T T (34 8) 34 Prob. Z s e = Prob.[Z ≤ - 1.33] σe 6

But Z = -1.33 from the normal distribution table is 0.0918. Students may please note that the values for the Prob. For a Z value correspond tot e shaded area as shown in the

diagram below:

Thus, the probability of completing the project within 26 months is 9.18%. (v) If the project due date is 38 months, then the probability of not meeting the due date is given by

T Te (38 34) Prob. Z s = Prob.[Z > 0.67] σe 6

But Z = 0.67 from the normal distribution is 0.2514. Thus, the probability of not meeting the due date is 25.14%.

Ans. 28: The required network is drawn below:

The expected time marked in the above network diagram for various activities is calculated in the table below: Activity Time (in weeks) Expected

2 t p t0 2

-8-

Optimistic (to)

1-2 2-3 2-4 3-5 4-6 5-6 5-7 6-7

3 3 2 4 4 0 3 2

Most likely (tm)

3 6 4 6 6 0 4 5

Pessimistic (tp)

3 9 6 8 8 0 5 8

time (weeks) te = (t0 + 4tm

+ tp) / 6 3 6 4 6 6 0 4 5

0 1

4/9 4/9 4/9 0

1/9 1

(i) Variance of each of the activities has been calculated in the last column of the above table. (ii) Critical path is given by 1 – 2 – 3 – 5 – 6 – 7 and the expected project length is 20 weeks. (iii) Variance of the critical path = σ² = 0 + 1 + 4/9 + 0 + 1 = 22/9 = 2.444

Mean = x = 20 weeks

To calculate the probability of completing the project in 23 weeks, we will first calculate the normal Z as below:

Z= D x

=

23 20 2.444

= 1.92

(from the normal table) P (x < 23) = P (z < 1.92) = 0.9726

Thus, the probability that the project will be completed in 23 weeks is 97.26%.

Ans. 29: The network for the given problem is drawn below:

17.67

1 17.83

2 17.83 3 19 5 7 22.83

9

4 17 6 8

20

16. 67

-9-

In the table below, we have calculated the expected duration and variance of each activity.

Activity Optimistic

a 1-2 2-3 2-4 2-8 3-4 3-5 4-6 5-7 5-9 6-7 6-8 7-9 8-9

Variance paths are: 1-2-3-5-7-9 1-2-3-5-9 1-2-3-4-6-7-9 1-2-3-4-6-8-9 1-2-8-9 1-2-4-6-8-9 1-2-4-6-7-9

14 14 13 16 -

15 13 -

14 - -

16 14

Time Most Likely

m 17 18 15 19 -

18 17 -

18 - -

20 16

Pessimistic b

25 21 18 28 -

27 21 -

20 - -

41 22

Expected duration

{(a+4m+b) 6}

17.83 17.83 15.17

20 -

19 17 -

17.67 - -

22.83 16.67

Variance {(b-a) 6}2

3.36 1.36

4

17.36

20.08

77.49 72.33 75.49 69.33 54.5 66.67 72.83

Hence the critical path is 1-2-3-5-7-9 with duration of 77-49 days or 78 days approximately.

Variances of various activities on critical path have been calculated in the last column of the above table.

Hence standard deviation of critical path = 26.08 = 5.12

Now we want to find out that within how many days the project should be completed so as to provide 95% probability of break even.

Z0.95 = 1.65

- 10 -

Hence, 1.65 = {(D-77.49) 5.12} Or, D = 1.65 5.12+77.49 = 85.94 or 86 days

The fixed cost of the project is Rs. 8 lakhs and the variable cost is Rs. 9,000 per day.

Thus, amount to bid = Rs. 8 lakhs+ Rs. 9,000 86 = Rs. 8 lakhs + Rs. 7,74,000 = Rs. 15,74,000

Ans. 34: (a) Critical Paths:

All are critical paths: (i) (ii)

1–2–5–6 1–3–5–6

2+8+5 3+7+5 4+6+5 3+1+6+5

= 15 = 15 = 15 = 15

(iii) 1 – 4 – 5 – 6 (iv) 1 – 3 – 4 – 5 – 6 (i) (ii)

Choose 5 – 6, common path; Crash by 1 day Choose: 1 – 2, 1 – 3, 1 – 4

Or (iii) Choose: 1 – 2, 3 – 5, 4 – 5

Or (iv) Choose: 2 - 5 , 3 – 5, 4 – 5 (v) Choose: 1 – 3, 1 – 4, 2 - 5

Ans. 35: (i)

Or

Assuming that the duration of activity 3 – 5 is 4 weeks. The various critical paths are:

1-2-5-8-9 15 weeks 1-3-4-7-8-9 15 weeks 1-3-4-6-7-8-9 15 weeks 1-3-5-8-9 15 weeks

(ii) Note: Since the duration for activity 3-5 is not specified it is open for you to assume the duration. Depending upon the duration assume three possibilities emerge. 1.

2.

3.

If the duration assumed is more than 4 weeks then that path (13, 35, 58, 89) alone will be critical. In that case you can choose any of the activity in the critical path. If the duration assumed is exactly 4 weeks then it will be one of the 4 critical paths and the various possibilities are given below. If the duration assumed is less than 4 weeks then the solution should be based on 3 of the critical paths namely 12,589, 1346789 and 134789. This has 16 combinations. Reduce in the following ways, the project duration is. Since all the paths are critical, reduction is possible by combining activities. The activities can be independent, common to few paths and common to all the paths. The various categories are as follows: 1. Common to all the paths. 8-9 2. Independent : Combination 1. 1-2,3-5,4-6 and 4-7.

Combination 2. 2-5,3-5,4-6 and 4-7.

- 11 -

Combination 3. Combination 4.

3. Activities common to two of the paths. Combination 1. 1-2,1-3. Combination 2. 1-3,2-5. Combination 3. 3-4,5-8. Combination 4. 5-8,7-8.

4. Activities common to two of the paths and two independent activities. Combination 1. 1-2,3-4,3-5. Combination 2. 1-2,3-5,7-8. Combination 3. 2-5,3-4,3-5. Combination 4. 2-5,3-5,7-8. Combination 5. 4-6,4-7,5-8. Combination 6. 4-7,5-8,6-7.

(Any three of the above combination.)

Ans. 36: (i) Project network based on the given activities is as under :

1-2,3-5,4-7, 6-7. 2-5,3-5,4-7, 6-7.

(ii) A review of the above network clearly shows that there are four paths 1 – 4 – 5; 1 – 2 –5 ; 1 –2 – 3 – 5;& 1 – 3 – 5 of duration 10 days; 11 days; 13 days and 4 days respectively. The longest path of 13 days viz,. 1 – 2 – 3 – 5 is the critical path of the drawn network.

(iii) The optimum duration of a project is that duration of the project for which the total cost (direct & indirect) will be minimum. The cost corresponding to optimal duration is known as resultant cost of the project. To determine optimum duration and resultant cost of the project based on the given activities we proceed as follows:

Activity Normal Time (days)

4

2

5

Crash Time

(days)

3

2

4

Normal Cost

Rs.

1,500

1,000

1,875

Crash Cost Rs

2,000

1,000

2,250

Cost slope per day

Rs.

500

--

375

1–2

1–3

1–4

- 12 -

2–3

2–5

3–5

4–5 Total direct cost

7

7

2

5

5

6

1

4

1,000

2,000

1,250

1,500 10,125

1,500

2,500

1,625

2,125

250

500

375

625

The normal total cost (direct & Indirect) of completing the project in 13 days is :

Normal direct cost : (Rs)

Indirect cost 13 days x Rs. 500

Total normal cost : (Rs)

10,125

6,500

______ 16,625

To determine the optimum duration and resultant cost we crash activities on the critical path by properly selecting them as under :

Activities

No. of available crash days

Cost slope per day (Rs)

Indirect cost per day (Rs)

Saving in cash

Ranking

1–2

1

500

500

--

--

2–3

2

250

500

250

1

3–5

1

375

500

125

2

The above ranking clearly shows that we should select the activity 2 – 3 and crash it for one day, as it results in maximum saving of Rs. 250 per day.

Let us crash 2 – 3 by 2 days.

Normal direct cost

Cost slope (2 days x Rs. 250)

Indirect cost (11 days x Rs. 500)

Total cost

After crashing the activity 2 – 3 we are left with the following paths as under :

1–2

1–2

1–4

1–3

2–3

2–5

4–5

3–5

3–5 of 11 days duration

of 11 days duration

of 10 days duration

of 4 days duration

Rs. 10,125

500

5,500 ______ 16,125

1 – 2 is a common activity in the first two paths with cost slope of Rs. 500/- per day. There is no profit or loss in crashing this actively. Hence crash it by one by.

Normal direct cost Rs.

10,125

- 13 -

Total cost slope (Rs. 500 + 1 day x Rs. 500)

Indirect cost (10 days x Rs. 500)

Total cost

Now we have the following four paths are as under :

1–2

1–2

1–4

1–3

2–3

2–5

4–5

3–5

3–5

1,000

5,000 ______ 16,125

of 10 days duration

of 10 days duration

of 10 days duration

of 4 days duration

To reduce the duration of project further, we are required to select the activities on all the three paths. These activities may be 3 – 5, 2 – 5, and 1 – 4. if all of these activities are crash by even 1 day each, then the total increase in cost would be (Rs. 375 + Rs. 500 + Rs. 375) or Rs. 1,250/- for saving Rs. 500. At this stage, we stop the process of crashing.

Hence optimal project duration

Resultant project cost/optimal cost : (Rs)

10 days

16,125

Ans. 38: (i) The required network is given below:

The various paths in the network are: 1 – 2 – 4 – 5 with project duration = 16 days 1 – 4 – 5 with project duration = 17 days 1 – 3 – 4 – 5 with project duration = 20 days

The critical path is 1 → 3 → 4 → 5. The normal length of the project is 20 days and minimum project length is 12 days.

(ii) Since the present schedule consumers more time than the minimum project length, the duration can be reduced by crashing some of the activities. Also, since the project duration is controlled by the activities lying on the critical path, the duration of some of the activities lying on critical path can be reduced. It is given that overhead cost is Rs.60 per day. Step I: First, the crashing cost of activity (3, 4) being minimum, the duration of this activity can be compressed from 10 days to 9 days. The total cost for 19 day’s schedule

= Rs.15 + Rs.19 × 60 = Rs.1,155

- 14 -

Step II: Since the critical path remains unchanged, the duration of activity (3, 4) can be further reduced from 9 days to 8 days resulting in an additional cost of Rs.15 so that total cost for 18 days schedule = Rs.30 + Rs.60 × 18 = Rs.30 + Rs.1,080 = Rs.1,110. Step III: Continue this procedure till the minimum project length schedule. The calculations are given below:

Normal Project

length (days) 20 19 18 17 16 15 14 13 12

-- 3–4 3–4 3–4 4–5

Job crashed Crashing Cost (Rs.) Overhead cost @

Rs.60 / day 20×60 19×60 18×60 17×60 16×60 15×60 15×60 13×60 12×60

Total Cost. (Rs.)

1,200 1,155 1,110 1,065 1,045 1,030 1,035 1,040 1,055

-- 1 × 15 = 15 2 × 15 = 30 3 × 15 = 45 3×15+1×40 = 85 4×15+1×40+1×30= 130 130+1×30+1×25+1×10=195 195+1×25+1×30+1×10=260 260+25+30+20=335

3–4, 1–4 1–3, 1–4, 2–4 1–3, 1–4, 2–4 1–3, 1–4, 1–2

(iii) Since the total cost starts increasing from 14 days duration onwards, the minimum total cost of Rs.1,030 for the optimum project duration of 15 days occurs for optimum duration of each job as given below: Job: Optimum:

Duration (day)

(1,2) 9

(1,3) 8

(1,4) 14

(2,4) 5

(3,4) 6

(4,5) 1

Path 1 → 2 → 4 → 5 = 9 + 5 + 1= 15 days Path 1 → 4 → 5 = 14 + 1 = 15 days Path 1 → 3 → 4 → 5 = 8 + 6 + 1 = 15 days. Hence, the optimum duration of the project is 15 days.

Ans. 39 : (a) (i) Net work diagram

- 15 -

Critical Path is 1-2-5-6-7-8 = 32 weeks Associated Cost = 4220 + 32×50 = 5820

(ii) Total floats

Activity

1-2 2-3 2-4 2-5 3-5 4-5 5-6 6-7 6-8 7-8

Duration weeks

3 3 7 9 5 0 6 4

13 10

Early start

0 3 3 3 6 10 12 18 18 22

Latest start

0 4 5 3 7

12 12 18 19 22

Early finish

3 6 10 12 11 10 18 22 31 32

Latest finish

3 7 12 12 12 12 18 22 32 32

Total float

0 1 2 0 1 2 0 0 1 0

(iii) Calculation of crashing

Activity

1-2 2-3 2-4 2-5 3-5 4-5 5-6

Nt

3 3 7 9 5 0 6

Nc

300 30 420 720 250 0

320

Ct

2 3 5 7 4 0 4

Cc

400 30 580 810 300 0

410

Slop = (Cc-Nc) / (Nt-Ct)

100 0 80 45 50 0 45

- 16 -

6-7 6-8 7-8

4 13 10

400 780 1000

3 10

9

470 900

1200

70 40

200

The critical path activities are Slope

1-2 100

2-5 45

5-6 45

6-7 70

7-8 200

Two activities cost slope cost is minimum (2-5 and 5-6) but activity 5-6 is common and critical, it also continuing so reduce by 2 weeks, then reduce activity 2 -5 by one week.

Activity I II

So

Slope cost

5-6 2-5

From-to 6-4 weeks 9-8

1-2

100

3-5 2-5

Project durations 32-2 = 30 30-1 = 29

6-7

70

Cost 4220 + (2×45) + (30×50) = 5810 4220+90+(1×45)+(29×50) = 5805

After this reduction now two paths are critical 1-2-3-5-6-7 = 28 and 1-2-5-6-7 = 28

50+45=95 As cost per week for every alternative is greater than Rs.50 (overhead cost p er week). Therefore, any reduction in the duration of project will increase the cost of project completion. Therefore, time for projects is 29 weeks, minimum cost is Rs.5805.

Answer 40: The network is given below:

(i)

(ii)

The critical path of the project is A C E G or 1-2-3-4-6-7 with normal duration of 25 days. The minimum duration of the project is 18 days.

The cost slope for various activities is given below:

Activity Normal Duration

Crash duration

Normal cost (Rs.)

Crash cost (Rs.)

Cost slope (Rs.)

- 17 -

A (1-2)

B (2-4)

C (2-3)

D (2-5)

E (4-6)

F (5-6)

G (6-7)

7

4

5

6

7

5

6

5

2

5

4

4

2

4

Total

500

400

500

800

700

800

800

4,500

900

600

500

1,000

1,000

1,400

1,600

900 500 200

7 5 600 400

100 42

N.A. 1,000 800

100 6 4

1,000 700 100

7 4 1,400 800

200 5 4

1,600 800 400

6 4

Step –1: Various paths of the network are given below: 1-2-3-4-6-7 With duration = 25 days 1-2-4-6-7 With duration = 24 days 1-2-3-5-6-7 With duration = 23 days 1-2-5-6-7 With duration = 24 days

In order to determine the cost of completing the project in 21 days, let us crash that activity on the critical path, which has minimum cost slope. It can be seen that the minimum cost slope of Rs.100 corresponds to activity E (4-6) and it lies on the critical path. Hence, we crash activity E (4 –6) by 1 day at an additional cost of Rs. 100.

Step- 2: Various paths now are: 1-2-3-4-6-7 1-2-4-6-7 1-2-4-6-8 1-2-4-6-9

With duration = 24 days With duration = 23 days With duration = 23 days With duration = 24 days

An examination of the above four paths clearly points out that there are two critical paths namely 1-2-3-4-6-7 and 1-2-5-6-7, each with duration = 24 days. To reduce the project duration by three days more, there are following possible combination of activities.

1.

2.

3.

Crash activities 4-6 on the path 1-2-3-4-6-7 and 5-6 on the path 1-2-5-6-7 by one day each at an addition cost of Rs. 100 +Rs. 200 = Rs. 300.

Crash activities 4-6 on path 1-2-3-4-6-7 and 2-5 on path 1-2-5-6-7 by one day each at an additional cost of Rs. 100 +Rs. 100 = Rs. 200

Crash activity 1-2 by one day at an additional cost of Rs. 200.

It can be observed that the additional cost of reducing the project duration by one day in combination 2 as well as combination 3 is Rs. 200. Hence any of these two can be selected for crashing. However, since crashing activity 1-2 by 1 day reduces the duration of all the paths by1 day, we will crash it by I day. The project duration becomes = 23 days at an additional cost = Rs. 200.

- 18 -

Step 3: Crash activity 1-2 by 1 day further, it would reduce the project duration to 22 days at an additional cost = Rs. 200. Step 4: Activity 1-2 can not be crashed further. So, we now select the combination 2 stated above for crashing. Crash activities 4-6 and 2-5 by one day each at an additional cost of Rs. 100 +Rs. 100 = Rs. 200.

Hence, in order to complete the project in 21 days, an additional cost of Rs. 100 +Rs. 200 +Rs. 200 +Rs. 200 = Rs. 700 will be incurred. The normal cot of completing the project in 25 days =Rs. 4,500. Hence, the percentage increase in cost to complete the project in 21 days

= Rs.700

100 = 15.5%. Rs.4,500

Answer 42 The requires network based on the given activities and duration is drawn below :

The critical path of the network is 1-3-4-5-6 i.e. B-E-G-H. The duration of the project is 14 weeks.

E=4 L=6

A 4

2

D 3

B E 2

E=9 L=9

C 3

3 H

G 2

E = 14 L = 14

1

E=0 L=0

7

6 4

F 3

E=7 L=7

2

5

E = 11 L = 11

The time scale diagram for various activities along the resource accumulation table showing the number of workers required on each day are drawn on next page.

C(2) 3

A(4)

4

7

2 D(4)

3 2

B(2) E(6) 3

G(3) H(4)

1

7

4

2

F(3)

2 2

2

5

3

6

- 19 -

Crew size

1 6

6

2 6

6

3 6

6

4 6

6

5 8 -2 6

6 8 -2 6

7 8 -2 6

8 9

9

9 9

9

10 3

3

11 3

3

12 4

+2 6

13 4

+2 6

14 4

+2 6

It can be seen that the demand on the resources is not even. On the 8th and 9th week, the demand of workers is as high as 9 whereas on the 10th and 11th week, it is only three. If 9 workers are to be hired for the entire project duration of 14 weeks, then during most of the days they will be idle. We will attempt to re-schedule our activities in such away so as to utilize the workers in a fairly uniform manner. As can be seen from the above network diagram, activity C has a float of 7 weeks and activity F has a float of 2 weeks. The maximum demand on the resources occurs during 5th week to 7th week. (i.e. 8 workers) and during 8th to 9th week (i.e. 9 workers). We will shift activity C by seven weeks so that it starts on 12th week instead of 5ht week. This reduces the demand of the workers from 8 to 6 during 5th to 7th weeks. The modified resource requirements are shown in the last row of the above table.

Activity F has a float of two weeks. It is shifted by two weeks so that it starts on 10th week instead of 9th workers required earlier. The modified resource accumulation table is given:

Crew size

1 6

6

2 6

6

3 6

6

4 6

6

5 8

6

6 8

6

7 8

6

8 9 -3 9

9 9 -3 9

10 3

+3 6

11 3

+3 6

12 4

6

13 4

6

14 4

6

It is evident from the last row of the above table that there is a uniform demand of 6 workers throughout the duration of the project.

Ans. 46: The network diagram is drawn below:

2

4

E=0 L=0 1

E= 4 L=4

8

4 6

6

3

4 3

E=3 L=4

4 E=8 L=8

5 E = 14 L = 14

- 20 -

The critical path is 1-2-4-5. The total floats of all the activities are calculated below:

Activity 1-2 1-3 1-4 2-4 2-5 3-4 3-5 4-5

(b)

Duration 4 3 6 4 8 4 4 6

Total float 0 1 2 0 2 1 7 0

The resource allocation table is given below:

Starting day Equipment X job done No. of men required day completed Equipment Y Job done No. of men required Day completed Equipment Z Job done No. of men required Day completed Total no. of men

Explanation:

1st (1,2) 30 4

(1,3) 20 3

4th (1,2) 30 4

5th (2,4) 30 8

9th 10th 13th (4,5) 30 18

18th (4,5) 30 18

(3,5) 20 21

21st

50

(1,4) 20 9

50

(1,4) 20 9

50

(3,4) 20 12

(1,4) 20 9

40

(3,4) 20 12

(2,5) 20 17 40

(3,5) 20 21

(2,5) 20 17 50 50 20

This is basically a problem of resource-leveling whereby the main constraint would be on the resources. It the maximum demand on any resource is not to exceed a certain limit, the activities will have to be rescheduled so that the total demand on the resources at any time will be within the limit and consequent the project duration time is exceeded. The criterion to be followed in such a case is to delay the job with a large float. In this way we tend to absorb the float and cutdown the demand on the resource. If two or more jobs are competing

Ans. 47:

Paths 1-2-5-7-8

Duration 7+16+9+8 = 40

- 21 -

1-2-4-7-8 1-4-7-8 1-3-4-7-8 1-3-6-7-8 1-3-6-8

Critical path = 1-3-6-7-8 = 47 days

7+12+19+8 = 46 6+19+8 = 33 8+6+19+8 =41 8+24+7+8 =47 8+24+4 = 36

-1-

Ans. 6 The numbers 00-99 are allocated in proportion to the probabilities associated with each event as given below:

Daily Demand

0 10 20 30 40 50

Probability

0.01 0.20 0.15 0.50 0.12 0.02

Cumulative Probability

0.01 0.21 0.36 0.86 0.98 1.00

Random Numbers Allocated

00-00 01-20 21-35 36-85

86—97 98-99

Let us simulate the demand for the next 10 days using the given random numbers in order to find out the stock position if the owner of the bakery decides to make 30 breads every day. We will also estimate the daily average demand for the bread on the basis of simulated data.

Day Random Number Simulated Demand Stock if 30 breads are prepared every

day 0 0 20 20 20 20 40 60 60 80

1 2 3 4 5 6 7 8 9 10

48 78 19 51 56 77 15 14 68 9

Total

30 30 10 30 30 30 10 10 30 10

220

Daily average demand of the basis of simulated data = 22

Ans. 7: The random numbers are established as in Table below:

Production Per day 196 197 198 199 200 201 202 203 204

probability

0.05 0.09 0.12 0.14 0.20 0.15 0.11 0.08 0.06

cumulative probability

0.05 0.14 0.26 0.40 0.60 0.75 0.86 0.94 1.00

Random number

00-04 05-13 14-25 26-39 40-59 60-74 75-85 86-93 94-99

Some solutions of simulation

-2-

Based on the 15 random numbers given we simulate the production per day as above in table 2 below.

Random No. Estimated Production Per day

No. of mopeds waiting

Opening Balance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

82 89 78 24 53 61 18 45 04 23 50 77 27 54 10

202 203 202 198 200 201 198 200 196 198 200 202 199 200 197

-- 2 5 7 5 5 6 4 4 0 0 0 2 1 1

No. of empty spaces in the lorry

current current Total excess short waiting

Production production

2 3 2 --

--- 1

--- --- --- --- -- 2

--- --

---

-- --- --- 2 --

--- 2 -- 4 2 -- -- 1 -- 3

Total

2 5 7 5 5 6 4 4 0 0 -- 2 1 1

_-- 42

=

=

--- --- --- --- --

--- --- --- --- 2

--- --- --- ---

__2 __4

2.80

0.266

Average number of mopeds waiting

Average number of empty spaces in lorry

=

=

42 15 4

15 Ans. 8:

If the numbers 00-99 are allocated in proportion to the probabilities associated with each category of work, then various kinds of dental work can be sampled, using random number table :-

Type

Filling Crown Cleaning Extraction Checkup

Probability

0.40 0.15 0.15 0.10 0.20

Random Numbers

00-39 40-54 55-69 70-79 80-99

Using the given random numbers, a work sheet can now be completed as follows :-

FUTURE EVENTS

PATIENT SCHEDULED ARRIVAL RN CATEGORY SERVICE TIME 1 2 3 4

8.00 8.30 9.00 9.30

40 82 11 34

Crown Checkup Filling Filling

60 minutes 15 minutes 45 minutes 45 minutes

-3-

5 6 7 8

10.00 10.30 11.00 11.30

25 66 17 79

Filling Cleaning Filling Extraction

45 minutes 15 minutes 45 minutes 45 minutes

Now, let us simulate the dentist’s clinic for four hours starting at 8.00 A.M.

STATUS

Time

8.0 8.30 9.00

9.15 9.30 10.00

10.30 10.45 11.00 11.30

11.45 12.00 12.30

Event

patient arrives nd 2 “ arrives st 1 departs rd 3 “ arrives nd 2 departs th 4 “ arrives rd departs 3 th 5 “ arrives th 6 “ arrives th 4 departs th 7 “ arrives th 5 departs th 8 “ arrives th 6 departs

End -

1st

Number of the patient being served (time to go)

1st(60) 1st(30)

2nd(15) 3rd(45) 3rd(30)

4th(45) 4th(15) 5th(45) 5th(30)

6th(15) 7th(45) 7th(30) 8th(45)

Patients waiting

- 2nd

3rd - 4th

5th 5th & 6th 6th 6th & 7th

7th & 8th 8th 8th -

The dentist was not idle during the entire simulated period :- The waiting times for the patients were as follows :-

Patient

1 2 3 4 5 6 7 8

Arrival

8.00 8.30 9.00 9.30

10.00 10.30 11.00 11.30

Service Starts

8.00 9.00 9.15

10.00 10.45 11.30 11.45 12.30 Total

Waiting (Minutes)

0 30 15 30 45 60 45 60 285

35.625 minutes. The average waiting time of a patient was 285 15

=

Ans. 9: Random allocation tables are as under: Time Arrival (Mts) (Proba.)

1

Arrivals cumulative Probability

0.05 0.05

Random No.

allocated

00-04

Time (Mts)

Service (Proba.)

1

Service Random Cumulative No. Probability allocated

0.10 0.10 00-09

-4-

2 3 4 5 6

0.20 0.35 0.25 0.10 0.05

0.25 0.60 0.85 0.95 1.00

05-24 25-59 60-84 85-94 95-99

2 3 4 5

0.20 0.40 0.20 0.10

0.30 0.70 0.90 1.00

10-29 30-69 70-89 90-99

Simulation of ten trails: R. No. Arrival Mts. Time Start R. No. Time Mts. Finish

Time

09 12 18 65 25 11 79 61 77 10

1 2 2 3 2 2 4 3 4 2

9.05 9.08 9.10 9.14 9.16 9.18 9.22 9.25 9.29 9.31

Waiting Time

Clerk 4 1 1

_ 6

Passanger 60 16 08 36 38 07 08 59 53 03

4 2 2 3 3 2 2 3 3 1

Total

9.04 9.06 9.08 9.11 9.14 9.16 9.18 9.21 9.24 9.25

9.04 9.06 9.08 9.11 9.14 9.16 9.18 9.22 9.25 9.29

1 1 4 6

In half an hour trial, the clerk was idle for 6 minutes and the passengers had to wait for 6 minutes.

Ans. 10: From the frequency distribution of arrivals and service times, probabilities and cumulat ive probabilities are

first worked out as shown in the following table:

Time between arrivals

1 2 3 4 5 6

Frequency Probability

5 20 35 25 10 5

0.05 0.20 0.35 0.25 0.10 0.05

Cum. Prob.

0.05 0.25 0.60 0.85 0.95 1.00

Service Time

1 2 3 4 5 6

Frequency

1 2 4 2 1 0

Prob.

0.10 0.20 0.40 0.20 0.10 0.00

Cum. Prob.

0.10 0.30 0.70 0.90 1.00 1.00

Total 100 10 The random numbers to various intervals have been allotted in the following table:

Time between arrivals

Probability Random numbers allotted

Service Time Probability Random numbers allotted

-5-

1 2 3 4 5 6

0.05 0.20 0.35 0.25 0.10 0.05

00-04 05-24 25-59 60-84 85-94 95-99

1 2 3 4 5 6

0.10 0.20 0.40 0.20 0.10 0.00

00-09 10-29 30-69 70-89 90-99

-

Simulation Work Sheet Random Time till Number next

arrival

64 04 02 70 03 60 16 18 36 38 07 08 59 53 01 62 36 27 97 86 20

4 1 1 4 1 4 2 2 3 3 2 2 3 3 1 4 3 3 6 5 57

Arrival Time a.m.

11.04 11.05 11.06 11.10 11.11 11.15 11.17 11.19 11.22 11.25 11.27 11.29 11.32 11.35 11.36 11.40 11.43 11.46 11.52 11.57

Service Random Service begins number time a.m.

11.04 11.07 11.11 11.14 11.16 11.19 11.20 11.22 11.24 11.27 11.29 11.31 11.35 11.38 11.42 11.44 11.46 11.49 11.52 11.57

30 75 38 24 57 09 12 18 65 25 11 79 61 77 10 16 55 52 59 63

3 4 3 2 3 1 2 2 3 2 2 4 3 4 2 2 3 3 3 3 54

Service Clerk Customer Ends Waiting waiting a.m. Time time

11.07 11.11 11.14 11.16 11.19 11.20 11.22 11.24 11.27 11.29 11.31 11.35 11.38 11.42 11.44 11.46 11.49 11.52 11.55 12.00

04 - - - - - - - - - - - - - - - - - - 2 6

- 2 5 4 5 4 3 3 2 2 2 2 3 3 6 4 3 3 - -

56

Time spend by customer in system

3 6 8 6 8 5 5 5 5 4 4 6 6 7 8 6 6 6 3 3

Length of

waiting line - 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 - -

26

Average queue length = Number of customers in waiting line 26 � 1.3 = Number of arrivals 20

56 � 2.8 minutes 20

Average waiting time per customer =

Average service time = 54 � 2.7 minutes

20

Ans. 11: Cumulative frequency distribution for Ramu is derived below. Also fitted against it are the eight given random numbers. In parentheses are shown the serial numbers of random numbers.

-6-

10 20 30 40 50 60 70 80

4 10 20 40 80 91 96 100

01 (2)

14 (1)

44 (4) 82 (6) 95 (3)

00 (7) 03 (8)

61 (5)

Thus the eight times are: 30, 10, 70, 50, 60, 10 and 10 respectively. Like wise we can derive eight times for Raju also.

Col-1 10 20 30 40 50 60 70 80

Col-2 4 9 15 22 32 40 46 50

Col-3 8 18 30 44 64 80 92

100 97 (5)

25 (4) 36 (1) 55 (3) 76 (2)

34 (8) 56 (7)

41 (6)

(2× Col-2)

(Note that cumulative frequency has been multiplied by 2 in column 3 so that all the given random numbers are utilized). Thus, Raju’s times are: 40, 60, 50, 30, 80 40, 50 and 40 seconds respectively. Ramu’s and Raju’s times are shown below to observe for waiting time, if any.

1 Ramu

30 10 70 50 50 60 10 10

2 Cum. Times

30 40 110 160 210 270 280 290

3 Raju Initial

40 60 50 30 80 40 70 40

4 Raju’s cumulative time with included 70 130 180 210 290 330 400 440

30 seconds

Since col. 4 is consistently greater than Co.2, no subsequent waiting is involved.

Ans. 12: The numbers 00-99 are allocated in proportion to the probabilities associated with each event. If it rained on the previous day, the rain distribution & the random no allocation are given below:

-7-

Event Probability Cumulative Probability

0.50 0.75 0.90 0.95 0.98 1.00

Random numbers Assigned 00-49 50-74 75-89 90-94 95-97 98-99

No rain 1 cm rain 2 cm rain 3 cm rain 4 cm rain 5 cm rain

0.50 0.25 0.15 0.05 0.03 0.02

Table 1 – Rain on previous day Similarly, if it did not rain the previous day, the necessary distribution and the random number allocation is given below:

Event Probability Cumulative Random Probability numbers

Assigned No rain 1 cm rain 2 cm rain 3

0.75 0.15 0.06 0.04

0.75 0.90 0.96 1.00

00-74 75-89 90-95 96-99

Table 2- No rain on previous day Let us now simulate the rain fall for 10 days using the given random numbers. For the first day it is assumed that it had not rained the day before:

Day 1 2 3 4 5 6 7 8 9 10

Random Numbers 67 63 39 55 29 78 70 06 78 76

Event No rain No rain No rain No rain No rain 1 cm rain 1 cm rain No rain 1 cm rain 2 cm rain

(from table 2) (from table 2) (from table 2) (from table 2) (from table 2) (from table 2) (from table 1) (from table 1) (from table 2) (from table 1)

Hence, during the simulated period, it did not rain on 6 days out of 10 days. The total rain fall during the period was 5 cm.

Ans.13: The probabilities of occurrence of A, B and C defects are 0.15, 0.20 and 0.10 respectively. So, tile numbers 00-99 are allocated in proportion to the probabilities associated with each of the three defects

Defect-A Defect-B Defect-C Exists Random Exists? Random Exists? Random

Numbers numbers numbers Assigned assigned assigned

Yes 00-14 yes 00-19 yes 00-09 No 15-99 No 20-99 no 10-99

-8-

Let us now simulate the output of the assembly line for 10 items using the given random numbers in order to determine the number of items without any defect, the number of items scrapped and the total minutes of rework time required:

Item RN for RN for RN for whether Rework Remarks No. defect A defect B defect C any defect time (in

Exists minutes) 1 48 47 82 none -- -- 2 555 36 95 none -- -- 3 91 57 18 none -- -- 4 40 04 96 B 15 -- 5 93 79 20 None -- -- 6 01 55 84 A -- Scrap 7 83 10 56 B 15 --- 8 63 13 11 B 15 --- 9 47 57 52 None -- -- 10 52 09 03 B,C 15+30 =45 --

During the simulated period, 5 out of the ten items had no defects, one item was scrapped and 90 minutes of total rework time was required by 3 items.

Answer 14: The question is not happily worded, if we go by the language of the question, the following solution can be worked out: First of all, random numbers 00-99 are allocated in proportion to the probabilities associated with demand as given below:

Demand 0 1 2 3 4

Probability 0.05 0.10 0.30 0.45 0.10

Cum. Probability 0.05 0.15 0.45 0.90 1.00

Random Nos. 00-04 05-14 15-44 45-89 90-99

Based on the ten random numbers given, we simulate the demand per day in the table given below. It is given that stock n hand = 8 and stock on order = 6 (expected next day). Let us now consider both the options stated in the question. Option A: Order 5 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books:

Day Random No.

Sales Demand

Op. Stock in

hand

8 5 9 6

Qty. Order

Qty. Recd. At end of the day

- 6 - -

Total Qty. on order

6 - - 5

Closing Stock

1 2 3 4

89 34 78 63

3 2 3 3

- - - 5

5 9 6 3

-9-

5 6 7 8 9 10

61 81 39 16 13 73

3 3 2 2 1 3

3 0

- 0

- 5 0

Now on day 6, there is stock out position since 5 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it will into be possible to proceed further and we will have to leave the answer at this stage.

Random No.

Sales Demand

Opening Stock in

hand

8 5 9 6 3 0

Qty. Order

Qty. Recd. At end of the day

-- 6 -- -- -- 8

Total Qty. on order

6 -- -- 8 8 --

Closing Stock

1 2 3 4 5 6 7 8 9 10

89 34 78 63 61 81 39 16 13 73

3 2 3 3 3 3 2 2 1 3

-- -- -- 8 -- --

5 9 6 3 0

Now on day 6, there is stock out position since 8 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it is not possible to proceed further and we may leave the answer at this stage. Alternatively, if we assume that the demand occurring during the day can be met out of stock received at the end of the day, the solution will be as follows: Stock in hand = 8 and stock on order = 6 (expected next day)

Random No.

Sales Demand

Opening Stock in

hand

8 5 9 6 3 0 2 0 3 7

Qty. Order

Qty. Recd. At end of the day

-- 6 -- -- -- 5 -- 5 5 --

Total Qty. on order

6 -- -- 5 5 5 10 5 -- 5

Closing Stock

1 2 3 4 5 6 7 8 9 10

89 34 78 63 61 81 39 16 13 73

3 2 3 3 3 3 2 2 1 3

-- -- -- 5 -- 5 5 -- -- 5

5 9 6 3 0 2 0 3 7 4

- 10 -

Carrying Cost = 39 × 0.50 = Rs.19.50 Ordering Cost = 4 × 10 = Rs.40.00 Total Cost = Rs.59.50 Option B: Order 8 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books:

Random No.

Sales Demand

Opening Stock in

hand

8 5 9 6 3 0 5 3 1 8

Qty. Order

Qty. Recd. At end of the day

-- 6 -- -- -- 8 -- -- 8 --

Total Qty. on order

6 -- -- 8 8 -- 8 8 -- --

Closing Stock

1 2 3 4 5 6 7 8 9 10

89 34 78 63 61 81 39 16 13 73

3 2 3 3 3 3 2 2 1 3

-- -- -- 8 -- -- 8 -- -- --

5 9 6 3 0 5 3 1 8 5

Carrying Cost = 45 × 0.50 = Rs.22.50 Ordering Cost = 2 × 10 = Rs.20.00 Total Cost = Rs.42.50 Since Option B has lower cost, Manager should order 8 books.

Ans.15 Demand (Tons) 1 2 3 4

Option-I RN Demand

Probability 0.15 0.30 0.45 0.10

Opening Stock 8 5 9 6 3 0 2 0 3 7 4 1

Receipts

- 6 - - - 5 - 5 5 - - 5

Cumulative Probability 0.15 0.45 0.90 1.00

Closing Stock 5 9 6 3 0 2 0 3 7 4 1 4

Op.Stock on Order - - - 5 5 5 10 5 - 5 5 5

Random Nos. Allocated 00-14 15-44 45-89 90-99

Order

- - 5 - 5 5 - - 5 - 5 -

Cl.Stock on Order

6 - 5 5 10 10 10 5 5 5 10 5

88 41 67 63 48 74 27 16 11 64 49 21

3 2 3 3 3 3 2 2 1 3 3 2

- 11 -

44 (Rs.)

No of order placed 5 Ordering cost Closing Stock Carrying cost Total

Option-II RN Demand

88 41 67 63 48 74 27 16 11 64 49 21

3 2 3 3 3 3 2 2 1 3 3 2

(5x1000) 44

(44x50)

5,000

2,200 7,200

Closing Stock 5 9 6 3 0 5 3 1 8 5 2 0 47

Op.Stock on Order - - - 8 8 - 8 8 - - 8 8

Order

- - 8 - - 8 - - - 8 - -

Cl.Stock on Order

6 - 8 8 8 8 8 8 - 8 8 8

(Rs.) 3,000 2,350 5,350

Opening Stock 8 5 9 6 3 0 5 3 1 8 5 2

Receipts

- 6 - - - 8 - - 8 - - -

No of orders 3 Closing stock 47

Ordering cost 3 x 1000 Carrying cost 47x50 Total

Analysis: Since the cost of inventory is less in Option II, it is suggested to implement.

Ans. 16 (i) Allocation of random numbers

Demand 0<300 300 < 600 600 < 900 900 < 1200 1200 <1500 1500 < 1800

Probability 0.18 0.32 0.25 0.15 0.06 0.04

Cumulative probability 0.18 0.50 0.75 0.90 0.96 1.00

Allocated RN 00—17 18—49 50—74 75—89 90—95 96—99

(ii) Simulation: twelve months sales, monthly and annual profit/loss Month RN Demand Sold Return Profit

on sales (Rs.)

Loss on return (Rs.)

Net (Rs.)

Loss on lost units

- 12 -

1 2 3 4 5 6 7 8 9 10 11 12

27 15 56 17 98 71 51 32 62 83 96 69

450 150 750 150 1650 750 750 450 750 1050 1650 750

450 150 750 150 750 750 750 450 750 750 750 750

300 600 -- 600 -- -- -- 300 -- -- -- --

3375 1125 5625 1125 5625 5625 5625 3375 5625 5625 5625 5625 54000

12000 2400 -- 2400 --- -- -- 1200 -- -- --

7200

2175 -1275 5625 -1275 5625 5625 2175 5625 5625 5625 5625 5625 46800 2100

300 900

900

(iii) Loss on lost sale 2100×7.5 = Rs15750.

Ans. 17 The demand and supply patterns yield the following probability distribution. The numbers 00-99 are allocated in proportion to the probabilities associated with each event.

Availability (Kg.)

10 20 30 40 50

Prob. Cum. Prob.

0.08 0.18 0.56 0.86 1.00

Random Numbers allocated

00-07 08-17 18-55 56-85 86-99

Demand (Kg)

10 20 30 40 50

Prob. Cum. Prob.

0.10 0.32 0.72 0.92 1.00

Random number

allocated 00-09 10-31 32-71 72-91 92-99

0.08 0.10 0.38 0.30 0.14

0.10 0.22 0.40 0.20 0.08

Let us simulate the supply and demand for the next six days using the given random numbers in order to find the profit if the cost of the commodity is Rs.20 per kg, the selling price is Rs.30 per kg, loss on any unsatisfied demand is Rs.8 per kg and unsold commodities at the end of the day have no saleable value.

Day Random no.

31 63 15 07 43 81

Supply availability

30 40 20 10 30 40

Random no.

18 84 32 32 75 27

Demand Buying cost Rs. 600 800 400 200 600 800

Selling cost Rs. 600 1200 600 300 900 600

Loss for unsatisfied

demand -- --

160 160 80 --

Profit

1 2 3 4 5 6

20 40 40 30 40 20

-- 400 40 -60 220 -200

During the simulated period of six days, the net profit of the retailer is = (400 + 40 + 220) – (60 + 200)

- 13 -

= =

660 – 260 Rs.400

Ans. 19:

Amount (Rs. In crores) 30 42 36 99

Amount (Rs. In crores) 33 60 39 57

Week

1 2 3 4 5 6 7 8 9

10 11 12

Op.Balance

15 -12 -30 -33 -51 -54 -69 -66 -63 -3

-18 42

Random No. Coding Table - Receipts Probability Cum. Probability

0.20 0.20 0.40 0.60 0.25 0.85 0.15 1.00

Random No. Coding Table - Payments Probability Cum. Probability

0.15 0.15 0.20 0.35 0.40 0.75 0.25 1.00

Random No. Interval 00-19 20-59 60-84 85-99

Random No. Interval 00-14 15-34 35-74 75-99

Cl.Balance

-12 -30 -33 -51 -54 -69 -66 -63 -3

-18 42 15

Simulation Table Receipts Payments

Random Amount Random Amount No. (in crores) No. (in crores) 17 30 78 57 43 42 16 60 74 36 35 39 31 42 23 60 72 36 44 39 46 42 92 57 51 42 58 39 68 36 8 33 93 99 58 39 54 42 78 57 96 99 54 39 9 30 77 57

(i) Probability is = 10 ÷ 12 = 0.83

(ii) Total Shortfall is Rs. 399 crores. Therefore average shortfall is 399 ÷ 12 = Rs. 33.25 crores Alternatively, average shortfall is 399 ÷ 10 = Rs. 39.90 crores

(iii) There will be a shortfall in 5 months i.e. 4,5,6,7,8. therefore the probability is 5 ÷ 12 = 0.42