solutions of activity based costing -...

-1-

Ans. 9 The total production overheads are `26,00,000: Product A: 10,000 × `30 = `3,00,000 Product B: 20,000 × `40 = `8,00,000 Product C: 30,000 × ` 50 = `15,00,000 On the basis of ABC analysis this amount will be apportioned as follows:

Statement of Activity Based Production Cost Activity Pool

Stores Receiving Inspection Dispatch

Machine Setups Total Cost

Activity

Cost Cost Driver Ratio Total Amount (`) 2,96,000

8,94,000 2,10,000

12,00,000

A (`)

71,040

2,23,500 50,400

3,60,000 7,04,940

B (`)

1,06,560

3,12,900 75,600

3,90,000 8,85,060

1,18,400

3,57,600 84,000

4,50,000 10,10,000

C

Purchase requisition Production Runs Orders Executed Set ups

6:9:10

5:7:8 6:9:10

12:13:15

Quantity Sold Unit Cost Add: Conversion Cost Total

10,000 70.49 80

150.49

20,000 44.25 80

124.25

30,000 33.67 90

123.67 Ans 10:

(i) Traditional Method

`, Cost per Unit P

Direct Method Direct Labour Overhead @ `6/Hr on Machine Hour

90 80 60 (10 x6) 230

Q 80 240 108 (18 x 6) 428

R 120 160 84 (14 x 6) 364

Workings under ABC Product No. of Units

P 3000

Q

R

5000

20000

M Hrs/Unit 10

Batches Inspection Purchase Order 20 100 60

(20 x 3) (3000/150) (20 x 5) 18 90000 40 100 10

(10 x 4) (10 x 10) (5000/500) 14 280000 20 60 160

(20 x 8) (20000/1000) (20 x 3) 400000 50 200 320

Overhead @ `6/Hr =4L x 6�`24L

[`In ooo’s] Cost Pool C Driver

480 Batches

M Hrs 30000

(ii) Activities MC Setup

CA. Parag Gupta

% 20

CDQ 50 Batches

CDQ Rate(`) 9600

Costing & O.R. Ph.: +91 9891 432 632 [email protected] World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

Solutions of Activity Based Costing

-2-

Mc Operation Inspection Mat

30 40 10

100

720 960 240

2400

M Hrs Inspection Purchase Order

4L 200 320

1.80 4800

750

Product

P

Q

R

Set up cost

192000 (20 x 9600)

96000 [10x9600]

192000 [20x9600]

(iii) Link of overheads Machine Inspection Cost

Operation Cost 54000 480000

[30000x1.8] [100x4800] 162000 192000

[90000x1.8] [40x4800] 504000 288000

[280000x1.8] [60x4800]

Purchase Order Cost

45000 [60x750]

75000 [100x750]

120000 [160x750]

Total

771000

525000

1104000

Rate

257

105

55.2

Cost sheet under ABC

Direct Material Direct Labour Overhead

P 90 80

257 427

Q 80

240 105 425

R 120.00 160.00

55.20 335.20

Ans. 11: (i) Computation of the activity based overheads Step 1: Compute cost per unit of cost driver = Cost pool / cost driver volume

Activity

Purchasing Setting Materials handling Inspection Machining

Cost Driver

Purchase orders Batches produced Material movements

Cost Pool (a)

Cost driver volume/yr (b)

1,500 2,800

8,000 2,800

50,000

Cost/Unit of cost driver (a)/(b)

`75,000 `112,000

`96,000

`50/pruchse order `40/batch

`12/movement `25/batch `3/machine hour

Batches produced Machine hours

`70,000 `150 000

Step 2: Compute the volume of cost drivers consumed by Product Nova Shaft

Purchase orders (given) = 25 Batches = 15,000/100 = 150

Materials movement = 150 batches × 6 = 900 Machine hours = 15,000 units × 0.1 = 1,500 Step 3: Compute the Activity Based Overheads Cost for Product Nova Shaft Activity Cost Driver Costing

Rate / Cost

Driver Unit `

CA. Parag Gupta Ph.: +91 9891 432 632 [email protected] Costing & O.R. World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

-3-

Purchasing Setting Material handling Inspection Machining

Purchase orders Batches produced Material movements Batches produced Machine hours

50 25 order × `50 40 150 batches × `40 12 900 movement × `12 25 150 batches × `25 3

1,500 hours × `3

`1,250

`6,000

`10,800

`3,750

`4,500

`26,300 (ii) Computation of budgeted overheads costs for Product Nova Shaft using absorption

costing Budgeted overheads = (`75,000 + `96,000 + `112,000 + `70,000 + `150,000)

= `503,000 Budgeted absorption cost/machine hour = `503,000 / 50,000 = `10.06 Budgeted machining hours for Product Nova Shaft = 1,500 Budgeted absorbed overhead = 1,500 × `10.06 = `15,090

(iii) Ways in which the company can reduce the ABC for product Nova Shaft:

Reduce the number of batches by increasing the batch size which will then reduce the setting up overhead, materials handling and inspection costs. Reduce the number of purchase orders

Innovate ways of speeding up production so that the machining hours are reduced.

Ans. 12: (a)

(i)

(ii) (iii) (iv) (v) (vi)

Sales Units ` Selling price/unit Sales Value (`) Prime Cost Overhead No. of units/run Prime Cost ` Gross Margin (ii v)

A 25,000

18 4,50,000

12 2,520

3,02,400 1,47,600

B 56,000

14 7,84,000

9 2,810

5,05,800 2,78,200

C 27,000

12 3,24,000

8 3,010

2,16,720 1,07,280 5,33,080

15,58,000

Total 1,08,000


-4-

Workings: A

Gross Production/unit /run (1) Defectives/run (2) Good units / run (3) Sales (Goods units)(4) No. of runs (5) Gross Production (6) = (1) (5) Prime Cost / unit (7) Prime Cost (8) ` Inspection hours/run (9) Inspection hours (10) = (9) (5) M/c hours / run (11) M/c hours (12) = (1) (5) Dye Cost/run (13) Dye cost (14) (13) (5)

2,520 20

2,500 25,000

10 25,200

12 3,02,400

3 30 20

200 200

B 2,810

10 2,800

56,000 20

56,200 9

5,05,800 4

80 12

240 300

C 3,010

10 3,000

27,000 9

27,090 8

2,16,720 4

36 30

270 250

2,250

A B 56,000

2,78,200 1,16,797

84,000 2,00,797

77,403

10,250

C 27,000

1,07,280 56,313 40,500 96,813 10,467

Costing & O.R.

Total

10,24,920

146

710

2,000 6,000 Conventional Accounting System

Total 1,08,000 5,33,080 2,25,250 1,62,000 3,87,250 1,45,830

Sales – units / Production (good units) Gross Margin (`) Production overheads (`) Selling Overhead (`) Sub-Total Overhead (`) Net profit (`)

CA. Parag Gupta Ph.: +91 9891 432 632

25,000 1,47,600

52,141 37,500 89,641 57,959

[email protected] World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

-5-

Ranking Activity Based System

II I III

Sub-Total Overhead (`) Net profit (`) Ranking

62,787 84,813

I

2,16,963 61,237

II

1,07,500 (220)

III

Ans. 13: (i) Factory overhead applicable to machine oriented activity = `37424 Total Machine hours = Volume × Machine hour required for each period

= (500 × ¼) + (5000 × ¼) + (600×1) + (7000 ×3/2) = 12475 hours Machine overhead charges = `37424/12475 hours = `3 per hour Setup Costs = `4355/17 i.e., total number of setups = `256.18 Material ordering cost = `1920/10 operations = `192 Material handling cost = `7580/27 operations = `280.74 Spare parts = `8600/12 parts = `716.67

Products Overheads Items Machine Overhead Setup cost Material ordering cost Material handling cost Spare parts cost

A 1/4×`3 = 0.75

1×256.18/500 = .51 1×192/500=.38

2×280.74/500=1.12

2×716.67/500=2.87

B 1/4×`3 = 0.75

6×256.18/5000=.31 4×192/5000=.15

10×280.74/5000=.56

5×716.67/5000=.72

C 1× `3 = 3.00

2×256.18/600=.85 1×192/600=.32

3×280.74/600=1.40

12×716.67/600=1/19

D 3/2×`3 = 4.50

8×256.18/7000=.29 4×192/7000=.29

12×280.74/7000=.48

4×716.67/7000=.41

(ii) Competition of overhead per unit based on two system and their difference Products Machine Material Setup Material Spare Total Old Difference

overhead ordering handling parts (ABC system ` system) ` ` ` ` `

A 0.75 0.51 0.38 1.12 2.87 5.63 1.20 +4.43 B 0.75 0.31 0.15 0.56 0.72 2.49 1.20 +1.29 C 3.00 0.85 0.32 1.40 1.19 6.76 4.80 +1.96 D 4.50 0.29 0.11 0.48 0.41 5.79 7.20 -1.41

The traditional system does not make correct assumptions that all overheads are related to volume and machine time. Under traditional system products A and C are under costed because it misallocates costs for small volume products. The activity based costing system recognizes the amount of input to each cost unit. Product B previously avoided its full share of overheads because of its low machine time and may still do so if part of `37425 of machine oriented overhead should be apportioned on some other basis. Product D is overcosted because the additional system loaded it with overhead attributable to activities concerned with products A, B & C as a result of using a volume-based and machine oriented rate which failed to pay proper attention to activity costing.

Ans.: 14

(i) Statement of Operating income and Operating income as a percentage of revenues for each product line


-6-

(When support costs are allocated to product lines on the basis of cost of goods sold of each product) Soft Fresh Packaged Total Rs.

Drinks Produce Foods Rs. Rs. Rs.

Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost of Goods sold (COGS): 6,00,000 15,00,000 9,00,000 30,00,000 (B) Support cost (30% of COGS): 1,80,000 4,50,000 2,70,000 9,00,000 (C) Total cost: (D) = {(B) + (C)} 7,80,000 19,50,000 11,70,000 39,00,000 Operating income: E= {(A)- 13,500 1,50,600 39,900 2,04,000 (D)} Operating income as a 1.70% 7.17% 3.30% 4.97% percentage of revenues: (E/A) x 100)

Working notes: 1. Total support cost:

Bottles returns Ordering Delivery Shelf stocking Customer support Total support cost

2.

=

Rs. 12,000

1,56,000 2,52,000 1,72,800 3,07,200 9,00,000

Percentage of support cost to cost of goods sold (COGS):

Total support cost 100 Total cost of goods sold

Rs.9,00,000 100 = 30%

Rs.30,00,000

3. Cost for each activity cost driver: Cost allocation Activity Total cost Rs. base (1) (2) (3) 1,560 purchase Ordering 1,56,000 orders

Delivery 2,52,000 3,150 deliveries Shelf-stocking 1,72,800 8,640 hours

Customer support 3,07,200 15,36,000 sold

Cost driver rate (4)=[(2)÷(3)]

100 per purchase order 80 per delivery 20 per stocking hour

items 0.20 per item sold

(ii) Statement of Operating income and Operating income as a percentage of revenues for each product line


-7-

(When support costs are allocated to product lines using an activity-based costing system) Fresh Soft drinks Packaged Total

Produce Food Rs. Rs. Rs. Rs.

Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost & Goods sold 6,00,000 15,00,000 9,00,000 30,00,000 Bottle return costs 12,000 0 0 12,000 Ordering cost* 36,000 84,000 36,000 1,56,000 (360:840:360) Delivery cost* 24,000 1,75,200 52,800 2,52,000 (300:2,190:660) Shelf stocking cost* 10,800 1,08,000 54,000 1,72,800 (540:5,400:2,700) Customer Support cost* 25,200 2,20,800 61,200 3,07,200 (1,26,000:11,04,000:3,06,000) Total cost: (B) 7,08,000 20,88,000 11,04,000 39,00,000 Operating income C:{(A)- 85,500 12,600 1,05,900 2,04,000 (B)} Operating income as a % of 10.78% 0.60% 8.75% 4.97% revenues

* Refer to working note 3 (iii) Comment: Managers believe that activity based costing (ABC) system is more credible

than the traditional costing system. The ABC system distinguishes with different type of activities at family store more precisely. It also tracks more precisely how individual product lines use resources. Soft drinks consume less resources than either fresh produce or packaged food. Soft drinks have fewer deliveries and require less shelf stocking time. Family store managers can use ABC information to guide their decisions, such as how to allocate a planned increase in floor space. Pricing decision can also be made in a more informed way with ABC information.

Ans. 15 (a) Statement showing total cost of different products, assuming absorption of overhead on a machine hour basis

Direct material Direct labour* Overhead Cost of production per unit Output in units 120 100

17760 13100 Total Costs (`) * Rate per machine hour = `26000/1300 hours = `20 Machine Hours = 480 + 300 + 160 + 360 = 1300 hours (b) Cost Drivers ` Setups 5250 Production runs Stores/receiving 3600 Requisitions Inspection/quality 2100 Production runs

CA. Parag Gupta Ph.: +91 9891 432 632

Product A 40 28 80

148

Product B 50 21 60

131

Product C 30 14 40 84

80 6720

Product D 60 21 60

141

120 16920

No. 21*

80@ 21

Cost/unit of driver `250

45 100

Costing & O.R. [email protected] World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

-8-

Handling/dispatch 4620 Orders 42 110 * Production runs = (120/20) + (100/20) + (80/20) + (120/20) @ Requisitions = 20 for each product or 80 in total. It may be pointed out that machine department cost of `10430 will continue to be absorbed on a machine hour basis as before. The relevant absorption rate will be = `10430/1300 = `8.02 per machine hour.

Total cost (`) A B C S

Direct material 4800 5000 2400 7200 Direct labour 3360 2100 1120 2520 Set-ups 1500 1250 1000 1500 Stores/receiving 900 900 900 900 Inspection/quality 600 500 400 600 Handling/dispatch 1320 1100 880 1320 Machine dept. 3851 2407 1284 2888 costs

16331 13257 7984 16928 Cost per unit 136.09 132.57 99.80 141.07 (c)

A B C D Cost per unit (a) 148 131 84 141 Cost per unit (b) 136.09 132.57 99.80 141.07 Difference (11.91) 1.57 15.80 0.07 The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially in respect of products A and C. A change from traditional machine hour rate to an activity based system may have effect on:

(a) pricing and profits tot the extent that pricing is based on a ‘cost plus’ approach. (b) Reported profits to the extent that stock levels fluctuate between reporting periods.

Ans. 16 (a) Total cost of different products (overhead absorption on Machine hour basis)

A `

B `

C `

D `

Direct material Direct labour Overhead Cost of production per unit Out put in unit Total cost

42 10 72

124 720

89,280

45 09 54

108 600

64,800

40 07 36 83

480 39,840

48 08 18 74

504 37,296

Machine hours (720 4 + 600 3 + 480 2 + 504 1) = 6,144 hours.

Rate per hour = Rs 1,10,592

= `18 per hour. 6,144 hours

Set up Store receiving

Inspection (b) Activity based costing system

Machine operation and maintenance cost of ` 63,000 to be distributed in the ratio of 4: 3: 2.

CA. Parag Gupta Ph.: +91 9891 432 632

28,000 21,000 14,000

[email protected] Costing & O.R. World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

-9-

Cost ` Drivers

48,000 Production runs 36,000 Requisitions raised 24,000 Production runs

2,592 Orders

No Cost per unit of driver (`)

Set up Store receiving Inspection Material handling and disp

96 200 96

192

500 180 250

13.50

Production Run for A (720/24) = 30 ; B (600/24) = 25 ; C (480/24) = 20 ; D (504/24) = 21. A (`) B(`) C(`) D(`)

Direct material Direct labour Setup Store receiving Inspection Material handling and dispatch Total cost Per unit cost

(c)

30,240 7,200

15,000 9,000 7,500

810 69,750 96.875

A

27,000 5,400

12,500 9,000 6,250

675 60,825

101.375

B

19,200 3,360

10,000 9,000 5,000

540 47,100 98.125

C

24,192 4,032

10,500 9,000 5,250

567 53,541 106.23

D Cost per unit (a) Cost per unit (b) Difference

124 96.88

(27.12)

108 101.38 (6.62)

83 98.13 15.13

74 106.23 32.23

The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially: in respect of product A and D a change from traditional machine hour rate to an activity system may have effect on price and profits to the extent that pricing is based on cost plus approach.

Ans. 17: (a)

Activity Budget Cost Statement

Activity Cost Activity Driver (`)

(Budgeted) 8,00,000 ATM

Transaction 10,00,000 Computer

Transaction 20,00,000 No. of

Statements 3,60,000 Telephone

Minutes 41,60,000

No. of Units of Activity Driver

(Budget) 2,00,000

20,00,000

5,00,000

7,20,000

Activity Rate (`)

4

0.50

Deposits Loans Credit Cards

- 2,00,000 1.ATM Services

2. Computer Processing 3. Issuing Statements 4. Customer Inquiries Budgeted Cost

6,00,000

7,50,000 1,00,000 1,50,000

4.00 14,00,000 2,00,000 4,00,000

0.50 1,80,000 90,000 90,000

8,40,000 29,30,000 3,90,000


- 10 -

Units of product as estimated in the budget period Budgeted Cost per unit of the product

58,600 50

13,000 30

14,000 60

Working Notes: (i) (ii)

(iii)

ATM 4,00,000 + 2,00,000 + 2 × 1,00,000 = 8,00,000 Computer

Issuing Statements

5,00,000 (Fixed = 2,50,000) Variable= 10,00,000 2,50,000 increase to 3 times = 7,50,000

2,00,000 + 80% × 2,00,000 = 2 + 1.6 = 3,60,000

Ans. 18: (a) Working:

Calculation of Direct Labour hours:

Total Indirect Costs (`)* Total Direct labour hours (30,000 + 9,750)

Overhead absorption rate

(i)

` 23,85,000

39,750

Rs. 23,85,000 Rs. 60 per hour 39,750 hours

Product B (15,000 units)

Per unit 45.00 13.00 58.00 39.00

(5,85,000/ 15,000

units)

97.00 137.00

40.00

Amount (`) 6,75,000 1,95,000 8,70,000 5,85,000

(9,750 hours @ `60 per

hour) 14,55,000 20,55,000

6,00,000

Statement showing total manufacturing costs and profits Product A

(60,000 units) Per unit Amount (`)

18.75 11,25,000 10.00 6,00,000 28.75 17,25,000 30.00 18,00,000

(18,00,000/ (30,000 hours 60,000 @ `60 per

units) hour) 58.75 63.00

4.25

35,25,000 37,80,000

2,55,000

Total (`)

Direct materials Direct labour Prime cost Indirect costs (absorbed on the basis of direct labour hours) Total cost Sales Profit (Sales – Total cost)

18,00,000 7,95,000

25,95,000 23,85,000

49,80,000 58,35,000

8,55,000

* Calculation of total Indirect Cost: `

Cleaning and maintenance wages Designing costs Set-up costs Manufacturing operations cost Shipment costs Distribution costs Factory Administration Costs

Indirect cost allocation to products A and B:

CA. Parag Gupta Ph.: +91 9891 432 632

2,70,000 4,50,000 3,00,000 6,37,500

81,000 3,91,500 2,55,000

23,85,000


- 11 -

Direct labour hours Direct labour hour rate:

Product A 30,000

`

Product B 9,750

60 60

Indirect costs Output (units) Cost per unit of output

`18,00,000 5,85,000 15,000

39 60,000

` 30

Statement showing the total manufacturing costs and profits using direct labour hour basis of absorption and treating cleaning and maintenance cost as indirect cost:

Output (units)

Sales Direct Materials Direct Labour Prime Cost Indirect costs Total costs Profit

(ii)

Product A `/unit Amount

60,000 `

Product B `/unit Amount

15,000 `

Total

` 63.00 37,80,000 18.75 11,25,000

10.00 6,00,000 28.75 17,25,000 30.00 18,00,000 58.75 35,25,000

4.25 2,55,000

137.00 20,55,000 45.00 6,75,000

13.00 1,95,000 58.00 8,70,000 39.00 5,85,000 97.00 14,55,000 40.00 6,00,000

58,35,000 18,00,000

7,95,000 25,95,000 23,85,000 49,80,000

8,55,000

Product B 15,000

50

5 hours

Calculation of Setup hours

Total Output (in units) No. of quantity produced per batch Setup time per batch Setup hours (Total) (No. of batches set up time per batch)

Product A 60,000

240

2 hours 60,000 2 = 500 240

15,000 5 = 1,500 50

Calculation of Cost Driver, Rates and summary of indirect cost relating to Product A & B:

Activity and Cost Drivers Amount (`)

A Cleaning & Maintenance (Direct Labour hours) Designing costs (square feet)

CA. Parag Gupta

2,70,000

4,50,000

30,000

30 sq. feet

B

9,750

70 sq. feet

39,750

100

(Amount / total of cost driver)

6.7925 per Direct labour hour

4,500 per sq. feet

Product A 2,03,775

1,35,000

Product B

66,227

3,15,000

Cost Drivers for Product Activity Cost Rates Indirect Costs

Ph.: +91 9891 432 632 [email protected] Costing & O.R. World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

- 12 -

Setup costs (setup hours) Manufacturing operations costs (molding machine hours) Shipment costs (No. of shipments) Distribution costs (area in cubic feet)

Factory administration costs (direct labour hours) Production (units)

3,00,000 6,37,500

500 hours 9,000

1,500 hours 3,750

2,000 12,750

150 per setup hour 50 per molding hours

75,000 4,50,000

2,25,000 1,87,500

81,000

3,91,500

100 100

22, 500 cubic feet

9,750

200

67,500

405 per shipment

5.80 per cubic feet

40,500

2,61,000

40,500

1,30,500 45,000

cubic feet 2,55,000 30,000 39,750 6.4151 per labour

hour 1,92,453

13,57,728 60,000

22.63

62,547

10,27,274 15,000

68.48 Cost Sheet based on activity based costing system:

Description Product A Total cost

` Per unit

`

Product B Total cost Per unit

` ` Sales Direct Cost

Direct Materials

Direct Labour

Total Indirect costs Total costs Profit

(iii) Comparison of results:

37,80,000

11,25,000

6,00,000

17,25,000 13,57,728 30,82,728

6,97,272

63.00

18.75

10.00

28.75 22.63 51.38 11.62

20,55,000

6,75,000

1,95,000

8,70,000 10,27,274 18,97,274

1,57,726

137.00

45.00

13.00

58.00 68.48

126.48 10.52

Description Product B Traditional Activity Traditional Activity

Costing Based Costing Based System System System System

` ` ` `

Product A

Selling Price Direct costs Indirect costs Total cost per unit Profit per unit

Opinion:

63.00 28.75 30.00 58.75

4.25

63.00 28.75 22.63 51.38

11.62

137.00 58.00 39.00 97.00

40.00

137.00 58.00 68.48

126.48

10.52

In the traditional costing system, Product B appears to be more profitable than Product A whereas under the activity based costing system, Product A appears to be more profitable than product B. The activities


- 13 -

like designing, set up, manufacturing operation cost, shipment and distribution are support service activities and the consumption of resources relating to these activities are not dependent on direct labour hours. The quantum of consumption of resource of each support service activity is different in respect of the two products manufactured and hence activity based costing presents a true view of cost of production. Moreover, the suggestion to treat cleaning and maintenance activity as a direct cost pool is commendable because costs should be charged direct wherever possible. The results reveal that the company should concentrate upon product B.

Alternative Solution: Cleaning and maintenance activity will not find a place in the statement of calculation of cost driver rates. However, other cost driver rates will be unchanged. Statement showing total cost and profits on the basis of Activity Based Costing

Product A

Direct materials Direct labour Cleaning & maintenance expenses

Prime cost

Per unit

18.75 10.00

2.00

Amount (`)

11,25,000 6,00,000

1,20,000*

Product B Per unit Amount

(`) 45.00 6,75,000 13.00 1,95,000 10.00 1,50,000*

Total (`)

18,00,000 7,95,000 2,70,000

30.75

2.25 1.25 7.50

0.67 4.35 3.21

19.23 49.98 63.00

13.23

18,45,000

1,35,000 75,000

4,50,000

40,500 2,61,000 1,92,453

11,53,953 29,98,953 37,80,000

7,81,047

68.00

21.00 15.00 12.50

2.70 8.70 4.17

64.07 132.07 137.00

4.93

10,20,000

3,15,000 2,25,000 1,87,500

40,500 1,30,500

62,547

9,61,047 19,81,047 20,55,000

74,953

Product A

28,65,000

4,50,000 3,00,000 6,37,500

81,000 3,91,500 2,55,000

21,15,000 49,80,000 58,35,000

8,55,000

and balance

Indirect costs: Designing Setup Manufacturing operation Shipments Distribution Factory administration Total indirect costs

Total costs Sales Profits (Sales – total costs)

* `1,20,000 for The Cost Accountant identified `1,50,000 of cleaning and maintenance wages for Product B.

(iii) Comparison of results:

Product A Allocation basis Direct

Labour Activity

Based

Product B Direct Activity

Labour Based

Costing & O.R. CA. Parag Gupta Ph.: +91 9891 432 632 [email protected] World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

- 14 -

Selling Price Prime cost Total Indirect costs Total costs (Prime cost + Total indirect costs) Profit per unit

Comments:

Hour 63

28.75 30.00

Costing 63

30.75 19.23

Hour 137.00

58.00 39.00

Costing 137.00

68.00 64.07

58.75 4.25

49.98 13.02

97.00 40.00

132.07 4.93

It is evident from the comparison of results that under single cost pool system the product A is overcost and product B is undercost. This is due to allocation of indirect cost on the basis of blanket rate based on direct labour hour and considering one of the significant cost as an indirect one. Cost Accountant’s decision for allocation of indirect costs on the basis of ABC methods and identifying be cleaning and maintenance cost as direct element of cost appears to be a good decision. Result show that the firm enjoys competitive advantage with regards to product A.

Ans. 19

(1) Single factory direct labour hour overhead rate =

Computation of unit cost ( existing system)

Rs 3,10,000 = ` 155 per direct labour hour

2,000

R (`) 300

1,200 3,875 5,375

560 9.60

S(`) 5,760 2,900

74,400 83,060 12,800

6.49

T(`) 600

1,800 7,750

10,150 2,400 4.23

Direct labour cost @ ` 12 per hour Direct material Overheads(direct labour hours ` 155 per hour

Quantity Produced (No) Cost per unit

(2) ABC system involves the following stages, 1. 2. 3. 4.

Identifying the major activities that take place in an organisation. Creating a cost pool /cost centre for each activity Determining the cost driver for each activity Assigning the cost of activities to cost objects (e.g. products, components, customers etc) The most significant activities have been identified e.g. receiving components consignments from suppliers, setting up equipment for production runs, quality inspections, and despatching orders to customers. The following shows the assignment of the costs to these activities,

(` ,000) Receiving

supplies Equipment operation expenses Maintenance Technicians wages initially

CA. Parag Gupta

Set ups

87.50 17.50 17.85

Quality Despatch inspection

18.75 3.75 3.82

Total

125.00 25.00

25.50

Costing & O.R.

18.75 3.75 3.83

Ph.: +91 9891 432 632 [email protected] World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

- 15 -

allocated to Maintenance(30% of ` 85,000= ` 25,500 and then reallocated on same basis on maintenance) Balance of technicians wages allocated to set ups and quality inspections Stores wages - Receiving Despatch wages - Despatch

61.33 156.85 25.50

35.00 40.00 66.32

34.00 25.50 59.50

35.00 40.00

310.00

Note : Equipment operation expenses and Maintenance allocated on the basis 15%,70% and 15% as specified in the question. The next stage is to identify the cost drivers for each activity and establish cost driver rates by dividing the activity costs by a measure of cost driver usage for the period. The calculations are as follows :-

Receiving supplies (

Performing set ups (

Despatching goods (

Quality inspection (

Rs 61,330 ) = ` 62.58 per component.

980 1,56,850

) = ` 153.77 per set up 1,020

66,320 ) = ` 157.93 per despatch

420 25,500

) = ` 39.84 per quality inspection 640

Finally, costs are assigned to components based on their cost driver usage. The assignments are as follows,

R (`) S(`) T(`) Direct labour Direct materials Receiving supplies Performing set ups Quality inspections Despatching goods Total costs No of units produced Cost per unit

300 1,200

2,628.36 2,460.32

398.40 3,474.46

10,461.54 560

18.682

5,760 2,900

1,501.92 2,767.86

318.72 13,424.05 26,672.55

12,800 2.08

600 1,800

1,752.24 1,845.24

717.12 7,264.78

13,979.38 2,400 5.82

For components, the overhead costs have been assigned as follows, (Component R) Receiving supplies (42 receipts at ` 62.58) Performing set ups (16 production runs at ` 153.77) Quality inspections (10 at ` 39.84)


- 16 -

Despatching goods ( 22 at ` 157.93).

Ans 20: Overhead rate per labour hour = Overhead incurred in first half year = `21,00,000 = `52.50 per labour hour Direct labour hours worked 40,000 hours Apportionment of technical staff salaries Machine maintenance = 6,37,500 X 31/100 = ` 1,91,250 Set up = 6,37,500 X 40/100 = ` 2,55,000 Quality Inspection = 6,37,500 X 30/100 = ` 1,91,250 Statement showing apportionment of ‘Machine operation’ and ‘Machine maintenance’ between stares and production activity (set up) in ratio 20:80

Particulars Total Stores / Set up/ Expenses Receiving Production run

Machine operation 10,12,500 2,02,500 8,10,000 Machine maintenance 3,78,750 75,750 3,03,000 (`1,87,500 + `1,91,250)

Particulars Total Stores / Set up /

Expenses Receiving Production run Wages and salaries of stores staff Component of set‐ up cost Total

Rate per activity cost driver Particulars

Total overheads (`) Units of activities carries out Rate per activity cost driver (`)

2,62,500 2,55,000

19,08,750

2,62,500 ‐

5,40,750

‐ 2,55,000

13,68,000

Stores / Receiving 5,40,750 1,960 275.89

Set up/ Production run 13,68,000 2,040 670.59

Quality inspection 1,91,250 1,280 149.41

Statement showing computation of cost of products P and Q (Based on the existing system of single overhead recovery rate) Particulars Product

P Q 100 Direct Labour hours 960 5,000 Unit made 15,000 4,000 Direct materials cost 6,000 600 Direct labour cost (@ `6 per D.L.H.) 5,760 5,250 Overheads ( @ `52.50 per D.L.H.) 50,400 9,850 Total cost of products 62,160

Cost per unit 4.144 1.97 Statement showing computation af cost of products P and Q (Using activity based costing system)


- 17 -

Particulars

Units Direct materials cost Receiving/ Stores cost Receiving Stores cost (48 X 275.89) (52 X 275.89) Production runs / Set ups cost (36 X 670.59) (24 X 670.59) Inspection cost (30 X 149.41) (10 X 149.41) Total Cost products Coat per unit

Product P 15,000 6,000 5,760 13,243 24,141 4,482 53,626 3.58

Q 5,000 4,000 600 14,346 16,094 1,494

36,534 7.31

Computation of sales value per quarter of component K (Using activity based costing system)

Units of component K To be delivered per quarter Component of initial design cost per quarter ( `60,0000/8 quarters) Direct material costs Direct labour cost (600 hours X `6) Receiving cost (50 X `275.89) Production runs cost (6 X `670.59) Inspection cost (24 X `149.41) Total cost Add: Mark up (25% of cost) Sales value Selling price per unit of K (`43,035/3,000 units)

3,000

` 7,500 12,000 1,800 5,518 4,024 3,586 34,428 8,607 43,035 16.34

Ans 21 (i) Job cost sheet for Host Restaurant and Pizza Hut (using a simplified costing system)

Host Restaurant

(`) Professional labour cost: 25 hours @ `60 per hour 40 hours @ `60 per hour (Refer to working note 1) Professional Support staff 25 hours @ `120per hour 40 hours @ `120 per hour (Refer to working note 2) Total

(ii) Job cost sheet using an Activity based costing

1,500 2,400

Pizza Hut

(`)

3,000 4,800

4,500

Host Restaurant

7,200

Pizza Hut (`)

Professional labour cost

CA. Parag Gupta Ph.: +91 9891 432 632

(`) 500


- 18 -

5 hours @ `100 per hour 30 hours @ `100 per hour (Refer to working note 3) Associate labour cost 20 hours @ `40 10 hours @ `40 (Refer to working note 4) Design support 1,690

800

3,000

400

`1.30 × `1,300 `1.30 × `3,400 (Refer to working note 5) Staff support 25 hours @ `42.22 40 hours @ `42.22 (Refer to working note 6)

4,046

1,056

4,420

1,689

9,509 (iii) Determining the amount by which each job was under or overcosted using a simplified costing

system. Host Restaurant

(`) 4,500 4,046

454

Pizza Hut

Cost using simplified system Cost using Activity Based system Difference

(`) 7,200 9,509

(2,309) The simplified costing system overcosted Host Restaurant job by `454 and undercosted Pizza Hut job by `2,309.


- 19 -


- 20 -

Ans. 22: (i) Comparison of manufacturing cost per unit.

Audio Player Model ‘AB 100’ ‘AB 200’

` Direct material cost Direct manufacturing labour cost Machining costs Testing costs Rework costs Ordering costs Engineering costs Total manufacturing cost per unit Working notes for audio player model ‘AB 200’ (i) Machining hours and cost:

(ii) Testing hours and cost:

(iii) Rework cost per unit:

Machining hours = (1 hour–0.20 hours) or 0.80 hours) Machining cost is 0.80 hours × `200 or `160

1,000.00 200.00 200.00 250.00 150.00

2.00 198.00

2,000.00

` 800.00 180.00 160.00 200.00 75.00 1.25

198.00 1,614.25

Testing hours = 2 hours × (1 hour – 0.20) or 1.60 hours. Testing cost is 1.60 hours × `125 or `200

Rework units = 5% × 10,000 units or 500 units. Rework cost = 500 units × `1,500 or `7,50,000. Rework cost per unit `7,50,000 / 10,000 units or `75 per unit.

(iv) Ordering cost: No. of orders per month 50 components × 2 orders = 100 Ordering cost per month 100 orders × `125 per order = `12,500 Ordering cost per unit = `12,500 / 10,000 units = `1.25 per unit.

(v) It is assumed that total available engineering hours will be used for manufacturing ‘AB 200’ model of audio player.

(ii) Effect of design change and pricing decision on operating income of ABC. (`Lakhs)

Revenue loss on 10,000 units (`10,000 units × `400) Saving in cost: Direct material costs (`200 × 10,000 units) Direct manufacturing labour costs (`20 × 10,000 units) Rework costs

CA. Parag Gupta Ph.: +91 9891 432 632

(40)

20.00

2.00

7.50 [email protected]

29.50 Costing & O.R.

World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta

- 21 -

(5% × 10,000 units × `1,500) Net effect on operating income Conclusion: Operating income per month will be reduced by `10.50 Lakhs. Effects of reduction in components, machining time, and testing time will not have any immediate effect, because it is difficult to adjust the available facilities in ordering department, machining department and testing department.

(10.50)


-1-

Ans.1: Statement showing ranking

Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material Direct labour Other variable costs Contribution per unit (Rs.) Machine hours/unit Contribution/machine hour Ranking

P 25.00

11.00 2.50 1.50

10.00 0.67 15 III

Products Q

30.00

16.25 2.50 2.25 9.00 0.33 27 I

R 35.00

21.00 2.50 3.50 8.00

0.4167 19.2

II

Ans: 2 Working Note The limiting factor in the company is the No. of labour hours in department II. Hence, contribution per labour hour of department II has to be found and products ranked on that basis.

A B C 130 175 Selling price / unit 100

Less: Variable cost: 50 64 Direct materials 40

Direct Labour: 12 15 Department I 10 12 12 Department II 6 15 18 Department III 12 11 16 125 80 100 Variable overhead 12

20 30 50 Contribution per unit

0.5 hr. 1 hr. 1 hr. Time taken in department II Contribution per labour hour of Department II 20/0.5 = 40 30 50 Ranking for allotment of department II labour hour II III I

Solution

Product (a) Current mix profit and total labour hour in dept. IIs

No. of units Contribution Total Labour time Total labour / unit contribution in time in

department department II per unit II

30,000 Rs.20 Rs.6 lakhs 0.5 hr. 15,000 hr. 40,000 Rs.30 12 lakhs 1.0 hr. 40,000 hr. 25,000 Rs.50 12.50 lakhs 1.0 hr. 25,000 hr.

80,000 hr. Total 30.50 FOH 25.00 Profit 5.50

A B C

Solution’s of Budget and Budgetary Control

-2-

The suggested product mix is the optimum one because the first ranked product C is proposed to be produced & sold to the maximum of 30,000 units. Similarly, the second ranked product A can be produced and sold up to 50,000 units. The balance hours can be utilized to produce B to the extent of 25,000 units only. This will be optimum mix as indicated below:

Product C A B

Product C A B

Less: FOH Profit Profit under proposed plan in question Increase in profit

No. of Units 30,000 (Maximum) 50,000 (Maximum) 25,000 (Balance)

Total (b) Statement of increase in profit

No. of Units Contribution per unit 30,000 50 50,000 20 25,000 30

Total

Ranking I II III

No. of hours in Dept. II 30,000 25,000 25,000 (Balance)

80,000

Amounts (Rs.lakhs) 15.00 10.00 7.50

32.50 25.00 7.50

5.50 2.00

If the suggestion for optimum product mix is implemented, the increase in profit would be Rs.2.00 lakhs.

Ans: 3 Working Notes

Statement of contribution per machine hour (Limiting factor ) and ranking Particulars PIE SIGMA Selling price 20 30 Less: Variable cost 16 11 Contribution per unit 9 14 Contribution per machine hour = 14/2 9/1

=Rs.9.00 Rs.7.00 Ranking I II

Solution (a) Best combination: Pie should be produced fully one lakh units. Then , sigma should be produced within the balance machine hours. This combination will give optimum contribution as follows:

Product Ranking No. of Units No. of CPU Total Machine contribution(Rs.) Hours

Pie I 1,00,000 1,00,000 9.00 9,00,000

-3-

Sigma

Less: Fixed Profit

II

Total

1,50,000 (300000 /2 )

3,00,000 (Balance) 4,00,000

14.00 21,00,000

30,00,000 (Optimum) 26,00,000 4,00,000

(b) There is market for Sigma for one lakh units (i.e., 2,50,000 – 1,50,000 units). Two machine hours are required per unit of production of Sigma. That is 1,00,000 units at 2 hours = 2,00,000 machine hours required. For this purpose, 7 machines are to be taken on rental basis. Then, the profit will improve as follows:

(Rs.lakhs) Pie 1 lakh units at Rs.9 9.00 Sigma 2.5 lakh units at Rs.14 35.00 Total contribution 44.00 Less: Fixed cost 26.00

36.50 Rent 7 X 1.5 = 10.50 Profit 7.50

(c) There is no change in number of machines required on rental basis. Total rental charges will come down and profit will improve further as follows: (Rs.lakhs) Total contribution (as calculated above) 44.00 Less: Fixed cost 26.00 Rent 7 X 1.25 = 8.75 34.75 Profit 9.25

Ans. 4: Working Notes Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Contribution per unit Machine hours/unit Contribution/machine hour Ranking

Products Y

2400 1200 1200

2 600 II

X 1900 700

1200 3

400 III

Z 4000 2800 1200

1 1200

I

CPU Total contribution 1200 1200000 1200 2400000 1200 6000000

Rs. 9600000

(b) Machine hours available will be only 20000 hours Product Ranking No. of units DLH

Z I 1000 1000 Y II 2000 4000 X III 5000 (15000/3) 15000 (B.F.)

Total 20000

Ans. 5: Statement of Ranking Working Notes Particulars

Products Y X Z

-4-

Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) Direct labour(@Rs. 8 p.h.) Variable overheads(@Rs. 5.6 p.h.) Sellling commission (10% of SP)

Contribution/unit

Raw material per unit (kg) Contribution per kg (Rs.) Ranking

30

5.6 8

5.6 3

22.2 7.8

0.7 11.14

II

40

3.2 16

11.2 4

34.4 5.6

0.4 14 I

50

12 12 8.4 5

37.4 12.6

1.5 8.4 III

Statement of Ranking (if additional 4500kg are made of RM is available) Products

Particulars X Y Selling Price/unit (Rs.) 30 40 Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) 5.6 3.2 Direct labour(@Rs. 10 p.h.) 10 20 Variable overheads(@Rs. 7 p.h.) 7 14 Sellling commission (10% of SP) 3 4

25.6 41.2 Contribution/unit 4.4 (1.2)


0.7 6.28

I

0.4 (3) -

RM (kgs) 2400 5600

2400 (B.F.) 10400

CPU 5.6 7.8

12.6

Z 50

12 15

10.5 5

42.5 7.5

1.5 5 II

Total contribution 33600 62400 20160

Rs. 116160 50000 66160

Total contribution 35200 37500

- Rs. 72700

75000 (2300)

(a) Raw material available will be only 10400 kg Product Ranking No. of units

Y I 6000 X II 8000 Z III 1600 (2400/1.5)

Total Less: Fixed overheads Profit

(b) Raw material available will be only 14900(10400+4500) kg Product Ranking No. of units RM (kgs)

X I 8000 5600 Z II 5000 7500

Balance 1800 Total 14900 Less: Fixed overheads Profit

CPU 4.4 7.5

-5-

Hence firm should not go into further production

Ans. 6: Statement of Ranking Working Notes Particulars Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material Direct labour Variable overheads

Contribution/unit Units Total contribution Ranking


DLH required per unit Contribution per DLH Ranking

Products B 16

4 3 1 8 8

12000 96000

II

0.4 20 II

0.20 Rs. 40

III

A 20

6 3 2

11 9

10000 90000

III

0.6 15 III

0.20 Rs. 45

II

C 10

2.00 1.50 1.00 4.50 5.50

20000 110000

I

0.10 27.50

I

0.10 Rs. 55

I

Solution (a) Raw material available will be only 12100 kg

Product Ranking No. of units C I 20000 B II 12000 A III 5500 (3300/0.6)

Total Less: Fixed overheads Profit

RM (kgs) 4000 4800

3300 (B.F.) 12100

CPU 5.50

8 9


Rs. 255500 138000 117500


Rs. 240000 138000 102000

(b) Direct labour hours available will be only 5000 hours Product Ranking No. of units DLH

C I 20000 2000 A II 10000 2000 B III 5000 (1000/0.2) 1000 (B.F.)

Total 5500 Less: Fixed overheads Profit

CPU 5.50

9 8

(c) No shortage of materials and labour: Ranking as per total contribution is to be considered. Product Ranking No. of units CPU Total contribution

C I 25000 (20000 + 25%) 5.50 137500

-6-

B A

Total Less: Advertisement cost Net contribution Less: Fixed overheads Profit

Ans 7:

II III

12000 10000

9 8

96000 90000

Rs. 323500 20000

303500 138000 165500

Working Notes Statement of comparative contribution and Ranking (Direct labour Hour (DLH) is key

factor) Particulars A B C

60 125 Selling 28 Less: Variable cost 45 95 23 Contribution per unit (CPU) 5 15 30 DLH per unit 10/10 = 1 2 5 Contribution per DLH 5/1 15/2 30/5 =CPU/DLH =5.00 =7.50 =6.00 Ranking III I II

Solution (a) Profit according to current plan

Product

A B C D

Less :Fixed overheads Profit

(b) Alternative plan for maximum profit

Product B is a Rank No. 1. Hence, instead of C Product. B should be manufactured by using surplus labour hours. This will maximize the profit as follows:

Product

A B

No. of Units

500 (Minimum) 500 (Minimum)

DLH

500 1,000

CPU

5 15

Total amount(Rs.)

2,500 7,500

No. of Units

500 (Minimum) 500 (Minimum) 500 (Minimum) 1,400(from surplus DLH) Total

DLH

500 1,000 2,500 7,000

(Balance) 11,000

CPU

5 15 30 30

Total amount(Rs.)

2,500 7,500

15,000 42,000

67,000 25,000 42,000

-7-

C D

500 (Minimum) 3,500(from surplus DLH) Total

2,500 7,000

(Balance) 11,000

30 15

15,000 52,500

77,500 25,000 52,500

Less :Fixed overheads Profit

Note: This profit of Rs.52,500 is higher than current plan.

( C ) BEP (units and value) At BEP, contribution is equal to fixed overheads, i.e., and C=F. In such case, the company

has to earn the contribution of Rs.25,000 in order to get BEP as follows:

Rank

I II II

Total contribution Less: Fixed overheads Profit

BEP (Units and Value) Product No. of Units

Product

B C A

No. of Units

500 (Minimum) 500 (Minimum) 500 (Minimum)

CPU

15 30 5

Total amount(Rs.)

7,500 15,000 2,500

25,000

25,000 Nil

Selling Price Per unit 60 125 28

Sales Value at BEP (Rs.)

30,000 62,500 14,000

1,06,500

Rs.24,000 Rs.48,000

Rs.24,000 24,000

B 500 C 500 A 500 Total 1500 BEP in terms of units: 1,500 units BEP in terms of Sales Value : Rs.1,06,500

(d) Profit after tax (PAT) 24% on 1,00,0000 Tax Rate 50% Hence, Profit Before tax 24,000 x 100

50 Less: Tax at 50% PAT

Note: By production and selling minimum quantities of A,B and C, BEP is achieved. Hence, in order to earn profit before tax of 48,000, Rank No.1, Product B should be sold to the extent of 3,2000 units (48,000 / CUP rs.15).

Then, the position will be as follows: Product No. of Units DLH CPU Total

amount(Rs.)

-8-

A B C

B

Less: Fixed overheads Profit

500 500 500

3,200 Total

500 1,000 2,500

6,400 10,400

5 15 30

15

2,500 7,500

15,000 25,000 48,000 73,000

25,000 48,000

No. of Units and Sales value:

Product

A B C Total

No. of Units

500 3,700 500

4,700

Selling Price Per unit 28 60 125

Sales Value (Rs.)

14,000 2,22,000 62,500

2,98,500

The sales value of Rs.2,98,500 will earn the profit of Rs.48,000 (Profit Before Tax) as worked out in the previous statement.

PBT 48,000 Less: Tax at 50% 24,000 PAT 24,000 (24% on capital employed of Rs.1,00,000)

Ans: 8 Working Notes

Statement of contributions per unit of raw material (Key factor)

A B C Contribution per 2,00,000/20,000=Rs.10 4,00,000/40,000=Rs.10 3,00,000/20,000=Rs.15

unit= Contribution per 10/4 = Rs.2.50 10/5 = Rs.2.00 15/6 = Rs.2.50 unit of Materials

Ranking I II I

Solution (i) Production / Sales mix.

Product Units

A C B Total Less: Fixed Cost Loss

20,000 20,000 20,000 60,000

Materials (Units)

20,000 X 4 = 80,000 20,000 X 6 = 1,20,000 Balance 1,00,000

3,00,000

CPU

10 15 10

(-)

Total Amount(Rs.)

2,00,000 3,00,000 2,00,000 7,00,000 7,50,000

50,000

-9-

(ii) Product No. of Units CPU Total Amount(Rs.) A 20,000 10 2,00,000 C 20,000 15 3,00,000 B 20,000 10 2,00,000 B 40,000 6.25(Notes) 2,50,000 Total 1,00,000 9,50,000 Less: fixed Cost 7,50,000 + 50,000 = 8,00,000 Profit 1,50,000

Yes, The company can optimize production of 1,00,000 units with local substitute materials. Note 1. Imported Raw material cost Rs.3.00 per unit x 5 units = Rs.15.00

18.75 Local substitute materials 3.75 per unit x 5 unit = 3.75 Extra cost of materials 0.75 per unit

Contribution = 10.00-3.75= Rs.6.25 per unit

(iii) Product A C B

Total Add: Lease amount

No. of Units 20,000 20,000 10,000

50,000

CPU 10 15 10

Total Amount(Rs.) 2,00,000 3,00,000 1,00,000

6,00,000 2,75,000 8,75,000 7,50,000 1,25,000

Less: Fixed cost Profit

60,000-50,000 = 10,000 The company cannot enhance profits by leasing out a part of the plant. Conclusion – The proposal at (ii) will maximize the profit at Rs.1,50,000.

Ans:9 Working Notes Sales Less: Variable cost Contribution

Product A (Rs.per unit) 2,500 1,500 1,000 1,000 2,500 =40%

P/V ratio = C x 100 = S

Solution (i) When total sales in value is limited: Product A is more profitable as its P/v ratio is 40% which is higher than that of B. (ii) When raw material is in short supply: Product A B Raw material required per unit 10 kg. 25 kg. Rs.500/50= (Rs.1,250/50) Contribution per kg of material

Product B (Rs. per unit) 5,000 3,250 1,750

1,750 x 100 5,000

=35%

- 10 -

=Contribution per unit /kg 1,000/10 kg. =Rs.100

1,750/25 Rs.70

In this case also, product A is more profitable as its contribution per kg of raw material is Rs.100 which is higher than that of B. (iii) When Production capacity is the limiting factor:

Product A B Direct Labour hours (DLH) Required per unit = Rs.750/30 25 hours 1,500 / 30 = 50 hours Contribution per DLH =Contribution per unit/No. of DLH 1,000 / 25 hours =Rs.40 1,750 /50 hours =Rs.35 In this case also, Product A is more profitable as its contribution per DLH is Rs.40 which is higher than that of B (iv) Statement of Product Mix and Maximum profit:

Product Raw No. of Units. Contribution per Unit Amount (Rs.) Material (kg) (Rs.)

A 10,000 1,000 1,000 10,00,000 B 10,000 400 1,750 7,00,000

(Balance) (10,000/25) Total 20,000 17,00,000 Less: Fixed 10,00,000 Overheads 7,00,000 Profit (Maximum)

Ans:10 To maximize Profit. (a) Statement of current profit

Products A Direct Materials : 10,000 x 20 2.00 Direct labour : 10,000 x 12 1.20 Variable overheads : 10,000 x 8 0.80 Marginal cost 4.00 Sales 10,000 x 64 6.40 Contribution 2.40 Less: Fixed overheads 10,000 x 6 0.60 Profit 10,000 x 18 1.80 Ranking according to I profitability P/v Ratio = C x 100 2.40 x 100

S 6.40

=37.5%

(Rs.lakhs) C

1.44 0.96 0.48 2.88 4.16 1.28

0.32 0.96 II

1.28 x 100 4.16

30.77%

B 0.80 0.70 0.50 2.00 3.00 1.00

0.30 0.70 III

1.00 x 100 3.00

1 33 -- %

3

Total 4.24 2.86 1.78 8.88 13.56 4.68

1.22 3.46

( b) Though the contribution per unit of C is lowest, it should not be discontinued. Instead, B should be discontinued. Total contribution from C is more than that of B.

- 11 -

Analysis: Product A Selling price 64 Less: Variable cost 40 CPU 24

If C is discontinued, Sales of A and B will increase by 50%.

Contribution A 10,000 + 50% = 15,000 units at 24= 3.60 B 5,000 + 50% = 7,500 units at 20= 1.50


If B is discontinued, sales of A and C will increase by 50%

Contribution A C


B 60 40 20

C 52 36 16

Rs.lakhs

5.10 1.22 3.88

8,000 + 50% = 12,000 units at 16 = 3.60 1.92 5.52 1.22 4.30

Hence, C should not be discontinued. Product B should be discontinued. Then , the profit will improve to Rs. 4,30,000.

Present profit 3,46,000 Proposed profit 4,30,000 Increase in profit 84,000

C. Product D: Selling Price Less: Marginal cost Contribution per unit

48 25 23 Rs.

Total contribution Rs.5,52,000 less contribution from a & C 3,68,000 = 1,84,000 Minimum sales = Rs.1,84,000/23 = 8,000 units are to be sold in order to ensure maximum

profit as per (b) above, i.e., Rs.4,30,000. Statement of Profitability

Rs.lakhs Contribution from A (original level) 2.40 Contribution from C (original level) 1.28 Contribution from D ( proposed ) 8,000 x 23 1.84 Total 5.52 Less: Fixed overheads 1.22 Profit 4.30

- 12 -

Ans:12 Working Note

Statement of contribution per labour hour (limiting Factor) P Q

60 Selling price / unit (Rs.) 80 49 Variable cost / unit (Rs.) 62 11 Contribution (Rs.) 18

2 Labour hrs/unit 20/10= 1.5 9 Contribution /labour hr(Rs.) 18/2= 7.33

15,000 Current sales (Units) 20,000

Solution (a) Current Profit

Contribution: P : 15,000 x Rs.18 Q : 20,000 x Rs.11 R : 10,000 x Rs.14 Total contribution Less: Fixed overheads Profit as per estimate

R 50 36 14

1 14

10,000

= = =

Rs.2,70,000 Rs.2,20,000 Rs.1,40,000 Rs.6,30,000 Rs.5,50,000 Rs. 80,000

(b) Labour is the limiting factor Total Labour Hours utilized for the above production units : (Production and sales same).

P = 30,000 hrs.(15,000 x 2) Q = 30,000 hrs.(20,000 x 1.5) R = 10,000 hrs.(10,000 x 1)

70,000 hrs Available hrs. 75,000 hrs.

Since contribution per labour hour is Maximum for R, and since labour hour is the limiting Factor, normally this excess 5,000 hrs have to be allocated to R. But, increase in production / sales is limited to 25% of current sales of any one of the products:

Product Labour hours Production/sal 25% of Lower of Contributio Total available es possible current sales the (iii) & n per unit contrib

(i) (ii) (iii) (iv) (iv) (Rs.) ution Rs.

P 5,000 2,500 3,750 2,500 18 45,000 Q 5,000 3,333 5,000 3,333 11 36,663 R 5,000 5,000 2,500 2,500 14 35,000

Contribution is highest for P.P should be chosen and after deduction of Rs. 30,000 for advertisement, profit is Rs.15,000.

© If selling price is reduced by 5% the position will be as follows:

Product Reduced Variable cost Contribution Labour hrs Contribution Ranking

- 13 -

Selling price Rs.

P Q R

80-5%=76 60-5%=57 50-5% 47.50

Rs.

62 49 36

per unit Rs.

14 8

11.50

reqd per unit

2 1.5 1

per labour hour

7 5.33

11.50

for production Rs.

II III

I

Since labour hours are limited to 75000 hours only,product mix will be as follows: Product No of units with Labour hrs. reqd. Total contribution

increase R 15,000 15,000 @ Rs.11.5=1,72,500 P 22,500 45,000 @ Rs.14 =3,15,000 Q 10,000 (15,000/1.5) 15,000 (Bal.Fig) @ Rs. 8 = 80,000

5,67,500 75,000


This proposal is not recommended because of lower profit.

Ans. 13:

5,50,000 17,500

- 14 -

- 15 -

- 16 -

Contribution per unit Option 1: Units Contribution (Rs.) Option 2: Units Contribution (Rs.) Option 3: Units Contribution (Rs.)

120 - -

100

80 9,600

125 115

115

- -

121 100

- -

135 16,335

- 215

26,475 215

26,375 215

25,935 24,780 1,155

22,000 4,375

26,780 (305) 14,375 12,100

12,000 14,375

Best strategy is to produce 100 units of product A and 115 units of product B during off - season. Maximum profit = Rs. 4,375. (i) Best strategy for peak-season is to produce 202 units of A. (ii)

Maximum profit for off-season Rs. 4,375.

Ans:14

Products Sale Value Per acre 10 x 1000= Variable cost per acre Contribution per acre Area occupied (acres) Total contribution 25 x 5,300= Less: Fixed overheads Profit

(a) Profit for the current year (Rs.) A B C

13,500 10,000 10,000

4,700 5,300

25

1,32,500

5,100 4,900

20

98,000

5,950 7,550

30

2,26,500

D 16,200

6,600 9,600

25

2,40,000

Total

100

6,97,000 5,40,000 1,57,000

(b) profit for the product mix The land which is being used for A and B can be used for either items. A gives higher

contribution per acre. Hence, b should be produced to the minimum of 40 tonnes and in balance land A should be produced.

Similarly, the land which is being used for C and D can be used for either items. D gives higher contribution per acre. Hence, C should be produced to the minimum of 36 tonnes and in balance land , D should be produced. Then, the position will be as follows:

A + B Area occupied = 25 + 20 = 45 acres.

B : Minimum production : 40 tonnes i.e., 40 = 5 8

Acres required.

- 17 -

A : Balance 40 acres : A should be produced

C + D : Area occupied = 30 + 25 = 55 acres

C : Minimum production = 36 tonnes, i.e., 36 = 4 acres required.

D : Balance 51 acres : D should be produced. Then, the profitability will improve as follows:

Products A B C No of acres 40 5 4 Contribution per 5,300 4,900 7,550 acre 2,12,000 24,500 30,200 Total Contribution Less: Fixed Overheads Profit

The profit will improve from Rs.1,57,000 to Rs.2,16,300

Ans. 15: Calculation of area to be cultivated in respect of each crop to achieve the largest total profit

Available information: Land available for all four vegetables Land available for peas and carrots Total land available Min. requirement of each variety Max. requirement of each variety

Boxes per hectare (a) Market price (b) Variable costs: Direct material Labour – Growing

- Harvesting & Packing Transport per box Total variable costs (c) Contribution per box (a)-(b) Contribution per hectare × Boxes per hectare (c)

2.72* 5.12* 7.20 10.40 25.44 5.32 1862

4.32 12.16 6.56 10.40 33.44 (1.70) (170)

5.49 10.63 8.80 8.00 32.92 3.88 271.60

3.47 5.87 10.40 19.20 38.94 5.61 1009.80

350 Rs. 30.76

Potato

500 boxes 113750 boxes

Peas 100 Rs. 31.74

Carrots 70 Rs. 36.80

Tomatoes 180 Rs. 44.55

340 hectares 140 480

D 51

9,600 4,89,600

Total 100 Rs.

7,56,300 5,40,000 2,16,300

- 18 -

Ranking *Cost per hectare ÷Boxes per hectare

I IV III II

Best cultivation plan: From 140 hectares for peas and carrots: Peas: Minimum 5000 boxes = 5000÷100 = 50 hectares Carrots: Balance land 140 hectares – 50 hectares = 90 hectares From 340 hectares all four vegetables: Tomatoes: Minimum 5000 boxes = 5000÷180 = 28 hectares

(in terms of complete hectares) Potatoes: Balance of land i.e. 340 -28 = 312 hectares

Area to be cultivated for each variety and total contribution Potatoes

Hectares Contribution per hectares Contribution Total contribution Less: Fixed expenses Profit

(ii) Analysis to show whether land development should be undertaken Carrot yield a lower contribution per hectare than Potatoes and Tomatoes, but it is grown in excess of the requirement of 5000 boxes or 72 hectares i.e. 5000 boxes ÷700. Therefore, 18 hectares i.e., 90 hectares – 72 hectares can be made available for Potatoes and Tomatoes by land improvement. After land improvement the contribution per hectare of Tomatoes will be foloows: Present contribution per hectare Saving per hectare after land improvement Rs. 2.60 ×180 boxes

Allocation of 18 hectares available Crop Maximum Sales

(Boxes)

Potatoes Tomatoes

113750 113750

Present Production (Boxes) 109200* 5000

4550 900

Addl. Reqt. (Boxes)

Yield hectare (Boxes) 350 180

per Additional hectares to be allotted

13 5(B.F.)

Rs. 1009.80 460.00

1477.80

312 Rs. 1862

Rs. 580944

Peas 50

(170)

(8500)

Carrots 90

271.60

24444

Tomatoes 28

1009.80

28274.40 Rs. 625162.40

424000.00 201162.40

* 312 hectares X 350 boxes = 109200

- 19 -

Profit by revised Cultivation plan Potatoes

Hectares Contribution per hectare Total contribution Less: Fixed cost (revised)* Profit *Capital expenditure Interest ( 108000 X 0.15) Existing fixed expenses

= 18 hectares X 6000 = 108000 = Rs. 16200

424000 440200

Conclusion: Since the profit after land development is greater, the company should implement the proposal to develop 18 hectares of land.

Question 16: (i) Statement of Cost break-up Sambalpur

Total cost (Rs. Lacs)

Material cost (Refer to working note)

198 (6,000 M. T. ×

Rs.1,800 + 3,600 M. T. ×

Rs.2,500) 156

Cost per M.T. of output (Rs.)

1,650 (Rs.198 lacs/ 12,000 M. T.)

Bilaspur Total cost (Rs.

Lacs) 240

(12,000 M. T. × Rs.12,000)

Cost per M.T. output (Rs.)

1,600 (Rs. 240 lacs/ 15,000 M. T.)

Peas 50 (170)

Carrots 72 271.60

Tomatoes 33 1477.80 48767.40

Total 480

664972.60 440200.00 2224772.60

325 Rs. 1862 Rs. 605150 (8500) 19555.20

Other variables 1,300 (156 lacs/

12,000 M. T.)

192 1,280 (192 lacs/

15,000 M. T.) Fixed Cost 108 900

(108 lacs/ 12,000 M. T.)

120 800 (120 lacs/

15,000 M. T.) Total Cost

Working Note: 462 3,850 552

Sambalpur

3,680

Bilaspur 15,000 25,000

(15,000/60%) 12,000

(15,000 × 80%)

Annual output (M. T.) Maximum possible output (M. T.)

Basic raw material requirement (M. T.)

12,000 15,000

(12,000/80%) 9,600

(12,000 × 80%)

- 20 -

Material available locally (M. T.) Possible output from local material (M. T.)

6,000 7,500

(6,000 / 80%)

Sambalpur

16,000 20,000

(16,000 / 80%)

Bilaspur 25,000

1,600

(ii) Quantity of production at each unit from the availability of local supplies of basic raw material:

Maximum output/ possible (M. T.) (Refer to above working note) Material cost/ M. T. of output from locals (Rs.) 1,440 (6,000 ×

Rs.1,800) / 7,500 M T. 1,300

2,740 7,500

15,000

Other variables / M. T. of output from locals (Rs.) [Refer to part (i)] Total variable cost / M. T. of output Possible output (M. T.) from local supplies of basic raw material

(iii) Cost saving as per revised schedule of production : Sambalpur (Rs. lacs)

Total variable cost of output (Refer to part ii)

Fixed Cost Total cost: (A) Previous total cost: (B) [as per (i) above] Cost savings: {(B) – (A)}

Ans. 17

1,280

2,880 19,500

(Balancing Figure)

Bilaspur (Rs. lacs)

561.6 (19,500 M. T. ×

Rs.2,880) 120.0 681.6 552.0

(129.6)

Total (Rs. lacs)

767.1 205.5 (7,500 M. T. ×

Rs.2,740) 108.0 313.5 462.0

148.5

228.0 995.1 1014.0

18.9

Statement of cost per tonne and net profit earned in respect of each factory

Present production tonnes: (A)

Cost of raw material (Rs. in lacs) (Refer to working note 1) Other variable costs (Rs. in lacs) Fixed cost (Rs. in lacs) Total cost (Rs. in lacs): (B) Cost per tonne (Rs) : (C) = [(B) / (A)]

Lucknow 7,200

Rs. 59.04

22.32 18.00 99.36 1,380

Pune 10,800

Rs. 87.48

32.94 24.84

145.26 1,345

- 21 -

Selling price (Rs. Per tonne: (D) Net profit per tonne (Rs.) : [(D) – (C)] Total net profit (Rs. in lacs)

Total profit of the company = Rs.15.46 lacs (Rs.5.04 lacs + Rs.12.42 lacs)

1,450 70

5.04 (Rs.70 ×7,200 tonnes)

1,460 115

12.42 (Rs.115×10,800 tonnes)

Alternative production plan to earn optimum Lucknow

Maximum production capacity (tonnes) Present production (tonnes)

Cost per tonne of output: Cost per tonne of output manufactured from locally purchased raw material: (A) (Refer to working note 2) Cost per tonne of output manufactured from material purchased from Bhopal : (B) (Return to working note 3) Other variable cost (Rs.) : (C) 310 305

880 880

9,000 7,200

Rs. 800

Pune 11,880 10,800

Rs. 810

Rs.22.32 Lacs 7,200 tonnes

Selling price per tonne (Rs.) : (D) Contribution per tonne of Output : [(D)–{(A)+(C)}] Contribution per tonne of Output : [(D) – {(B)+(C)}]

1,450 340 260

Rs.32.94 Lacs 10,800 tonnes

1,460 345 275

(When material was purchased from Bhopal) The priority to produce 18,000 tonnes of total output is as below as apparent from the above data:

Priority Pune factory (Local purchase of raw material) Lucknow factory (local) purchase of raw material) Pune factory (raw material purchased from Bhopal) Lucknow factory (raw material purchased from Bhopal) Suggested alternative production plan :

Production priority

I II III IV

11,700 tonnes 5,400 tonnes (11,880 – 11,700) = 180 tonnes 720 tonnes balancing figure

Raw Material Input(in tonnes)

13,000 6,000

200 800

Output (in tonnes) Lucknow

-- 5,400

-- 720

Pune 11,700

-- 180

--

Total 11,700 5,400

180 720

1st 2nd 3rd 4th

- 22 -

(18,000 – 17,280 tonnes) 20,000

Working Notes: Lucknow

1. Present production output (tonnes) Total raw material required for present production (tonnes)

7,200 8,000

Pune 10,800 12,000

6,120 11,880 18,000

100 7,200

90 Raw material produced locally (tonnes) Raw material product from Bhopal Cost of raw material purchased locally and from Bhopal (Rs. in lacs)

2. Cost per tone of output manufactured from locally purchased raw material (in Rs.)

3. Cost per tonne of output manufactured from material purchased from Bhopal (in Rs.)

6,000 2,000 59.04

(Rs.720×6,000+ Rs.792 × 2,000)

800

100 10,800

90 12,000

-- 87.48

(12,000 × Rs.729)

810

100 720

90 880

100 729

90 880

100 792

90

Ans.: 20:Throughout Accounting ratio is highest for ‘Machine 2’. ‘Machine 2’ is the bottleneck

Contribution per unit of bottleneck machine hour : A

Total ‘Machine 2’ hours available = 6,000

A. B. C. D. E.

Contribution per unit (Rs.) ‘Machine 2’ hours Contribution per ‘Machine 2’ hours (A / B) Ranking Maximum Demand ‘Machine 2’ hours required (B E) ‘Machine 2’ hours available Units

Ans. 21:

30 15 2 3

500 7,500 1,500 100

25 3

8.33 1

500 1,500 1,500 500

15 6

2.50 2

500 3,000 3,000 500

B C

- 23 -

A Production

B C Total Mach Capacity

TA ratio

Demand (units) 200 200 200 Hrs. required in Dept. Machine 1 2,400 800 400 3,600

2 3,600 1,200 600 5,400 3 1,200 400 200 1,800

∴Machine 2 is the bottleneck Note-2:

Through put contribution & rank

(a) Throughput Contribution (b) MR/unit in Machine 2 (c) Contribution/hr. Machine –2

Rank Identification of product mix.

Available Less: Rank I C

Less: Rank II B Less: Rank III A

A 24 18

1.33 III

Hrs. in machine 2 3,200 _600

1,200 18

B 20

6 3.33

II

3,200 112.5% 3,200 168.75% 3,200 56.25%

C 12

3 4 I

units

200 2,600

200 77.77

i.e. 77 units

Ans. 22: (a)

Machine A

1 2

2000 2000

Time required for products B

1200 1800

C 400 600

D 200 300

Total Time

3800 4700

Time Machine Available utilization

3000 3000

126.67% 156.67%

3 2000 600 200 100 2900 3000 96.67% Since Machine 2 has the highest machine Utilization it represents the bottleneck activity hence product, ranking & resource allocation should be based on contribution/machine hour of Machine 2.

Allocation of Resources A B C D Machine

Utilization Spare

Capacity

- 24 -

Contribution unit (Rs.)

per 1500

10 in

150

3r d

200×10 = 2000

200 2000

2000

1200

9

133.33

4th

100 (balan

cing figure)

100/9=11.1 1

11.11×6 = 66.66

11.11×3 = 33.33

1000

3

333.33

2n d

200×3 = 600

200 400

200

600

1.5

400

1st

200×1.5 = 300

200 200

100

3000

Time required Machine 2 Contribution per Machine – hour (Rs.) Rank as per contribution / mach. Hour Allocation of Machine 2 time Production Quantity Allocation Machine 1 time Allocation of Machine 3 time

2666.66

2333.33

333.34

666.67

Ans. 23: W. Note 1 Rs. p. u A

Material Variable production overhead cost TVC Selling price (a) (b) (c) (d) (e) (f)

W. Note-2: Fixed overhead recovery rate =(Amount Budgeted hours) = 14,70,000 36,750 = Rs. 40/hr.

Rs. p. u. B

40 4

44 70 26

0.15 173.33

II 45,000 54,000

2 28 30 60 30

0.25 120

II 1,20,000 1,44,000

14,70,000

Contribution Limiting factor (hr./u) Contribution/hr. (a/b) Rs. Rank Budgeted production & sales Maximum demand Total Fixed cost Rs

Budgeted hours A B

1,20,000 units @ Rs. 0.25 = 30,000 hrs. 45,000 units @ Rs. 0.15 = 6,750 hrs.

36,750 hrs.

(a) Contribution per unit Rs.

A 30

B 26

- 25 -

Less: Fixed overhead per unit Rs. (a) (b)

Profit per unit Rs. Units

10 20

1,20,000

6 20

45,000 Total (a b)

(b) (a) (b)

Rank

Hrs. Available Less: for Rank I For Rank II Product A

3,075 810

2,265/0.02

Contribution per unit Rs. Limiting time/unit

24 lakhs + 9 lakhs = 33 lakhs Management is indifferent on the basis of profit per unit however this is wrong concept on selecting the product mix.

A 30

0.02 Rs. 1,500

II Statement of product mix & profit

units

54,000 1,13,250

Less: Fixed cost Profit

B 26

0.015 Rs. 1,733

II

Contribution/u

26 30

Total

14,04,000 33,97,500 48,01,500 14,70,000 33,31,500

Contribution /hr. (a/b)

(c) Return per bottleneck hour = (selling price – material cost)/ (Time on bottleneck resource)

Product A Product B

= Rs. 2,900 [(Rs. 60 – Rs. 2)/ Rs. 0.02 hours] = Rs. 2,000 [(Rs. 70 – Rs. 40)/ 0.015 hours]

Product A should be sold up to its maximum capacity of utilizing 2,880 bottleneck hours (1,44,000 units × 0.02 hours). This will leave 195 hours for product B thus enabling 13,000 units (195/0.015) to be produced. The maximum profit is calculated as follows:

Rs. Throughput return from product A (1,44,000 × Rs. 58) Contribution from product B (13,000 × Rs. 30)

Less: Variable overheads Fixed overhead cost Net profit

Note: It is assumed that the variable overheads (e.g. direct labour) are fixed in the short term. They are derived from part (a) – [(120,000 × Rs. 28) + (45,000 × Rs. 4)]

83,52,000 3,90,000 87,42,000 35,40,000 14,70,000 37,32,000

Ans. 30:

Installed Capacity for the machine = 365 * 8 *3 * 500 = 43.8 lakh units

- 26 -

Practical Capacity = ( 365 – 52 - 13 ) * ( 8 - 1) * 3 * 500 = 31.5 lakh units

Out of the past five years, normal capacity is average of 3 normal years. Normal Capacity = ( 30.1 + 29.7 + 30.2 ) / 3 = 30.0 lakh units

Actual Capacity Utilization = 30.1 lakh units = 68.7 %

Idle Capacity = ( 43.8 – 30.1) = 13.7 lakh unit = 31.3 %

Abnormal idle capacity = 31.5 – 30.1 = 1.4 lakh units

Ans. 31:

Details of Computation

1. Maximum capacity ( 365 days × 8 hours per day) 2. Practical capacity Maximum capacity (in hours) 2,920 Less: Idle capacity Sundays: (52 days × 8 hours) 416 Holidays (10 days × 8 hours) 80 Plant maintenance 200 3. Normal capacity 4. Expected capacity

Determination of Factory overhead application rate (a) Total Budgeted overheads Fixed overhead costs Variable overhead costs (2,000 hours × Rs. 100)

(b) Normal Capacity (machine-hours) (c) (i) Factory overhead application rate (Rs. 8,00,000÷2,000) per hour

(ii) Factory overhead application rate (Rs. 8,00,000÷2,0000) per unit

Ans. 32 Working Notes:

Capacity Machine hours Production units @ 10

units per hour 2,920 29,200

2,224 2,000 1,900

22,240 20,000 19,000

Rs. 6,00,000 2,00,000 8,00,000

2000 400

40

(Amount in Rupees) X

Selling price per unit (A) Variable costs per unit Direct material Direct labour Department 1 Department 2 Department 3 Variable overheads Total variable costs (B) Contribution per unit (A B)

45.00 15.00 20.00

8.00 120.00

15.00

25.00 12.00 10.00 4.50

127.50 12.50

50.00 21.00 40.00 10.50

180.00 20.00

32.00 76.00 58.50

135.00

Y

140.00

Z

200.00

- 27 -

(i)

Budgeted quantity (units)

Statement of budgeted profitability X

19,500 15.00

2,92,500 Contribution per unit (Rs.) Total contribution (Rs.)

Contribution fund (Rs.) Fixed overheads (Rs.) Profit (Rs.) 3,99,500

Contribution per direct labour hour for Department 2 X

Contribution per unit (Rs.) Direct labour hours per unit Contribution per labour hour Rank

15.00 5

3.00

Y 12.50

4 3.125

Z 20 7

2.857 III

Y 15,600 12.50

1,95,000

Z 15,600 20.00

3,12,000

(ii)

(iii) X Y Z Total

II I Total hours available in department 2 19,500 units 5 = 97,500 hours 15,600 units 4 = 62,400 hours 15,600 units 7 = 1,09,200 hours

= 2,69,100 hours

Y X Z

19,500 23,400 19,500

2,69,100 1,91,100

74,100

4 5 7

19,500 23,400 10,585

78,000 1,17,000

74,095

1,91,100 74,100

5

Optimal profit (Rs.) Contribution (Rs.) Y X Z Total Contribution Less fixed cost

19,500 Rs. 12.50 = Rs. 2,43,750 23,400 Rs. 15 10,585 Rs. 20

= Rs. 3,51,000 = Rs. 2,11,700 = Rs. 8,06,450 = Rs. 4,00,000

- 28 -

Profit = Rs. 4,06,450

Ans 33: (a)

Output level (units)

Sales Direct Material 12.5 per unit (reduction for 1,00,000 units by Rs.0.50) Direct wages (5.00 per unit) Semi variable cost (variable) Factory overhead (V) Rs.5 per unit) Selling and Adm. (25% variable) Total variable cost Contribution Fixed factory overheads (5×60,000) Selling and adm. (6 × 60,000) Semi variable fixed part Increase due to expansion Interest Depreciation Special Advertisement exp. Total fixed costs

Flexible Budget 50,000

(Rs. in lakhs) 80,000

(Rs. in lakhs) 1,00,000

(Rs. in lakhs) 20.00 6.25

32.00 10.00

36.00 12.00

4.00 0.40 4.00 1.60

20.00 12.00 3.00 3.60

.30 2.00

.60

.50 . .50

6.90 10.50 0.60 1.50

Therefore activity level 80,000 units is most profitable level. Calculation of Break even point P/V ratio

2.50 0.25 2.50 1.00

12.50 7.50 3.00 3.60

.30

5.00 0.50 5.00 2.08

24.58 11.42 3.00 3.60 .30

2.80 .60 .50

. 10.80 0.62

7.5/20.00 × 100 = 37.5%, 12.00/32.00 × 100 = 37.5%, 11.42/36.00 × 100 = 31.72%BEP (value) = 6.90/37.5% = Rs.18,40,000, 10.50/37.5% = Rs.28,00,000, 10.80/31.72% = 34,04,792 BEP (Units)

= 46,000 units = 70,000 units = 94,571 units Alternative Solution (BEP in Sales) Break Even Point in value of sales: At 50000 units’ level : At 80000 units’ level : At 100000 units’ level :

6.90lakhs Rs.15

10.50lakhs Rs.15

10.80lakhs Rs.15

(F x S) / (S – V) = Rs. 18,40,000 = Rs. 28,00,000 = Rs. 34,04,553

(6,90,000 x 20,00,000)/7,50,000 (10,50,000 x 32,00,000)/12,00,000 (10,80,000 x 36,00,000)/11,42,000

- 29 -

Budget statement for April Budget

Fixed Variable Total Management Rs.30,000 - 30,000 Shift premium - 3,600 3,600 ESI 6,000 7,920 13,920 Inspection 20,000 9,000 29,000 Supplies 6,000 6,480 12,480 Power - 7,200 7,200 Lighting and heating 4,000 - 4,000 Rates 9,000 - 9,000 Repairs 8,000 5,400 13,400 Materials handling 10,000 10,800 20,800 Depreciation 15,000 - 15,000 Administration 12,000 - 12,000 Idle time - - -

1,20,000 50,400 1,70,400

Ans. 34: Overheads Actual

30,000 4,000

15,000 28,000 12,700

7,800 4,200 9,000

15,100 21,400 15,000 11,500

1,600 1,75,300

Variance Adverse Favourable

- - 400 -

1,080 - - 1,000

220 - 600 - 200 -

- - 1,700 -

600 - - - - 500

1,600 - 6,400 1,500

Rs.4,900 (A)

(b) E.S.I. This variance may be due to increase of E.S.I. rates. If this assumption is correct, then the variance will be beyond the control of management. It should be noted that actual activity is less than budgeted activity. It is , therefore, unlikely that increase is due to increase in the number of labour hours worked. Another possibility is that E.S.I. Payment might have got increased due to increase in E.S.I. rates. Inspection: There is a possibility that standard inspection has been lowered, thus resulting in a saving in costs. If this is not due to management policy, then the variance requires immediate investigation. Another possibility is that a number of staff members have resigned and consequently actual inspection is less than the budget. Repairs and Maintenance: This increase may be due to unexpected repair, which might not have been envisaged. The variance for this item over a period of several months should be studied to form an opinion. Idle Time: No Idle time has been included in the budget. Consequently this idle time must be of an abnormal nature. Possible uncontrollable causes include a power failure or machine breakdown. Controllable causes may include poor scheduling or lack of material.

(c ) (i) Calling for comments on variances in excess of a specific figure may not be satisfactory for control purpose. For decision on whether to investigate or not, Cost of investigation should be compared with benefits of investigation. Statistical tests may also be applied.

(ii) The statement could be improved by analyzing the expense items into their controllable and non- controllable elements. Variances should be analysed according to whether they are due to price and quantity changes. Analysis should include non- financial measures such as a comparison of actual hours worked with standard hours produced.

(d) (i) Overhead absorbed = Rs.1,58,400, i.e.,36,000 hrs x Rs.4.40 (ii) Over spending = Rs.4,900 (iii) Actual production was 4,000 standard hours less than budgeted production and this decline

in output has resulted in a failure to recover Rs.12,000 fixed overheads. This under recovery of Rs.12,000 is also known as the volume variance.

- 30 -

Ans. 35: A.Z. Limited Analysis of the information required for preparation of cash budget (Rs.’000)

April May June July August Sales receipts - 401.70 450.28 425.88 - Variable cost of sales (60%) 240.00 270.00 312.00 252.00 288.00 Variable production costs: In the month of sales (60%) 144.00 162.00 187.20 151.20 - In prior month (40%) 108.00 124.80 100.80 115.20 -

252.00 286.80 288.00 266.40 Material costs 60% of production cost 151.20 172.08 172.80 159.84 Purchases: In the month of production (50%) 75.60 86.04 86.40 79.92 In prior month (50%) 86.04 86.40 79.92 Payment to supplier 161.64 172.44 166.32 Labour costs (Variable production cost x 0.3) 75.60 86.04 86.40 79.92 Variable overhead 25.20 28.68 28.80 26.64 (Variable production cost x 0.1) Variable cost was paid as follows: Paid in the month of incurrence (40%) 10.08 11.47 11.52 10.66 Paid in the following month (60%) 15.12 17.21 17.28 Variable overhead expenditure 26.59 28.73 27.94

Cash budget for the month of May to July 1997 May June 401.70 450.28

161.64 86.04 26.59 75.00

349.27 52.43 40.00 92.43

172.44 86.40 28.73 75.00

552.57 (102.29) 92.43 (9.86)

Receipts from sales Payments: Materials Labour Variable overhead Fixed costs (12,00,000-3,00,000)/12 Capital expenditure Total expenditure Net inflow (outflow) Balance b/f Balance c/f

July 425.88

166.32 79.92 27.94 75.00

349.18 76.70 (9.86) 66.84

Note. In this question language should be given particular attention: (a) Variable production cost 60% in the same month 40% in the prior month.

Production cost relevant for cash budget for each month should be found. (b) 60% of production cost is material 50% in the same month and 50% in the prior month.

30% of production cost is labour which is paid the same month. 10% of production cost is variable overhead, 40% is paid the same month. 60% is paid in the following months.

(c) This question illustrates the interaction of sales, purchase and manufacturing process and requires the reader to think clearly about these relationships

Ans. 36

Note: Since question has not clearly specified that whether labour efficiency is lower by

- 31 -

ANOTHER 1% or by 1%, also it is unclear that efficiency is to reduced based on BUDGETED EFFICIENCY OR ACTUAL EFFICIENCY, hence this question can be solved in following 3 ways (after giving prompt assumption)

Solution – Way 1

Production Cost Budget (for 6 months ending 30th September, 2009)

30,000 units Cost per unit Total

Rs. Rs. Material cost 180 54,00,000 Labour cost 115.47 34,64,208 Variable overhead 23.65 7,09,500 Fixed overhead 23.2 6,96,000

342.34 1,02,69,708

Assumption : Here, difference in actual and standard time is also considered for calculating the lower efficiency i.e. 3.74% + 1% = 4.74% based on budgeted efficiency

Working Notes: I. Material cost

Material consumption per unit = 1,600MT ÷16,000 = 0.10 MT

Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000.

II. Labour cost can be calculated as follows: 2008 – Total Budgeted Hour = 16,00,000 ÷40

Labour hour budget for each unit = 40,000÷ 16,000

Actual time paid = 15,99,840÷ 44

= 40,000 hours

= 2.5

= 36,360 hours

Less: Standard labour hours for 14,000 units (i.e. 14,000×2.5)= 35,000 hours Difference in actual and standard hours = 1,360

3.74% = Difference in actual and standard hours ÷ Actual hours ×100 = 1,360 hours÷ 36,360 hours

Budget unit (2008) for each labour hour = 16,000÷40000 Less: (3.74% + 1%) = 4.74% for lower efficiency Budget unit (2009) for each labour hour

Time required for 30,000 units (30,000 ÷ 0.38104)

Labour cost = 78,732 hours× 44 per hour = Rs. 34,64,208.

III. Variable overhead Actual rate = Rs.2,76,000 ÷14,000 units Add: 20 % New rate

= 19.71 per unit = 3.94 23.65

= 0.4 units = 0.01896 units = 0.38104 units

= 78,732 hours

- 32 -

Total variable overhead = 30,000 ×23.65 = Rs. 7,09,500 IV. Fixed overhead

Actual = Rs. 5,80,000 Add: 20% = Rs. 1,16,000

= Rs. 6,96,000

According to above the production cost budget will be as follows:

Solution – Way 2 Production Cost Budget

(for 6 months ending 30th September, 2009) 30,000 units Cost per unit

Rs. Material cost 180 Labour cost 111.11

Variable overhead 23.65 Fixed overhead 23.2

337.96

Total Rs.

54,00,000 33,33,352 7,09,500 6,96,000

1,01,38,652

Assumption : Here, lower efficiency of 1% is based on budgeted efficiency


Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000.

II. Labour Cost: 2008 – Total Budgeted Hour = 16,00,000 ÷40

Budget unit (2008) for each labour hour = 16,000÷40000 Less: 1% for lower efficiency Budget unit (2009) for each labour hour


Labour cost = 75,758 hours × 44 per hour = Rs. 33,33,352

III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units Add: 20 % New rate Total variable overhead = 30,000 ×23.65

IV. Fixed overhead Actual Add: 20%

= 19.71 per unit = 3.94 23.65

= Rs. 7,09,500

= Rs. 5,80,000 = Rs. 1,16,000 = Rs. 6,96,000

= 40,000 hours

= 0.4 units = 0.004units = 0.396 units

= 75,758 hours

- 33 -

Solution – Way 3 Production Cost Budget

(for 6 months ending 30th September, 2009) 30,000 units Cost per unit

Rs. Material cost 180 Labour cost 115.44

Variable overhead 23.65 Fixed overhead 23.2

342.29

Total Rs.

54,00,000 34,63,196 7,09,500 6,96,000

1,02,68,696

Assumption : Here, lower efficiency of 1% is based on actual efficiency


Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000.

II. Labour Cost: 2008 – Total Actual Hour = 15,99,840 ÷44

Actual unit (2008) for each labour hour = 14000÷36360 Less: 1% for lower efficiency Budget unit (2009) for each labour hour


Labour cost = 78,709 hours × 44 per hour = Rs. 34,63,196

III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units Add: 20 % New rate Total variable overhead = 30,000 ×23.65

IV. Fixed overhead Actual Add: 20%

= 19.71 per unit = 3.94 23.65

= Rs. 7,09,500

= Rs. 5,80,000 = Rs. 1,16,000 = Rs. 6,96,000

= 36,360 hours

= 0.385 units = 0.00385units

= 0.38115 units

= 78,709 hours

Cash Budget for October, November and December 1990 October November

Rs.35,000 Opening balance of bank (overdraft) Rs.(9,100) Cash inflows – Sales: -

5,000 From cash sales of current month 6,000 15,000 From credit sales of previous month 18,000

Total Receipts (A) 55,000 14,900 Cash outflows:

Ans. 37: (a) December

Rs.(12,600)

8,000 20,000 15,400

- 34 -

Creditors for purchases of the preceding month Equipment Wages Administration Rent Dividend Total payment (B) Closing balance (Overdraft) (A-B)

40,000 16,000

3,000 1,500 3,600

- 64,100 (9,100)

23,000 -

3,000 1,500

- -

27,500 (12,600)

27,000 -

3,000 1,500

- 15,000 46,500

(31,100)

Rs.82,000 (b) Budgeted Income Statement for three months ending 31st December 1990 Sales Less: Cost of Goods Sold:

Rs.20,000 Material- Opening Stock Add: Purchases (23,000 + 27,000 + 26,000) 76,000

96,000 Less: Closing stock 43,500 Cost of material consumed 52,500 Wages (3,000 x 3) 9,000

Gross profit Less: Rent [ 3,600 x (3 / 12 ) ] 900

Administration (1,500 x 3) 4,500 Depreciation [3,000 x (3 / 12)] 750 Loss on sale of asset ( Rs.15,000 – Rs.14,000) 1,000

Net profit

61,500 20,500

7,150 13,350

Working Notes: (i) Total Sales

October 1990 November 1990 December 1990

Credit Sales Rs.18,000

20,000 25,000 63,000

Cash Sales Rs.5,000

6,000 8,000

19,000

Rs.82,000 20,500 61,500

Rs.61,500 9,000

52,500

Rs.20,000 76,000 96,000 52,500

43,500

Total Rs.23,000

26,000 33,000 82,000

For Cost of Sales: (ii) Sales for the quarter

Less: Gross Profit 25% of Sales Cost of sales

(iii) For Material consumed: Cash of sales for three months Less: Wages (3,000 x 3) Cost of material consumed

(iv) For closing stock of material Opening stock of material Add: Purchases (23,000 + 27,000 + 26,000)

Less: Material consumed Closing stock of material

- 35 -

Ans. 38:

Shirt Dec 6242

15300 21542 6120

15422

Short Dec 8320

20400 28720 8160

20560

Cl. Stock( 40% Of next month) Sales Total Op. Stock Production

Nov 6120

15000 21120 6000

15120

Jan 6367

15606 21973 6242

15731

Feb -

15919

Nov 8160

20000 28160 8000

20160

Jan 8490

20800 29290 8320

20970

Feb -

21224

Shirts Opening stock Sales November

December January February

6000 40%

= 15,000

6000 8000 Shorts

8000 = 20,000

40% 1.02 X 20,000 = 20400 1.02 X 20,400 = 20,808 1.02 X 20,808 = 21,224

1.02 x 15,000 = 15,300 1.02 x 15,300 = 15,606 1.02 X 15, 606 = 15, 919

Alternative: Opening Stock Shirts = 6000 = 40% of November Sales

November sales

Dec. Sales Closing Stock November

6000 40%

= l5,000

Opening Stock of Shorts = 8000 =40% of November Sales 8000

= 20,000 40%

l.02 x 20,000 = 20400 40% x 20,400 = 8l60 20,l60

l.02 x l5,000 = l5,300 40% x l5, 300 = 6,l20

November Production = l5, l20 Closing Stock + sales – Opening stock December Production January Production

Ans39:

l.02 X l5, l20 = l5422 l.02 Xl5422 = l5, 73l

l.02 X 20,l60 = 20, 560 l.02 X 20,560 = 20, 970

(a) Production Budget for product A and B A units

Inventory at the end of the year Sales forecast

1,000 8,000

B units 2,000

15,000

- 36 -

Total requirements Less: Beginning inventory Production

Budgeted requirements of components P, Q and R Components For Product A: Production 6,000 units P: 6,000 × 1 per unit Q: 6,000 × 2 per unit For Product B: Production 12,000 units P: 12,000 × 2 per unit Q: 12,000 × 1 per unit R: 12,000 × 2 per unit For comp R: Production 24,000 comp Q: 24,000 × 1 per component R Total requirements

(b) The company is advised to adopt EOQ system. P Q

9,000 3,000 6,000

17,000 5,000

12,000

P

6,000

Q R

12,000

24,000 12,000

24,000

24,000 30,000 48,000 24,000

EOQ 2 30,000 15

2 20% 2 48,000 15

0.8 20% = 1,500 components = 3,000 components

(c) Calculation of savings arising from switching over to the new ordering system. Existing situation:

P Present order quantity (units) (equivalent to 3 months consumption) Average stock (units) Investment in inventory of P & Q Total investment Carrying cost @ 20% p.a. of average inventory investment Ordering cost: Total cost

After switching over: P

Economic order quantity (units) 1,500 Q

3,000

7,500 × ½ 3,750 × Rs. 2

Rs. 7,500 + Rs. 12,300 × 20%

P = 4×Rs. 15 = Rs. 60

3,750 7,500

Rs. 4, 800

12,000 × ½ 6,000 × Re. 0.80 =Rs. 12,300

Rs. 2,460

Rs. 120 Rs. 2,580

6,000 4,800

30,000 × ¼ 7,500 48,000 × ¼ Q

12,000

- 37 -

Average stock (units) Investment in inventory of P & Q Total investment Carrying cost @ 20% p.a. of average inventory investment Ordering cost:

Total cost

1,500 × ½ 750 × Rs. 2

Rs. 1,500 + Rs. 2,700 × 20%

P = 20×Rs. 15 Q = 16×Rs. 15

750 1,500

Rs. 1,200

3,000 × ½ 1,500 × Re. 0.80 =Rs. 2,700

1,500 1,200

Rs. 540

= Rs. 300 = Rs. 240 Rs. 540

Rs. 1,080 Saving in costs: Rs. 2,580 – Rs. 1,080 = Rs. 1,500 Reduction in working capital: Rs. 12,300 – Rs.2,700 = Rs. 9600

Ans. 42: Production Budget (showing quantities to be manufactured)

Chairs 4,200 Units to be sold (Note 1)

Add: Closing inventory as per budget 200 4,400

Less: Opening inventory as per budget 400 4,000

(b) Material Purchase Budget (in quantities)

Timber (cu. ft.) 4,450

650 5,100

600 4,500

Tables 800 300

1,100 100

1,000

Benches 500 50

550 50

500

Material required for production (Note 1) Add: Closing stock as per budget

Less: Opening stock as per budget Raw materials to b purchased

Upholstery (Sq. yards) 1,000

260 1,260

400 800

Materials Purchase (in rupees)

Quantities to be purchased Timber (c.ft.) 4,500 Upholstery (sq. yds.) 860

(c) Direct wage Cost Budget

Total hrs. 4,625 1,500

Rate p.h. 6.00 4.80

Amount Rs.27,750

7,200 34,950

Rate 50 20

Amount Rs.2,25,000

17,200 2,42,200

Carpenter’s time and wages Fixer’s and finisher’s time and wages

(d) Statement showing the variable cost of manufacture per unit of all three products. Chairs Tables Benches

- 38 -

Raw materials – Timer

Upholstery

Fixing and finishing materials cost (Note 2) Wages Carpenters

Fixer’s and finisher’s

Rs.25.00 (0.5 x Rs.50)

5.00 (0.25 x 20)

1.50

4.50 (45/60) x Rs.6

1.20 (15/60) x 4.80

37.20

60.00 (1.2 x Rs.50)

-

3.00

6.00 (60/60) x Rs.6

1.20 (15/60) x 4.80

70.20

125.00 (2.5 x Rs.50)

-

6.25

7.50 (75/60) x Rs.6

2.40 (30/60) x 4.80

141.15

(e) Budgeted Net Income Statement (For the quarter)

Chairs Rs.50.00

37.20 12.80 4,200

53,760

Tables Rs.85.00

70.20 14.80

800 11,840

Benches Rs.158.00

141.15 16.85

500 8,425

Total Rs. Selling price (per unit)

Less: Variable cost Contribution per unit (A) Units to be sold (B) Total contribution Fixed cost for the quarter (Rs.8,000 x 30 Budgeted net income

74,025

24,000 50,025

Working Notes: 1. Raw Materials, Carpenter’s Time and Fixer’s and finisher’s Time

Benches Tables Chairs 500 1,000 4,000 Units to be manufactured

1,250 1,200 2,000 Timber (c. ft.) (500 x 2.5) (1,000 x 1.2) (4,000 x 0.5)

- - 1,000 Upholstery (sq. yards) (4,000 x 0.25)

625 1,000 3,000 Carpenter’s time (hrs.) 500 x (75/60) 1,000 x (60/60) (4,000 x(45 /60)

250 250 1,000 Fixer’s and Finisher’s 500 x (30/60) 1,000 x (15/60) 4,000 x(15/60) time(hrs.)

2. Per unit cost of materials of fixing and finishing

Total cost of Timber and Upholstery Fixing and Finishing Material will cost 5% Of total cost of timber and upholstery

Ans. 43:Necessary Calculations

Chairs Rs.30

1.5 (5% of 30)

Tables Rs.60

Benches Rs.125

Total

4,450

1,000

4,625

1,500

3 6.25 (5% of Rs.60) (5% of Rs.125)

- 39 -

Statement showing total cost and selling price and sales in units for each product (Working Note 1) Working A Working B Working C Materials Rs. Rs. Rs. M1 (Rs.2x5 units) 10 - 2x12 24

M2

M3

Labour Department I Department II Department 1II Variable overhead

(Rs.1x5 units)

-

5 15

10 12

3 10

(4x10)

(1x5)

40

5 45

5 4 6

20

10 6

24 120

24 48

192 24

(2.5x2) (2x3) (1.5x6)

(4x9) 36

60

5 6 9

15

10 9

36 150

30 60

240 40

280 16,80,000

6,000

C (Units) 6,000 2,500 3,500

2,000 5,500

(Rs.2.5x4) (Rs.2.0x6) (Rs.1.5x2)

(2.5x2) (2x2) (1.5x4)

Fixed Cost(Working Note 2) Department I (Rs.5x4 hrs.) 20 Department II (Rs.3x6 hrs) 18 Department 1II (Rs.6x2 hrs.) 12 Total production cost 100 Adm.(Based on 20% of production cost) 20 Selling and Distb. Cost (40% of prod. Cost) 40 Total cost 160 Profit (25% of total cost) 40

Selling price per unit 200 Sales in rupees 15,00,000 Sales in units 7,500 Sales in rupees / Selling price (per unit)

(a) Production Budget for July 1986

Sales Less: Closing stock (given)

Add: Closing stock : 20% reduction (working Note 3) Production

(b) Material Usage budget for July 1986 Product Units of Qty. per

product unit of product

A B C Total usage in unit

6,900 4,600 5,500

5 - 12

A (Units) 7,500 3,000 4,500

2,400 6,900

(5x2) (3x2) (6x4)

(5x2) (3x3) (6x6)

(12 ½ % of total cost)

(16 2/3% of total cost

216 10,80,000

5,000

B (units) 5,000 2,000 3,000

1,600 4,600

M1 total Qty reqd.

34,500 -

66,000 1,00,500

Qty. per unit of product

- 10

9

M2 Total Qty reqd.

M3 Qty Total per units Qty.

reqd. of product

- 5 34,500 46,000 5 23,000

- 49,500 - 95,500 57,500

- 40 -

(c ) Material Purchase Budget

Usage (price is given Less: O/stock

(Add: C/stock) (10% reduction)

M1 Units Rs. 1,00,000 2,01,000

24,500 76,000

22,050 98,050

49,000 1,52,000

44,100 1,96,100

Units 95,500

20,500 75,000

18,450 93,450

M2 Rs. 3,82,000

82,000 3,00,000

73,800 3,73,800

Units 57,500

17,500 40,000

15,750 55,750

M3 Rs. 57,500

17,500 40,000

15,750 55,750

Total Rs.42,60,000

36,00,000 6,60,000

(d) Budgeted profit and loss account for each product and in total A B C

Sales Rs.15,00,000 Rs.10,80,000 Rs.16,80,000 Less: cost (Working Notes) 12,00,000 9,60,000 14,40,000 Profit 3,00,000 1,20,000 2,40,000

Working Notes Note: 1. Price per unit of material and material units required for each product should be multiplied.

Note:2. Fixed overhead rate Deptt. I = Rs.2,39,000 or Rs.5 per hour

47,800

Deptt. II = Rs.2,01,300 or Rs.3 per hour 67,100

Deptt. II = Rs.3,91,200 or Rs.6 per hour 65,200

or 2,400 , B = 2,000 x 80 100

or 1,600, C = 2,500 x 80 or 2,000 100

B - 5,000 x 192 Rs.9,60,000;

Note:3. A = 3,000 x 80 100

Note:4. A -7,500 x 160 C – 6,000 x 240

=Rs. 12,00,000; =Rs.14,40,000

Ans. 44: Responsibility Accounting Reports

For the production manager Cutting Department Cloth Cutting Labour

Budgeted Rs. 31,000

6,000

Actual Rs. Variance Rs. 36,000

6,600 5,000 (A)

600 (A)

- 41 -

Cutting utilises Total cutting Deptt. (A)

Sewing Department: Thread Sewing Labour Sewing utilities Total Sewing Dept. (B) Total (A + B)

Production Department * Production engineering expenses Production manager-office expenses Total

800 37,800

500 17,000

900 18,400 56,200

56,200 13,000 18,000 87,200

For the Direct-Marketing

700 43,300

450 18,400

950 19,800 63,100

63,100 12,200 17,000 92,300

100 (A) 5,700 (A)

50 (F) 1,400 (A)

50 (F) 1,400 (A) 6,900 (A)

6,900 (A) 800 (F)

1,000 (F) 5,100 (A)

For the director-Manufacturing

(* As per responsibility accounting report for the production manager)

Sales representative: Travelling expenses Sales commission Total (A) Sales Management: Office expenses Advertising Total (B) Credit Department: Salaries Credit reports Bad debt Losses Total Total (A + B + C)

8,000 1,200 5,000

14,200 50,200

8,000 1,050 3,000

12,050 48,950

150 (F) 2,000 (F) 2,150 (F) 1,250 (F)

16,000 4,000

20,000

15,700 4,000

19,700

300 (F) —

300 (F)

9,000 7,000

16,000

10,200 7,000

17,200

1,200 (A) --

1,200 (A)

Note: ‘F’ denotes favourable variance while ‘A’ denotes adverse variance.

Ans. 45: Performance Budget

Original Plan Rs. 50,000 40,000

20,000 16,000

18,000 2,000 (A)

Revised Budgeted Rs.

Actual Variance Result Rs. Rs.

Revenue (5,000×10) (4,000×10) (4,000×11)

Variable (5,000×4) Costs (4,000×4)

(4,000×4.5)

44,000 4,000 (F)

- 42 -

Contribution (5,000×4) (4,000×6) (4,000×6.5)

Fixed costs Net Profit

30,000 24,000

20,000 10,000

26,000 20,000

4,000

2,000 (F) 21,000

5,000 1,000 (A) 1,000 (F)

Summary Report on Profit Plan Planned Income (from Project plan) Rs. 10,000 Activity variance (lost contribution margin due to shortage of materials) (6,000) Selling price variance (increased Selling price of Re. 1/- per unit) 4,000 Variance cost variance (increased production Costs at 0.50 per unit) (2,000) Fixed cost variance (new research programme to Develop raw materials and processes) (1,000) Actual income (from income statement) 5,000

Ans. 13 (Pg. 11): Margin of Safety(%) = MoS Units/Actual Sales Units = 7500/(7500+2500) = 75%

Total Sales Profit

P/V Ratio

= 187500/0.75 = Rs.2,50,000/- = Total sales – Total Cost = 250000 – 193750 = Profit/MoS (Rs.) x 100 = 56250/187500 x 100 = 30% BEP Sales =

Total Sales / (100 – MS) = 2,50,000 x 0.25

Fixed Cost

Alternate Answer 1

Margin of Safety = Selling Price per unit x ( 7500 units) Rs. 187500 = Selling Price per unit x ( 7500 units)

Therefore , Selling Price per unit = Profit Sales Less: Total Cost Profit P/V Ratio

BEP Sales Fixed Cost Alternative Answer 2

Profit/Margin of Safety 56250/187500 2500 x25 62500 x 30%= Rs.

30% Rs. 62,500

10000 x 25

187500/7500 =Rs. 25 Rs.

2,50,000 1,93,75

56,250

= Sales x P/V Ratio = 250000 x 0.30-56250 = 18750

= Rs.62,500

= Rs.56250

Selling price = Rs 187500/ 7500 = Rs.25 Total Cost at Break Even point=Rs.25 x 2500 = 62500 = Break Even Sales (Total Cost – Total Cost of BE)/(Total Units – Break Even Units) = Variable Cost per Unit (93,750 – 62,500)/(10,000 – 2,500) = 1,31,250/7,500 = Rs.17.50 per unit Selling Price Variable Cost Contribution P/V Ratio Fixed Cost Profit

= 25.00 = 17.50 = 7.50 = 7.50/25

= 7.50 x 7500

=

=

30% Rs.18750. Rs. 56,250

= 7.50 x 2500 units =

Ans. 12 (Pg. 11) (1) P/V Ratio In year 2, additional NP which means additional contribution 8,000

Solution’s of CVP

Additional sales

P/V Ratio

40,000

20%

Fixed cost = Contribution – NP = (2,40,000 * 20%) – 18,000 BEP = FC/PV Ratio

(3) Margin of Safety

Year 1 Year 2

48,000 – 18000 30,000/0.20

30,000 1,50,000

2,40,000 – 1,50,000 2,80,000 – 1,50,000

90,000 1,30,000

() fi (Contribution*PV Ratio) – Fixed Cost (2,00,000 * 20%) – 30,000 10,000

OR

Cap Sales

(-) BEP

Margin of Safety

(-) PV Ratio

NP

2,00,000

1,50,000

50,000

20%

10,000

5) Sales Required 100/20 ( 30,000(FC) + 40,000(NP)) 3,50,000

OR

BEP

Margin of Safety Req (100/20*40,000) Sales Required

1,50,000

2,00,000 3,50,000

(6) a) 20% decrease in sale Qty Reduction in Contribution & in net profit

Reduction in Contribution & in net profit

(b) Revenue Sales

(-) Revenue Cost

Revenue contribution

(-) Revenue Fixed Cost

Revenue NP

(-) Given NP

Increase in NP OR

( 2,80,000*80%) *110%

(2,80,000*80%) * 80%

20% *(2,80,000*20%) 20% (56,000)

Rs.11,200

2,46,400

1,79,200

67,200

(26,500)

40,700 (26,000)

14,700

(b) Revenue Sales

P/V Ratio (now)

(new)

(Reconciliation of NP change)

Change

1) Reduction in Sales Qty (as per (a))

2) Increase in Sales Price (2,80,000*80%*10%)

3) Reduction in Fixed Cost

Increase in NP

(2,80,000*80%) *110%

100-80 = 20

110–80 =30

2,46,400

3/11

Effection NP

(11,200)

22,400

3500

14,700

Ans. 3 (Pg. 14) (1) Evaluation of proposal to replace product Z with product S. a: net profit if we continue with product Z. X Y

Z

Total contribution

(-) Fixed Cost

Net Profit

(5,00,000*40%/20)*(20-10) (5,00,000*35%/25)*(25-25)

(5,00,000*25%/30)*(30-18)

1,00,000 70,000

50,000

2,20,000

1,50,000

70,000

b) Net profit if we replace with S X Y

Z

Total contribution

(-) Fixed Cost

Net Profit

(4,50,000*50%/20)*10 (4,50,000*30%)/25*10

(4,50,000*20%)/28*14

1,12,500 54,000

45,000

2,11,500

1,60,000

51,500

The company should continue with product Z because the replacement of ‘Z’ with ‘S’ would result in reduction net profit.

2) Statement showing the overall breakeven point of the 2 alternatives. XYZ XYZ

Contribution

Sales

Fixed cost

BEP 50/22*1,50,000

2,20,000

5,00,000

1,50,000

3,40,909

2,11,500

4,50,000

1,60,000

3,40,426

The above calculation are based on the presumption, in addition to the usual presumptions that the sales of products X, Y & Z would always be in the ratio of Rs.40:35:25 and that of X, Y & Z would be in the ratio of 50:30:20

Ans. 6 (Pg. 15) a) Statement showing the budgeted net income for 2003

Fees collected (4,000 *50)

Less: Budgeted cost

Evaluation 4000*20

G.B 4000* 10

Hall rev.

Hon. To Chief Adm.

Super changer (50*4 * 4000/100)

Total

Budgeted N.I

b) (i) Calculation of supervision cost Fees per student

Less: Variable cost + semi variable cost

Evaluation

QB

20

10

30

Semi- variable

(supervision)

Gross contribution

Gross Fixed Cost

Gross BEP

Therefore, no. of Supervisory required.

Therefore, Supervision Cost

Net fixed cost

12*200

20,000+2,400

20,000/18

2

32

18

20,000

1111.11

12

2,400

22,400

80,000

40,000

8,000

6,000

8,000

1,48,000

52,000

2,00,000

50

(ii) BEP

Fixed Cost

Net CTR per student

Fees 50

20

1,120

22,400

(-) Variable Cost (30)

BEP

(C) (i) Calculation of total contribution required

Gross contribution per student

Gross Fixed Cost

Net Profit Required

Gross Total Contribution Required

Gross no. of students (40,000/18)

No. of Supervision required

Supervision cost (23*200)

Net Fixed Cost (20,000+4,600)

Net Contribution Required (20,000+24,600)

Net Total Contribution required

Net Contribution per Student

Fees

(-) Variable Cost

50

(30)

18

20,000

20,000

40,000

2,222.22

23

4,600

24,600

44,600

44,600

20

2230 No. of Students required

Ans. 7 (Pg.15): (i) Department

Statement of profitability of Special Health Care

(for the years 2001 and 2002) Year 2001

Rs.

Year 2002

Rs. Total contribution : (A) 8,225 bed days × Rs. 260 21,38,500

8,225 bed days × Rs. 243.50 (Refer to working notes 1, 2, & 3)

Fixed costs : Department fixed costs Apportioned fixed costs (Refer to working note 4) Nursing staff 6

20,02,788

6,22,500 10,00,000

2,88,000 (6 Nurse × Rs. 48,000

19,10,500

6,84,750 12,50,000

3,24,000 (6 Nurse ×

Rs. 54,000) 22,58,750 Total fixed costs : (B)

Profit (Loss) : { (A) – (B)} 2,28,000 (2,55,962)

Working notes :

1. Total number of bed days of occupancy = Total fees collected ÷ Fee per bed days = Rs. 34,95,625 ÷ Rs. 425 = 8,225

2. Variable cost per bed day Variable cost per bed das (Rs.) (Rs. 13,57,125 / 8,225) Variable cost per bed day (Rs.) in the year 2002 (Rs. 165 + 10% × Rs. 165)

3. Contribution per bed day Contribution per bed days in the year 2001 (Rs.) (Rs. 425 -- Rs. 165) Contribution per bed days In the year 2002 (Rs.) (Rs. 425 -- Rs. 181.50)

4. Departmental fixed costs Departmental fixed costs (Rs.) for the year 2001 Department fixed cost (Rs.) for the year 2002 (Rs. 6,22,500 + 10% × Rs. 6,22,500)

(ii) Break even bed capacity for the year 2002

= Total fixed costs ÷ Contribution per bed day = Rs. 22,58,750 ÷ Rs. 243.50 = 9,276 bed days (approx.) (this is not a valid answer because for 9,276 bed days 8 nurses service will be

required)

165.00

181.50

260.00

243.50

6,22,500

6,84,750

Nursing staff required; Remuneration of 8 nursing staff (Rs.) 8 nurses × Rs. 54,000 Department fixed costs (Rs.) Apportioned fixed costs (Rs.) Total fixed costs

8 4,32,000

6,84,750 12,50,000 23,66,750

Break even point = Rs. 23,66,750 ÷ Rs. 243.50 = 9,720 bed days

Increase in fee per day required to justify continuance of the Special Health Care department

Desired contribution (Rs.) Bed days of occupancy

Contribution per bed days (Rs. ) ; (a) (Rs. 22,58,750 / 8,225)

Variable costs (Rs.) ; (B) Required fee per bed day; {(A) + (B) } Increase in fee per bed day (Rs.) (Rs. 456.12 – 425)

Ans. 9 (Pg. 16): (i) yearly basis.

22,58,750 8,225

274.62

181.50 456.12

31.12

Profit Statement of M/s Satish Enterprises for first and second year on monthly and

First year Monthly

Rs. Yearly

Rs. 7,200

2,160

900

720

540

288

Second Year Monthly

Rs. 600

180

75

60

45

24

Yearly Rs.

7,200

2,160

900

720

540

288

Sales revenue: (A)

Material cost

Labour cost

Variable overheads

Primary packing cost

Boxes cost

600 (3,000 units × Rs.200)

180 (3,000 units × Rs.60)

75 (3,000 units × Rs.25)

60 (3,000 units × Rs.20)

45 (3,000 units × Rs.15

24 � Rs.3,000 units � � � ×400 � 12 months �

Total fixed overhead 108 1,296 110 1,320

(Refer to note 1)

working � Rs.1,296 � � � � 12 months �

492 108

5,904 1,296

� Rs.1,320 � � � � 12 month �

494 106

5,928 1,272

Total cost : (B) Profit : C = [(A)-(B)]

Working Note : 1. (i)

Fixed overhead Depreciation

First year : (Rs.) 8,96,000

Second year (Rs.) 8,96,000

Rs, 24,00,000 + Rs.2,88,000 duty 3 years

Other fixed overheads Total Fixed overheads

Levels – No. of units (Refer to working note)

Fixed costs (A) Total fixed overheads per month (Refer to working note) Semi – variable costs (Special boxes cost) – (B)

1,08,000

11,200

(28 boxes × Rs.400)

Total fixed and semi variable costs : (A+B) Break-even level of units:

1,19,200

1490

1,08,000

11,600

(29 boxes × Rs.400) 1,19,600

1495

1,08,000

12,000

(30 boxes × Rs.400) 1,20,000

1500

1,08,000

12,400

(31boxes × Rs.400 1,20,000

1505

1351 1400 Rs.

4,00,000 12,96,000

– 1401 1450 Rs.

– 1451 1500 Rs.

–

4,24,000 13,20,000

1501 1500 Rs.

–

(ii) Statement of monthly break – even units of the first year.

(Rs. (Rs. (Rs. (Rs. 1,19,200 / 1,19,600 / 1,20,000 / 1,20,000 Rs.80) Rs.80) Rs.80) / Rs.80)

The first and second break-even level of unit viz. 1490 and 1495 units falls outside the range of 1351 – 1400 and 1401 – 1450 units respectively. Here a monthly break-even level of units is 1,500 units which lies in the range of 1451 – 1500 units.

� Total fised and semi - variable costs � � �

Contribution per unit � �

Statement of yearly break-even points of the first year Levels No. of units

Fixed Costs (A) Semi-variable costs (Special boxes costs): (B)

17851-17900 Rs.

12,96,000 1,43,200

17901-17950 Rs.

12,96,000 1,43,600

17951-18000 Rs.

12,96,000 1,44,000

18001-18050 Rs.

12,96,000 1,44,000

(358 boxes × Rs.400)

Total fixed and semi- variable costs (A + B) Break-even level units

14,39,200

17,990

(359 boxes × Rs.400)

14,39,600

17,995

(360 boxes × Rs.400)

14,40,000

18,000

(361 boxes × Rs.400)

14,40,400

18,005 (Rs.14,39,200 (Rs.14,32,600 (Rs.14,40,000 (Rs.14,40,400

/ Rs.80) / Rs.80) / Rs.80) / Rs.80) Have a break-even level of units (on yearly basis) is 18,000 units which lies in the range of 17,951 – 18,000 units as well. The other first two figures do not lie in the respective ranges, so they are rejected. Working note:

Rs. 1. Fixed overhead in the first year

Fixed overhead per month Contribution per unit (S.P. per unit – VC per unit) Hence the break-even number of units will be above 1,350 units

12,06,000 1,08,000

80

� Rs.1,08,000 � � �

Rs.80 � � (iii) If the number of toys goes beyond the level of 1,500 numbers, one more box will be required to

accommodate each 50 additional units of toys. In that case the additional cost of a box will be Rs.400/- this amount can be recovered by the additional contribution of 5 toys. Hence, the second break-even point in such a contingency is 1,505 toys. (Refer to 1(b) (ii) last column of first statement).

(iv) Comments: Yearly break-even point of 18,000 units of toys in the first instance is equal to 12 times the monthly break-even point of 1,500 units, because the monthly and yearly figures of break-even point fell on the upper limit of the respective range. In the second instance, it is not so because the monthly and early break-even point fell within the range of 50 toys.

Ans. 10 (Pg. 16): (a) Statement showing total costs indicating each item of cost

60 Rs.

Variable costs: Break fast Lunch Tea Entrance fee Aquarium

for Zoo &

420 1,800

180 300

840 3,600

360 600

1,260 5,400

540 900

1,680 7,200

720 1,200

2,100 9,000

900 1,500

120 Rs.

180 Rs.

240 Rs.

300 Rs.

No. of students

Total (A) Rent of buses (Refer to working note 1) Special permit fee (Refer to working note 2) Daily allowance paid to teacher (Refer to working table) Block entrance fee (Refer to given table) Cost of prizes (Refer to given table) Total (B) Grand Total (A) + (B)

No. of students: (A) Total Costs (Rs.) : (B) [Refer to (a) Part] Average cost (Rs.): (B)/(A)

(c)

97.50

60 5,850

2,700 1,400

100

400

5,400 2,100

150

600

8,100 2,800

200

800

10,800 3,500

250

1,000

13,500 4,200

300

1,200

200

1,050

3,150 5,850

120 9,600

80

300

1,050

4,200 9,600

180 13,500

75

300

1,300

5,400 13,500

240 17,400

72.50

450

1,400

6,600 17,400

300 21,150

70.50

450

1,500

7,650 21,150

(b) Average cost per student at each of the above levels

Statement showing number of students to break-even

51-100

2

101-125

3

126-150

3

151-200

4

201-250

5

251-300

6

No. of students in the trip No. of buses Semi costs

variable

Bus Rent (Rs.) Permit fee (Rs.) Block entrance fee (Rs.) Daily allowance paid to teachers (Rs.) Cost of prizes Total cost (Rs.) No. of students to break even: (Total semi

1,400 100 200

400

2,100 150 300

600

2,100 150 300

600

2,800 200 300

800

3,500 250 450

1,000

4,200 300 450

1,200

1,050 3,150

105

(Rs.3,150

1,050 4,200

140

Rs.4,200/

1,200 4,350

145

Rs.4,350/

1,300 5,400

180

Rs.5,400/

1,400 6,600

220

Rs.6,600/

1,500 7,650

255

Rs.7,650

variable cost/contribution per student)

/ Rs.30 Rs.30 Rs.30 Rs.30 Rs.30 / Rs.30

As the figure of 105 and 140 student fall outside the limits (No. of students in the trip), therefore there are four break-even points in this case viz., 145,180, 220 and 255 students. The college authorities should keep these figures in mind while hiring 3, 4, 5 and 6 buses respectively to avoid losses. The college incurred loss during the previous year s they hired 5 buses and 72% of total students (216 out of 300 students) joined the trip. The break-even in case college authorities hire 5 buses for the trip comes to 220 students. Working Notes: 1. No. of buses required and Rent of buses @ Rs.700/- per bus

No. of students Bo. of buses Rent of buses (Rs.) (No. of buses × Rs.700)

2. Special permit fee:

No. of buses × Rs.50) 100 150 200 250 300

60 2 1,400

120 3 2,100

180 4 2,800

240 5 3,500

300 6 4,200

3. Allowance paid to Teachers (Rs.)

No. of buses × Rs.200) 400 600 800 1,000 1,200

4. Contribution per student towards semi-variable costs Rs.

Collection from each student Subsidy provided by the college

Less: Variable cost per student Contribution per student

65 10 75 45 30

-1-

Decision Making

Answer: 11

1. Material A is not yet owned. It would have to be purchased in full at the replacement cost of `6.00 per unit. Relevant cost is therefore 1,000 units at the replacement Cost.

2. Material B is used by the Company regularly. There is already existing a stock of 600 units. If these are used in the contract, a further 400 units would have to be purchased.

3. Material C: 1,000 units of material C are required. 700 units are already in stock. If it is used for the contract, a further 300 units will have to be purchased at a replacement cost of `4.00 each. The existing stock of 700 units will not be replaced. If they are used for the contract, they cannot be used @ `2.50 each unit. The realisable value of these 700 units @ `2.50 per unit represent opportunity cost.

4. Material D is already in stock and will not be replaced. There is an opportunity cost of using D in the contract. It has following two uses: It can be sold to fetch `1,200 i.e. 600 X `2 It can also be used for E, which would cost `1,500 i.e. 300 X `5. Since substitution is more useful, `1,500 is the opportunity cost.

Summary of Relevant Costs:

` Material A Material B Material C

Material D Other expenses Total Relevant Cost

1,000 units X `6 1,000 units X `5 700 units X `2.5 300 units X `4 300 units X `5

6,000 5,000 1,750 1,200 1,500

550 16,000

Contract should be accepted since offer is of `22,000 in relation to relevant Cost of `16,000.

Answer: 12

Retain Present Machine

Variable Costs: (20,000 units @ `0.30 for 3 Years Sale Proceeds of Old Machine Capital Cost of New Machine

18,000

- - 18,000

Buy New Machine

12,000

(4,000) 7,000 15,000

Relative Benefit of Replacement (6,000)

(4,000) 7,000 (3,000)

Thus, it is advantageous to replace the equipment. Note. Depreciation charge and loss on sale of old machine should be ignored for this decision.

Answer: 13

Relevant costs of producing one unit of the finished product

Cost of material ‘M’ (realisable value) Cost of labour (Being sunk cost) Out-of-pocket expenses

` 80 0 30

110 Allocated overhead is not relevant for the decision. The customer should be charged `110 per unit.

Answer: 14

Solution’s of Decision Making

-2-

(i) The down payment of `2,50,000 represents a sunk cost. The lost profit from subletting the shop of `1,20,000 per annum arrived as: (18,000 × 12) – 96,000 = 1,20,000 is an example of an opportunity cost. The salary amount is not given is also an opportunity cost lost. (ii) The relevant information for running the shop is:

(`) Net Sales Less: Costs (22,02,000 – 2,50,000) (sunk cost excluded for decision making purpose) Gross Margin Less: Opportunity cost from subletting

22,20,000 19,52,000 2,68,000 1,20,000

Profit 1,48,000 As profit is more than opportunity cost, the most profitable decision is to carry on business in the shop.

Ans. 15: Analysis of Cost and profit:

Direct material Direct labour Prime cost Overhead:

Variable factory overhead Fixed factory overhead Administration overheads Selling commission Fixed selling overheads Total cost Profit Rate of profit on costs (2/18) = 1/9

`(lakhs) 3.60 6.40

2.20 2.60 1.80 1.00 0.40

`(lakhs)

10.00

8.00 18.00

2.00

Overhead absorption rate based on direct wages = (8.00 / 6.40) 100 = 125% of direct wages

Break up of new order: Direct Materials Direct Labour Overheads 125% of direct wages Total costs Profit 1/9 Selling Price The following points emerge:

` 36,000 64,000 80,000

1,80,000 20,000

2,00,000

(i) Factory overheads only are to be recovered on the basis of direct wages. (ii) The special order is a direct order. Hence commission is not payable. (iii) The budgeted sales are achieved. Hence all fixed overheads are recovered. Hence, no

fixed overheads will be chargeable to the special order.

Based on the above, the factory variable overheads recovery rate may be calculated as under:

Total variable factory overheads Direct wages

`2.20 lakhs `6.40 lakhs

-3-

Factory overhead rate = (2.20 / 6.40) 100 = 34.375%

Applying this rate the cost of the special order will be as under:

Direct materials Direct labour Overheads 34.375% of direct wages Total costs Price offered Margin

` 36,000 64,000 22,000

1,22,000 1,50,000

28,000 (more than 1/9)

Hence, the order is acceptable at the price of `1,50,000.

Answer: 16 Statement of minimum price which the company can afford to

quote for the new customer (based on relevant cost)

Cost to be incurred to bring the equipment in its original condition. Opportunity cost of the direct material Direct wages: Dept. A : 15 man days × `120 Dept. B : 25 man days × `100 Opportunity cost of contribution lost by department B (`2,500 × `2.30) Variable overheads 25% × (`1,800 + `2,500) Delivery costs Supervisory overtime payable for modification Control device to be used in another job (Refer to working note 1) Net loss on material cost savings, in the original equipment (Refer to working note) Opportunity cost of remaining materials which can be sold as scrap Opportunity cost of sale drawings Total minimum price which may be quoted Working notes: 1. Cost of control device to be used in another job:

1,350 1,050

(10,350) 11,700

11,400 1,500

61,975

1,800 2,500 8,000 1,075

29,700 2,250

` Cost of control device Less: Dismantling & removal cost of control mechanism

(1 man day × `120) Less: Variable cost )25% × `120) Balance cost of control device 2. Net loss on material cost saving of equipment: Loss on material cost saving of equipment Less: Conversion cost (2 man days × `120) Less: Variable overheads (25% × `240) Net loss on material cost saving of equipment

240 60

11,700

12,000

30 10,350

10,500 120

-4-

Answer: 17 Working Notes:

1. The book value of Material K `40,000 is a sunk cost and is not relevant for decision making. 2. The Scrap Value of Material K `10,000 will affect the cashflow and is relevant.

Alternative I Relevant Costs

Material A (Replacement Cost) Direct Labour – Skilled Contribution Lost (Opportunity Cost) Unskilled (not relevant) Variable Overheads Total Relevant Cost

Cost per unit Selling Price Profit

= `60000 / 500 units

= 500 units (`150 – `120)

(600kgs. X `70) (200 hrs X `6) (2000 X `2)

(`) 42,000 12,000 4,000 - 2,000 60,000

= `120 p.u. = `150 p.u. = `15,000

Alternative II 1. The Cost of substitute material `8,000 is relevant. 2. The regular profit of a job `6,000 is not relevant.

Analysis: From the above analysis it is suggested to convert the materials into a specified product.

Answer:18 Working Notes: 1. Relevant cost of labour

Grade

Grade 2 2. Relevant cost of material

Material A

Material B

: `100 per unit, the replacement cost because the material is widely used.

: `250 per unit, the net realisable value, being the opportunity cost.

: Nil, labour cost for Grade 1 labour as it will not be affected by the decision.

: `20 per hour

3. Statement of loss of contribution from the reduction in the sale of product Y. `

Sales revenue per unit: (A) Variable cost per unit Grade 2 labour: (4 hour × `20) Materials relevant variable costs Variable production overheads: (B) (4 hours × `30) Contribution per unit: [(A) – (B)]

80 120 120

` 700

320

380

-5-

Loss of contribution from the reduction in sale of 5,000 units (5,000 units × `380) Less: Avoidable fixed factory overhead cost Net Loss

19,00,000

5,90,000 13,20,000

Relevant costs and benefit analysis from the acceptance of the contract. (`’000)

Sales revenue: (1) (20,000 kgs. × `1,000) Relevant costs: Labour: Grade 1 Grade 2 (20,000 kgs. × 6 hours × 20) Material A (20,000 × 2 units × `1,000) Material B (20,000 kgs. × 1 litre × `250) Variable production overhead (20,000 kgs. × 8 hours × `30) Total variable cost Incremental fixed costs

4,000 5,000 4,800

16,200 2,280

18,480 Add: Loss of contribution on product Y (Refer to working note 3) Total relevant cost: (ii) Excess of relevant revenue over relevant cost:

19,800 200

NIL 2,400

20,000

Advice to A Limited: to accept the contract, as it will enhance the pre-tax operating income by `2,00,000

Answer: 19:Working Notes: Calculation of contribution margin The company expects that each per cent point increase in on-time performance will result in revenue increase of `18,000 p.a. Additional revenue increase = `18,000 X 10 = `1,80,000 Contribution margin on additional revenue = `1,80,000 X 45/ 100 = `81,000

Costs incurred annually on the installation of new scheduling and tracking system Additional annual cost Interest Foregone on Fixed (Opportunity Cost) (10% X `2,00,000) deposit Total Costs

Expected Savings in costs on the installation of new scheduling and tracking system Contribution margin from additional annual revenue (45% X `1,80,000) Decrease in variable costs due to reduced numbers of (3,000-1,000) X `50 carton lost

(`) 1,50,000 20,000

1,70,000

(`) 81,000 1,00,000

-6-

Total savings in cost Net saving (1,81,000 - 1,70,000)

1,81,000 11,000

Suggestion: The expected savings are more than annual costs, hence it is suggested to install a new scheduling and tracking system.

Answer: 20 Statement showing Revised Cost Estimates:

1. Steel Sheets (`12/kg. x 5,000kg.) 2. Steel Rods (1,000 kg. @ `17 kg.) 3. Bearing, hardware items, etc. 4. Labour Cost 5. Overheads:

Fabrication Shop (500 hrs @ `25) Welding Shop (300 hrs @ `16) Planning engineers cost Design engineers cost Total Estimated Relevant Cost

`60,000 17,000 15,000

Nil

12,500 4,800

Nil Nil

1,09,300

Relevant costs are estimated future costs pertinent to a decision. Imputed costs do not form part of relevant costs. All costs accumulated for stock valuation purposes may not be relevant cost. Reasons for Variation in the Cost Elements

1. Current rate of steel sheets is quite relevant. Past rate of `12 per kg has no impact on the decision and therefore not adopted in the cost estimates.

2. Steel rods purchased five years ago cannot be used (non- moving) and as such it represents sunk cost. This material can now be substituted for alloy steel rods (`17/kg). Alloy rods are cheaper than steel rods and therefore relevant to the decision.

3. Fixed costs are past costs, not relevant to the decision. Labour costs are fixed in nature. 4. It is assumed that Fabrication Shop is working at optimum level. Therefore rate charged from

outsiders (`25 per hour) is relevant. 5. It is assumed that Welding shop is not working at full capacity. Therefore variable cost of `16 per

machine hour is adopted. 6. Planning and design engineers costs are fixed cost and, therefore, irrelevant.

Answer: 21 Revised Cost Estimate

1. Direct Material: - Paper

- Ink 2. Direct Labour (Skilled) Normal (250 hrs x `4)

Overtime (125 hrs x `1) 3. Variable Overhead (350 hrs x `4) 4. Printing Revised Cost Estimate

Working Notes:

1. With no alternative use, the paper would not be replaced; the alternative, therefore, being to scrap the stock receiving proceeds of `2,500.

2. The surplus ink could not be used or sold and therefore the whole cost of the ink purchased should be charged to the cost of the programme.

3. The direct employees are currently usefully employed, therefore, their wage cost is being recovered from an existing customer. Before, transferring them to the work on the programme, the ability of the programme work to bear this cost must be determined.

2,500 3,000

1,000 125

5,500

1,125 1,400

600 8,625

-7-

4. The overtime premiums are directly caused by the programme work, which should be able to bear this additional cost.

5. There is no additional cost associated with the employment of the unskilled labour. Current idle time 200 hrs Printing Work 75 hrs (No additional cost)

125 hrs Week-end work 25 hrs Paid time off 50 hrs The 50 hrs of paid time off is more than covered by the 125 hrs of idle time, which is also paid for and, therefore, there is no additional cost.

6. Variable overhead is the incremental cost. 7. The variable overhead and other variable costs associated with running the printing press have been

separately dealt with. The additional recovery required is, therefore, the lost contribution associated with 200 printing press hours.

8. Fixed production overheads are not associated with incremental cashflows, and therefore should be ignored. a) The cost of estimating time is a small cost, since it has already been incurred. It does not involve

incremental cash flow. Therefore, it has been ignored. b) In short-term decision making, resources usage is best measured by using ‘variable cost’ which

change in proportion to changes in output. When variable cost is matched with the sales revenue with which it is associated, the resulting difference or contribution gives a good indication of the expected benefit to the organisation of any course of action. If fixed assets are unaffected by a decision, contribution will be close approximation of cash flow and therefore, it is very real figure which may also be usefully used as a basis for ranking alternatives where limiting factors are involved.

c) For evaluating the economic benefit derived from a product, it is necessary to match the revenue generated with he cost incurred. Opportunity cost represents the benefit forgone for taking one course of action rather than alternative. It gives a measure of sacrifice made in order to generate income. Conventional contribution approach normally extracts variable costs from the internal costing records (i.e., stock accounts, etc.). Opportunity costs may be derived from internal or external sources depending on such factors as whether there are alternative uses for internal resources consumed and whether, if used, they would be replaced.

Answer:22: Research Project

Particulars

Project cost till date Sale price of the project

Cost of materials received

Cost of labour Contribution lost on the alternative use

Absorbed Fixed overheads

Relevancy

Not relevant Relevant

Not relevant

Not relevant Relevant

Reason

Sunk cost Incremental revenue/opportunity gain Sunk cost Avoidable/opportunity cost Common costs Opportunity cost [Sales – (Prime cost labour) Sunk cost

(125)

Amount (Rs’000s)

400

15 Cost of disposal of materials Relevant

Not relevant

Cost of Research Staff Relevant Incremental / out of pocket (160) Common costs

Sunk costs

Redundancy and severance Not relevant pay Share of General Not relevant

-8-

B ildi Total incremental inflow if the project is proceeded with

Decision: Better to continue the project.

Answer. 23 Statement of cost of product NP Particulars

Direct materials A B

130

Total cost (100000

units)

2,50,000 60,000

1,20,000 6,00,000

75,000

50,000

- 36,000 24,000 30,000 5,000

1,25,000 1,50,000

(`) Cost per unit

C Direct labour

Skilled (25,000 hrs X `3) Unskilled Opportunity loss (25,000 X `2)

Variable overhead (1,00,000 X 1.50) Fixed Overheads: Factory overheads: Addl. Overheads- Foreman

Supervisor Depreciation: Type P

Type Q Total Costs profit Sales

(1,00,000 X 2.50) (60,000 X 1.00) (40,000 X 3.00) (1,00,000 X 6.00) 10,30,000 10.30

1.25 1.50

60,000

35,000 14,00,000

4,00,000 18,00,000

0.60

0.35 14.00.

4.00 18.00

Working Notes: 1. Cost of Direct Material Material A- It is in regular use and hence replacement cost of `2.50 will be charged. Material B- Total requirement is of 1,00,000 units:

Stock available 60,000 units - opportunity cost `1.00 each 40,000 units - purchase price `3.00 each.

Material C- Purchase price of `6.00

2. Cost of Direct Labour Skilled Labour: (i) 1,00,000 units at `0.25 per hour

(ii) Loss of contribution on existing product opportunity cost 25,000 X 2=`50,000

Unskilled labour: Available in surplus and is to be paid even without work. Hence, not relevant 3. Cost of Additional Staff

(`) 36,000 Foreman

Supervisor 24,000 Total 60,000

4. Variable Overheads 5. Fixed Overheads 6. Depreciation

Type P:

Type Q:

`1.50 per unit is relevant cost Not relevant hence excluded

The machine is used on other product. Hence, replacement cost is relevant Depreciation =`1,60,000-1,30,000 =`30,000 Since it can be sold if not used resale value is relevant. Depreciation =`22,000-`17,000 =`5,000

-9-

7. Market Survey Costs: It is a sunk cost. Hence it is not a relevant cost.

Answer: 24 Working Notes:

1. Machine manufacturing cost Costs of `50,000 incurred to date in manufacturing the machine is irrelevant for the decision, since It is a sunk cost. The payment of `15,000 received from the customer prior to the liquidation is also not relevant for decision making.

2. Material Cost. The purchase cost of `6,000 of materials bought in the past is irrelevant for decision making. Only the scrap value of materials i.e.`6,000 is relevant for decision making since it is the opportunity cost of materials bought in the past.

3. Labour Costs. Opportunity cost of labour when the workforce, is in short supply, and switched to another job,it could fetch the additional contribution of (`30,000-`8,000-`12,000)=`10,000.

4. Consultancy fees (`) 4,000 Cost of completing the work

Cost of canceling the contract 1,500 Incremental cost of completing of work 2,500

5. General Overheads The general overheads are absorbed on allocation and therefore, these costs are not relevant for the decision.

Statement showing economics of proposition (`) Revenue from completing work 34,000 Less:

2,000 Materials (opportunity cost) Labour: Actual costs 8,000

18,000 Opportunity costs 10,000 Cost of consultancy (Incremental cost) 2,500 22,500

Additional profit by accepting the offer of new customer in completion of the 11,500 work. In view of incremental profit of `11,500, the offer of new customer can be accepted.

Answer: 25: For solving this question, it is necessary to take the following into consideration. SV Ltd. Has two departments A and B. Dept. A is manufacturing FLOTAP, but Dept. B is manufacturing the containers for this product. It also stores this product. This is the existing situation. Now three alternatives are given. Alternative 1.- Close Dept. B and manufacturing & storing may be given to PH Ltd. Alternative 2 – Continue Dept. B and manufacturing may be given to PH Ltd and storing to Dept. B. Alternative 3 – Continue Dept. B, Manufacturing may be done by Dept. B but storing may be given to PH Ltd. Company should either select one of the alternative or continue the existing practice. Working Notes: (i) (`)

4,20,000 Direct Materials including germicide th 1,20,000 Use of germicide (1/5 of `6,00,000)

Direct materials other than germicide 3,00,000

This material will be avoidable cost if Division B is to Close-down. (ii) 10% of all materials = 10% of `3, 00,000

(a) Savings: `3, 00,000-`30, 000=`2, 70,000 if manufacture is given to PH Ltd. And storage is with SV Ltd.

(b) Savings: 3, 00,000- 90% of `3, 00,000=`30, 000. If manufacture is done by SV Ltd and storage given to PH Ltd.

(iii) Direct Labour cost Less: Terminal benefit if B is closed Avoidable cost, if Dept .B is closed (saving)

(`) 3,00,000

45,000 2,55,000

- 10 -

If manufacturing is given to PH Ltd. And SV Ltd. continues to store the product, saving on account of labour retrenchment will be only `15,000.(It means in this alterative 3,00,000-15,000=2,85,000 will be spent any way and avoidable cost will be only `15,000). If manufacturing is done by SV Ltd. Then Labour force will continue. It means impact of labour cost in 3rd alternative will be nil.

(iv) Supervisory staff will be transferred to another department in the lst alternative. It means cash flow will not be affected. In the second and third alternative, supervisory staff will be retained and it means no additional cash flow or relevant cost due to decision.

(v) Depreciation does not affect the cash flow. Therefore it is not relevant for these decisions.

(vi) The hire charges of warehouse is `54,000 per annum. The remaining space of the warehouse is idle. It means, when department B is closed, cash outflow of `54,000 will be avoided. Therefore `54,000(and not `27,000) is the avoidable cost for this decision. If Department B continues, this expenditure of `54,000 continue. Therefore cash flow for alternatives 2 and 3 will not be isturbed on this account.

(vii) Maintenance of machine is required for manufacturing. If means `21,600 will be avoidable cost for alternative 1 and 2. In 3rd alternative this cost will continue to be there. Besides this machine will not be required in alternative 1 and 2. It will be sold at `1,50,000.It will be a one time cash inflow for alternatives 1 and 2.

(viii) Miscellaneous overhead of `94,500 will be avoidable cost for alternative 1. For 2nd alternative 80 % of this i.e `75,600 will be avoidable cost. For 3rd alternative 20% of `94,500 i.e. `18,900 will be avoidable cost.

(ix) Germicide- Stock: Stock in 2002 Used last year (1/5th) Balance Stock

It is given that original price is `3,000

Therefore, `4,80,000/`3,000=160 tonne Germicide is there.

(x) Germicide-value Alternative 1 : Storage is done by PH Ltd. Therefore it will be sold at `2,400 per tonne. Cash inflow

will be 2,400 X 160=`3,84,000. Note that original price and replacement cost are irrelevant for the decision.

10% of all material will be used. It means 90% of 160 tonne will be sold. Cash inflow will be 160 X 0.90 X `2,400= `3,45,600

(`) 6,00,000 1,20,000 4,80,000

Alternative 2 :

Alternative 3 : In this situation storage is done by PH Ltd. Therefore only 10% of whole quantity of 160 tonne will be sold in market at `2,400 per tonne . Cash inflow will be 16 X `2,400 `38,400.

(The replacement cost is irrelevant information in the question and it will be relevant only, when germicide has competing demands.)

(xi) Machine is used for manufacturing of containers. It is not required in alternatives 1 and 2. Therefore , it will be sold and there will be one time cash inflow of `1,50,000 under alternatives 1 and 2. Written down value is irrelevant for decision under consideration.

(`) Alternative 1 Alternative 2 Alternative 3

Division B Close Continue Continue Manufacture of containers PH Ltd PH Ltd. SV Ltd. Storage of product PH Ltd. SV Ltd. PH Ltd. Cash Inflows

(Including avoidable cost)

- 11 -

Direct materials other than germicide Direct labour Rent of a part of warehouse Maintenance of machine Miscellaneous overhead Total avoidable cost p.a. (A) Cash outflows Contract fee to PH Ltd. For Manufacturer For packing and storage Total outflow (B) Net Cash outflow p.a. (A-B)-( C ) Total cash outflows for 4 years ( C X 4) One time income Sales of germicide Sale of machine Net cash outflow

3,00,000 2,55,000

54,000 21,600 94,500

7,25,100

7,50,000 1,50,000 9,00,000

(1,74,900) (6,99,600)

3,84,000 1,50,000

(1,65,600)

2,70,000 15,000

- 21,600 75,600

3,82,200

7,50,000 -

7,50,000 (3,67,800)

(14,71,200)

3,45,600 1,50,000

(9,75,600)

30,000 - - -

18,900 48,900

- 1,50,000 1,50,000

(1,01,100) (4,04,400)

38,400 -

(3,66,000)

Recommendations: All the alternatives result in net cash outflow. Therefore it is interest of SV Ltd. To continue and to manufacture containers and store them in Division B.

Answer: 26: Comparative Statement of Relevant Costs for use of own distribution division or use of Countrywide distributions. (`’000) Particulars Own Distribution Countrywide Distribution

95-96 96-97 97-98 95-96 96-97 97-98 Relevant Cash outflow: Operating Costs 2,100 2,100 2,100 - - - Sub-Contract costs - - - 1,950 1,950 1,950 Total 2,100 2,100 2,100 1,950 1,950 1,950 Less: Relevant cash inflow: Sale of delivery vehicle On 1-4-2002 - - - 600 - - On 31-3-2005 - - 240 - - - Net Relevant Cash outflows: 2,100 +2,100 +1,860 1,350 +1,950 +1,950 Total =6,060 =5,250 Suggestion: From the above comparative statement it is observed that the net relevant cash outflow is more in case of own distribution. Hence, selection of countrywide distributors is recommended. It is based on the assumption that no portion of the common corporate cost of which `3,00,000 is apportioned to distribution division which would be avoided even if, the distribution division is closed down. (b) Reasons for reluctancy to accept countrywide distributors in distribution of Soft Drinks. (1) Loss on Sale of Delivery Vehicles presently owned by the company: (`)

Cost of Vehicles Less: Depreciation for 2003-04 Book Value on 1-4-2004 Less: Sales realization Book Loss on sale of Vehicles

(8 Vehicles on 1-4-2003)

(8 Vehicles X `75,000)

19,20,000 4,20,000

15,00,000 6,00,000 9,00,000

(`’000) 1996-97

660 330

(`’000) 660

6. Possibility of reduction in reported income as per Security Analyst’s recommendation Forecast of operating income as per Security Analyst

Particulars 1995-96 Estimated Profit when own distribution division is used 630 Net income if the offer of countrywide distributors is accepted 630

Working Notes: Projected Profit for 95-96

- 12 -

Add; Depreciation avoided Add: Saving in operating cost (`2,100- `1,950)

Less: Book loss on the disposal of delivery vehicles Net income, if Countrywide distributors selected

Analysis: In view of short- run benefit, countrywide distributors can be opted. But when the long-run benefits are recognized, and to focus on customer needs, the company’s own distribution function is recommended.

Answer: 27: Statement showing value of total work undertaken by X Ltd. at customer’s price

(`’000) Material costs (for appliances covered under agreement) [Rate to working note 1 (i)] Material costs (for appliances not covered under agreement) [Refer to working note 2 (i)] Labor cost (for appliances covered under agreement) [Refer to working note 1 (ii)] Labour cost (for appliances not covered under agreement) [Refer to working note 2 (ii)] Total receipts Break up of receipts:

Big appliances Small appliances

60% 40%

Profitability Statement (`’000)

Option 1 Income Big appliances

Small appliances

Total receipts: (A) Costs: Material

Heat, rent, light etc. Management costs Service staff costs Transport costs Total costs: (B) Profit: [(A) – (B)]

Recommendation: Option 3 is most profitable one. Working Notes: 1. Material and labour cost (for appliances under after sales agreement):

129.6 (60%×`216)

936 .

1,065.6

320 40%×(825+275)

137.5% 125 108 230

25 808

257.6

Option 2

1,404

86.4 (40%×`216)

1,490.4

480 60%×(825+275)

137.5% 50 83

440 220

1,273 217.4

Option 3

1.404

936 .

2,340

800 (825+275)

137.5% 150 150 750 230

2,080 260

1.404 936

240 _____ 2,340

1,000

275

825

420 150

1,230 900 330

- 13 -

` (i) Cost of Material per unit charged to customer’s by X Ltd.

(`100 + 10% x `100 + 25% x `110) Cost of material charged to customer’s by X Ltd.

137.50

Rs.60,000 × `137.50 Rs.10

(ii) Cost of labour charged to customer by X Ltd.

8,25,000

Rs.1,00,000 × `100 Rs.10

2.

10,00,000

Material and labour cost (for appliances not covered under sales agreement): `

(i) Cost of material charged to customer by X Ltd. Rs.20,000 × `137.50

Rs.10 (ii) Cost of labour charged to customer by X Ltd.

2,75,000

Rs.36,000 × `100 Rs.15

Answer: 28

2,40,000

Statement of relevant cost of Mahila Griha Udyog Industries If the contract is accepted/rejected

Decision Relevant costs (if contract is

accepted) `

18,00,000 -

. 18,00,000

1,35,000

for the use of -

3,00,000 5,70,000

Relevant costs (if contract is rejected)

`

- Cash inflows Contract price Sale of material Y (Refer to working note I) Total cash inflows: (A) Cash outflows Material X substitute (Refer to working note 2) Adaptation required obsolete material X Material Z Replacement of semi-skilled labour by skilled labour (Refer to working note 3) Non-skilled labour cost (Refer to working note 4) Supervisory staff cost (Refer to working note 5) Avoidable overheads 1,25,000 -

35,000 -

3,00,000 -

27,000

- -

-

2,10,000 .

2,10,000

- 14 -

(Refer to working note 6) Total cash outflows: (B) 14,65,000 27,000 Net cash inflows: (A) – (B) 3,35,000 1,83,000 The net benefit on accepting the contract is : `3,35,000 – `1,83,000 = `1,52,000. Conclusion The contract should be accepted as it yields a net incremental cash inflow of `1,52,000. Working notes: 1. Material Y will have to be paid for whether or not the contract is accepted, therefore its cost is irrelevant.

The relevant cost figure here is that which has an opportunity cost of `2,10,000. This means that the company can resell material Y at this price.

2. Regarding material X, if the contract is accepted, alterative material will have to be purchased for the other product at a cost of `1,35,000. If the contract is rejected material X will be adapted for a product not included in the list of special range of namkeens at a cost of `27,000.

3. The relevant skilled labour cost of `5,70,000 is the extra cost to the company because of this contract. It is the replacement cost of semi-skilled labour by skilled labour.

4. Non-skilled labour cost is the incremental cost of the contract. 5. If the company accepts the contract it will have to pay `35,000 for the two position that the supervisory

staff can replace. 6. Only `1,25,000 of avoidable overheads are relevant to this contract.

Answer: 29

M/s Ranka Builder’s Statement of relevant costs on the

Acceptance of contract form Excel Ltd. (Figure in lakh of `)

S.No. Particulars Basis for cost to relevant

the be

Relevant cost if contract is accepted `

20

-

Incremental

Replacement Opportunity Incremental

10

8 5

10 9

7 (Sunk cost)

-

Irrelevant cost if the contract is

accepted ` 1.

2.

3. 4.

Land cost (Refer to working note 1) Drawings and design

Registration Materials : Cement and sand Bricks and Tiles Steel Others (Refer to working note 2)

5. Labour : Skilled Unskilled

Opportunity Incremental

2 8

- 15 -

Supervisor’s Salary

6. Overheads : General

Depreciation

Replacement machine

7.

cost of

Opportunity foregone

Relevant (avoidable)

4

-

7

10

93

5 (Sunk Cost)

6 (Sunk Cost)

Estimated profit foregone on other project Total

Decision : Since the offer price of contract is `1 crore and its total relevant cost is `93 lacs; these figures clearly shows that the offer should be accepted. Working notes : 1.

Total cost of 3 grounds of land Cost of ground of land will be borne by Excel Ltd. Cost of 1 ground of land will be borne by M/s Ranka Builders

`(Lacs) 60 40 20

2. Others material cost is `10 lacs, it includes material worth `2 lacs, relating to interior decoration, which is a sunk cost, this material can be sold for `1 lac, (which is a relevant opportunity cost) and `8 lacs, material is an incremental cost. Hence total relevant cost of others material is `9 lacs. (`8 lacs, incremental + `1 lac, opportunity cost).

3. Since the equipment can also be used on ths contract. Its current replacement price is `32 lacs, and after one year its cost will be `25 lacs. Therefore the relevant opportunity cost of machine is : (`32 lacs – `25 lacs).

Answer: 30 Alternative 1 – (Conversion versus immediate sale)

` Sales revenue 900 units at `300 per unit (Refer to working note 1) Less: Relevant costs Material XY opportunity cost (Refer to working note 2) Material A – units @ `90 per unit (Refer to working note 3 Material B – 1,000 units @ `45 per unit (Refer to working note 4) Direct Labour : Unskilled – 5,000 hours @ `3 per hour Semi-skilled Highly skilled – 5,000 hours @ `11 (Refer to

15,000 Nil

55,000

` ` 2,70,000

21,000

54,000

45,000

70,000

- 16 -

working note 5) Variable overheads 15,000 hours @ Re.1 (Refer to working note 6) Extra selling and delivery expenses Extra advertising Fixed advertising (To remain same, not relevant) Excess of relevant revenues Alternative 2 – (Adaptation versus Immediate Sale) Saving on purchase of sub-assembly Normal spending – 1,200 units @ `900 per unit Less: Revised spending – 900 units @ `1,050 per unit (Refer to working note 7) Less: Relevant costs: Material XY opportunity cost (Refer to working note 2) Material C – 1,000 units @ `37 (Refer to working note 8) Direct labour Unskilled – 4,000 hours @ `3 per hour Semi-skilled Highly skilled – 4,000 hours @`11 per hour (Refer to working note 5, 6) Variable Overheads – 9,000 hours @ Re.1/- per hour (Refer to working note 6) Fixed overheads Net relevant savings

Evaluation : The evaluation of two alternatives clearly shows that Alternative 1, yields higher net revenue of `8,000 (`20,000 – `12,000). Hence because of higher net revenue of Alternative 1, it is advisable to convert material XY into a specialized product. Working notes : 1. There will be a additional sales revenue of `2,70,000 if Alternative 1 is chosen. 2. Acceptance of either Alternative 1 or 2 will mean a loss of revenue of `21,000 from the sale of the

obsolete material XY and hence it is an opportunity cost for both of the alternatives. The original purchase cost of `75,000 is a sunk cost and thus not relevant.

3. Acceptance of Alternative 1 will mean that material A must be replaced at an additional cost of `54,000. 4. Acceptance of Alternative 1 will mean diversion of material B from the production of product Z. The

excess of relevant revenues over relevant cost for product Z is `180 (`390 – `210) and each unit of product Z uses four units of material B. The lost contribution (excluding the cost of material B which is incurred for both alternatives) will therefore be `45 for each unit of material B that is used for converting the obsolete materials into a specialised product.

Nil

12,000 Nil

44,000 56,000

9,000 1,23,000

. 12,000

21,000

37,000

10,80,000 9,45,000 1,35,000

27,000 18,000 45,000

Nil .

20,000

2,50,000

15,000

- 17 -

5. Unskilled labour can be matched exactly to the company’s production requirements. Hence acceptance of either alternative 1 or 2 will cause the company to incur additional unskilled labour cost at `3 for each hours. It is assumed that the semi-skilled labour will be able to meet the extra requirements of either alternatives at no extra cost to the company. Hence, cost of semi-skilled labour will not be relevant. Skilled labour is in short supply and can only be obtained by reducing the production of product L, resulting in a loss of contribution of `24 (given) or `6 per hour of skilled labour. Hence the relevant labour cost will be `6 (contribution lost per hour) + `5 (hourly rate of skilled labour) i.e. `11 per hour.

6. It is assumed that for each direct labour of input, variable overhead will increase by Re.1 hence for each alternative using additional direct labour hours, variable overheads will increase.

7. The cost of purchasing the sub-assembly will be reduced by `1,35,000 if the second alternative is chosen and so these savings are relevant to the decision.

8. The company will incur additional variable costs, of `37 for each unit of material C that is manufactured, so the fixed overheads for material C viz. `18/- per unit is not a relevant cost.

Ans. 31 Calculation minimum price to be quoted for a quotation, based on relevant costs only Opportunity cost of:

(1) Retaining materials already in the original machine - Sale of Brass scrap - Sale of Steel scrap - Balance material , cost of scrapping )saved)

(2) Conversion materials - Department M - Department A

(3) Conversion work (a) Department M

Labour Variable overhead Contribution foregone

(b) Department A Labour

(`)

1,00,000 25,000 (5,000)

12,000 3,000

60,000 12,000

1,80,000

Nil

2,52,000

Variable overhead 6,000 63,000 Off-loading cash flow foregone 57,000 60,000 (4) Sales proceed of design and specifications

(5) Incremental fixed overhead-cost of supervision 10,000 Minimum price to be quoted 5,20,000

Note: For the above minimum price of `5,20,000 profit can be added. The existing overheads are committed costs and are not relevant for decision making.

Answer: 32 1. Value of Material X in stock : (which can be used as substitute for other materials)

= `54,000 X 90 / 100 = `48,600

2. Value of Material X for which firm order has been placed = `76,000 X 90 / 100 = `68,400

3. Value of Material Y in stock = 2 times x `62,000 = `1,24,000

4. Irrelevant Costs: Following costs are irrelevant therefore, they have been ignored Site manage costs – being fixed costs Depreciation of plants Interest on capital Notional interest in estimated working capital

- 18 -

Head office expense allocated to contracts.

(`) Contract AX 48,600 68,400 1,50,000 - -

2,15,000 17,000 (15,000) -

4,84,000 7,20,000 2,36,000

Contract BX Comparative statement of Net Benefit resulting from each contract Particulars

Material X – in stock Material X – firm orders placed Material X – not yet ordered Material Y - in stock Material Z – not yet ordered

Labour – to be paid Travel and other expenses Income from the hire of plant Penalty for rescinding the contract ‘AX’ is relevant Total Cost Contract Price Expected net benefit

(at current cost)

(at replacement cost)

(future outflow)

1,24,000 1,78,000

2,75,000 14,000

70,000

6,61,000 8,80,000 2,19,000

Advice- Since the expected net benefit of contract AX, is more than Contract BX, it is suggested to continue with Contract AX.

Answer: 33:Relevant Cost of ‘Jeet’ bicycle Material Labour Variable Overhead (0.4 X 300) Cost of Capital (0.15 X 6,00,000) / 25,000

300.00 200.00 120.00

3.60 623.60

If Star Bicycle company accept the offer of making ‘Jeet’ for the chain stores the loss in contribution due to sale of Smart is going down by 1,00,000 units is relevant, which causes a loss of `(899-300-200-120)= `279 The price of Jeet then should be `623.60 + 279 = `902.60. This is higher than the price of `800 as offered by the chain store. So, the offer cannot be accepted. Since the chain store has decided to launch a product like ‘Jeet’, it will do so whether or not Star Bicycle Company accepts the proposal as there is excess capacity in the industry it will be able to do so. In that case, the loss of contribution is `279 is not relevant and Star Bicycle Company can accept the proposal of the chain store. Star Bicycle Company should have a closure look in the market condition and the chain store’s ability to get a replica of ‘Jeet’ from other manufacturer before Star Bicycle Company reaches a final decision.

Answer 34: Minimum recommended price per unit of 5,000 units of a product (obsolete model) of ACE Ltd. (i) Historical cost of `11.50 per unit of 5,000 units of a product is irrelevant (as it is a sunk cost) for

determining the recommended price per unit. (ii) If at all this model is sold in the market through normal distribution channels it will entail a variable selling

and distribution cost of `3 per unit. (iii) If the stock is disposed off by asking someone to take them on “as is where is basis”, the company would

have to spend `5,000 over 5,000 units i.e. `1/- per unit. In view of (ii) and (iii) the option of selling 5,000 obsolete units of the model using regular channels will nave a

differential cost of `2 (`3 – Re.1) per unit. Recommendation: Hence, if the company can get anything more than `2/- per unit, then it is worthwhile to sell the stock of 5,000 units and earn an additional contribution.

- 19 -

Answer: 35

Statement of Increment Cost and Incremental Revenue Capacity in units (a) 200 3000

Unit cost `

(b) 40 35

Total cost ` (c)=(a)×(b) 80,000 1,05,000 (`1,05,000 – `80,000)

4000 34 1,36,000 `1,36,000 – 1,05,000)

5,000 32 1,60,000 24,000 (`1,60,000 – `1,36,000)

6,000 31 1,86,000 26,000 (`1,86,000 – `1,60,000)

Decision: At 4,000 units capacity told sales revenue is `3,76,000 and the total cost is `1,36,000 leaving a profit of `2,40,000. The profit figure at this level clearly shows that the fixed expenses stand fully recovered. Hence, we have to take incremental cost for further level levels of output. For an additional sales of 2,000 units

incremental cost is `50,000 (`1,86,000 – `1,36,000) and the cost per unit is `25

- - -

- -

31,000 94 3,76,000

Incremental cost ` (d) - 25,000

Unit price ` (e) 100 95

Total price ` (f)=(a)×(e) 2,00,000 2,85,000

Incremental revenue ` (g) - 85,00,000 (`2,85,000 - `2,00,000) 91,000 (`3,76,000 – `2,85,000) -

Rs.50,000 2,000 units

Since the price quoted per unit is `28, which is more than `25, therefore, the order should be accepted.

Answer: 36 ABC Ltd is facing Direct material constraint and special steel plates are in short supply but the stock is available only 500 M.T. Alternatives available to maximize profit Alternative I: - Manufacture and Supply only 20,000 cylinders at the risk of reduced order in future. Alternative II: - Make 40,00 upper halves, buy 40,000 button halves from outside and supply 40,000

cylinders.

Profitability Statement

No. of Cylinders

Sales Realisation @ `700 Welding and other costs @ 30 Transportation, loading etc. (at `5 per half) Net Differential Income

Alternatives I

20,000 140 (6) -

134

II 40,000

280 (12) (2) 266

Differential Cost 140 (6) (2) 132

The additional net income when 40,000 halves are purchased is `132 lakhs which is the maximum price that ABC Ltd. Can afford to pay keeping for itself at least the contribution it would earn by its own operation (a).

- 20 -

i.e. The Price = ` 120 Lakhs 40,000

= `330 per bottom half.

Answer: 37 Option 1: Profitability to continue only in season period Particulars Incremental Revenue (i) Differential cost: Cost of Sales Supplies Electricity Charges Total (ii) Incremental revenue over differential cost (i)-(ii) Less: Cost of advertisement Net incremental revenue

Gift shop 6,000

3,300 300

40 3,640 2,360

Restaurant 8,000

4,400 800 160

5,360 2,640

(`) Lodge 20,000

- 1,600

400 2,000

18,000

Total 34,000

7,700 2,700

600 11,000 23,000 12,000 11,000

Working Notes: (1) Incremental revenue Gift shop Restaurant Lodge

(2) Differential cost of sales Gift shop Restaurant

(`) (`48,000 X 10/80) (`64,000 X 10/80) (`1,80,000 X 10/90)

Total

6,000 8,000

20,000 34,000

(`) 3,300 4,400 7,700

(`) (`6,000 X 5/100) (`8,000 X 10/100) (`20,000 X 8/100)

Total

300 800

1,600 2,700

(`) (`900-`640) X 10/80) (`3,200 –`1,920)X 10/80) (`13,500-`9,900) X 10/90)

Total

40 160 400 600

Total

- 1,59,800 1,59,800

46,200 19,400 60,000 18,920 4,400

1,48,920 10,880

(`6,000 X 55/100) (`8,000 X 55/100)

Total

(3) Differential cost of supplies Gift shop Restaurant Lodge

(4) Differential cost of Electricity Charges Gift shop Restaurant Lodge

Option 2: Profitability to continue throughout the year including season and off season periods (`) Particulars Gift shop Restaurant Lodge Incremental Revenue:

- - - Season Period Off Season period 34,200 45,600 80,000 Total (i) 34,200 45,600 80,000 Differential Cost Cost of Sales 19,800 26,400 - Supplies 1,800 4,800 12,800 Salaries 9,600 9,600 40,800 Electricity –Fixed 1,280 3,840 13,800 Electricity- Variable 240 960 3,200 Total (ii) 32,720 45,600 70,600 Net incremental Revenue (i)-(ii) 1,480 - 9,400

Working Notes: (a) Incremental Revenue in off season period (`)

- 21 -

Gift shop Restaurant Lodge

(b) Differential Cost of Sales Gift shop Restaurant

(`48,000 X 2 X 30 / 80X 95/100) (`64,000 X 2 X 30 / 80X 95/100 (`1,80,000 X 2 X 40 / 90X 50/100

Total

34,200 45,600 80,000

1,59,800

(`) 19,800 26,400 46,200

(`36,000 X 55/100) (`48,000 X 55/100)

Total

(c) Differential cost of supplies Gift shop Restaurant Lodge

(d) Differential cost of Salaries Gift shop Restaurant Lodge

(`) (`36,000 X 5/100) (`48,000 X 10/100) (`1,60,000 X 8/100)

Total

(`) (`4,800 X 2) (`4,800 X 2) (`25,200-`4,800) X 2)

Total

(`) 1,280 3,840

13,800 18,920

(`) 240 960

3,200 4,400

9,600 4,600

40,800 60,000

1,800 4,800

12,800 19,400

(e) Differential cost of Electricity (Fixed Element) Gift shop (`640 X 2) Restaurant (`1,920 X 2) Lodge (`6,900 X 2)

Total

(f) Differential cost of Electricity (Variable element) Gift shop (`900-`640) X 30 X2 /80) Restaurant (`3,200 –`1,920) X 30X 2/80) Lodge (`13,500-`9,900) X 40 X 2 /90)

Total

Decision : By adopting the Option 1, the net increase in incremental revenue by `120 (i.e. `11,000-`10,880) over the Option 2.Therefore, Option 1 is suggested to adopt. Incremental profitability by adopting strategies of both advertisement insertions and operating during off season period. (`) Incremental Revenue with Advertisement 11,000 Incremental Revenue with the continue of operations during off season 10,880 Total incremental revenue 21,880 Therefore, both the strategies can be implemented simultaneously for increase of profitability of the organization.

Answer: 38 (a) Consequences of undertaking: Nagpur & Delhi Contracts

Nagpur Contract Contract revenue Sales of materials held for the Nagpur contract (Note 1) Saving in material purchases by alternative use of materials of Delhi contract (Note2) Hire of plant

Incremental costs:

(`’000) Delhi Contract

170 180 24

48 2

220 204

- 22 -

Materials to be ordered (Note 3) Project manager’s travel, lodging etc. Local labour Penalty for canceling the other contract

Excess of revenue/saving over incremental costs

40 4

70 8

122

98

34 4

56 16

110

94

Note: (1) If the Delhi job is undertaken sales of materials no longer required for the Nagpur job would be

(`) Materials held, at cost Current money value (add 60%) Sales price )x90%) Less: transportation etc. costs (16.67%) Net sales revenue

(2) If the Nagpur job is undertaken, the materials for the Delhi job might be refused on a different contract, thereby saving the purchase of additional materials: (`’000)

Materials held Contracted for Cost of unwanted materials Saving in purchase on different contract (80%)

20 32

28.8 4.8

24.0

24 36 60 48

(3) The materials contracted for to carry out the Delhi job must be paid for whatever happens. Although not yet received, they must be paid for whichever (if either) contract is undertaken. It is therefore not an incremental cost chargeable to the Delhi contract. For similar reason, materials already held are not an incremental cost to their respective contracts. The alternative use of materials not required is , however, significant and this has been taken into account on the revenue side of the analysis.

(4) It is assumed that the project manager’ salary is a fixed cost, whichever contract (if either) is undertaken. Incremental labour costs are therefore travel, lodging etc. and local labour.

(5) The penalty cost of failing to undertake one contract should be treated as a consequential cost of undertaking the other contract.

(6) The excess of revenue/ saving over incremental costs calculated for each contract shows the comparative effect on profits of undertaking each job in preference to the other. The difference between the two figures (`98,000 a and `94,000) shows that there is a difference between the two project of `4,000 in favour of Nagpur job.

(c) The approach usef has assumed that one project or the other will be undertaken. Some costs have already been incurred (some materials , plant): other costs have been committed (project manager’s salary, head office administration) and others are notional (interest on plant).

These are not relevant to any decision about future action. The only relevant consideration should be: (i) Future revenues or cash savings as a consequence of the decision. (ii) Future costs, incurred as an additional expense as a consequence of the decision. In the solution in part (a), incremental revenues are the revenues from the contract undertaken , alternative uses of materials held but not required and hire of plant. Incremental costs are only those additional costs which would be incurred as a result of the decision to undertake one of the contracts. The cost accounting profit or loss recorded for each contract might be: Nagpur: `1,70,000-`1,60,000 = `10,000 Delhi: `1,80,000-`1,82,000 =(`2,000) There figures are irrelevant to a decision because the costs include past , committed or notional costs, and other revenues and penalty costs to the company are ignored. ( c) Other factors to consider are: (i) The constraints on working which make the contract mutually exclusive. If there is a shortage of

labour, funds etc., it might be possible to overcome and carry out both projects: (ii) The likelihood of another contract being offered for the same period of time, which is more

profitable than either the Nagpur or Delhi jobs. (iii) Loss of goodwill and future contracts by not undertaking either projects: (iv) Reliability of the prospective customer in each contract:

- 23 -

(v)

(vi)

Reliability of costs forecasts, lobour availability etc. on both contacts. The net difference between the two jobs, `4,000 is relatively small and sensitivity / risk analysis will be very important: The preference for the Nagpur contract (by `4,000) has assumed that the alternative use for the Delhi contract materials will exist. It is only a likelihood, however. Failure to obtain this saving would shift the preference strongly in favour of accepting the Delhi job.

Answer: 39 Working Notes: Calculation of Balance Capacity

Products Units

‘AB’ 5,000 ‘CD’ 10,000 Total

At 65% Capacity At 100% Capacity Balance Capacity (i) Statement of Profit for 2003-04 Products Production & Sales (Units) Sales Revenue (i) Variable Costs: Direct Material Direct Labour

Products Variable overheads

( 100% on Wages) Total Contribution Less: Fixed Costs Profit

Labour Hours (per unit)

5 4

Total Labur Hours 25,000 40,000 65,000

Capacity utilized (%) 25 40 65

= 65,000 Labour hours used = Labour hours used would be 1,00,000 = 1,00,000 hours-65,000 hours = 35,000 hours

‘AB’ 5,000 4,00,000 (@`80)

50,000 (@`10) 1,25 ,000 (@`25)

‘AB’ 1,25,000

‘CD’ 10,000 10,00,000(@`100)

300000 (@`30) 200000 (@`20)

‘CD’ 2,00,000

7,00,000 3,00,000

(`) Total

14,00,000

3,50,000 3,25,000

Total 3,25,000

10,00,000 4,00,000 2,25,000 1,75,000

(ii) (i)-(ii)

3,00,000 1,00,000

Working Notes: Proposals

(1) Utilise balance capacity to Produce ‘AB’ (2) Utilise balance capacity to Produce ‘CD’ (3) Utilise balance capacity to produce a new product ‘EF’ Additional Units= Balance Capacity / Labour hours per unit AB = 35,000 hrs. / 5 hrs = 7,000 units CD = 35,000 hrs. /4 hrs. = 8,750 units

Less: Decrease in 1,400 units Efficiency by 16%

= 7,350 units EF = 35,000 hrs. / 7 hours 5,000 units

Statement showing utilization of Balance Capacity

Products AB - Existing

- Additional

Proposal (a0 5,000 7,000

12,000 10,000

-

10,000 -

Proposal (b) 5,000

-

5,000 10,000 7,350

17,350 -

Proposal ( c ) 5,000

-

5,000 10,000

-

10,000 5,000

CD – Existing Additional

EF – New Units

- 24 -

Statement showing contribution per unit of Products ‘AB’ ‘CD’ AND ‘EF’.

Product Units

Selling Price (i) Variable Costs:

Direct Material Direct Labour Variable Overheads

(100% of Wages) Total Variable Costs (ii) Contribution (i) – (ii)

AB Existing 5,000 84.00

10.50 26.25 26.25

63.00

21.00

Addl. 7,000 80.00

10.50 26.25 26.25

63.00

17.00

Existing 10,000 104.00

31.50 21.00 21.00

73.50

30.50

CD Addl. 7,350

104.00

31.50 25.00 25.00

81.50

22.50

EF New

5,000 145.00

40.00 36.75 36.75

113.50

31.50

Note: 1. The selling price of additional units of Product ‘CD’ is assumed to be `104 as is for existing units. 2. The direct labour cost per unit of additional units of Product ‘CD’ is calculated as below:

Time taken for each additional unit of Product ‘CD’ = 35,000 hours/ 7,350 units = 4,762 hours Direct Labour Cost per unit = 4,762 hours x `5.25 per hour = `25000

The variable cost per unit of Products ‘AB’ and ‘CD’ were `60 and `70 respectively in the year 2003-04. In the year 2003-04 it became `63 and `73.50 respectively. Then the differential cost for product ‘AB’ for 5,000 units comes to `3 per unit and for product ‘CD’ for 10,000 units comes to `3.50 per unit. The differential cost per unit for each additional unit produced during unutilised capacity is equal to its variable cost.

Profitability Statement using incremental revenue and differential cost approach (`) Products Units Incremental Total Differential Total Difference

Revenue per Incremental cost per unit Differential unit revenue cost

Proposal (a) AB 5,000 4.00 20,000 3.00 15,000 5,000

7,000 80.00 5,60,000 63.00 4,41,000 1,19,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 Total 6,20,000 4,91,000 1,29,000 Proposal (b) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000

7,350 104.00 7,64,400 81.50 5,99,025 + 1,15,375 50,000 (*)

Total 8,24,400 6,99,025 1,25,375 Proposal (c) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 EF 5,000 145.00 7,25,000 113.50 5,67,500+ 1,27,500

30,000(**) Total 7,85,000 6,47,000 1,37,500 * Selling and Distribution Expenses ** Special Advertising Expenses The Profit as per Statement of Profit for 2003-04 is `1, 75,000. By utilising the Balance capacity 35,000 hours in manufacture of product ‘EF’ the said profit will increase by `1,37,500

Statement of Profit for 2004-05 with the selection of Proposal (C) to Introduce Product ‘EF’ Existing Profit on manufacture of Products ‘AB’ and ‘CD’ Add: Profit from Product ‘EF’ by utilising to balance capacity Total Profit

Answer: 40

(`) 1,75,000 1,37,500 3,12,500

- 25 -

Differential Cost of the job Increase `

Material cost Labour cost Additional Overheads Other expenses Total

(`1,50,000 – `44,750) Note: Depreciation, rent, heat and light and power are not going to affect the costs.

(b) Full Cost of the jobs: `

Cost as above at (a) (i.e. increased costs) Depreciation Power Rent Heat & Light Total

(c) Opportunity cost of taking the order: `

Sale of Product A Less: Material Labour Power Other expenses Total

(d) Sunk cost of the jobs: `

Depreciation Power* Rent Heat & Light Total

9,000 1,000 2,500

250 12,750

20,000 20,500

1,000 2,250 45,750

16,750

` 62,500

9,000 1,000 2,500

250 1,62,750

1,50,000

50,000 90,000 10,000

- 1,50,000

Decrease `

20,000 22,500

- 2,250

44,750 Net differential cost of the job : `1,05,250

*If a student treats power as a relevant cost, in that case it would not appear here. Advice regarding the jobs : ZED Ltd. should not accept the job as there will be a chase disadvantage of `42,750/- as computed below:

` `

- 26 -

Incremental revenue 5,000 units @ `25 Less: Sale of product A Differential costs (a) Cash disadvantage 42,750

(`per unit) 100

60 40

(`) Relevant cost per unit 10+(2M.H. X `8) Suppliers price per unit Excess of relevant cost over supplier’s price.

26 25

1

1,25,000 62,500 62,500

1,05,250

Ans 41:Working Notes: Contribution per hour in manufacturing Product B is as follows: Selling Price Less: Variable Cost Contribution per unit Contribution per machine hour =`40/5 hours =`8

Analysis-The relevant cost of production of component is higher by Re 1 over the purchase price of component part X-100.therefore buy decision is recommended.

Ans. 42:

Selling price per unit of product ‘A’ Less: marginal cost per unit Contribution per unit Contribution per hour of product ‘A’

`

50 35 15

3 Since one unit of product ‘B’ needs 2 hours, therefore if a unit of B is produced, then the contribution lost by not producing ‘A’ = 2 hours × `3 = `6 Real cost of producing one unit of product ‘B’

` Marginal cost per unit Add: Contribution lost per unit Total cost of producing a unit of Product ‘B’

5 6

11 As the suppliers price per unit of product ‘B’ is `10 and that of producing in the factory is `11, therefore it is suggested that it is better to buy product ‘B’ from outside.

Ans. 43: Calculation of total number of hour required in department P and Q

Particulars Demand units Department P: Hours per unit Total hour required

Particulars Department Q: Hours per unit Total hours required

Component A B 900 900

2 2 1800 1800

Component A B

3 2700

3 2700

C 1350

1.5 2025

C

1 1350

Total

5625

Total

6750

- 27 -

From the above, we can observe that department Q is facing the capacity constraint of 750 hours Statement showing the qualities of components to be purchased to maintain cost Particulars A C Purchase cost 129 70 Less: variable cost of manufacture 99 50 Saving in manufacture 30 20 Hours required per unit in dept. Q 3 1 Saving in manufacture per hour 10 20 Suggestion: since the saving in manufacture per hour is more in case of component C, component A should be purchased from outside. No. of components of A to be purchased from outside =750 hrs/3 hrs =250 units

Ans. 44: (a) Selling price per unit 600 Less: Variable cost of `

Component A 32 Component B 54 Component C 58 Component D 12 Component E 4 Assembly 40 200 Contribution per unit 400 Total contribution for 132 units ` 52800

Less: Fixed cost 132×316 41712 Net profit 11088

(b) The company may buy any one of the components. The number of units that can be produced under the three options:

Buy component “A” Buy component “B” Buy component “C” Component Machine Component Machine Component Machine

Hrs reqd Hrs reqd Hrs reqd A 10 A 10 A -

B 14 B - B 14 C 12 C - C 12

Total machine 22 24 Hrs/unit 26

Total machine hours available is 4752 under all options

Number of units that can be Number of units that can be Number of units that can be manufactured, if “A” is bought manufactured, if “B” is bought manufactured, if “C” is bought

= 4752/22 = 216 units = 4752/24 = 198 units = 4752/26 = 182.77 units Additional capacity that can be Additional capacity that can be Additional capacity that can be

created created created (182.77 132) 100 (216 132) 100 (198 132) 100

38.5% 63.6% 50% 132 132 132

(c) If the increase in demand during the next period is 50% it is not possible to meet it by buying Component “A” as additional capacity created is only 38.5%. Of the remaining two options, the cheaper one has to be accepted.

Buy “B” Buy”C” ` `

- 28 -

Market price Less: Variable cost if made by the company Additional cost to be incurred Machine hours saved Cost per hour

160 54

106 14 7.57

125 58

67 12 5.58

Since it is cheaper to increase capacity by buying “C” this option has to be exercised.

(d) Profitability statement Selling price per unit of equipment Less: Variable cost of: Making A Making B Buying C Making D Making E Assembly

`600

`32 `54 `125 `12 `4 `40

267 Contribution per unit Total contribution for 198 units (Note 1) Less: Fixed cost (as worked out above) Net profit Net increase over period for current period Note: 1. Maximum capacity = 4752 machine hours.

Machine hours reqd for one unit of equipment : 36 hours. No. of equipment that can be produced = 4752/36 = 132 Nos.

Marketing department of the company anticipates 50% increase in demand during the next period. i.e. 132 + 50% = 198 Nos.

Ans. 45: Working Notes:

1. Present demand of components (in batches) from 10,800 (maximum) available machine hours and projected estimates of components demand (in batches) in the next year. Maximum available machine hours Machine hours needed to manufacture components. A, B and C (Per batch of ten numbers) of water purifier Components

A B C

20 28 24

Machine hours Machine hours Machine 72 hours

Total

10,800

267 333

65934 41712 27222 13134

Present demand (in batches) of components A, B and C (10,800 hours/ 72 hours) 150 Projected estimate of demand of components A, B and C (add 50% increase) in 225 the next year

2. Present and future fixed costs: Present fixed cost of 150 batches @ `200/- per batch 30,000

- 29 -

Add: Increase in fixed cost to meet 50% increase in demand Total future fixed cost for 225 batches

3. Expected purchase cost of components View point Probability

A Expected

price

Component B

Expected Price

10,000 40,000

` `

C Expected

Price `

Pessimistic

Most likely

Optimistic

Total

0.25

0.50

0.25

30 (`120×0.25)

55 (`110×0.50)

20 (`80×0.25)

105

50 (`200×0.25)

65 (`130×0.50)

35 (`140×0.25)

150

40 (`160×0.25)

70 (`140×0.50)

30 (`120×0.25)

140

4. Present contribution (per batch) `

Selling price (per batch) Less: Variable production cost Less: Variable assembly cost Contribution (per batch) Total Present contribution on 150 batches

320 50

` 800

370 430 64,500

(i) Maximum number of batches that could be produced in 10,800 machine hours each of the three alternatives namely buying A or B or C is considered respectively. (a) Buy component

Make component Make component

A (from outside) B C Total

(10,800 hours/52 hours) (b) Buy component

Make component Make component

B (from outside) A C Total

(10,800 hours/744 hours) But in view of projected (expected) market demand of 225 batches, production would be restricted to 225 batches only.

(c) Buy component Make component Make component

C (from outside) A B

20 28

No machine hours required Machine hours required Machine hours required

20 24 44

No machine hour required Machine hours required Machine hours required

28 24 52

No machine hour required Machine hours required Machine hours required

Number of batches that could be produced internally 207.69 batches

Number of batches that could be produced internally 245.45 batches

- 30 -

Total 48 Number of batches that could be produced internally 225 batches (10,800 machine hours 748 hours)

(ii) Statement of financial implication when purchases of component A, B and C are made from outside(in view of the fact that production capacity will be limited to 50% increase) Component bought

Total variable cost per batch (I) Expected purchase cost (II) (Refer to working note 3) Increase I variable cost per batch (III) = (II – I) Present contribution per batch (IV) (Refer to working note 4) Revised contribution per batch (V) = (IV – III) Total revised contribution

389

80,791 (207.69

batches × `389)

388

87,300 (225 batches ×

`388)

406

91,330 (225 batches ×

`406)

41

430

42

430

24

430

A B C `

64 105

` 108 150

` 116 140

Advise: Purchase component C from outside as it gives maximum contribution on manufacturing A and B internally.

(iii) Profit Statement (When C is bought from outside and A, B were manufactured internally and extra production is made and sold)

Per Batch ` Total (for batches)

225

` Sales revenue: (I)

Less: Variable costs (`(Per batch) : (II) Production cost of A Production cost of B Production cost of D Production cost of E Production cost of C

(Refer to working note 3) `344 Assembly cost `50 394.00 88.650

(225 batches × `394)

Contribution : (III) – (-II) Less: Fixed costs (`40,000 / 225 batches)

406.00 177.78

91,350 40,000

`64 `108 `24 `8 `140

800.00 1,80,000 (225 batches × `800)

- 31 -

(Refer to working note 2) Profit 228.22 51.350

Ans: 46:The components are made in a machine shop using three identical machines each of which can make any of the three components.

Total machine hours required for 3 components = 4+5+6 = 15 hours Total capacity of 3 machines is 12,000 machine hours per month and is just sufficient to meet the current demand. Hence, the current demand is 12,000/15 = 800 units of product z per month. Profit made by the company for current month.

Sale price 300 Less: Variable cost 48+60+80+30= 218 Contribution per unit 82 Total contribution 800 x 82= 65,600 Less: fixed cost per month 50,000 Profit for current month RS. 15,600

(a) From next month onwards, the company expects the demand for z to rise by 25% i.e., 800+25% = 1,000 units per month. One component should be bought from the market. Which component ?

Statement of extra cost of component per unit Component A B C

Market price 64 75 110 Less: Variable cost 48 60 80 Extra cost of buying one unit 16 15 30 Machine hours required per unit 4 5 6 Extra cost per machine hour 16/4= `4 15/5=`3 30/6=`5 Ranking II I III Because of Ist rank (lowest extra cost), component b should be bought from the market.

Manufacturing Hours C 1,000 units x 6 hours = 6,000 A 1,000 units x 4 hours = 4,000 B 400 units x 5 hours = 2,000 (Balance)

Total 12,000

Balance 600 units of B should he bought from the market. ( c) Profit made by the company

Component Element of cost Cost per unit No. of units 1,000 48 Variable cost A 400 60 Variable cost B 600 75 Market price B

1,000 80 Variable cost C 1,000 30 Variable cost Assembling

Total variable cost Add: Fixed cost Total cost Sales 1,000 units at `300 per unit

Amount(`) 48,000 24,000 45,000 80,000 30,000

2,27,000 50,000

2,77,000

3,00,000

- 32 -

Profit on 1,000 units

Ans. 47:i) Statement showing Profit / Loss of company

(If it accepts the order of manufacturing moulded toys) Total available machine hours: (A) (8 machine × 7.5 hours / day × 300 days) Machine hours required for producing 4,20,000 cans: (B) (4,20,000 cans /30 cans) Balance machine hours: {(A) – (B)] Total number of production of moulded toys in balance hours (4,000 hours × 15 toys / hour) Total contribution on 60,000 moulded toys (`) (60,000 × `10) Less: Fixed expenses of mould (`) Net profit

2,25,000 (`) 3,75,000

6,00,000

4,000 60,000

14,000

18,000

23,000

Decision: It is advisable for the company to accept the order of 60,000 moulded toys as it will increase its profit by `3,75,000.

(ii) Statement showing Profit / Loss (If the order of manufacture of cans increase to 5,40,000)

If 5,40,000 cans are produced, no machine hours would be available for manufacturing toys `(Lacs)

Total contribution on 5,40,000 cans 5,40,000 cans × `6) Less: Fixed cost Profit Alternatively, the production would be 4,20,000 cans and 60,000 moulded toys

20.00 12.40

32.40

`(lacs) A. Profit from 4,20,000 cans:

Contribution (4,20,000 cans × `6) Less: Fixed cost Profit

B. Profit from 60,000 moulded toys (Refer to (i) above) Total profit: (A + B) 8.95

20.00 5.20 3.75

25.20

- 33 -

Decisions: The production of 1,20,000 additional cans instead of 60,000 moulded toys will result an additional profit of `3.45 lacs (`12.40 lacs – `8.95 lacs). Therefore, the company is advised not to accept the order of manufacturing moulded toys.

(iii) Let the minimum excess capacity needed to justify the manufacturing of any portion of the moulded toys order be x. If toys are manufactured, the profit is = (`60 – `50) x – `2,25,000 and, if toys are sub-contracted, the profit is = (`60 – `57.50) x Indifference point would be 10x – `2,25,000 = 2.5x

or x Toys produced per hour

= 30,000 moulded toys =15 toys

Therefore, 2,000 (30,000 toys / 15 toys) excess machine hours are required to justify manufacturing of toys by the company, instead of sub-contracting.

(iv) Profit under existing production plan: (`Lacs)

Contribution from 4,50,000 cans (4,50,000 × `6)

Contribution from 45,000 toys (45,000 × `10) Total contribution Less: Fixed cost

(20 lacs + 2.25 lacs) Profit Profit from 15,000 sub-contracted toys (15,000 × `2.50) Total profit 9.625

9.25 0.375

31.50 22.25

4.50

27.00

If demand was accurately forecasted & 4,80,000 cans were manufactured, excess machine hour capacity available was 2,000 hrs, such excess being the pint of indifference i.e. profit from toys order would be the same by either manufacturing 30,000 toys or sub-contracting them along with the rest of 30,000 toys.

(v) Profit under properly negotiated production plan: (`Lacs)

Contribution from 4,80,000 cans (4,80,000 × `6) Less: Fixed cost Profit Profit from Toys 60,000 Nos. sub-contracted (60,000 × `2.5) Total profit 10.30

20.00 8.80 1.50

28.80

- 34 -

Therefore, the loss for improper prediction and negotiation is `10,30,000 – `9,62,500 or `67,500.

Ans. 48: Working Notes: 1. (i) Fixed manufacturing overhead per unit

“XY 100”; `3,00,000 / 5,000 units or `60 “XY 200”; `3,00,000 / 12,000 units or `25

(ii) Variable manufacturing overhead per unit “XY 100”; (`180 – `60) or `120 “XY 200”; (`60 – `25) or `35

2. Variable costs of production of “XY 100” and “XY 200” Product Per unit

‘XY 100’ ‘XY 200’ `

Direct material Variable machine operating costs Variable manufacturing overheads Total variable costs per unit

200 150 120 470

` 200

50 35

285 3. (i) machine hours for the production of one unit of each of the two products.

“XY 100”; `150/-`100 per hour = 1.5 hours. “XY 200”; `50/- `100 per hour = 0.50 hours.

(ii) Total machine hours available 5,000 units × 1.5 hours = 7,500 hours

Ranking between manufactured “XY 100” and manufactured “XY 200” Manufactured

“XY 100” Manufactured

“XY 200” `

Variable cost of production (Refer to working note 2) Variable marketing and administrative cost Total variable cost per unit: (A) Selling price per unit: (B) Contribution per unit: [(B) – (A)] Contribution per hour [Refer to working note 3(i)] Ranking

80 350 900 350 233

(`3.50/1.5 hrs) II

470 `

285

60 345 600 255 510

(`255/0.5 hrs) I

Ranking between manufactured “XY 100” and purchased “XY 100” Manufactured Purchase

- 35 -

“XY 100” “XY 100” `

Variable cost of production (Refer to working note 2) Purchase price Variable marketing and administrative cost Total variable cost per unit: (A) Selling price per unit: (B) Contribution per unit: [(B) – (A)] Ranking “XY 200”: 12,000 units × 0.50 hours or 6,000 hours “XY 100”: (7,500 – 6,000) hours = 1,500 hours

-- 80

550 900 350

II

470 ` --

650 40

690 900 310

I

Quantity of each product that XYZ Limited should manufacture and / or purchase to maximise operating income Manufactured “XY 200” Manufactured “XY 100”: 1,500 hours / 1.5 hours Purchased “XY 100” Maximum number of units Which ABC can supply.

12,000 units 1,000 6,000

Ans. 49: (i) Profitability as per original Budget Rs

(‘000s) Rs(‘000s)

23,400 5,400 1,296

5,040

2,160

2,160 (B) (A – B)

2,160 720 396 900 4,176

3,168

16,056 7,344

Sales(1,80,000 units Rs 130) Direct Material (1,80,000 units Rs 30)

Rs 28)

(A)

Component ‘EH’ ( variable cost = Rs 7.20 per unit) Direct wages (1,80,000 units Variable factory overheads (1,80,000 units Rs 24 50% ) Variable selling & distribution (1,80,000 units

Rs 24 50% ) Total variable cost Contribution Fixed factory overheads Fixed selling & distribution overheads Component ‘EH’ @2.20 Administrative overhead Profit

(ii) Export order Rs per Unit Rs per Unit

- 36 -

Direct material 56 70 30 14

170 175

5

= 6000 units(per annum)

Rs 7 per hour) Variable factory overhead ( Rs 3 10 labour hours) Direct labour (10 hours

Selling and distribution overheads Total variable cost Selling price (export) Contribution Since the product earns contribution of `5 per unit, it should be accepted. Total units 500(per month) Therefore additional contribution (6000 units Rs 5) = `30,000 Total hours on product ‘43 grade’ (1,80,000 units 4) = 7,20,000 Hrs Total hours on component ‘EH’ (1,80,000 units 0.5*) = 90,000 Hrs

* Direct Labour cost Rs 52,500

= = No of units produced Labour rate per hour 15,000 units Rs 7 per hour

0.5 Hrs Total hours utilised at 90% capacity = 7,20,000 hours + 90,000 hours = 8,10,000 hours

100% capacity hours = 8,10,000 hours 100

= 9,00,000 Hrs 90

Balance hours available = 90,000 hours p.a Hours required for export order 60,000 hours. Both contribution per unit of export order and availability of capacity confirm its acceptance.

(iii) Component ‘EH’ make or buy (per 15,000 units) Make (`) Buy (`) Direct material 30,000 Direct labour 52,500 Variable factory overhead 25,500 Total 1,08,000 1,18,500 Per unit 7.20 7.90 If the company makes the component the out of pocket cost is `7.20 per unit whereas if the component is bought , the out of pocket cost is `7.90. Decision : If the capacity remains idle it is profitable to make.

(iv) Alternative use of the spare capacity Units required = 1,80,000 units and hours required = 1,80,000 0 .5 = 90,000 Hrs Cost of buying component ‘EH’ = (1,80,000 units Rs 7.90) =Rs 14,22,000 Cost of making component ‘EH’ = (1,80,000 units Rs 7.20) = Rs 12,96,000 Hence , excess cost of buying = `1,26,000

Rent income (90,000 hours Re1) = `90,000

Contribution per unit from making component ‘GYP’ = Rs 8 -

Rs 0.5 per unit.

Direct labour cost per unit of ‘GYP’ =

Rs 1,12,500 =

15,000 Units

Rs 31,500 = `2.10 per unit.

15,000 Units

- 37 -

Rs 2.10 = 0.3 Hrs

Rs 7 90,000 hours

No. of units of ‘GYP’ in 90,000 hours = =3,00,000 0.3 hours

Contribution from component ‘GYP’ = 3,00,000 Rs 0.50 = Rs 1,50,000

No. of labour hours required for one unit of ‘GYP’ =

Since the contribution from ‘GYP’ is greater than the extra variable cost of buying component ‘EH’ , component ‘GYP’ should be manufactured and component ‘EH’ should be purchased.

Hence, accept export order and buy the component.

Ans. 50: (i) If the reliable suppliers offered to supply P44E at a guaranteed price of `50 p.u. variable manufacturing cost p.u. Direct material 14 Direct labour 12 Variable overheads 8 Total variable manufacturing cost 34

(`) Purchase price Less: variable manufacturing cost Saving, if manufactured internally

50 34 16

(ii) If the company incur additional inspection and testing charges of `56,000 p.a. = `56,000/`16 p.u. = 3500 units

The company can purchase, if yhe requirement of P44E, is less then 3500 units. If the requirement is more then 3500 component, it can manufacture its own requirement.

(iii) when the direct labour hours is limiting factor : Calculation of contribution per labour hour Particulars

Selling price Cost of purchase of P44E (saving)

Less: variable cost

Contribution Labour hours Contribution per labour hour Rank

(i) (ii)

(i)/(ii)

Own P44E - 50 50

34

16 4 4 II

manufacture of Extra sale of another existing product 90 - 90

50

40 8 5 I

Analysis: since the labour hours are the limiting factor, it is suggested to opt for extra sale of another existing product then to manufacture component P44E. (iv) The cost of the machine bought last year is a sunk cost and not relevant to the present decision of ‘make or buy’. Book value of the machine is merely an accounting treatment.

buy Ans. 51: (a)This is a make or buy decision so compare the incremental cost to make with the incremental cost

- 38 -

Incremental cost per unit Direct material (`75000 ÷ 10,000) Direct labour (`65000 ÷ 10,000) Variable Overhead (`55000 ÷ 10,000) Supervision (`35,000 ÷ 10,000)

Make the Blades `7.50

`6.50

`5.50

`3.50 Total cost `23.00 Compare the cost to make the blades for 10,000 motors. `23.00, with the cost to buy, `25.00 There is a net loss of `2.00 if ‘X’ chooses to buy the blades.

(b) ‘X’ will be indifferent between buying and making the blades when the total costs for making and buying will be equal at the volume level where the variable costs per unit times the volume plus the fixed avoidable costs are equal to the supplier’s offered cost of `25.00 per unit times the volume. (Direct materials + Direct labour + Variable overhead) × Volume + Supervision =, Cost to buy × Volume. Let volume in units = x (7.50 + 6.50 + 5.50) × x + 35,000 = 25.00x 19.50 x + 35,000

35,000 35,000

of blades As volume of production decreases, the average per unit cost of in house production increases. If the

volume falls below 6,364 motors, then ‘X’ would prefer to buy the blades from the supplier.

= 25.00 x = 25.00 × x – 19.50 × x = 5.50 × x x = 6,364 units

(c) If the space presently occupied by blade production could be leased to another firm for `45,000 per year, ‘X’ would face an opportunity cost associated with in house blade production for the 10,000 units of `4.50 per unit. New cost to make = 23.00 + 4.50 = 27.50 Now ‘X’ should buy because the cost to make, 27.50, is higher than the cost to buy, 25.00.

Ans. 52: (i) Deciding whether B Ltd. Should accept the offer from an outside vendor instead of

manufacturing chains internally. Price of chain offered by vendor `12

7 Less: Variable cost of (`5 + `2) Excess of quoted price over variable cost 5 Total excess of quoted price over variable cost (24,000 x `5) `1,20,000 Less: Avoidable cost

Inspection, set-up, etc. `24,000 - Machine rent 24,000 48,000

Excess of bought –out price over variable cost and avoidable cost 72,000

Decision- B Ltd. Should not accept the offer from outside vendor, because this decision will lead to reduction in profit by `72,000.

(ii) Deciding whether the use of internal facilities for upgrading the quality of chains would be useful in comparison to purchase from outside.

Incremental revenue per unit `22

- 39 -

Less: Differential cost per cycle Contribution Total Contribution (24,000 x `4) Less: Tooling costs Net contribution

18 4

`96,000 16,000 80,000

Decision – B Ltd. Should accept the offer of alternative use of facilities for upgrading the bicycle. It will lead to increase of `80,000 in contribution. This is more than the excess of bought-out price over variable and avoidable cost [i.e.`72,000 as per (i)]. Thus company will benefit by `8,000 i.e.,(`80,000 – `72,0000)

(iii) Deciding whether use of internal facilities for upgrading the bicycle ( chain) internally would be profitable, if batch size becomes 4,000 units in comparison to their purchases from an outside vendor. Bought- out price offered `12 Less: Variable internal cost 7 Excess of bought – out cost over variable cost 5 Total excess of bought – out cost over variable cost (24,000 x `5) `1,20,000

`12,000 - Less: Inspection cost Machine rent 24,000 36,000

Excess of bought – out price over variable and avoidable costs 84,000 Decision – If inspection cost (Which varies with batch size) decreases, then excess of bought- out price over variable and avoidable costs would be `84,000. In comparison to this, net contribution from using the internal facilities for upgrading quality of chains will `80,000[refer to (ii).] There fore, if batch size increases and inspection cost reduces, then use of internal facilities of updation of quality of chain is advocated. If decision to update is taken in (ii), it will increase profit by `4,000 (i.e..`84,000 – `80,000)

Ans. 53: For taking a make or buy decision, it is necessary to find out the relevant cost of both the decisions, i.e. manufacturing vis-à-vis purchasing the component from outside.

Departmental Expenses Budget (`000)

Items Total Allocation ratio Gadgets Components 24,000 24,000 Production

Variable Costs 3,072 80 : 20 3,840 768 Direct material 1,152 75 : 25 1,536 384 Direct labour

576 80 : 20 720 144 Indirect labour 360 75 : 25 480 120 Inspection and testing 360 75 : 25 480 120 Power

5,520 7,056 1,536 Fixed Costs

40 Lighting 30 Insurance 96 Depreciation 54 Misc. Fixed Exp.

220 7,276 Total cost

Variable cost per unit `230 `64

- 40 -

(i) Variable cost of component is `64 per unit. The purchase price is `70 per unit. For each unit net cash outflow will be `6. Therefore, company should take decision to make.

(ii) Evaluation of decision to export Inflow (a) Additional contribution due to export 12,000 units x (`245 – 230) `1,80,000

15,36,000 (b) Saving in variable cost of components (24,000 units x `64) 17,16,000

Less: Outflow Payment to be made to supplier (24,000 units x `70) 16,80,000 Net Cash Inflow 36,000

Ans. 54 (a)

Demand

Direct Material

M/c Other Variable Cost Total Variable Cost Selling Price Contribution (`/u) M/s Hours per unit Contribution (`/ M/c hr.) Ranking Cost `/u) Cont (`/u) on (Subcontract)

52,000 A 64

48 32

144 162 18 6 3 III

146 16

48,500 B 72

32 36 140 156 16 4 4 II

126 30

26,500 C 45

64 44

153 173 20 8

2.5 IV

155 18

30,000 D 56

24 20

100 118 18 3 6 I Sub-Contract

108 8

I Division: It is more profitable to sub-contract B, since contribution is higher subcontract. 1st Level of Operations: 1,50,000 hours, Produce D as much as possible. Hours required = 30,000 units × 3 = 90,000 hours Balance hours available: 60,000 hours. Produce the next best (i.e. A, Since B is better outsourced) 60,000 hrs = 10,000 units of A.

6 hrs / u

1st Level of Operation: Contribution (units) Contribution (`)

A A B

Produce 10,000 units Outsource 42,000 units 48,500 units Outsource fully

18 16

30

1,80,000 6,72,000

14,55,000

- 41 -

C

D

26,500 units Outsource fully 30,000 units Fully produce Total Contribution: Less: Fixed cost Net Gain

18 5,40,000 33,24,000 10,00,000 23,24,000

18

2nd Level of Operation: Both A and C increase contribution by own manufacture only by `2/ - per unit. 1,50,000 hrs can produce 25,000 units of A.

Contribution increases by 25,000 × 2 = 50,000 (Difference in Contribution sub -contract and own manufacturing) = 2 But increase in fixed Cost = 50,000 At the 2nd level of operation, the increase in contribution by own manufacturing is exactly set up by increase in fixed costs by `50,000/-. It is a point of financial indifference, but other conditions like reliability or possibility of the sub -contractor increasing his price may be considered and decision may them but towards own manufacture. 3rd Level Additional: 1,50,000 hrs available Unit of A that are needed = [52,000 – 25,000 (2 nd Level) – 10,000 (1 st Level)] = 17,000 units × 6 hrs/u = 1,02,000 hrs. Balance 48,000 hrs are available for C to produce 6,000 units. Increase in Contribution over Level 1 st or 2nd : A: C:

17,000 × 2 6,000 × 2

= `34,000 = `12,000 = `46,000

Increase in fixed costs Additional Loss

= `50,000 = `4,000

4th Level Additional 150000 hrs. can give 150000 ÷ 8 = 18,750 unit of C Increase in Contribution 18,750 × 2 Increase in Cost c/fd will order by expand capacities; sell maximum No. of units by operating at 1,50,000 hrs. capacity (level 1 st ) and gain `23,24,000. Summary:

Product

= ` 37,500 = (`50,000) Level 3rd loss = (` 4,000) Level 1st profit =(` 16,500) Advice: Do not

Produce (Units)

10,000 -

Sub-Contract (Units)

Contribution Contribution (Production) (Sub-Contract)

Total Contribution

A B

42,000 48,500

1,80,000 -

6,72,000 14,55,000

8,52,000 14,55,000

- 42 -

C D

Fixed Cost Profit

- 30,000

26,500 -

- 5,40,000

4,77,000 -

4,77,000 5,40,000

33,24,000 10,00,000 23,24,000

Ans. 55 Calculation of contribution per unit Particulars (a) selling cost P.U. Variable cost P.U. Dept. 1 Direct materials

Direct labour

Variable overheads (5 hrs*`2.40) (7.5 hrs*`2.40)

EXE 375

58 5 50

WYE 540

100 hours 7.5

75 hours

12 - - 18

(i) 120 193 Dept.2 Direct materials 21 26

Direct labour 90 120 27 - (7.5 hrs*`3.60) - 36 (10 hrs* `3.60)

(ii) 138 182 Total variable cost (i)+(ii) 258 375 Contribution P.U. (a)-(b) 117 165 Calculation of contribution per unit if facilities of Dept.1 were sub-contracted but facilities of Dept.2 used internally

(`) Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting Dept.1 facilities 138 212 Cost of manufacture in Dept.2 internally 138 182 Total variable manufacturing cost per unit 276 394 Contribution per unit (a)-(b) 99 146

Calculation of contribution per unit if facilities of Dept.1 and Dept.2 are sub-contracted Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting P.U.

Dept.1 138 212 Dept.2 150 192

Total variable cost P.U. (b) 288 404 Contribution P.U. (a)-(b) 87 136 Statement showing number of units to be produced and sold to earn maximum profit by using own manufacturing capacity Particulars EXE WYE

- 35,000 Dept.1 (1,75,000 hrs/5 hrs) 23,333 - (1,75,000 hrs/7.5 hrs) - 37,333 Dept.2 (2,80,000 hrs/7.5 hrs) 28,000 - (2,80,000 hrs/10 hrs)

Maximum unit can be produced and sold by using facilities of 35,000 23,333

- 43 -

both departments. Maximum contribution

40,95,000 - (35,000 units* `117) - 38,49,945 (23,333 units*`165)

Les: fixed cost 15,00,000 15,00,000 (Dept.1 `5,00,000 + Dept.2 `10,00,000)

Maximum profit 25,95,000 23,49,945 Suggestion: by production and sale of 35,000 units of EXE is maximum, it is suggestion to manufacture EXE internally. Calculation of profit from EXE (`)

40,95,000 Contribution on internally produced units (35,000 units * `117) 2,30,967 Contribution when Dept.1 services were sub-contracted (2,333 units * `99) 1,01,529 Contribution when Dept.1 & Dept.2 services were sub-contracted (1,167 units * `87)

Total contribution of EXE 44,27,496 Less: fixed cost 15,00,000 Profit 29,27,496 Calculation of total contribution of WYE (`)

38,49,945 Contribution on internally produced units (23,333 units * `165) 6,81,382 Contribution when Dept.1 services were sub-contracted (4,667 units * `146)

Contribution when Dept.1 and Dept.2 services were sub-contracted (3500 units * `136) 4,76,000

Total contribution of WYE 50,07,327 Less: fixed cost 15,00,000 Profit 35,07,327 Suggestion: profit is maximum for product WYE. Hence 31,500 units of WYE should be produced to yield a sum of `35,07,327 as profit.

Ans. 56:

Working notes: 1.

(a) Total normal and overtime hours available. Department

A Normal capacity hours Overtime hours (50% of normal hours in each department)

Total available hours 900 780

600 300

B 520 260

(b) Total hours required to meet fully the market demand of 2,500 units of P and 2,000 units of Q. Department

A Hours required for manufacturing P 2,500 units of Product

250 B

500

(2,500 Units × 0.1 hour)

Hours required for manufacturing Q 2,000

600

(2,500 Units × 0.2 hour) 400

- 44 -

units of Product (2,000 Units × 0.3 hour)

Total hours required 2. Sub-contracting should be resorted:

To meet the market demand of 2,500 units of product P and 2,000 units of product 850 and 900 hours [Refer to working note 1(b)] are required in departments A and B respectively. In department B only 780 hours are available and thus does not meet fully the requirement of 900 hours. Hence, sub-contracting should be resorted to meet the market demand fully.

3. (i) Contribution per unit; Product

Normal hours

Director material cost (`) Direct labour cost Dept. A (`)

10.00 1.00

(`10 × 0.1 hr.)

Dept. B: (`) 2.40 (`12 ×

0.2 hrs.) Total variable cost per unit (`) : (A) Sub-contract price per unit (`) : (B) Contribution / cost saving / (Loss per unit (`) (C) = [(B) – (A)]

(ii) Contribution per hour Hours required per unit Dept. A Dept. B Contribution hour Dept. A (`)

per

46 (`4.60/0.1 hrs.)

Dept. B (`) 23 (`4.60/0.2 hrs.)

29 (`2.90/0.1 hr.)

14.50 (`2.90/0.2 hr.)

5.33 (`1.60/0.3 hrs.)

8.0 (`1.60/02. Hrs.)

Loss --

Loss --

0.1 0.2

0.1 0.2

0.3 0.2

0.3 0.2

13.40 18.00 4.60

P Overtime

hours 10.00 1.50

(`15 × 0.1 hrs.)

3.60 (`18 ×

0.2 hrs.) 15.10 18.00 2.90

Normal hours 5.00 3.00

(`10 × 0.3 hrs.)

2.40 (`12 ×

0.2 hrs.) 10.40 12.00 1.60

Q Overtime

hours 5.00 4.50

(`15 × 0.3 hrs.)

3.60 (`18 ×

0.2 hrs.) 13.10 12.00 (1.10)

850

(2,000 Units × 0.2 hour) 900

4. Utilization of normal and overtime available hours to meet fully monthly market demand of 2,500 units of P and 2,000 of Q. (i) An analysis of contribution statement (Refer to working note 3) clearly shows that 2,500 units of the

product P should be manufactured by utilising the normal capacity hours of departments A and B. The

- 45 -

manufacturing of 2,500 units of P will consume 250 normal hours of department A and 500 hours of department B (Refer to working note 1(b).

(ii) For manufacturing 2,000 units of product Q, it is beneficial to utilise the remaining normal available hours of departments A and B. The normal available hours in the department B are only 20 hours, [520 hours – 500 hours] and in department A 350 hours [600 hours – 250 hours]. 100 units of product Q can be manufactured by utilising the normal available hours of departments A and B. The manufacturing of 100 units of Q in normal available hours will utilise 30 hours in department A and 20 hours in department B.

(iii) Now for manufacturing the remaining 1,900 units of product Q, we have 320 normal hours plus 300 overtime hours in department A and 260 overtime hours in the department B. The manufacturing cost per unit of product Q comes to `11.60 when normal hours of department A and overtime hours of department B are utilized. {`5 (Material Cost) + `3 (Direct Labour in Department A) + `3.60 (Direct Labour in Department B)} On comparing `11.60 with sub-contracting price of `12 per unit, we arrive at a contribution of 0.40 per unit. Hence maximum number of units of product Q should be manufactured by using normal hours of department A and overtime hours of department B. since 0.3 and 0.2 hours are required respectively for manufacturing one unit of product Q in the two departments, therefore, utilising 320 normal hours and 213 overtime hours in departments A and B respectively, 1066.66 units (or say 1,067 units) of product Q are manufactured.

(iv) Finally, to manufacture remaining 833 units of Q, the available time is 300 overtime hours and 47 overtime hours in department A and B respectively. According to (working note 1) the available time in department B is short by 120 hours (900 required hours – 780 available hours) therefore 833 units of Q cannot be made internally. But few units can be made by utilising the available overtime hours in departments A and B. The manufacturing cost of 1 unit of Q by utilizing overtime hours in departments A and B comes to `13.10 (Refer to working note 3) which on comparison with subcontract price of `12 gives rise to a situation of loss of `1.10 per unit {`13.10 – `12}. Hence it is advisable not to manufacture the remaining 833 units internally. These 833 units should be sub-contracted at a price of `12/- per unit.

(i) Statement of quantity of each product to be manufactured / or to be sub-contracted for fulfilling the market demand in most economical way.

Departments A

Normal time hours

Available hours working note 1(i)

(Refer to 600

250

30

320

Overtime hours 300

--

--

--

Normal time hours

520

500

20

--

B Overtime

hours 260

--

--

213

Production 2,500 units of P (Refer to working note 4 (i)) 100 units of Q (Refer to working note 4 (ii) 1067 units of Q (Refer to working note 4(iii))

(ii)

(2,500 units × 0.1 hrs.)

(100 units × 0.3 hrs.)

(1,067 units × 0.3 hrs.)

(2,500 units × 0.2 hrs.)

(100 units × 0.2 hrs.)

(1,067 units × 0.2 hrs.) Statement Showing Total Cost

(Based on the solution in (i) above) Products

- 46 -

Particulars P Q Sub contract price

Total

` Direct Material Cost 25,000

(2,500 units × `10)

Direct Wages: Dept. A 2,500

(250 hours × `10)

Dept. B 6,000 (500 hours ×

`12) Fixed overhead Cost of 833 units @ `12 per unit on sub- contracting Total Cost

18,000 --

` 5,835

` -

(1,167 units × `5)

` 30,855

3,500 -- 6,000 (350 hours × `10)

4,074 -- 10,075 (20 hours × `12 + 213 hours × `18

6,400 --

- 9,996

24,400 9,996

51,500 19,809 9,996 81,305

Ans. 57:

(i) Option Statement of Profit (Loss)

(if the firm discontinue all the operations during notice period of 3 months) (`Crores)

Products Sales* Costs: Material & Labour Allocated overheads: Manufacturing Admin. & Selling Total allocated overheads during notice period of 3 months Profit / (Loss)

1.5 0.6 2.1

(2.1)

1.2 0.3 1.5

(1.5)

1.8 0.9 2.7

(2.7)

1.2 0.6 1.8

(1.8)

5.7 2.4 8.1

(8.1)

- - - - -

A -

B -

C -

D -

Total -

*The option (i) would not yield any revenue. Conclusion: The option (i) will result in a loss of `8.1 crores due to the committed costs account of 3 months notice period. (ii) Option

Working note: Ascertaining profitable products (if their production is continued during 3 months of notice period)

(`Crores)

Products Sales (X)

A 18

B 13.5

C 21

D 15

- 47 -

Variable cost: Materials Labour Total variable costs: (Y)

12.0 4.5

16.5

7.5 3.0

10.5

13.5 7.5

21.0

9.0 7.5

16.5 Contribution: (X – Y) 1.5 3.0 - (1.5) A review of contribution figures in the above statement of four products A, B, C and D clearly reveals that products A and B are only profitable.

Statement of Profit (Loss) (If the firm continues the operations of profitable products A and B during 3 months of notice period)

(`Crores) Products Contribution (Refer to above working note) Less: total manufacturing administrative overheads (Refer to part (i) above) Profit / (Loss)

& selling

A 1.5

B 3.0

Total 4.5 8.1

(3.6) Conclusion: Under this option the total loss is (`3.6) crores which is less than the loss of option (i).

(iii) Option Working Note: Ascertaining profitable products (when notices are issued to the staff and the landlord – only in the manufacturing unit, resort to subcontracting only on profitable products)

(`Crores) Products Sales: (X) Variable Cost: Materials Sub-contracting charges

48.0 16.0

(20 lacs × `80)

Total variable costs : (Y) 64.0

30.0 10.5

(15 lacs × `70) 40.5

54.0 27.0

(30 lacs × `90) 81.0

36.0 26.0

(20 lacs × `130) 62.0

A 72.0

B 54.0

C 84.0

D 60.0

Contribution: (X – Y) 8.0 13.5 3.0 (2.0) A review of contribution figures in the above statement clearly shows that products A, Band C are only profitable.

Statement of Profit / (Loss) (If the firm resorts to manufacturing of profitable products by sub-contracting)

(`Crores) Product

A Contribution: (X) (Refer to above working note) Total manufacturing overheads of 3 months notice period : (Y) (Refer to option (i) above)

5.7

8.0 B

13.5 C

3.0 24.5

Total

- 48 -

Total administrative & Selling overheads: (Z) Profit/(Loss): {X – (Y+Z)}

Decision:

9.6 9.2

Out of the three options the option (iii) is the most viable one. Not only it will help the company with a turn around, but from the year 2002, the company can look forward to even higher profitability, since the manufacturing overhead would no longer be incurred thereafter.

Ans. 58: Working Notes: 1. FOB price of dismantled kit:

FOB price of dismantled kit (in$) FOB price of dismantled kit (in `) ($510 × `47.059)

2. Cost of a dismantled kit to Z Inc. If `120 is the S. P. of kit to Z Inc. then its C `100

Re 1

If `24,000 is the S. P. then C. P. is =

=

24,000 510

Rs.100 Rs.120

Rs.100 Rs.120

× `24,000

= `20,000 3. Cost of local procurements:

140% of the supplies made by Z Inc. or 140% × `10,000* = `14,000 *Being 50% of cost of a dismantled kit to Z Inc.

4. Landed cost of a dismantled kit: `

FOB price (50% × `24,000) (Refer to working note 1) Add: Insurance & freight CIF price Add: Customs duty (30% × `12,500) Landed cost of a dismantled kit

5. Cost of the standard items procured locally: 48% of the cost of locally procured goods = =

48% × `14,000 `6,720

16,250

500 12,500

3,750

12,000

6. Royalty payment per computer: Let x = Selling price per unit of personal computer y = Royalty paid per computer Since 20% is the margin of profit on S.P. it main a margin of 25% on C.P. Therefore we have

- 49 -

X = 1.25 (`32,250+ `150 + y) Y = 10% {x – (`6,720 + `16,250)} On solving the above equations we get: X = `43,000 Y = `2003.43 or `2,000 (Approx) Statement showing the selling price of a personal computer in India A.

B.

C. D. E.

F.

G. H. I.

Ans. 59: Capacity Output (units)

Landed cost of a dismantled kit (Refer to working note 4) Cost of local procurement (Refer to working note 3) Cost of assembly and other overheads per computer Total cost of manufacture: (A+ B + C) Technology fee per computer (`3,00,00,000 / 2,00,000 computer) Royalty payment per unit (Refer to working note 6) Total cost (D + E+ F) Profit (20% on selling price of 25% of total cost) Selling price (per computer)

Statement of Differential cost FOB cost per unit (`)

Total cost(`) Differential cost(`)

Differential cost per unit (`)

34,400 8,600

43,000

14,000 2,000

32,250 150

16,250

`

70% 80% 90% 100%

70,000 80,000 90,000

1,00,000

97 92 87 82

67,90,000 73,60,000 78,30,000 82,00,000

5,70,000 4,70,000 3,70,000

57 47 37

Statement showing gain or loss for various export order

If proposal A is accepted the company will suffer a loss of `10,000 with an idle capacity of 5,000 units. If proposals A and B are accepted, the company will suffer a loss of `10,000 with an idle capacity of `5,000 units. If the company accepts all the three proposals, it will earn profit of `80,000 with an idle capacity of 5,000 units.

- 50 -

Therefore, the company should accept all three proposals.

Ans. 60: Shut down point = Avoidable Fixed cost - Shut down cost

P/V Ratio

= [120000-40000] - 0 = `400000 1-0.8

Ans. 61:

Continue Fixed expenses at 50% activity Additional shut down cost Fixed expenses during shut down

30,000 Additional fixed cost incurred due to continued operations = 18,000

30,000 Shut Down

- 2,000

10,000 12,000

If contribution from operation is less than 18,000, a shut down is recommended.

i.e. Contribution per unit

i.e. Contribution i.e Selling price – variable cost or S.P. – 3.6 3.60

<

< <

18,000 5,000

Rs 3.60 per unit Rs 3.60 per unit

< Variable cost i.e. 14.00 – < Variable Cost or variable

cost is more than Rs 10.40 For a variable cost more than Rs 10.40 per unit, a shut down is recommended. Alternative Contribution from operation must be less than 18,000 `for a shut down. Sales value = 14x5,000 = 70,000

Sales – variable cost < 18,000 or variable cost is more than 70,000-18,000 = 52,000 Variable cost of 5,000 units above `52,000

Or Variable Cost V.C. per unit > 52,000 = `10.40 5,000

For a variable cost per unit above `10.40, shut down is recommended.

Ans. 62: If plant is continued

Sales Less:Variable Cost

Contribution Less:Fixed Cost

Additional Cost

7,60,000 5,70,000 1,90,00

If plant is shutdown - -

1,30,00 15,000

3,50,000

- 51 -

Operating Loss 1,60,00 1,45,00 A comparison of loss figures indicated as above points out that loss is reduced by (16,000-14,500) `15,000 if plant is shut down.

Shut down point = 3,50,000 - 14,5000 20,500 = 1,02,500 units =

8-6 2

95,000 Capacity level of shut down point:

At 100% level production is = 1,18,750 0.80

Capacity level at shut down =

Alternative Solution

1,02,500 = 86.31%

1,18,750

` If the plant is shut down, the sunk cost or fixed expenses If it is working at 80% capacity, the fixed cost Additional fixed expenses Contribution (95000*2) Incremental Loss on Continuing Decision - better to shut down Production at shut-down point

2 x – 350000 2x x Capacity %

= = = =

1,45,000

1,45,00 3,50,000 2,05,000 1,90,00 0 15,00

2,05,000 1,02,500 Units 1,02,500/(95,000/0.8) =

Ans. 63: (a) Contribution per tin = Selling Price – Variable cost

= 21 – (7.8 + 2.1+ 2.5 + 0.6) = `8 per tin.

Loss on operation: Fixed cost per annum = 2,00,000 units 4 per unit = 8 lakhs Fixed cost for 1 quarter = 8/4 = 2 lakhs

Fixed cost for the quarter Less: Contribution on operation (8 10,000) Expected loss on operation

Loss on shut down:

Unavoidable Fixed Cost Additional shut down cost Loss on shut-down

2,00,000 80,000

(1,20,000)

`

74,000 14,000 (88,000)

`

- 52 -

Conclusion: Better to shut down and save `32,000.

Shut-down point (number of units) = Avoidable Fixed Cost ÷ Contribution per unit = (2,00,000 88,000)/8 = 14,000 units.

Ans. 64: The Directors, XYZ Co.

New Delhi Date…….

Dear Sir As desired, we have analysed the cost implications of the decision of temporary closure of the trade recession. We find that if the factory is run at 50% capacity and with reduced sales revenue, the loss likely to be incurred in one full year (the estimated period of recession), would be around `200000 as detailed below:

`In’000 Direct materials Direct labour Production overhead Administrative o v e r h e a d Selling & distribution overhead

Loss

300 400 240 120 130

1190 200

Sales If the factory is closed, the following costs will be incurred:

Fixed costs Settlement cost Maintenance costs Cost of resuming operations

990 `In ‘000

220 150

20 80

470 It is obvious from the above, that despite the fact that running at 50% capacity would imply a loss of `200000, it is better not to close down the factory since in that case the loss would be higher. In our views, even if running the factory entailed a somewhat bigger loss as compared to the loss incurred by closing it down temporarily, it may be better to keep the factory in operation. This is because a closure, even if temporary, results in the loss of regular and old customers, suppliers and skilled personal. This, coupled with a loss of goodwill in the market, may give rise to substantial losses at the time of restarting the factory. We trust that the above analysis would be helpful to you in reaching an appropriate decision in the matter. We shall be glad to be of any further assistance that may be required in this regard.

Yours faithfully X and Co.

Chartered Accountants.

- 53 -

Working Note:

Production overhead

(`Lakhs) (i) (ii) (iii) (iv) (v) (vi)

Ans. 65:

(i)

Details Sales Revenue Less: variable cost Contribution Less: fixed cost Profit

(ii)

M/s supreme Ltd. Comparative statement of sales and profit under marginal costing

2002 `6,00,000 4,50,000 1,50,000 1,20,000 30,000

2003 5,62,500 4,50,000 1,12,500 78,750 33,750

Amount at 60% Amount at 80% Variable cost for 20% Variable cost for 60% Fixed Cost Amount at 50% (iii×2.5+v)

2.52 2.76 0.24 0.72 1.80 2.40

Admn. overhead

(`Lakhs) 1.24 1.32 0.08 0.24 1.00 1.20

Selling overhead

(`Lakhs) 1.36 1.48 0.12 0.36 1.00 1.30

Minimum sales required, if the firm decides to shut down in units in 2003: Minimum sales required is the sales which should yield at least the contribution, which is sufficient to meet

increase in fixed cost. Increase in fixed costs in 2003 = `78,750 – 60,000 = `18,750 Sales required to yield contribution equal to increase in fixed cost X* P/V retio = `18,750 Or x = `18750 / 0.20 = `93,750 Working notes 1. Computation of variable costs, break even point, profit and fixed cost for the year 2002: Sales revenue `6,00,000 P/V ratio 25% Margin on safety 20% So, margin of safety = sales * 0.20

= `6,00,000 * 0.20 = 1,20,000 We know that margin of safety * P/V ratio = Profit So, Profit: `1,20,000 * 0.25 = `30,000 Total contribution = sales * P/V ratio

= `6, 00,000 * 0.25 = `1,50,000 Variable cost = sales – contribution So, variable cost = 6, 00,000 – 1,50,000 = 4,50,000 Fixed cost = contribution – Profit

= 1,50,000 – `30, 000 = `1,20,000 Break even sales * P/V ratio = fixed cost So, BES = 1,20,000 / 0.25 = `4,80,000

2. Computation of sales revenue, variable cost, fixed cost and profit in 2003 Let sales revenue for the year 2003 be x. the variable cost for the year 2003 is `4,50,000 (no. change). So, contribution = X – `4,50,000

= 20% (given) We know that P/V retio = contribution

Sales Or, 20

100 = X – 4, 50,000 X

- 54 -

Or, 20x Or, x Margin of safety So, margin of safety

We know that sales – margin of safety = B.E. sales So, B.E. sales

= `100x – `4, 50, 00,000 = `4, 50, 00,000/80 = 5, 62,500 = 30% (given) = sales * margin of safety ratio = `5, 62,500 * 0.30 = `1, 68,750

= `5, 62,500 – `1, 68,750 = `3, 93,750

Ans. 66 (i)

Option I At 75% in Feb and close in

March and April (`)

Option II At 25% each from Feb

– April (`) Direct Material Direct Labour

Factory Overhead : Indirect Material Two months idle Indirect Labour Training cost Indirect Exp. :

Repairs & Maintenance Over hauling cost Others Expenses Idle × 2

Office overhead: Staff Salaries Idle 67,550 × 2 Other overheads Idle Total overhead cost Total cost

5,25,000 5,23,600

10,48,600

8,400 9,800

1,01,500 65,800

28,000 14,000 52,500 53,200

1,48,400 1,35,100

28,000 22,400

6,67,100 17,15,700

5,25,000 5,19,750

10,44,750

14,700

1,78,500

84,000

1,02,900

2,94,000

59,850

7,33,950 17,78,700

The more economic course of action is to operate at 75% capacity for a month only, and close the plant for March and April. This option will save (`17,78,700 – `17,15,700) = `63,000.

Ans. 68: (i)

Statement of Profitability of E Ltd. in Existing Situation A B C Total

No. of units 10,000 25,000 20,000 ` ` `

Selling Price per unit 40 75 85 Less: Variable Cost per unit Direct Material 10 14 18 Direct wages 8 12 10 Variable Overhead 8 9 10

- 55 -

Contribution per unit Total Contribution Less: Fixed Cost Net Profit

14 1,40,000 1,60,000 -20,000

40 10,00,000 4,50,000 5,50,000

47 9,40,000 4,00,000 5,40,000

20,80,000 10,10,000 10,70,000

Calculation of overall profit under each proposal (ii)(a) If Product A is discontinued and capacity released is utilized for either B, either C or for both B and C

Revised contribution of Product B and Product C. B(`)

Selling Price per unit 73.50 (75 – 2% of 75)

Less: Variable cost per unit Direct Material 15.40

(14 + 10%of 14) Direct Wages 12.00 Variable Overhead 9.00

Contribution per unit 37.10

C (`) 80.75 (85 – 5% of 85)

18.90 (18 + 5%of 18) 10.00 10.00

41.85

Profitability Statement Option 1 Option 2 Option3- Both B and C

equally Only B Only C B C

No. of Units (as per W.N.1) 6,666 8,000 3,333 4,000 ` ` ` `

Additional contribution 2,47,308.6 3,34,800 1,23,654.3 1,67,400 2,91,054.3

Savings from Fixed Cost of A 1,60,000 1,60,000 1,60,000 Reduction in contribution from A 1,40,000 1,40,000 1,40,000 Net Increase in Profit 267308.6 3,54,800 3,11,054.3 Existing Profit 10,70,000 10,70,000 10,70,000

1337308.6 3,31,054.3 Total Profit 14,24800 Hence, it is better to produce Product C only.

(ii)(b) Discontinue Product A and divert the capacity to produce Product D A B C

Sales (units) 10,000 25,000 20,000 Labour Hrs. per unit 4 6 5 Total Labour Hours 40,000 1,50,000 1,00,000 Idle Capacity (hours) 2,90,000 * 20 / 80 Capacity released of A Total hours released Hours per unit No. of units that can be produced

Profitability Statement No. of units

Selling Price per unit Less: Variable Cost per unit Direct Material Direct wages Variable Overhead Contribution per unit Additional Contribution (D) Less: Additional Fixed Cost Additional Net Profit Add: Existing Profit (B & C) Total Profit

28,125 `

60

28 12 6

14 3,93,750 1,05,500 2,88,250

10,90,000 13,78,250

Total

2,90,000 72,500 40,000

1,12,500 4

28,125

- 56 -

(c) If we hire out the idle capacity

Idle hrs. Profit per hour (10,70,000 / 2,90,000) Total Profit Existing Profit Total Profit Decision : Better to produce product C as per proposal (a)

` 72,500

3.69 2,67,500

10,70,000 13,37,500

Working Note-1: Hours release on discontinuation of Product A = 10,000 * 4 Only B Only C B and C equally 40,000 / 6 = 6,666 40,000 / 5 = 8,000 B- 3333 and C- 4000

Ans. 69:

1. Quantity analysis Input in process A – total capacity – given = 2, 00,000 kg Less: loss in process A = 10% of Input = 20,000 kg (NRV at `1/ kg = 20,000) Balance transfer to process B = 1,80,000 kg Less: loss in process B = 5% of Input = 9,000 kg (NRV at `2 / kg = 18,000) Balance good output available for sale = 1,71,000 kg

2. Supplier Evaluation and Decision Supplier P Q R R Condition Max. 1,20,000 kg Max. 1,60,000 kg Any Quantity Qtty = 2,00,000 kg Price 10.00 11.20 11.60 11.00 Var. Transport cost 1.20 1.00 1.00 1.00 Total 11.20 12.20 12.60 12.00 The following can be planned in any of the following ways –

Total Purchase = 2, 00,000 kg Purchase entirely from R 2,00,000 kg Purchase first kg. from P(least cost) and

balance 80,000 kg from Q (Next least cost) 1,20,000 * `11.20 + 80,000 * `12.20)

Cost incurred = (2,00,000 * `12) = 23,20,000 = 24,00,000

Decision: hence the company should Buy 1,20,000 kg from P and 80,000 kg from Q Fixed transport cost being constant is not relevant to the above decision.

3. Customer evaluation and decision Customer k L M Condition Upto 80,000 kg only Upto 1,60,000 kg only All 1,71,000 kg Selling price 65.00 64.00 61.80 Less: discount 2% 1.30 1.28 NIL Net selling price 63.70 62.72 61.80 Less: var. transport cost 2.60 1.44 NIL Net realization 61.10 61.28 61.80 The sales can be made in any of the following way –

Total sale Quantity = 1,71,000 kg

Sold entirely to M 1, 71,000 kg

Amt realized = (1,71,000 * `61.80) = `1,05,67,800

Less: fixed delivery cost NIL Net amount = `1,05,67,800

sell first 1,60,000 kg to L (max. revenue)and Balance 11,000 kg to K (next max. revenue) (1,60,000 * `61.28 + 11,000 * `61.10) = 1,04,76,900 = `60,000 (`5,000 * 12 months) = 1,04,16,900

- 57 -

Decision: since revenue is higher, the company should sell the entire quantity to customer M. 4. Statement of process costs

Particular Process A Raw materials (`23,20,000 + fixed transport 25,20,000 2,00,000)

22,00,000 Transport from previous process 9,56,000 Direct wages

Overheads Total process costs 56,76,000 Less: scrap value of normal loss ( as in WN Above) 20,000 Net process costs transferred to subsequent 56,56,000 process/FG Net profit: sales revenue – costs of production = 1,05,67,800 – 90,83,800 = `14,84,000

Ans. 70: (i) = Safety Stock + lead time consumption

= 100 units + (3600 units/12) = 400 units (ii) Anticipated reduction in the value of the average stock investment

EOQ = 2 Annual consumption Buying cost per order Cost of carrying one unit of inventory for one year

Process B

56,56,000 21,00,000 13,45,800

91,01,800 18,000 90,83,800

Reorder level

= 2ab cs

Where a = Annual consumption b= Buying cost per order c= Storage and other inventory carrying cost rate

= 2 3600 units Rs. 40 0.2 Rs.100

The average stock to be held under new system: = minimum lavel + ½Reorder quantity = 100 + ½* 120 = 160 units

The average stock investment under new system: = 160 units * `100 = `16,000

The average stock under old system: = Minimum level + ½ EOQ = 0 + ½ (1800 units) = 900 units

The average investment under old system = 900 * `100 = `90,000 Therefore, anticipated average reduction in value of average stock investment

= `90,000 – `16,000 = `74,000 (iii) The anticipated reduction in total inventory costs (in the first and subsequent years) Under new system: Annual ordering cost ((3,600/120) * `40) = `1,200 Stock holding cost (0.20 * `16,000) = 3,200 Total inventory cost 4,400 Under old system: Annual ordering cost (2 orders * `40) = ` 80 Stock holding cost (0.20 * `90,000) = 18,000 Total inventory cost 18,080 Anticipated reduction in subsequent year: Thus anticipated reduction in total inventory cost is `13,680 (i.e., `18,080 – 4,400) in subsequent years. Anticipated reduction in the first year = `13,680 – `10,000 * = `3,680

- 58 -

* In the first year 100 units will have to be purchased.

Ans. 71: Particular Current Policy A Policy B Policy C Sales 4,50,000 5,00,000 5,40,000 5,65,000 Less: variable cost at 70% 3,15,000 3,50,000 3,78,000 3,95,500 Contribution 1,35,000 1,50,000 1,62,000 1,69,500 Less: fixed cost (given) 10,000 10,000 10,000 10,000 Profit before tax 1,25,000 1,40,000 1,52,000 1,59,500 Less: tax at 40% 50,000 56,000 60,800 63,800 Profit after tax 75,000 84,000 91,200 95,700

3,60,000 3,88,000 4,05,500 3,25,000 Cost of good sold (VC + FC) 4 times 6 times 8 times 10 times Inventory turnover ratio (given) 1,01,375 64,667 45,000 32,500 Average inventory (COGS /T/o ratio) 5,069 3,233 2,250 1,625 Carrying cost of inv. At 5% (a)

Opportunity cost at 20 % of capital blocked in 20,275 12,933 9,000 6,500 average inventory (b) 25,344 16,166 11,250 8,125 Total cost of inventory holding (a + b) 70,356 75,034 72,750 66,875 Net benefit = total cost of inventory

Decision: As net benefit is Maximum under policy B, it may be chosen (alternative assumptions exist)

Ans. 72:

Working Note: Fixed overheads Present sale value: (A) (15,000 units ×`100) Direct materials (30% of sale value) Direct labour (20% of the value) Variable overheads (`20 per unit) Total variable costs (B) Contribution: (C) = (A) – (B) Profit : (D) (15,000 units × `15) Fixed overheads: (current level) Add: Additional fixed overheads due to price escalation 50,000 Total fixed overheads: 2,75,000

Statement of profitability for various alternatives Alternatives I

Rejecting the

II Rejecting the proposal for

III Accepting the proposal of

IV Accepting the proposal of the

(C) – (D)

3,00,000 .. 10,50,000 4,50,000 2,25,000 .

2,25,000

3,00,000

4,50,000

` 15,00,000

- 59 -

proposal for the purchase of 10,000 units and continuing with present level of sales only

the purchase of 10,000 units from a party and attaining the maximum capacity by incurring additional selling expenditure

the party to take 10,000 units @ `90 per units by installing a balancing equipment and continuing with present level of sales

party to take 10,000 units @ `90 per cent by installing a balancing equipment and attaining sale of maximum available capacity by incurring additional selling expenditure

30,000 `

29,00,000 (20,00,000 ×

`100 + 10,000 × `90)

9,90,000*

Sale (units)

Sales Value: (A)

15,000 `

15,00,000 (15,000 ×

`100)

20,000 `

20,00,000 (20,000 ×

`100)

25,000 `

24,00,000 (15,000 ×

`100+10,000 × `90

8,25,000* Variable costs Direct material (33% of sales value) Direct Labour Variable overheads (@`20 per unit) Total variable costs: (B) Fixed costs Fixed overheads

Additional selling expenditure Depreciation for balancing equipment Additional administrative expenses Total fixed cost : (C) Total cost D: [(B)+(C)] Profit: (A)-(D)

2,75,000 2,75,000 2,75,000 2,75,000

11,70,000 15,60,000 19,50,000 23,40,000

3,75,000 3,00,000

5,00,000 4,00,000

6,25,000* 5,00,000

9,90,000* 6,00,000

4,95,000 6,60,000

(Refer to working note) - 50,000 - 50,000

- - 1,00,000 1,00,000

- - 50,000 50,000

2,75,000

14,45,000

55,000

3,25,000

18,85,000

1,15,000

4,25,000

23,75,000

25,000

4,75,000

28,15,000

85,000 Note: For computing the material and labour cost under alternative III & IV the notional sale price of `100 is taken for additional 10,000 units. Recommendation: Alternative II is the best as it gives maximum profit.

- 60 -

Ans. 73:

Comparative profit Statement (based on Revised Cost Structure) Proposal 1 Sell 20,000 units only

Proposal 2 Secure orders for 5,000 additional units (unused capacity) and sell 25,000 units ` 25,00,000

units × 25,000 `100) 6,25,000

units × (`25,000 units × `10) 2,50,000

units × (25,000 units × `10) 4,40,000

+

-

50,000

60,000

-

1,50,000

18,00,000 2,00,000

21,90,000 3,10,000

26,90,000 2,10,000

units ×

Proposal 3 Accept the new order for 10,000 additional units and sell 30,000 units ` 29,00,000 (30,000 `33) 7,50,000 (30,000 `10) 3,00,000 (30,000 `10) 4,40,000

units +

units +

units +

` Total sales revenue (A) 20,00,000

(`20,000 `100)

Director Labour 5,00,000 (20,000 `25)

Variable overhead 2,00,000 (20,000 `10)

Fixed overheads 4,40,000 (`4,00,000 `40,000)

Add: charges

Administrative

promotion

(New

-

- Add: Sales expenses Depreciation equipment) Total cots (B) Profit (C) = [(A) – (B)] Analysis An analysis of the profit figures of M/s Unique products under three proposals clearly shows that it is maximum under proposal 2. Therefore, it is advisable for the concern to produce and sell 25,000 units @ `100/- per unit and utilise its full production capacity.

(a) Statement of Profitability for the year 1993-94 (as originally envisaged by the company)

Products Ethylene EDC VCL 25,000 30,000 30,000 Annual Production Capacity (MT)

Annual Planned Productions (MT) 25,000 25,000 15,000 (Refer to Note -1)

Cost of production of annual planned production ` ` `

Ans. 74

Total

`

- 61 -

Variable costs (Refer to Note 2) Fixed cost (Refer to Note 3) Common cost (Refer to Note 4) Cost of Ethylene Cost of Ethylene (Used for EDC) Cost of EDC (25,000 MT) Cost of 10,000 MT of EDC (Refer to Note 5) Cost of 15,000 MT of EDC for (VCL) Cost of Sale (A) Sales Revenue (B) Profit (B-A)

5,00,000 5,00,000 2,50,000

12,50,000

7,50,000 9,00,000 4,50,000

12,50,000 33,50,000 13,40,000

6,00,000 12,00,000 6,00,000

20,10,000 44,10,000 57,50,000 13,40,000 45,00,000 60,00,000 15,00,000

2,50,000 90,000 1,60,000 Note: Only 25,000 metric tonne of ethylene is available and as such 25,000 metric tonne of EDC could be produced. Out of this 15,000 metric tonne of EDC is consumed for VCL production and the balance of 10,000 metric tonne of EDC is sold. Working Note: Note: 1 annual planned production

Ethylene EDC VCL - Proposed Sale 10,000 15,000

Production: - 10,000 15,000 For EDC 10,000 For VCL 15,000 15,000 - Total 25,000 25,000 15,000

2. Variable Costs Ethylene 25,000 MT x `20

=`5,00,000

EDC 25,000 MT x `30

=`7,50,000

30,000 MT x 30 =`9,00,000

30,000 MT x 15 =`4,50,000

VCL 15,000 MT x `40 =`6,00,000

30,000 MT x40 =`12,00,000

30,000 MT x 20 =`6,00,000

3. Fixed Cost (This will be based on 25,000 MT x 20 Production capacity) =`5,00,000

4. Common Cost (This will also be based 25,000 MT x 10

On production capacity =`2,50,000

5. Cost of 25,000 metric tones of EDC = `33,50,000 Cost of one metric ton of EDC = `33,50,000 * 25,000 = `134 Cost of 10,000 metric tones of EDC = 10,000 x `134 = `13,40,000 Cost of 15,000 metric tones of EDC = 15,000 x `134 = `20,10,000

6. Sales Revenue EDC = 10,000 MT x `150 VCL = 15,000 MT x Rs,300 Total

=`15,00,000 =`45,00,000

60,00,000

(b) Revised Statement of Profitability (When the company decides to accept offer of X)

Products Ethylene EDC Annual planned productions (MT) 25,000 25,000

VCL 30,000

Total

- 62 -

Cost of production Refer (a) Variable cost (30,000 MT x `40) 12,00,000

12,00,000 Production Fixed cost (30,000 MT x `40) 6,00,000 Common Fixed cost (30,000 MT x `20)

6,25,000 Purchases cost of 5,000 MT of EDC @ `125 per MT

39,75,000 Total of EDC used in VCL 39,75,000 Total cost (A) 69,75,000 Total Sales (Refer to note 1 below (B) 80,00,000 Profit (B-A) 10,25,000 Comment – Since the profit has increased the proposal of X should be accepted. Note 1: Total Sales :

20,000 MT of VCL to X @ `250 per MT =`50,00,000 =`30,00,000 10,000 MT of VCL X `300 (in open Market)

Hours Available capacity 20,000 First product D should be produced (2,800 x 6) 16,800 Balance hours 3,200 Second product A should be produced (2,000 x 1) 2,000 Balance hours 1,200 Third product B should be produced (600 x 2) 1,200

Thus, if 20,000 hours is the limiting factor, all requirements of D and A can be manufactured and only 600 units of product B can be manufactured. The balance requirement of product B. i.e.,3,500-600 =2,900 units will have to be bought – out or manufactured in the second shift. (b) Because purchase price of component c is `52 and cost of manufacturing is `57, it will not be profitable to manufacture C even in second shift. It should be purchased form outside, purchased from outside. The relative position is as follows:

Cost of producing 2,900 units of product B in second shift

Ans. 75: Solution (a) Working Notes

` 12,50,000

` 33,50,000

`

(i) Components Direct expenses Direct hours per unit

Marginal costs: Direct Materials Direct wages Direct expenses Marginal costs Bought – out price Excess of bought out price over marginal cost Process hours per unit

Press hours required A B

`10 `20 1 2

C `10

1

D `60

6

(ii) Marginal cost per unit vs. bought-out prices per unit

`37 10 10 57 60

`27 8

20 55 59

`25 22 10 57 52

`44 40 60

144 168

3 1

4 2

(5) 1

24 6

- 63 -

Excess of bought – out price per unit of limiting factor Ranking

4 3

11 2

111 (5) - 1

The bought – out price of component C is lower than the marginal cost by `5 and for this reason it should be purchased from outside. For the remaining products. Ranking is based on utilization of limiting factor. Optimal product mix has been, calculated as follows:

Calculation of optimal product mix

Variable Cost Increase in direct wages

`55

Total variable cost (2,900 x 57) Additional fixed cost Hours required = 2,900 x 2=5,800 hours Extra fixed cost of 5,800 hours at `500 for each 1,000 hours or part thereof 3,000 Total cost for producing 2,900 units of product B in second shift 1,68,300 Bought- out price for 2,900 units of product B will be 2,900 x `59 1,71,100 Disadvantage in buying B 2,800

2 57

`1,65,300

For the above-mentioned reasons, it is in the interest of company to manufacture product B in the Second shift instead of buying it from outside market .The disadvantage of the decision to buy product B from outside will be `2,800 .

80,00,000 Ans. 76:

Components P Q R S

i. Direct wages `17.50 `35.00 `17.50 `105.00 ii. D.L.H. @ `8.75 p.h 2 4 2 12 iii. Variable Mfg. cost `99.75 `96.25 `99.75 `252.00 iv. Purchase Price 105.00 103.00 91.00 294.00 v. Saving if components are

manufactured - 5.25 6.75 42.00 vi. Saving per hour (5 * 2) - 2.625 1.6875 3.50 Ranking 2 3 1

(i) Statement showing product-mix of the components to be manufactured (Available hrs. = 40,000)

Component Qty. reqd. Hrs. / unit Production Hrs. Used Balance hrs. 11,200 28,800 2,400 12 2,400 S 6,400 4,800 2,400 2 2,400 P - 6,400 1,600 4 4,800 Q

Components to be manufactured=

Components to be purchased =

*6,400 hrs * 4 = 1,600

S P Q Q R

= = =

= = 1,600 3,200 1,200

2,400 2,400

- 64 -

(ii) Statement showing impact of second shift working

Additional quantity of Q required = Hours required to manufacture (3,200 x 4) =

Say = Fixed cost (`875 * 1,0000 ) x 13,000 = `11,375 Fixed cost per component Q (11,375 * 3,200) Increase in labour cost (`35 x 25%) Total Saving in cost Loss if component Q is manufactured

Hence, second shift operation is not recommended Fixed cost given per 1,000 hours

3,200 12,800 13,000

=`3.55 8.75

12.30 6.75 5.55

Ans. 77: Since S and Y are produced simultaneously from an input of raw material Z, therefore when additional 60,000 kgs. of Y will be produced then 30,000 of S will also be produced simultaneously. The input of material Z required for these additional 60,000 kgs. of Y and 30,000 kgs. of S will be 90,000 kgs. of material Z. Hence the cost of processing 90,000 kgs. of material will be as follows:

` Cost of Raw material Z (90,000 kgs. × `3) Variable processing cost (90,000 kgs. × `2) Total cost of processing Less: Sales revenue from 60,000 kgs. of Y (60,000 kgs. × `8) Balance cost to be recovered Current sales revenue from the sale of 3,00,000 kgs. of S (3,00,000 kgs. × `8) Total sales revenue to be earned from the Sale of S (3,00,000 kgs. + 30,000 kgs.) Hence minimum reduced price per kg. of S to recover `26.10,000 from the sale of 3,30,000 kgs. of S (`26,10,000 / 3,30,000 kgs.)

Ans. 78: Working notes: 1. Statement of total available, utilized and surplus capacity hours when 9,000 units of product ‘X’ are

produced.

7.91

26,10,000

2,10,000 24,00,000

4,50,000 2,40,000

1,80,000

2,70,000

- 65 -

Departments Available Capacity hours

(2) 2,400

(300 days × 8 hours) 2,400 2,400 2,400

Capacity utilized

(in % (in hours) (4) = (2)×(3)

1,800

Surplus Capacity hours

(5)=(2)-(4) 600

(1) A

(3) 75

B C D

100 70 50

2,400 1,680 1,200

NIL 720

1,200 2. Statement of total available, utilized and surplus capacity hours when 12,000 units of product ‘X’ are

produced. Production Department

Available capacity

hours

Capacity utilization on 9,000 units Hours

Balance capacity

hours

Unit per hour Hours required for 3,000 additional

units (7)

600

Surplus capacity

hours

(1)

A

(2)

2,400

(3)

75

(4)=(2)×(3)

1,800

(5)

600

(6)

5

(8)=(5)- (7) Nil

9,000 units 1,800 hrs.

B 2,400 100 2,400 Nil 3.75 800 Nil 9,000 units 2,400 hrs.

C 2,400 70 1,680 720 5.36 560 160 9,000 units 1,680 hrs.

D 2,400 50 1,200 1,200 7.5 400 800 9,000 units 1,200 hrs.

Alternative I Statement of net Revenue (Under Alternative I)

Production Surplus capacity

hours (Refer to W.N.-1

(a) A B D

Total

Total return

600 720

1,200

Hire charges per hour

Total revenue in

(`Lacs)

Incremental costs per

hour `

Total cost in (`Lacs)

Net revenue

in (`)

(b) 2,500 1,800 1,600

(c)=(a)×(b) 15.00 12.96 19.20 47.16

(d) 2,000 1,500 1,200

(e)=(a)×(d) 12.00 10.80 14.40 37.20

(f)=(c)-(e) 3.00 2.16 4.90 9.96

180.00 189.96

Add: present income (10% of `1,800 lacs)

- 66 -

Return on investment

= Total return

Total investment × 100 =

189.96 1,800

× 100 = 10.553%

Alternative II Statement of Net Revenue when 12,000 units of product ‘X’ are produced and surplus plant capacity (hours) in departments C and D hired out. Production Surplus

capacity hours

(Refer to W.N.-2)

(1) C D

Total

160 800

Hire charges per hour

Total revenue in

(`Lacs)

Incremental costs per

hour `

Total cost in (`Lacs)

Net revenue in

(`Lacs)

(2) 1,800 1,600

(3)=(1)×(2) 2.88

12.80 15.68

(4) 1,500 1,200

(5)=(1)×(4) 2.40 9.60

12.00

(6)=(3)-(5) 0.48 3.20 3.68

48.00

231.69 180.00

Add: Revenue (in lacs) earned on 3,000 additional units sale (3,000 units is × `1,600) Add: Present income on investment (10% × `1,800 lacs) Total Return (in lacs)

Return on investment = 231.68 lacs 2,200 lacs

× 100 = 10.53%

Evaluation of two alternative proposals : Since the return on investment under alternative I is more than that under alternative II; therefore it should be accepted.

Ans. 79: (i) Statement of Profitability of three Joint Products resulting from the joint production process

of a popular line of colognes. Evergreen Morning

Flower Evening Flower

Total

` Sales revenue 4,00,000

(10,000 units × `40)

Less: cost after point of split off Net realization value at the point of spilt off Less: Joint cost apportioned (Refer to working note) Profit

2,00,000 (10,000 units ×

`20) 2,00,000

` 6,00,000

(6,000 units × `100)

2,40,000 (6,000 units ×

`40) 3,60,000

` 6,00,000

(4,000 units × `150)

2,00,000 (4,000 units ×

`50) 4,00,000

` 16,00,000

--

6,40,000 --

9,60,000

1,16,667 2,10,000 2,33,333 5,60,000

83,333 1,50,000 1,66,667 4,00,000

- 67 -

Response to the President’s question. Review of the above profitability statement clearly shows that the concern is not selling its largest-volume product viz. evergreen at a loss. It yields a profit of `83,333. In fact the figure of joint cost data given in the statement of the question is misleading. The total joint cost viz. `5,60,000 should have been apportioned ever the three joint products by using net realisable value method. The use of net realisable value method would give joint cost per-unit of three respective joint products as `11,666; `35 and `58.33. (Refer to working note) Working note: Statement of Joint cost apportionment over three products obtained under a joint production process.

Evergreen Morning Flower

Evening Flower

Total

` Total Joint cost 2,80,000

(10,000 units ×

`28) Joint cost apportionment (One the basis of net realization value i.e. (`2,00,000 : `3,60,000 : `4,00,000 or (5:9:10) Joint cost per unit

1,16,667

` 1,68,000

(6,000 units × `28)

2,10,000

` 1,12,000

(4,000 units × `28)

2,33,333

` 5,60,000

--

5,60,000 --

11,666 (`1,16,667

/ 10,000 units)

35 (`2,10,000 / 6,000 units)

58.33 (`2,33,333 / 4,000 units)

(ii) Should the company sell Morning Flower Cologne below cost: To compete successfully with the other company’s product, if the price of Morning Flower Cologne is reduced to `60, it will still contribute `20 per unit (`60 – `40) towards joint cost and profit. On a volume of 6,000 units it will contribute `1,20,000 in total. Hence the company should do so and go ahead to sell Morning Flower below cost.

(iii) Response to price reduction: (Refer to working note) A reduction in sales price of Morning Flower fails to maintain a gross margin of 20% on sales of three products obtained from the joint production process of a popular line of colognes. Hence the company cannot reduce the sales price of Morning Flower to `60. A reduction in sale price would result in a loss of revenue of `1,40,000. Working note:

` Total joint cost (20,000 units × `28) Total cost after split off (10,000 × `20 + 6,000 units × `40 + 4,000 units × `50) Total cost Add: Profit margin (20% on ales or 25% on total cost Expected desired sales revenue Less: Sales revenue of Evergreen and Evening Flower (10,000 units × `40) + (4,000 × `150) Expected sales revenue from Morning Flower By reducing sales price of morning flower to `60/- total sale revenue received will be Loss of revenue resulting from the sale of Morning Flower

(iv) Minimum price for Morning Flower

5,60,000 6,40,000

12,00,000 3,00,000

15,00,000 10,00,000

5,00,000 3,60,000

1,40,000

- 68 -

Expected Sales revenue from Morning Flower to maintain a gross margin of 20% of sales: (`) (Refer to (ii) part Quantity (in units) Hence minimum price per unit (`) (`5,00,000 / 6,600 units)

5,00,000

6,000 83.33

Ans. 80: (i) (a)

Products

Caustic soda Chlorine Total

Statement showing apportionment of joint costs sales value at split-off

Sales in tones (a)

2,400 1,600

Selling price per ton (`) (b) 100 150

Sales value (`) (c) = (a) * (b) 2,40,000 2,40,000 4,80,000

Apportioned cost (`) 1,00,000 1,00,000 2,00,000

joint

*Apportioned joint cost = Total joint cost * sale revenue of each product. Total sale value

Apportioned joint cost to caustic soda = `2,00,000 * `2,40,000 = 1,00,000 `4,80,000

Apportioned joint cost to chlorine = `2,00,000 * `2,40,000 = `1,00,000 `4,80,000

(b) Statement showing apportionment of joint costs on physical measure (tons) Products Sales in (tons) Caustic soda 2,400 Chlorine 1,600 Total 4,000

**Apportioned joint cost = Total joint cost * sales of each product (tons) Total sales (tons)

Joint cost apportioned to caustic soda = `2,00,000 * 2,400 tons = `1,20,000 `4000 tons

Joint cost apportioned to chorine = `2,00,000 * 1,600 tons = `80,000 `4,000 tons

(c) Statement showing apportionment of joint costs by using estimated net realizable value method

Products

Caustic soda (2,400 tons * `100) PVC (1,000 tons of PVC * `400) Total

Sales revenue (`)

2,40,000

4,00,000

Further cost (`) -

40,000

pro-cessing Net realizable value (`) 2,40,000

3,60,000

6,00,000

Total joint cost * Net realizable value of each product. Total net realizable value

Apportioned ** joint cost (`) 80,000

1,20,000

2,00,000

Apportioned ** joint costs (`) 1,20,000 80,000 2,00,000

***Apportioned joint cost =

Apportioned joint cost for caustic soda = `2,00,000 * `2,40,000 = `80,000 `6, 00,000

- 69 -

Apportioned joint cost for chlorine = `2, 00,000 * `3, 60,000 = `1, 20,000 `6, 00,000

(ii) Statement of gross margin percentage of caustic soda and PVC under sales value at split off: physical measure (tons) and estimated net realizable value method

Sale value at split off (`) Physical measure (tons) (`) Estimated net realizable value (`)

Caustic soda 2,40,000 2,40,000 2,40,000 Sale revenue : (A) 1,20,000 80,000 1,00,000 Joint cost allocated : (B) 1,20,000 1,60,000 1,40,000 Gross margin (C) : (A)-(B)

Gross margin (%) (C) * 100 (A)

(b) PVC: Sales revenue (A) Joint cost allocated Further processing cost Total cost Gross margin (c) : (A)-(B)

Gross margin (%) (C) *100 (A)

58.33%

4,00,000 1,00,000 40,000 1,40,000 2,60,000

65%

50%

4,00,000 80,000 40,000 1,20,000 2,80,000

70%

66.67%

4,00,000 1,20,000 40,000 1,60,000 2,40,000

60%

(iii) Consequence of the operating income of inorganic chemicals for November, 1998 by accepting the offer of daily swimming pools Ltd. to purchase, 1,600 tons of chlorine Incremental revenue (loss) due to processing of chlorine to PVC (`1, 60,000) (1,600 tons * `150) – (1,000 tons * `400 tons) Saving on further processing cost of chlorine into PVC 40,000 Incremental operating income (`1, 20,000)

The operating income of inorganic chemicals will be reduced by `1,20,000 in the month of November, 1998 if it accepts the offer of daily swimming pools Ltd., to purchase 1,600 tons of chlorine in November, 1998 at `150 per ton.

Ans. 81:

(i) Statement showing the product to be manufactured and sold and the result contribution Aristocrat deluxe

Maximum possible production in unit (Note1) S. P. per unit `90.00 `80.00 Less: variable costs: Aristocrat deluxe

Direct material `10.00 `10.00 Variable costs: Deptt. A (0.5*`50; 0.3 * `50) 25.00 15

27.00 Deptt. B (0.4 * `60; 0.45 * `60) 24.00 52.00 59.00 52.00 Total variable cost per unit 59.00

Contribution per unit 31.00 28.00 Total contribution per unit 6,800 * `31; 8,500 * `28 `2,10,800 `2,38000 Form the above, it is apparent that sale of `8,500 units of deluxe model produces the maximum contribution of `2,38000 within the capacity and material constraints. Therefore, 8,500 units of deluxe model should be produced.

(ii) statement showing the maximum contribution on the sale of aristocrat or deluxe models and hiring out the surplus capacity in departments A and B

Aristocrat deluxe Total contribution on sale of maximum possible production as per (i) above `2,10,800 `2,38,000

Contribution on hiring capacity (Note 2):

- 70 -

Deluxe Deptt. A 850 * `40 - 34,000

900 Deptt. B 15 * `60 67,200 Total contribution 2,78,000 2,72,900 It is noticed that total contribution of the company would be maximum i.e. `2,78,000 on the sale of 6,800 units of aristocrat model and hiring out the surplus capacity of the two departments.

(iii) Statement showing total contribution of company when 4,250 units of each product are manufactured and surplus capacity of Deptt. A and/or Deptt. B hired out

Aristocrat Deluxe Total (a) Production (units) 4,250 4,250 (b) Contribution per unit as at (i) above `31 `28 Total contribution (a) * (b) `1,31,750 `1,19,000 `2,50,750 Contribution earned on hiring the surplus capacity of Deptt. B (Note 3) 13,650*

2, 64,400 This proposal is less profitable then proposal at (ii) above

Working Note: Maximum capacity or production is given in hours. But part (i) required production to be stated in units. The same has been worked out as under:

Deptt. A Deptt. B Maximum capacity in hours 3,400 3,840

Aristocrat Deluxe Maximum hour per unit - Deptt. A 0.50 0.30

Deptt. B 0.40 0.45 Maximum possible production (in unit) – constant Maximum capacity

Deptt. A: 3,400/0.5; 3,400/0.30 6,800 11,333 Deptt. B 3,840/0.40; 3,840/0.45 9,600 8,533

Maximum possible production (in unit) – constant Available material 17,000 kgs/2 kgs 17,000/2 kgs 8,500 8,500

Maximum possible production considering both Capacity and material constants 6,800 8,500

2. Surplus capacities

(a) Maximum possible hours (b) Capacity used when 6,800 units of aristocrat model are produced (0.50 * 6,800; 0.40 * 6,800) (c) surplus capacity with aristocrat model (d) Capacity used when 8,500 units of deluxe model are produced

(0.3 * 8,500; 0.45 * 8,500) (e) Surplus capacity with deluxe model (a)-(d)

3. Maximum possible hour as in unit Note 1 Hour utilized aristocrat 4,250 * 0.50; 4,250 * 0.45

Deluxe Surplus capacity (hours)

Deptt.A 3,400

3,400 NIL

2,550 850 Deptt. A 3,400 (-) 2,125 (-) 1,275 NIL

Deptt. B 3.840

3,840 1,120

3,825 15 Deptt. B 3,840 (-) 1,700 (-) 1912.5 NIL

Aristocrat Nil 1,120 * `60

Ans. 82: Brightly Unit price

`

Contrib ution

per unit Volume Units

`

Total contributi on (`in 000)

Increment al contributi on (`000)

Labou r hours

Increme ntal labour hours

Increment al contributi on per labour hour

Rank

`

- 71 -

276

272

268

264

260

254

176

172

168

164

160

154

12000

14000

16000

18000

20000

22000

2112

2408

2688

2952

3200

3388

2112

296

280

264

248

188

2400 0

2800 0

3200 0

3600 0

4000 0

4400 0

24000

4000

4000

4000

4000

4000

88

74

70

66

62

47

2

6

7

8

9

10

Lightly Unit price Contribution

per unit Volume Total

contribution (`in 000)

4120 4284 4444 4600 4608 4600

Incremental contribution

(`000)

4,120 164 160 156

8 (8)

Labour hours

Incremental labour hours

40,000 2,000 2,000 2,000 2,000 2,000

Incremental contribution

per labour hour 103 82 80 78 4

(4)

Rank

163 162 161 160 156 152

103 102 101 100 96 92

40,000 42,000 44,000 46,000 48,000 50,000

40,000 42,000 44,000 46,000 48,000 50,000

1 3 4 5

11 Loss

As the labour time is scarce source (time available 78,000 hours), the decision has to be taken on the basis of ranks based upon incremental contribution per labour hour.

Product Price Incremental volume

40,000 12,000 2,000 2,000 2,000 2,000 2,000

Incremental labour hours 40,000 24,000 2,000 2,000 2,000 4,000 4,000

Balance hours

38,000 14,000 12,000 10,000 8,000 4,000

Incremental Contribution

(in 000 `) 4120 2112 164 160 156 296 280

7,288

Lightly Brightly Lightly Lightly Lightly Brightly Brightly Total

163 276 162 161 160 272 268

Hence product mix is Brightly – 16,000 units and Lightly 46,000 units Optimal contribution per month Fixed costs per month Optimal profit per month

Working Notes:

Brightly Variable cost (p.u.)

Fixed cost (`)

Lightly

`72,88,000 `60,00,000 `12,88,000

(38,00,000 34,00,000) Rs. 100

(16,000 12,000) 22,00,000

(66,80,000 62,00,000) Rs. 60

( 48,000 40,000) 38,00,000

Contribution = Unit selling price less variable cost per unit.

- 72 -

Ans. 83:

Months Total number of unit

`60,000 Produced (Note 4) `28,125 Variable cost `2,81,250 `6,00,000 Labour cost (Note 2) 3,00,000 6,00,000 Overheads 1,12,500@ 2,40,000@ Total sami variable overheads (Note 3) Fixed overheads Total costs Add: profit: (20% on selling price or 25% on cost) Sales revenue Selling price per unit ( `40,10,063/1,21,875 on cost)

Statement showing computation of selling price per unit 1-3 4-9 10-12

`33,750 `3,37,500

3,37,500 1,35,000@

Total

1,21,875 `12,18,750

12,18,750 4,87,500 72,000# 1, 92,300

32, 08,050 8, 02,013

40, 10,063 32.90

Working notes 1. Average installed capacity per month (in units):

= Total annual installed capacity/12 month (in units): = 1, 50,000 units/ 12 months = 12,500 units per month.

2. Total labour cost at different capacity utilization: Capacity utilization 75%

Expected production per month ( in units) 9,375 Labour cost of expected production (`) 93,750 Minimum lqbour cost per month (`) 1, 00,000 Capacity utilization (in months) 3 Total labour cost at different capacity levels `3, 00,000

80% 10,000 1, 00,000 1, 00,000

6 `6, 00,000

90% 11,250 1, 12,500 1, 12,500

3 `3, 37,500

@28125 × `4; 60000 × `4; 33750 × `4 #This can also be taken based on average capacity utilization i.e. ( 121875÷150000) × 100 = 81.25%. Therefore, semi- variable overheads can also be taken as 68000 (refer note 3). In that case, selling price will be `32.87.

Ans. 84:

Part A

Target Price (`) Less : Variable Cost p.u. (`) Material(1.6 kg. @ `12.5 p.kg.) (`) Variable OH Machine A (0.6/0.25 hrs @ `80 p.h.) (`) Variable OH: Machine B (0.5/0.55 hrs @ `100 p.h.) (`) Total Variable Cost p.u. (`) Contribution p.u. (`)

Number of parts can be manufactured on the basis of: Alloy Available (13000kg ÷ 1.6/1.6) Machine A (4000 hrs ÷ 0.6/0.25) Machine B (4500 hrs ÷ 0.5/0.55) Maximum units that can be manufactured

Total Contribution (6,666 units × 27; 8,125 × 20) Hence it is recommended to produce Part A.

(b) Parts A to be Manufactured

145

20 48 50

118 27

8,125 6,666 9,000 6,666

179,982

Part B

115

20 20 55 95 20

8,125 16,000

8,181 8,125

162,500

6,666 units Hours utilized Idle hours

Machine A usage (6,666 × 0.6) 3,999.6 0.4 Machine B usage 3,333 1167 Compensation for unutilized machine hour (1167.4 @ Rs 60/ hour) `70,044 Revised contribution after reduction of 10% in S.P. [6,666 × (145 × 0.9 – 118)] `83,325

- 73 -

Total Contribution

Ans. 85:

`153,369

Capacity (units) Selling Price 1000 Material Cost 400 Throughput contribution 600 `/u.

(i) Throughput Contribution Subcontracting changes

600 400 200

Cutting 10,000

Finishing 5,000

Increase in throughput contribution = 200 x 5000 = 10,00,000 (ii) Already cutting has surplus capacity. It is not a bottleneck. Do not outsource as there will be

no benefit, instead there will be reduction of or throughput contribution of outsourced. (iii) Cutting has surplus capacity. Do not increase non-bottleneck capacity.

Ans. 86: Contribution analysis:

Product X Product Y `

Selling price Variable costs:

Direct materials Direct Labour:

40 48 24 72

Variable overheads Total variable costs

32 216

288 `

432

80 72 48

96 28

324 Contribution per unit 72 108

The direct labour hours required to manufacture the two products in each of the four departments at the wage rate of `8 per hour are as under:

Department

1 2 3 4

48 24 72

Product X Wage cost Hours/unit

6 3 9

72 48

96

Product Y Wage cost Hours/unit

9 6

12

Department 3 is used only for product X and department 4 is used only for product Y. Hence, these two departments will determine the maximum production of these two products as under: Department 3 : Maximum available hours:

Workers 27

Hours/day 8

Days/year 300 = 64,800 hours

- 74 -

Maximum possible production of product X:

Department 4 : Maximum available hours: Workers 36

Hours/day 8

64,800 = 7,200 units

9 hrs per unit

Days/year 300 = 86,400 hours

Maximum possible production of product Y: 86,400

= 7,200 units 12 hrs per unit

The company can produce 7,200 units each of products X and Y provided departments 1 and 2 have capacity to process this quantity of output. We can check the capacity of departments 1and 2 as under: Department 1: Maximum available hours: Workers 45

Product X Product Y Total

Hours/day 8

days/year 300

= = =

= 1,08,000 hours Hours required to produce 7,200 units each of X and Y:

7,200 6 hours 7,200 9 hours

43,200 hours 64,800 hours 1,08,000 hours

Department 1 has capacity to produce 7,200 units each of products X and Y. Department 2 : Maximum available hours: Workers 24

Product X Product Y Total

Hours/day 8

days/year 300

= = =

= 57,600 hours Hours required to produce 7,200 units each of X and Y:

7,200 3 hours 7,200 6 hours

21,600 hours 43,200 hours 64,800 hours

Department 2 has scarce capacity. Since department 2 capacity is scarce, link the contribution to the key factor of department 2 hours as under:

Contribution per unit Department 2 hours per unit Hours Contribution per hour of Department 2 Rank

Optimal product mix: Product Max.

units

7,200 7,200

Lab. Hours/unit

3 6

Prod. units

7,200 6,000

Product X 72

3

` 24 1

Hours used

21,600 36,000

Balance hours

36,000

Cont./unit

Product Y 108

6

18 2

Total cont.

` X Y

Fixed costs Optimal profit

Alternative Solution:

72 108

` 5,18,400 6,48,000

11,66,400 5,00,000 6,66,400

Total optimal contribution

- 75 -

The maximum possible production of product X is 7,200 units and that of product Y is 7,200 units. The following two methods shall be used to determine the optimal profit: (a) Produce 7,200 units of product X and use the balance capacity to produce product Y. (b) Produce 7,200 units of product Y and use the balance capacity to produce product X.

Profitability based on (a): Direct labour hours are scarce in Department 2. Maximum available hours in Department 2 Product X requires 7,200 3= Balance hours on Y Production of Y 36,000 6= Contribution: @ `72

@ `108 Total Fixed costs Profit

Profitability based on (b): Maximum available hours in Department 2 Product Y requires 7,200 6= Balance hours on X Production of X 14,400 3= Contribution: X 4,800 72

Y 7,200 108 Total Fixed costs Profit

Profitability of (a) is better.

Ans. 87: (a) Statement of Cash Receipts, Disbursements and cumulative difference in Cash flows for four years taken

together under both alternatives (`in thousands)

Alternatives Keep old machine Year

1 2nd 3rd & 4th year each

All 4 years

Buy new machine Year 1 2nd 3rd

& 4th year each

All 4 years

Cumulative difference in cash flows

for four years taken

together

57,600

14,400 4,800 units

`3,45,600 `7,77,600

`11,23,200 `5,00,000 `6,23,200

43,200 hours

X 7,200 units

Y 6,000 units

57,600 21,600 hours 36,000 6,000 units

`5,18,400

`6,48,000

`11,66,400 `5,00,000 `6,66,400

Receipts Sales revenue Self of old

150 -

150 -

600 -

150 8

150 -

600 8

- 76 -

equipment Total receipts : (A) Disbursements Annual operating cost Other cash costs Purchase cost of “old” machine Purchase of “new” machine Total disbursements (B)

:

5 25 80 (5) 31 88 08

15

110 20

-

145

15

110 -

-

125

60

440 20

-

520

9

110 20

24

163

9

110 -

-

119

36

440 20

24

520

150 150 600 158 150 608

Net cash inflows: (A)-(B)

Alternatives (b) Statement of income for each of the four years and cumulative difference in operating income.

Keep old machine 1st, 2nd 3rd &

4th year each

Income Sales revenue Total revenue : (A) Costs: Annual cost

operating 15

110 5

the old

-

60

440 20

-

9

110 6

12

9

110 6

-

36

440 24

12

150 150

600 600

150 150

150 150

600 600

All years

Buy new machine Year 1 2nd 3rd

& 4th year each

All 4 years

Cumulative difference operating income

Other cash costs Depreciation (Refer to working note 1) Loss on disposal of machine

Total costs: (B) Operating (A)-(B)

income:

(Refer to working note 2) 130 20

520 80

137 13

125 25

512 88 08

(c) The purchase of cost old machine `20,000; the sale revenue `1.50,000 and other cash costs of `1,10,000 as irrelevant items for the presentation in requirements (a) and (b) above. These items are irrelevant because their amounts are common to both the alternatives.

(d) The net difference in requirements under (a) and (b) will not change if the cost of ‘old’ machine becomes `10,00,000 instead of `20,000. This is so because the cost of old machine is common for both the alternatives.

(e) In the decision about eh replacement of machine the book value of the machine is irrelevant because it is a past (historical) cost. All past costs are down the drains. Nothing can change what has already happened. As apparent from (a) and (b) above; we can completely ignore the cost of old machine i.e. `20,000 and still have a correct analysis.

- 77 -

Working note: 1. Depreciation (according to straight line method):

Old machine (i) cost of machine (`) (ii) Terminal disposal value (iii) Useful life

Depreciation

20,000 Zero 4

New machine 24,000

Zero 4

5,000 (i) - (ii)

` (iii) 5,000

2. Loss on the disposal of old machine: `

Purchase price of old machine Disposal value Less: Removal cost

Ans. 88:

Evaluation of Make or Buy proposal (All figures are in lakhs in rupees)

Year P.V. factors at 10%

When the manufactured

Cash outflow (Capital cost + manufacturing cost + opportunity cost)

component is

10,000 2,000

` 20,000

8,000 12,000

When the component is bought from an outside supplier Cash outflow (Buying cost)

Present Value

Present Value

` (a)

0 1 2 3 4

Total

(b) 1.000 0.909 0.826 0.751 0.683

(c) 4

6+2 7+2 8+2

10+2

` (d)=(b)×(c)

4.000 7.272 7.434 7.510 8.196

34.412

` (e)

- 9

10 11 14

` (f)=(b)×(e)

- 8.181 8.260 8.261 9.562

24.264

Saving in cash outflow (when brought from outside)

total present value of Total present value of cash outflow, when the cash outflow, when the

component is manufactured component is bought

internally from outside.

= `24.412 – `34.264 = `0.148 (lakhs)

Conclusion: Since there is a saving of `0.148 (lakhs) in buying the component from outside, therefore, we should stick to this decision.

- 78 -

Note: The loss of `2 lakhs cash inflow for each of the four years due to the inability of the firm to operate another machine if it manufactures the component has been treated as an opportunity cost.

Ans. 89: Proposal I

Year (a)

1 2 3 4 5

Proposal II

Year (a)

Quantity of Price per Variable Net price per Net sales Discount PV of net sales medium in metric cost per metric tone (`) revenue in factor @ revenue metric tones tone metric tone (e) =(c)– (d) (`Lacs.) (f) = 12% (g) (`Lacs.) (h) = (b) (c) (`) (d) (b) * (e) (f) * (g)

1 1,000 1,200 200 1,000 10 0.89 8.90 2 2,000 1,300 200 1,100 22 0.79 17.38 3 3,000 1,400 200 1,200 36 0.71 25.56 4 4,000 1,500 200 1,300 52 0.64 33.28 5 5,000 1,600 200 1,400 70 0.57 39.90

Total 125.02 Note: since the selling price of medium is not given after second year, therefore an individual is free to talk any selling

price after second year. In view of this assumption the answer of each case may differ.

Year (a)

1 2 3 4 5

Quantity of mild in metric tones (b) 14,000 13,000 12,000 11,000 10,000

Price per metric tone (`) (c)

950 900 850 800 750

Sales revenue in (`Lacs) (d) = (b) * (c) 133 177 102 88 75

Discount factor @ 12% (e)

0.89 0.79 0.71 0.64 0.57

PV of sales revenue in (`Lacs) (f) = (d) * (e) 118.37 92.43 72.42 56.32 42.75

Statement of sales revenue of mild Quantity of mild in Price per metric metric tonnes (b) tonne (c)

15,000 15,000 15,000 15,000 15,000

950 900 850 800 750

Total amt of sales in (`Lacs) (d) = (b) * (c) 142. 5 135.0 127. 5 120.0 112. 5

Discount factor @ 12% (e)

0.89 0.79 0.71 0.64 0. 57

NPV of sales (`In lacs) (f) = (d) * (e) 126.825 106.65 90. 525 76.800 64.125 464. 925

Total 382.29 Total present value of sales of medium and mild under proposal II (`Lacs) 507.31 (`125.02 lacs – `382.29 lacs) Total net present value under proposal II (`507.31 lacs – `30 lacs) The net present value under proposal I is `464.925 lacs, and that under proposal II is `477.31 lacs. A comparison of the net present value under two proposal clearly shows that the proposal II is better as it yield a higher net present value of revenue, therefore it should be accepted.

Ans: 90 (i) 15,000 tins scrapped per month can be converted into 75,000 lids. (Each rejected tin can be converted into 5 lids) unusable tins are sold as scrap at `8 per unit. Hence, `8 can be taken as raw material cost for conversion into lids. 15,000 tines at `8 1,20,000

Add: Conversion cost `50 per 100 pieces. i.e. 50 paise per piece. 15000 x 5 = 75,000 lids x 0.50 = 37,500

- 79 -

Total cost of 75,000 lids 1,57,500 Less: Value of scrapped lids and off-cuts. Weight of tins: 15,000 kgs. 75,000 x 120 gms =

1,000 9,000 kgs. Weight of scrap 6,000 kgs. Sales value of scrap 6,000 x 5 30,000 Net cost of 75,000 lids 1,27,500 Cost of each lid 1,27,500 / 75,000 `1.70

`2.00 Cost of buying one lid Hence, there will be a saving of 30 paise on each lid converted instead of buying from outside. In view of saving , the proposal should be accepted.

`lakhs (ii) Saving in year: Buying 1,00,000 lids x

12 Months x `2.00 24.00

Less: Conversion cost: 75,000 lids x 12 months x 1.70 = Cost of buying the balance lids = 25,000 lids x 12 months x 2.00 = Saving in a year

15.30

6.00 21.30 2.70

Or else, 75,000 lids x 12 months = 9,00,000 lids at Re. 0.30 each = `2,70,000 savings in a year accrue to the company if the proposal is accepted. Ans. 91:

Order Qty Order Qty 100-140 (`) 141-200 (`)

Selling Price `/u 30,000 30,000 Commission @ 10% 3,000 3,000 Sales revenue p. u. 33,000 33,000 Less: Variable purchase cost Contribution / unit 29,000 26,000

4,000 7,000 (before shipping) Less: Shipping cost > 110 units 5,000 Contribution/ units after Shipping 2,000 (i) Upto 110 units, Reference will earn a contribution of `4,000/u.

(ii) Between 110 & 140 units, contribution of 4,000 will be wiped out by 5,000 on shipping costs. Hence we should not consider 110 – 140 range.

(iii) 101 – 110 not to be considered since additional fixed costs 2,25,000 will not be covered by 10 units.

(iv) Valid consideration, 100 units or 141 to 190 units. Fixed cost of box of 50 cameras is `2,25,000

- 80 -

Units 100 141 150 190 No. of Camera Boxes Cost of Cameras (`) Contribution (Rs/u) `4,000 Contribution (`) first 110 units @ 7,000/u

A B

C

D

2 3 4,50,000 6,75,000

400,000

7,70,000

3 6,75,000

4 9,00,000

7,70,000 7,70,000

62,000 80,000 1,60,000 E Contribution (`) Balance units @ 2,000/u

4,00,000 8,32,000 8,50,000 9,30,000 F Total Contribution

(F - 50 000 1 57 000 1 75 000 30 000

Best strategy buy 150 units from Comp. sell 110 at store and 40 outside. BEP

should be between 151 – 191 units

Extra Camera box cost beyond 150 units

Less: Profit for 150 units Extra profit acquired

= 2,25,000

= 1,75,000 = 50,000

No. of units to cover this additional costs at contribution 2000 `/u =25

BEP = 150 + 25 = 175 units

Ans:7 The problem may be summarized as follows:

Chemical A

Supplier X Supplier X2

Units required

1

Chemical B

2 1

60

Cost per mix Rs.

10 4

4 1

80

Let x1 be the number of mixes to be purchased from supplier X1 and x2 be of those to be purchased from supplier X2.

The conditions of the problem when symbolised, take the form: Minimize Z = 10 x1 + 4 x2 Subject to the restrictions x1 ≥ 0, x2 ≥ 0 4x1 + x2 ≥ 80, 2x1 + x2 ≥ 60. For the line 4x1 + x2 = 80, let x1 = 0,so that x2 = 80; let x2 = 0,so that x1 = 20. For the line 2x1 + x2 = 60, let x1 = 0,so that x2 = 60; let x2 = 0,so that x1 = 30.

Feasible region is shaded in the diagram which appears to be unbounded. We now try to determine the additional hidden conditions in the problem for which the feasible region becomes bounded. The column vector for the values of the objective function is given by

Solution’s of Linear Programming

Since 260 is the smallest element in EC, the minimum value is reached at the extreme point E2, whose coordinates are (10,40). Thus, to honour the contract and yet to minimize cost, the company should purchase 10 mixes from X1 and 40 mixes from X2.

Ans.8: Maximize x + 2y 720

5x + 4y 1800 3x + y 900 x 0y 0

where x = No. of units of A y = No. of units of B

By the addition of slack variables s1, s2 and s3 the inequalities can be converted into equations. The problem thus become

z = 80x + 100y subject to x + 2y + s1 = 720 5x + 4y + s2 = 1800 3x + y +s3 = 900

and x 0, Table I

Profit/unit 0

0

Qty. 720

1800

900

80 X

5

3 80

100 Y 2

4

100

0 S1 1

0

0 0

0 S2 0

1

0 0

0 S3 0

0

1 0

y 0, s1 0, s2 0, s3 0

z = 80x + 100y subject to

S1

S2

S3 0 Net evaluation row

1800 – 720 4/2 = 360 5 – I 2 = 3 4 – 2 2 =0 0 - I 2 = - 2 I - 0 2 = I 0 - 0 2 = 0

Table 2:

Program Y S2 S3

Profit/unit 100 0 0

Qty. 360 360 540

720 360 2

1800/4 = 450 900/1 = 900

900 - 720 1/2 = 540 3 - 1 ½ = 5/2 I – 2 1/2 = 0 0 – I 1/2 =- 1/2 0 – 0 1/2 = 0 I- 0 1/2 = I

80 X ½ 3 5/2

100 Y I 0 0

0 S1 ½ 2 1/ 2

0 S2 0 1 0

0 S3 0 0 I

360 1/2=720 360 3=120 540 5/2=216

Net evaluation row

360 – 360 1/6 = 300 ½ - 3 1/6 = 0 1- 0 1/6=1 ½ - -2 1/6 = 5/6 0 – 1 1/6 = - 1/6 0 – 0 1/6 = 0

Table 3:

30 0 50 0 0

540 – 360 5/6 = 240 5/2 –3 5/6 = 0 0 – 0 5/6 = 0 -1/2 - -2 5/6 = 7/6 0 – 1 5/6 = -5/6 1-0 5/6 = 1

80 100 Y I 0 0 0

0 S1 5/6 2/3 7/6 -500/6 +160/3

=

0 S2 -1/6 1/3 -5/6 +100/6 -80/3 0

0 S3 0 0 I

Program Y X S3 Net evaluation row

Profit/unit 100 80 0

Qty. 300 120 240

X 0 I 0 0

180 6

= 60 6

All the values of the net evaluation row of Table 3 are either zero or negative, the optimal program has been obtained. Here X = 120, y = 300 and the maximum profit

= 80 120 + 100 300 = 9600 + 30,000 = Rs. 39,600.

Ans. 9: Formulation of Linear Programming (LP) model :

Let X1 and X2 be the units of products A and B respectively which were manufactured and sold (within sales constraints) by the company in a month, by utilizing monthly available budgeted capacity in department A and B so as to maximize the profit of the company. The formulated LPP based on the given data is as under :

Max Z = 80 x1 + 100 x2

2 x1 + 4x2 < 1,400

5x1 + 4x2 < 2,000

X1 < 400

X2 < 400

X1, X2 > 0

--

--

--

--

(Refer to working note)

Department P Constraint

Department Q constraint

Product A Sales constraint

Product B sales constraint

Graphical Solution :

Draw the above four constraints by selecting X1 and X2 axes as shown in the diagram.

X2 - AXIS

X1 < 400

(0,500)

(0,350)

X2 < 400

P (200, 250)

0 (400,0) (700,0)

Put x2 = 0 in (i), then x1 = 700

Put x1 = 0 in (i), then x2 = 350

Put x2 = 0 in (ii); then x1 = 400

Put x1 = 0 in (ii); then x2 = 500

The point of intersection of (i) and (ii) viz, P is given by (200, 250)

The marked area represents the feasible area (common to all of the four constraints). The corner points of the identified feasible region are (0,0); (400,0); (200,250) and (0,350).

According to Dantzig, the objective function is maximum or minimum at the corner points of the feasible region.

Z (0,0)

Z (400, 0)

=

=

0,0

32,000

Z (0, 350)

Z (200, 250)

=

=

35,000

41,000

The objective function has maximum contribution viz, Rs. 41,000 at the point (200, 250). Hence, the concern should manufacture and sell 200 units of A and 250 units of B product.

Optimal contribution (Rs) (200 units x Rs. 80 + 250 units x Rs. 100)

Less : Fixed costs (Rs. 14,000 + Rs. 20,000)

Optimal profit

Working note :

Product A

Selling price per unit : (i)

Variable manufacturing costs

Sales commission

Total variable cost per unit : (ii)

Contribution per unit : (ii – I)

300

160

60

220

80

Product B

200

60

40

100

100

41,000

34,000

_____ 7,000

Ans. 11: Let x1, x2 x3 be the number of units produced of products A, B and C respectively. Then the profit gained by the industry is given by

Z = 3x1 + 8x2 + 2x3 Here it is assumed that all the units of products A and B are sold. In first operation, A takes 3 h of manufacturer’s time and B takes 4 h of manufacturer’s time. Therefore, total number of hours required in first operation becomes.

3x1 + 4x2 In second operation, per unit of A takes 2 h of manufacturer’s time and per unit B takes 5 h of manufacturer’s time. Therefore, the total number of hours used in second operation becomes

3x1 + 5x2 Since there are 18 h available in first operation and 21 h in second operation, the restrictions become

3x1 + 4x2 ≤ 18 3x1 + 5x2 ≤ 21

Since the maximum number of units of C that can be sold is 5, therefore, X3 ≤ 5 …… (3)

…… (1) …… (2)

Further, the company gets three units of by product C for every unit of product B produced, therefore X3 = 3x2 …… (4)

Now, the allocation problem of the industry can be finally put in the following linear programming problem:

Maximise Z = 3x1 + 8x2 + 2x3 Subject to the constraints

3x1 + 4x2 ≤ 18 3 x1 + 5x2 ≤ 21 x3 ≤ 5, x3 = 3x2 x1, x2 , x 3 ≥ 0

Ans. 15: Let X1, X2 and X3 respectively be the amounts in tons of grades A, B, and C used. The constraints are (i) Phosphorus content must not exceed 0.03%

.02 X1+ .04X2 + 0.3 X3 .03 (X1 + X2 + X3) 2X1 + 4 X2 + 3X3 3 (X1 + X2 + X3) or – X1 + X2 0

(ii) Ash content must not exceed 3% 3X1 + 2 X2 + 5 X3 3 (X1 + X2 + X3) or – X2 + 2X3 0

(iii) Total quantity of fuel required is not more than 100 tons. X1 + X2 + X3 100 The Mathematical formulation of the problem is Maximize Z = 12 X1 + 15X2 + 14 X3 Subject to the constraints: - X 1 + X2 - X 2 + X3 X1 + X 2 + X3 X1, X 2, X 3 >

0 0

100 0

12 15 Y2 1* -1 1 -15

Y2 1 0 0

14 Y3 0 2 1 -14

Y3 0 2 1

0 Y4 1 0 0 0

Y4 1 1 -1

0 Y5 0 1 0 0

Y5 0 1 0

0 Y6 0 0 1 0

Y6 0 0 1

Introducing slack variable X4 >0, X5>0, X6>0

Cb 0 0 0

Yb Y4 Y5 Y6 Z

Cb 15 0 0

Yb Y2 Y5 Y6

Xb 0 0 100

Xb 0 0 100

Y1 -1 0 1 -12

Y1 -1 -1 2*

Z Cb 15 0 12

Cb 15 14 12

Yb Y2 Y5 Y1 Z Yb Y2 Y3 Y1

Xb 40 20 40

Xb 50 50 50

-27 Y1 0 0 1 0 Y1 0 0 1

Y2 1 0 0 0 Y2 1 0 0

-14 Y3 1/2 5/2* 1/2 -1/2 Y3 0 1 0

15 Y4 1/2 1/2 -1/2 3/2 Y4 2/5 1/5 -3/5

0 Y5 0 1 0 0 Y5 -1/5 2/5 -1/5

0 Y6 1/2 1/2 1/2 27/2 Y6 2/5 1/5 2/5 68/5 Z 0 0 0 8/5 1/5

The optimum solution is X1 = 40, X2 = 40 and X3 = 20 with maximum Z = 1360. Ans.16:

40 Cj

Qty Cj

0 0 0

Variable

X3 X4 X5

Zj Zj-Cj

36 60 60

0

X1

3 5 2

0 -40

X2

3 2 6

0 -60

X3

1 0 0

0 0

X4

0 1 0

0 0

X5

0 0 1

0 0

12 30 10

60 Table 1 0 0 0 Ratio

40 Cj

Qty Cj 0 0

60

Variable X3 X4 X2 Zj

Zj-Cj

6 40 10

600

X1 2

13/3 1/3 20 -20

60 Table 2 0 0 0 Ratio

X2 0 0 1

60 0

X3 1 0 0 0 0

Table 3 60

X4 0 1 0 0 0

X5 -½ -1/3 1/6 10 10

3 120/13

30

40 Cj

Qty Cj 40 0

Variable X1 X4

3 27

X1 1 0

0 0 0

X2 0 0

X3 ½

-13/6

X4 0 1

X5 -1/4 3/4

60 X2 Zj

Zj-Cj

9 660

0 40 0

1 60 0

-1/6 10 10

0 0 0

1/4 5 5

Since all Zj –Cj are positive or zero, this is the optimum solution with, X1 =40 & X2 = 60 and optimum Z = 660.

Note: Alternatively, Cj-Zj may be used whereby maximum positive value may be considered.

Ans. 18: Under the usual notations where S1,

S2, S3 are stock Variables, A4 = the artificial variable S4 = Surplus Variable We have,

Max. Z = 100x 1 + 80x2 + 0S1 + 0S2 + 0S3 + 0S4 – M A4. S.t.

3x1 + 5x2 + S1 = x2 + S2 =

8x1 + 5x2 + S3 = x1 + x2 + - S4 + A4 =

x1 x2 S1

Basis

S1 S2 S3 A4 Zj Cj-Zj

Cj CB

0 0 0

-M

100

3 0 8 1

-M

80

5 1 5 1

-M

0

1 0 0 0 0 0

150 20

300 25 S2

0

0 1 0 0 0 0

S3

0

0 0 1 0 0 0

S4

0

0 0 0 -1 M -M

A4

-M

0 0 0 1

-M 0

150 20 300 25

-25M

√ √ √ √ √ √ 100+M 80+M

Ans.20: (i) Simplex Table

Basis

x1 x2 Zj NER

Cj → CB 8 6 → Cj - Zj

8 x1 1 0 6 0

6 x2 0 1 6 0

0 s1 ⅓ -⅙ 5

3 3 − 5

0 s2 -⅙ ⅓ ⅔ -⅔

(1 mark)

2 marks 1 marks

Note: Zj values are obtained by multiplying each row with cost and adding the values of the respective column as under:

X1

X1

X2 Adding Zj

8X1=8

6X0=0 8

X2

8X0=0

6X1=6 6

S1

8 X 1/3 = 2.2/3

6 X - 1/6 = - 1 5/3

S2 6 8 X - 1/ =

1.1/ 3 6 X 1/3 =

2/3 2

Net Evaluation Row (NER) is obtained by deducting Zj from Cj as under: 8–8=0 6–6=0 0 – 5/3 = - 5/3 0 – 2/3 = - 2/3

Since the values of NER are 0, the solution represented by this tableau is optimal. ≤

(ii)

X1 MI 60 X2 M II 48

Total optimal contribution

Ans.21: Let pi dj be the variable to denote the number of units of product from the ith plant to the jth

destination, so that P1d1 = transport from plant P 1 to D1 P2d2 = transport from plant P 2 to D2 etc. Objective function Minimize z = 400 p1d1 + 600 p1d2 + 800 p1d3 + 1000 p2d1 + 1200 p2d2 + 1400 p2d3

+ 500 p3d1 + 900 p3d2 + 700 p3 d3. Subject to:

p1d1 p1d 2 p1d 3 65

p 2 d1 p 2 d 2 p 2 d 3 24 (Plant constraints)

p 3 d1 p 3 d 2 p 3 d 3 111

p1d1 p 2 d1 p 3 d1 60 p1d 2 p 2 d 2 p 3 d 2 65 (destination constraints)

p1d 3 p 2 d 3 p 3 d 3 75

all pidj ≥ 0

x x

S1 5/3

-

S2

2/3

Rs. 100 32

132

and

Ans.22:

Route I Residence HO 600 400 300 180

Residence Route II Residence Br. Residence No. of vehicles Max. capacity No. of passengers

Let i be the ith route, and j be the type of vehicle, so that S11 = no. of vans (vehicles on Route I, Type I) S12 = no. of 8 seater cars on Route I S13 = no. of 5 seater cars on Route I S21 = no. of vans ─ on Route II

S22 = no. of 8 seater cars on Route II S23 = no. of 5 seater cars on Route II

Ans. 23:

500

4 80

300

10 80

200

20 100

260 220

40

Formulation. Let xi be the number of times cutting alternative i (j = 1,2, .....6) is employed. Minimise (waste produced) Z = 1x3 + 1x4 + 1x5 + 1x6 subject to 6x1 + 1x3 + 4x6 3x1 + 3x2 + 1x3 + 4x5+ 2x6 2x2 + 1x3 + 2x4 + 1x5+ 1x6

1x3 + 1x4 xj

Ans.24:

≤ 3000 ≤ 2000 ≤ 1500 ≤ 1000 ≥ 0, for

all j

The profits for each arrangement are: Economy = 6.00 – 4 (0.20) – 2(0.25) – 8 (0.15) May time Spring colour Deluxe rose

= 8.00 – 8 (0.20) – 5 (0.25) – 10 (0.15) – 4 (0.22) = 10.00 – 9 (0.20) – 10 (0.15) – 9 (0.20) – 6 (0.22) = 12.00 – 12 (0.20) – 12 (0.20) – 12 (0.22)

= Rs. 3.50 = Rs. 2.77 = Rs. 3.58 = Rs. 4.56

Let x1, x2, x3, x4 be number of units arrangements of type Economy, May time, Spring colour & Deluxe rose. Then the objective is Maximise Z = 3.5x1 + 2.77x2 + 3.58x3 + 4.56x4

subject to 4x 1 + 9x3 + 12x4 2x 1 + 5x2 8x 1 + 10x2 + 10x3 8x 2

≤ 800 ≤ 456 ≤ 4000

≤ 920 ≤ 422

+ 9x+ 12x 3 4x 2 + 6x3 + 12x4

All xi's ≥ 0

Ans. 26: The information given in the question can be presented in the following tabular form.

Raw material (in kg) required to produce one kg of product Products X1

1/2 3/7 --

Rs.30

20 kg

X2 1/4 2/7 2/3

Rs.50

15 kg

X3 1/4 2/7 1/3

Rs.120

10 kg

Selling price (per kg)

Y1 Y2 Y3

Cost of raw material (Per kg)

Availability of raw material

Rs.90 Rs.100 Rs.120

From the above table, the cost of producing 1 kg of Y1, Y2 and Y3 can be calculated as given below: Cost to produce 1 kg of Y1 =

= =

½ Rs.30 + ¼ Rs.50 + Rs.120 Rs.15 + Rs.12.50 + Rs.30 Rs.57.50 Rs.90 – Rs.57.50 = Rs.32.50 3/7 Rs.30 + 2/7 Rs.50 + Rs.120 1/7 (Rs.90 + Rs.100 + Rs.240) Rs.430/7 = Rs.61.43

Profit per kg of Y1

Similarly, cost to produce 1 kg of Y2 = = = =

Profit per kg of Y2 = Rs.100 – Rs.61.43 = Rs.38.57 and cost to produce 1 kg of Y3 = 2/3 Rs.50 + 1/3 Rs.120 = Rs.220/3 = Rs.73.33 Profit per kg of Y3 = Rs.120 – Rs.73.33 = Rs.46.67 Let the manufacturer produce y1, y2 and y3 units of the products Y1, Y2 and Y3 respectively. Since the manufacturer wants to maximise the profit, the objective function is given by Maximise Z = 32.50 y1 + 38.57 y2 + 46.67 y3 ½ y1 + 3/7 y2 ≤ 20 or 7 y1 + 6 y2 ≤ 280 ¼ y1 + 2/7 y2 + 2/3 y3 ≤ 15 or 21 y1 + 24 y2 + 56 y3 ≤ 1,260 ¼ y1 + 2/7 y2 + 1/3 y3 ≤ 10 or 21 y1 + 24 y2 + 28 y3 ≤ 840 where Y1, Y2 and Y3 ≥ 0

Ans. 27: Let x1 = No. of units of product 1 produced

X2 = No. of units of product 2 produced X3 = Amount of money borrowed

The profit contribution per unit of each product is given by the selling price minus the variable cost of production. Total profit ay be computed by summing up the profits from producing the two products minus the cost associated with borrowed funds (if any):- The objective function is thus stated as Maximize Z = (14 – 10 ) x1 + (11 – 8) X2 - 0.05 X3

= 4 x1 + 3 X2 - 0.05 X3

(Note that the interest rate is 20% per annum, hence 5% for a period of three months)

Subject to the following constraints:

The production capacity constraints for each department, as given by table 1 are:

0.5x1 + 0.3X2 ≤ 500 0.3x1 + 0.4X2 ≤ 400 0.2x1 + 0.1X2 ≤ 200

……….(1) ……….(2) ……….(3)

The funds available for production include both Rs.3,00,000 cash that the firm possesses and any borrowed funds maximum up to Rs.2,0,000. Consequently production costs. The constraint expressing this relationship is

Funds required for production ≤ Funds available. i.e 10x1 + 8X2 ≤ Rs. 3,00,000 + X3 or 10x1 + 8X2 - X3 ≤ Rs. 3,00,000 ……….(4)

The borrowed funds constraint (from condition (iii) of the Question) is X3 ≤ Rs. 2,00,000 ……….(5)

The constraint based on the acid-test condition is developed as follows:-

Surplus cash on hand after production + Accounts receivable Bank Borrowings + Interest accrued thereon

i.e. (3,00,000 +X3 - 10x1 – 8X2 ) + 14x1 + 11X2 (X3 + 0.05X3 )

or, 3,00,000 +x3 +4x1 +3x2 > (x3 +0.05x3) ≤ 3,00,000 Or, - 4x1 - 3X2 + 0.05X3

Thus, the linear programming problem is given by Maximize Z = 4x1 + 3X2 - 0.05X3

Subject to 0.5x1 + 0.3X2 ≤ 500 0.3x1 + 0.4X2 ≤ 400 0.2x1 + 0.1X2 ≤ 200 10x1 + 8X2 - X3 ≤ Rs. 3,00,000

X3 ≤ Rs. 2,00,000 - 4x1 – 3X2 + 0.05X3 ≤ Rs. 3,00,000

……….(1) ……….(2) ……….(3) ………..(4) ……….(5) ……….(6)

1

1

……….(6)

Where x1 X2 X3 0.

Ans. 28: Let x1, x2 and x3 be the number of acres allotted for cultivating radish, mutter and potato respectively. Since the average yield of radish is 1,500 kg per acre, and the selling price for radish is Rs.5/kg hence the selling amount which the agriculturist gets from one acre is:

Rs.5 × 1,500 = Rs.7,500 To produce 100 kg of radish, the manure cost is Rs.12.50, so the manure cost per acre will be Rs.12.50 × 1,500/100 = Rs.12.50 × 15.

Labour cost per acre for radish = Rs.40 × 6 = Rs.240 Profit per acre for radish = Rs.7,500 – Rs.12.50 × 15 – Rs.240 = Rs.7,072.50

Similarly, the selling price, manure cost, labour cost and profit per acre of land for mutter and potato are also calculated and presented in the following table. Per acre Radish Mutter Potato Selling price

Manure cost

Rs.5 × 1,500 = Rs.7,500

Rs.4 × 1,800 = Rs.7,200

Rs.5 × 1,200 = Rs.6,000

Rs.12.50 1,500 100

Rs.40 × 6 = Rs.240 (Rs.7,500-Rs.187.50

– Rs,240) = Rs. 7,072.50

Rs.12.50 1,800 100

Rs.40 × 5 = Rs.200 (Rs.7,200 – Rs.255 - Rs.200) = Rs.6,775

Rs.12.50 1,200 80

Rs.40 × 6 = Rs.240 Rs.6,000–Rs.187.50

– Rs.240) = Rs. 5572.50

Labour cost Profit

Since, the agriculturist wants to maximise the total profit, hence the objective function of the problem is given by:

Maximise Z = 7,072.5x1 + 6,775x2 + 5572.5x3 Subject to following constraints: x1 + X2 + X3 ≤ 125 6x1 + 5x2 + 6x3 ≤ 500 Where x1, x2 and x3 ≥ 0

Ans. 29: Maximize Z

…… (1) (land constraint) …… (2) (man day constraint)

= 60 (9x 1 + 5x2) + 90 (7x 1 + 9x2) = 1170x1 + 1110x2

Subject to 9x1 + 5x2 ≥ 500 commitment for A

7x1 + 9x2 ≥ 300 commitment for B 5x1 + 3x2 ≤ 1500 availability of Q 7x1 + 9x2 ≤ 1900 availability of P 2x1 + 4x2 ≤ 1000 availability of R and x1 ≥ 0, x2 ≥ 0.

Ans. 30: Let x1, X2 and X3 denote the number of P III, P II and Celeron Computers respectively to the manufactured in the company. The following data is given:

P III P II Celeron Selling Price per unit (Rs.) 3,000 5,000 15,000

Labour, Material and other Variable Costs p.u. (Rs.) Profit per unit (Rs.)

2,000 1,000

4,000 1,000

8,000 7,000

From the data given for time required for various models and the total number of hours available for machine time and assembly time, we get the following constraints:

20x1 + 15x2 + 12x3 ≤ 1,000 (Machine Time Restriction) 5x1 + 4x2 + 3x3 ≤ 1,500 (Assembly Time Restriction)

The level of operations in the company is subject to availability of cash next month i.e.; the cash required for manufacturing various models should not exceed the cash available for the next month. The cash requirements for x1 units of P III, x2 units of P II and x3 units of Celeron computers are:

2,000x1 + 4,000 x2 + 8,000x3 The cash availability for the next month from the balance sheet is as below: Cash availability (Rs.) Loan to repay to Nationalized bank (Rs. 50,000) Interest on loan from XYZ cooperative bank and Nationalized bank (Rs. 1500)

0.18 2,00,000 Interest on long term loans 12

…… (1)

Cash balance (Rs. 2,10,000)

Salary to staff (Rs. 15,000) Or, Cash availability

= Rs. 1,40,500 Thus, from (1) and (2), 2000 X1 + 4000 X2 + X3 < Rs. 1,40,500 The company has also promised to deliver 3 P III, 2 P II and 5 Celeron computers to M/s. Kingspen Ltd.

Hence, X1 > 3, X2 > 2, X3 > 5 Since the company wants to maximize the profit, hence the objective function is given by: Maximize Z = 1000X1 + 1000X2 + 7000X3- (Rs. 15000 + Rs. 3000 + Rs. 1500) The LP formulation of the given problem is as follow: Maximize Z = 1000 X1 + 1000X2 + 7000 X3 – (Rs. 15000 + Rs.15000) Subject to the constraints:

20X1 + 15X2 + 12X3 < 1000 5X1 + 4X2 + 3X3 < 1500 2000 X1 + 4000 x2 + 8000 X3 < Rs. 1,40,500 X1 > 3, X2 > 2, X3 > 5 X1, X2 and X3 can take only positive integral values.

Ans. 31: Let the firm produce x1 units of product A, x2 units of products B and x3 units of product

C.

= Rs. 2,10,000-(Rs. 50,000 + Rs. 1,500 + Rs. 3,000 + Rs. 15,000) ..…. (2)

The profit per unit of products A, B and C is Rs. 50, and Rs. 80 respectively. Since the objective of the firm is to maximize the profit, therefore, the objective function is given by

Maximize Z = 50x1 +50x2 +80x3

The firm uses two types of raw materials I and II of which 5,000 and 7,500 units respectively are available. As per the given data, the raw material constraints can be formulated as given below:

3x1 +4x2 +5x3 < 5,000 and 5x1 +3x2 +5x3 < 7,500

………….. (i) (ii)

The labour time for each unit of product A is twice that of product B and three times that of product C. Also the entire labour force can produce the equivalent of 3,000 units.

X1 + X2 X3 < 3,000

2 3 (iii) or, 6x1 +3x2 +2x3 < 18,000

The minimum demand of the three products is 600, 650 and 500 units respectively. Hence, x1 > 600, x2 > 650 and x3 > 500

Since the ratios of the number of units produced must be equal to 2:3:4, therefore,

½ x1 = 1/3 x2, and 1/3 x2 = ¼ x3 or, 3x1 = 2x2 and 4x2 =3x3

The linear programming model can be formulated as follows: Maximize Z = 50x1 +50x2 +80X3

Subject to the constraints: 3x1 +4x2 +5x3 < 5,000 5x1 +3x2 +5x3 < 7,500 6x1 +3x2 +2x3 < 18,000 3x1 = 2x2 and 4x2 =3x3 x1 >600, x2 > 650 & x3 > 500.

Ans. 32: Renco Foundries has to decide the amount of funds to be allocated to projects A, B, C, D, E and money market instruments. Let us define the decision variables as

a b c d e Si

(for i = 0,1,2)

: : : : : :

Rs. Invested in investment A Rs. Invested in investment B Rs. Invested in investment C Rs. Invested in investment D Rs. Invested in investment E Rs. Invested in money market instruments at time i

(iv)

(v)

The objective of Renco Foundries is to draw up the capital budget in such a way that will “maximize cash on hand at time 3”.

Now at time 3, the cash on hand for Renco Foundries will be the sum of all cash inflows at time 3. Since the firm earns interest at 8% p.a. by parking the un-invested funds in money market instruments, hence Rs. S0 which are invested in these instruments at time 0 will become 1.08 S0 at time 1. Similarly an investment of Rs. S1 at time 1 will become 1.08 S1 at time 2, and an investment of Rs. S2 at time 2 will become 1.08 S2 at time 3. From the table giving the description of various investments, it can be computed that at time 3,

Cash on hand = a Re. 0+b Re.1+c Re. 0+d Rs.1.9+ e Rs. 1.5+ 1.08S2 = Rs. (b+1.9d+1.5e+1.08S2)

The objective of Renco Foundries is to maximize the cash on hand at time 3. hence the objective function will be

Maximize Z = b+ 1.9d+ 1.5e +1.08 S2…………….(i)

It may be noted that Cash available for investment at time t = cash on hand at time

t ………..(ii)

At time 0, funds to the tune of Rs. 1,00,000 are available for investment. From the table, it can be seen that funds are invested in investment A, C, D and S0 at time 0.

Hence, a+c+d+S0 = 1,00,000………………….(iii)

At time 1, Rs. 0.5 a, Rs. 1.2 c and Rs. 1.08 S0 will be the available returns as a result of investments made at time 0. From the table Rs. B and Rs. S1 are invested in investment B and money market instruments respectively at time 1.

Using equation (ii), we get 0.5a+ 1.2c+ 1.08S0 = b+ S1……………….(iv)

At time 2, Re. 1 a, Rs. 0.5 b and Rs. 1.08S1 will be available for investment. However, Rs. E and Rs. S2 are invested at time 2………………………………..(v)

Further, since the firm will not commit an investment exceeding Rs. 75,000 in any project, we get the following constraints:

a b c d e

< < < < <

75,000 75,000 75,000 75,000 75,000

(vi) (vii) (viii) (ix) (x)

Also a, b, c, d, e and Si (for i = 0, 1, 2) are all > 0

Combining all the constraints, the linear programming model for the Renco Foundries is as given below:

Maximize Z = b+ 1.9d+ 1.5e+ 1.08S2

Subject to following constraints a+c+d+S0 = 1,00,000 0.5a +1.2c +1.08 S0 = b+S1 1a+ 0.5b +1.08S1 = e+ S2

a b c d e

< < < < <

75,000 75,000 75,000 75,000 75,000

a, b, c, d, e and si (I =0, 1, 2) are all > 0

Ans. 33: Let x1 and x2 be the amount to be invested in first and second stock portfolio respectively. The average rate of return for first portfolio is 10% and for second portfolio, it is 20%. Since the company wishes to maximize the return from investment, the objective function is as given below: Maximise Z = 0.1x1 + 0.2x2 The maximum amount available for investment is Rs.1,00,000. Hence, x1 + x2 ≤ 1,00,000 Further, the maximum investment allowed in either portfolio set is Rs.75,000. Therefore, x1 ≤ 75,000 and x2 ≤ 75,000

…… (2) …… (3)

…… (1)

The first portfolio has a risk rating of 4 (on a scale from 0 to 10) and the second has 9. The company will not accept a risk factor above 6. Therefore, 4x1 + 9x2 ≤ 6 (x1+x2) Further, the company will not accept an average rate of return below 12%. Hence, 0.1x1 + 0.2 x2 ≥ 0.12 (x1 + x2) Also, x1 and x2 ≥ 0

Maximise Z = 0.1x1 + 0.2x2 Subject to the constraints x1+x2 ≤ 1,00,000 x1 ≤ 75,000 x2 ≤ 75,000 4x1 + 9x2 ≤ 6 (x1 + x2) or – 2x1 + 3x2 ≤ 0 0.1x1 + 0.2x2 ≥ 0.12 (x1+x2)

…… (4)

…… (1) …… (2) …… (3)

…… (5) …… (6)

…… (4)

The linear programming model for the given problem can now be formulated as follows:

or – 0.02x1 + 0.08x2 ≥ 0 where x1, x2 ≥ 0 The problem is solved graphically below:

…… (5)

The point of intersection for the lines - 2x1 + 3x2 = 0

and x1 + x2 = 1,00,000 is given by B (60,000, 40,000) The point of intersection for the lines

X1 = 75,000 and x1 + x2 = 1,00,000 is given by C (75,000, 25,000) Similarly, the lines

x1 = 75,000 and – 0.02x1 + 0.08x2 = 0 intersect at point D (75,000, 18,750) Thus, the feasible region is bounded by ABCDA and feasible points are A (0, 0); B(60,000, 40,000); C(75,000, 25,000) and D(75,000, 18,750). Value of the objective function at the above mentioned feasible points is calculated below: At A, Z=0 At B, Z=0.1 × 60,000 + 0.2 × 40,000

= 6,000 + 8,000 = Rs.14,000 At C, Z=0.1 × 75,000 + 0.2 × 25,000

= 7,500 + 5,000 = Rs.12,500 At D, Z=0.1× 75,000 + 0.2 × 18,750

= 7,500 + 3,750 = Rs.11,250 We find that the value of the objective function is maximum (Rs.14,000) at point B(60,000, 40,000). Hence, the company should invest Rs.60,000 in first portfolio and Rs.40,000 in second portfolio to achieve the maximum average rate of return of Rs.14,000.

Ans. 35: Contribution analysis: Products

Selling price (A) Variable costs: Direct Materials Direct Labour Painting Variable Overheads Total variable costs (B) Contribution (A – B) Direct Material per unit Direct Labour hour per unit Painting hour per unit

100 80 30

190 400 100

100/25 = 4 kg. 80/20 = 4 hours 30/30 = 1 hour

100 40 60 175 375

75 100/25 = 4 kg.

40/20 = 2 hours 60/30 = 2 hours

A (Rs.) 500

B (Rs.) 450

Let A be the units to be produced of product A and B be the units to be produced of product B.

LP Problem formulation: Z Max Subject to:

4A + 4B 480 4A + 2B 400 A + 2B 200 A, B 0

Raw Material Constraint :

Raw material constraint Direct Labour hour constraint Painting hour constraint Non negativity constraint

Put B = 0, A = 120 Put A = 0, B = 120

Direct Labour Constraint : Put B = 0, A = 100 Put A = 0, B = 200

100A + 75B Maximisation of contribution

Painting Constraint : Put B = 0, A = 200 Put A = 0, B = 100

The graphical representation will be as under:

Q Intersects 4A + 2B = 400 and 4A + 4B = 480 Subtracting (2) from (1), we get 2B = 80

(1) (2)

B = 80/2 = 40 Putting value of B in (1), we get 4A + 2 40 = 400

A

R Intersects 4A + 4B = 480 2B = 200

400 80 80

4 (3) and A +

(4) Multiplying (4) by (2) and then subtracting from (3), we get

2A = 80 A = 40

Putting the value of A in (4), we get 2B = 200 – 40 B = 80.

Evaluation of corner points:

Point

A

P Q R S

0 80 40

100

Products

B

100 40 80 0

Contribution

A (Rs.) 100 per unit

0 8,000 4,000

10,000

B (Rs.) 75 per unit

7,500 3,000 6,000

0

7,500 11,000 10,000 10,000

Total Contribution

Rs.

Optimal product mix is Q Product

A B Total contribution Less: Fixed costs 400 D.L. Hrs. Rs. 17.50 Optimal Profit

Units

80 40

Contribution Rs.

8,000 3,000 11,000 7,000 4,000

(iii) If the painting time can be sold at Rs. 40 per hour the opportunity cost is calculated as under:

A (Rs.)

Income from sale per hour Painting variable cost per hour Opportunity cost Painting hours per unit Opportunity cost Revised contribution

40 30 10 1 10

100 – 10 = 90

B (Rs.) 40 30 10 2

20 75 – 20 = 55

Hence, modification is required in the objective function. Re-formulated problem will be:

41

Z Max. Subject to:

90A + 55B

4A + 4B 480 4A + 2B 400 A + 2B 200 A, B 0

Maximisation of contribution

Raw Material constraint Direct Labour hour constraint Painting hour constraint Non-negativity constraint

Ans 40: Dual:

Minimise S.T.

140u1 + 120u2 + 50u3 6u1 + 10u2 + 10u3 ≥ 100 4u1 + 10u2 + 12u3 ≥ 90 8u1 + 2u2 + 6u3 ≥ 40 4u1 + 6u2 + 2u3 ≥ 60 u1, u2 u3 u4 ≥ 0

-1-

Ans. 6: (a) Calculation of cost of per 100 units of good components:

(A) If not inspected Units required Estimated defectives

10,000 300 (3%)

Cost Purchase price (Rs.) Production damage (Rs.) Total Cost (Rs.) Good component (units) Cost per 100 good component (Rs.)

Rs. 18,000

540 18,540

9,700 191.13

10,000 500 (5%)

Rs. 17,400

900 18,300 9,500

192.63

X Ltd. Y Ltd.

(B) If inspected Defectives not detected Defectives detected Components paid for

Cost Purchase cost Inspection cost Production damage Total cost Good components Cost per 100 good components (Rs.)

30 270

9,730

Rs. 17,514

2,400 54

19,968 9,700

205.86

50 450

9,550

Rs. 16,61 7 2,400

90 19,107

9,500 201.3

Decision: (i) On the basis of the cost per 100 good component calculated at (A) and (B) above, it is

concluded that inspection at the point of receipt is not justified. (ii) It will be advantageous to purchase the component from X Ltd.

Ans. 7: 1. a. Percentage of defective units shipped

b. Customer complaints as a percentage of units shipped c. On-time delivery

d. Percentage of units reworked during production

2003 400 = 4% 10,000

500 = 5% 10000 8500 = 85% 10000

600 10000

=6%

2004 330 11000

517 11000 9900 11000

627 11000

= 3%

=4.7%

= 90%

=5.7%

2. The calculations in requirement I indicate that ESC’s performance on both quality and timeliness has improved. Quality has improved because (a) percentage of defective units shipped has decreased from 4% to

Solutions of Practical Questions in misc theory chapters

-2-

3%,(b) customer complaints have decreased from 5% to 4.7% , and (c) percentage of units reworked during production has decreased from 6% to 5.7% . Timeliness has improved as on –time delivery has increased from 85 % to 90% . Of course , there is a relationship between the improvements in quality and timeliness. Better quality and less rework reduces delays in production and enables faster and on-time delivery to customers.

3a. The output per labor- hour Between 2003 and 2004 Can be calculated as follows

2003

10000 =0.11 90000

2004

11000 =0.10 110000

3b . Output per labor-hour may have declined from 2003 and 2004 either because workers were less productive or more likely because the initial implementation of the quality program may have resulted in lost production time as employees were trained and became more adept at solving production quality problems. As workers implement good quality practices and defects and rework decrease over time, it is possible that both quality and productivity (output per labor-hour) will increase.

3c. it is not clear that the lower output per labor-hour will decrease operating income in 2004. the higher labor costs in 2004 could pay off in many ways. Higher quality and lower defects will likely result in lower material costs because of lower defects and rework. Internal and external failure costs will also be lower, resulting in lower customer returns and warranty costs. Customer satisfaction will likely increase, resulting in higher sales, higher prices, and higher contribution margins. Indeed the 10% increase in the number of units produced and sold in 2004 may well have been due to quality improvements. Overall, the benefits of higher quality in 2004 may very well exceed the higher labor costs per unit of output. Ans. 8: (i) Classification of Quality Costs

2007

Sales Prevention Quality training Appraisal Product Inspection Materials Inspection

Internal Failure Scrap Rework

External Failure Product warranty

6,000

75

200

80 280

600 500

1100

4.67

1.25

% of sales

Figures Rs. ’000 % of

2008 sales

6,000

150

240

60 300

300 400 700

5

2.5

18.33 11.67

300 5 150 2.5 1755 29.25 1300 21.67

(ii) Cost reduction was effected by 7.58% (29.25 – 21.67) of sales, which is an increase in profit by Rs.4,55,000. (6 Marks) Nov/08-NC& ICWA-June/03 [Adapted]

Ans. 9: Had there been no defectives for production of 1,00,000 pieces of P 1,00,000X5=5,00,000 units of raw material would be required. In case of high quality material , defective being 10% total raw material required is 5,00,000 units/0.90 =5,55,556 units. In case of lower quality material, defective being 20%, total raw material requirement is 5,00,000 units/0.08 =6,25,000 units. Similarly labour and variable overhead requirement are to be adjusted accordingly.

Ascertainment of Total cost I. Using high quality materials (scrap 10%) (Rs)

Material (5,00,000 units/0.90X Rs.1.05) 5,83,333 Labour (2,50,000 hours/0.90X Rs.0.50) 1,38,889 Variable overhead (Rs.1,00,000/0.90) 1,11,111 Fixed overhead 50,000 Less: Scrap (5,00,000/0.90)-5,00,000)XRe.0.30 8,83,333

-3-

Cost of 1,00,000 pieces of P

II. Using lower quality materials Material Labour Variable overhead Fixed overhead Machine and Tooling cost Additional laboour Additional overhead for additional labour

(scrap 10%) (5,00,000 units/0.80X Rs.0.80) (2,50,000 hours/0.80X Rs.0.50) (Rs.1,00,000/0.80)

(1,00,000units X 0.5hours XRe.0.50)

(1,00,000 units x 0.5 hours)X (Rs.1,00,000/2,50,000 hours)

Less: Realizable value of scrap Cost of 1,00,000 pieces of P

Analysis: Hence the high quality material should be used.

16,667 8,66,666

(Rs) 5,00,000 1,56,250 1,25,000

50,000 3,000 2,500

20,000

8,79,250 5000

8,74,250

Ans. 10:-Let the defectives be’d’ (I) If each components is tested before being sent to the agents for sales

No: of components in a batch Rs.2000 Cost of testing each components Rs.20 Cost of rectification before dispatch Rs.200 Total Cost Rs.(2000x25)+200d

(II) If components dispatch without pre-testing and defectives received back for rectification under warranty. Total Cost 400d In difference point of two alternatives (2000x25)+200d 400d 400d-200d 2000x25 200d 50,000 D 50000/20

250 Defective Components 250 components Percentage of defectives to total components 250/2000*100 =12.5% Analysis: If defectives exceed 12.5% of the total number of components per-testing is recommended. Ans. 11: Present Position (Based on 1,000 units Production)

Cost per unit. Direct material Direct wages (8 hours @ Re.0.50) Overheads (8 hours @ Rs.1.75) Total

Per unit Particular Sales price Firsts 30 Seconds 20 Thirds 10

Units Profit / Loss 2 (-) 8 (-) 18

900 50 50

(Rs.) 10 4 14 28

Total Profit 1,800

- -

1,800 Net Profit

Loss -

400 900

1,300 500

(Rs.) 4 4 7

15

Reprocessing of Inferior units (a) Additional expenditure for reprocessing per unit Direct Material Direct Wages 8 hrs. Variable overhead @ 0.875

Total expenditure for 100 units Rs.1,500

.

-4-

(b) Additional Revenue Second (Rs.30-Rs.20)x50units Thirds (Rs.30-Rs.10)x50

Note: No change in the profit position hence this need not be considered.

Ans. 12: (a)

Existing

i. Total production (Preinspection) Total sales requirements Specification losses 5%

Downgrading 12.5

� 5,250 87.5

(Rs.) 500

1000 1500

After TQM Programme

units

5,000 250

5,250 750

7.5 � 5,125

92.5

5,000 2.5% 125

5,125 416 at inspection

Total units before inspection ii Purchase of material ‘X’(Sq

Mtr) Material required to meet pre inspection production requirement 6,000 � 8 SqMtr

Processing loss 4 � 48,000

96

6,000 5,541

48,000 SqMtr

2,000

5,541�8 SqMtr

44,328 SqMtr

1,137 2.5

� 44,328 97.5

Input to the process

Scrapped

50,000

Total purchases iii

Gross Machine Hours Initial requirements 6,000 � 0.6

Idle time 20 � 3,600

80

50,000 5 �

95

45,465 1,406

3 � 45,465

97

material 2,632

52,632 46,871

3,600

900

4,500

5,541 � 0.5

12.5 � 2,771

87.5

2,771

396

3,167

Rs 50,00,000

Gross time (b)

Rs Sales revenue 5,000 Units� Rs 1,000 Sales downgraded 750 Units�Rs 700

55,25,00

50,00,00 0

5,25,000

Profit and loss statement

416 Units � Rs 700 2,91,200

52,91,200

-5-

0 Costs: Material 52,632 Sq Mtr �Rs 40

Inspection and storage costs 52,632 Sq Mtr �Re 1 Machine cost 4,500 Hrs � Rs 400 Inspection and other cost Product liability (3% � 50,00,000 Sundry cost of selling, distribution and administration. Preventive programme cost

21,05,28 0

52,632 18,00,00

0 2,50,000 1,50,000

46,871Sq Mtr � Rs 40

46,871Sq Mtr � Re 1 3,167 Hrs� Rs 400

2,50,000 � 60% 1% � 50,00,000

18,74,840

46,871 12,66,800

1,50,000 50,000

6,00,000 2,00,000 51,57,91

2

6,00,000 � 90% 5,40,000 6,00,000

45,28,511

7,62,689 Net profit 3,67,088

Ans. 13: (a) (i) Units Components worked on in the process 6120 Less: planned defective units 612 replacements to customer (2% X 5400) 108 Components invoiced to customers 5400 Therefore actual result agree with planned results (ii) Planned components cost = (3 X Rs.18 for material A) + (2 X Rs.9 for material B) + Rs.15 variable cost =Rs.87 Comparing with the data in appendix: Materials = Rs.440 640/6120 =Rs.72 Variable overhead = Rs.91 800/6120 = Rs.15 This indicates that prices were at the planned levels. (b) Internal failure costs = Rs.53 244(612 units X Rs.87)

External failure costs = Rs.9396 (108 units X Rs.87) (c) (i) Period 2 (units) Period 3 (units) Components invoiced to customers 5500 5450 Planned replacement (2%) 110 109 Unplanned replacement 60 (170-110) -69 (40-109) Components delivered to customers 5670 5490 Planned process defects (10% of worked on in the process) 620 578 Unplanned defects (difference to agree with with final row) -90 -288 Components worked on in the process 6200 5780

(ii) Period 2(Rs.) Period 3(Rs.) Internal failure costs 46,110 (620-90) XRs. 87 25,230 (578-288) X Rs.87 External failure costs 14,790 (110+60) X Rs.87 3,480 (109-69) X Rs.87 Appraisal costs 10,000 15,000 Prevention costs 5,000 8,000 (iii) The following points should be included in the report:

1. Insufficient detail is provided in the statistics shown in the appendix thus results in the need to for an improvement in reporting.

-6-

2. The information presented in (c) (i) indicate that free replacement to customers were 60 greater than planned in period 2 but approximately 70 less than planned in period 3. in contrast, the in process defects were 90 less than planned (approximately 15%) in period 2 and 288 less than plan (approximately 50%) in period 3.

3. Internal failure costs show a downward trend from period 1-3 with a substantial declined in period 3.External failure costs increased in period 2 but declined significantly in period 3.

4. The cost savings arising in period 2 and 3 are as follows: Period 2(Rs.) Period 3(Rs.)

Increase /decrease from previous period: Internal failure costs -1734(Rs.53244-Rs.46110) -20880(Rs.46110-Rs.25230) External failure +5394(Rs.9396-Rs.14790) -11310(Rs.14790-Rs.3480) Total decrease -1740 -32190 The above savings should be compared against the investment of Rs.10000 appraisal cost and Rs.5000 prevention cost for period 2 and Rs.15,000 and Rs.8,000 respectively in period 3. it can be seen that the cost exceed the savings in period 2 but the savings exceeds the cost in period 3. There has also been an increase in the external failure cost from period 1 to period 2. Investigations should me made relating to the likely time lag from incurring prevention/appraisal costs and their subsequent benefits. 5. The impact on customer goodwill from the reduction in replacements should also be explained.

Ans. 27: Return of 12% net (after tax of 40%) on capital employed is equivalent to 12%�(1-0.4) = 20%

(gross) on capital employed.

Let selling price per unit to be ‘x’

Since Total sales = Total cost + profit

i.e., 80,000x = 14,60,000+20% (12,00,000+0.5�80,000�) Or, 80,000x = 14,600+2,40,000+8,000x

Or, 72,000x = 17,00,000

17,00,000 = Rs. 23.61

72,000 Or, ‘x’ =

Hence selling price per unit will be Rs. 23.61

Ans. 28: (i) Statement showing price of Product Z Direct Material

Direct Labour

Deptt. A

Deptt. B

Deptt. A

Deptt. B

Variable overhead Deptt. A 3×6

Deptt B 4×3

Variable selling and distribution overhead 30,000/1,500

Total Variable Cost per unit

Total hours required for a target of 1,500 units of product Z

Deptt. A1500 × 3 4500 hours

30

25

30

40

18

12 30

20

175

70

55

-7-

Deptt. B1500 × 4 6000 hours

10500 hours

10500 hours represent 30% capacity

So total capacity per month 10500 / 0.30 = 35000 hours. Yearly

capacity is 35000 × 12 = 420000 hours.

Fixed capital employed in both department

(25 lakhs + 15 Lakhs)

Expected return

Contribution per hour

Working Capital

= 0.21 × 40,00,000

= 840000 / 4200000

= 0.21 × 400000

= 840000

= 2.00 per hour

= 84000 = 4.67 per unit

Rs.

= 14.00 = 4.67

18.67 Fixed charges recovery is based on usage. Full capacity is not being used by product Z and departments are also producing other products using same plant and machinery. Price of Product = Variable cost + contribution required = 175 + 18.67 = 193.67 per unit.

(ii) Price of product when product is well established in market: Variable Cost Fixed Cost (24 + 16) Total price

175 40

215

= 40.00 Lakhs

Contribution per unit 84000 / 18000 unit

Total contribution required

To cover fixed cost 3 hours of A and 4 of B = 7 × 2 To working capital

The product is first time launched in the market, and then variable cost Rs.175 should form the basis for price fixation.

Ans. 29: (a)

Materials: Iron 10kg @ Rs.5/- Copper 5 kg @ Rs.8/-

Wages X : 3 hrs @ 15 Rs./Hr. Y : 5 hrs @ 12 Rs./Hr

Variable OH (Production) X : 8 hrs × 3 hrs Y : 5 hrs × 5 hrs

Variable OH – Selling Total Variable Cost

45 60

24 25 49

20 264

105

50 40 90

Rs./u of alloy

-8-

Fixed Off: X : 8/hrs × 3 hrs. Y : 5/hrs × 5 hrs

24 25 49

313 Total Cost (i) If pricing strategy is to penetrate the market, the minimum price for a new product

should be the variable cost i.e. Rs.264/-. In some circumstances, it can also be sold below the variable cost, if it is expected to quickly penetrate the market and later absorb a price increase. Total Variable Cost is the penetration price.

(ii) When the alloy is well established, the minimum selling price will be the total cost – including the fixed cost i.e. Rs.313 per unit. Long run costs should cover at least the total cost.

Ans. 30: XYZ Ltd. Sales in X (rearranged for the purpose of ranking) Rank Category Stock(Rs.’000) 1 OTC 175 2 Toiletries 150 3 Photo 125 4 Food/ Drink 100 5 Baby 50 5 San. Prod. 50 5 Other 50 8 Foot Care 30 9 Cosmetics 25 10 Hair-care 25 11 Perfume 20

Stock in X (rearranged for the purpose of ranking) Rank Category Stock(Rs.’000) 1 Toiletries 60 2 Cosmetics 40 3 OTC 35 4 Photo 20 4 Food/ Drink 20 6 Other 13 7 Baby 10 7 San. Prod. 10 7 Hair 10 7 Perfume 10 11 foot care 2

Sales in Z (Rearranged for ranking) Rank Category Stock(Rs.’000) 1 OTC 120 2 Toiletries 100 3 Food/ Drink 75 4 Photo 60 5 Cosmetics 30 6 Baby 25 6 San. Prod. 25 6 Other 25 9 Foot care 20 10 Hair 10 11 Perfume 10

Sales in Z (Rearranged for ranking) Rank Category Stock (Rs.’000) 1 Toiletries 65

Cum. Sales(Rs.’000) 175 325 450 550 600 650 700 730 755 780 800

Cum. Sales(Rs.’000) 60

100 135 155 175 188 198 208 218 228 230

Cum. Sales(Rs.’000) 120 220 295 355 385 410 435 460 480 490 500

Cum. Sales(Rs.’000) 65

% 21.9 40.6 56.3 68.8 75.0 81.3 81.3 91.3 94.4 97.5

100.0

% 26.1 43.5 58.7 67.4 76.1 81.7 86.1 90.4 94.8 99.1

100.0

% 24 44 59 71 77 82 87 92 96 98 100

% 30.2

-9-

2 3 4 5 6 7 7 7 7 7

Cosmetics OTC Food/ Drink Photo Perfume Baby San. Prod. foot care Hair Other

45 40 20 12.5 7.5 5 5 5 5 5

110 150 170 182.5 190 200 200 205 210 215

51.2 69.8 79.1 84.9 88.4 93.0 93.0 95.3 97.7 100.0

System for Evans

Relevant Costs under

JIT Production

System Rs.1,50,000

- 24,000

1,40,000a 2,80,000b

(90,000)c Rs.5,04,000

Ans. 46:Annual Relevant Costs of Current Production System and JIT Production Corporation.

Relevant Costs under

Current Production

Relevant Items System Annual tooling costs - Required return on investment: 12% per year x Rs.9,00,000 of average inventory per year Rs.1,08,000 12% per year x Rs.2,00,000 of average inventory per year - Insurance , space, materials handling , and setup costs 2,00,000 Rework costs 3,50,000 Incremental revenues from higher selling prices - Total net incremental costs Rs.6,58,000 Annual difference in favor of JIT production Rs.1,54,000 a b Rs. 200,000 (1-0.30) = Rs.140,000 Rs. 350,000 (1-0.20) = Rs.280,000

c Rs. 3x30,000 units = Rs.90,000

(a) Personal observation by production line workers and managers is more effective in JIT plants than in traditional plants. A JIT plant’s production process layout is streamlined. Operations are not obscured by piles of inventory or rework. As a result, such plants are easier to evaluate by personal observation than cluttered plants where the flow of production is not logically laid out.

Besides personal observation, non financial performance measures are the dominant methods of control. Non financial performance measures provide most timely and easy to understand measures of plant performance. Examples of non financial performance measures of time, inventory, and quality include:

� Manufacturing lead time � Units produced per hour � Machine setup time / manufacturing time4 � Number of defective units / number of units completed.

In addition to personal observation and non financial performance measures. Financial performance measures are also used. Examples of financial performance measures include.

� Cost of rework � Ordering costs � Stock out costs � Inventory turnover

(3b) The success of a JIT system depends on the speed of information flows from customers to manufactures to suppliers. The Enterprise Resource Planning (ERP) system has a single database, and gives lower-level managers, workers, customers, and suppliers access to operating information. This benefit, accompanied by tight coordination across business function, enables the ERP system to rapidly transmit information in response to changes in supply and demand so that manufacturing and distribution plans may be revised accordingly. Ans. 47: (i) Comparative Statement of cost for purchasing from Y Co Ltd under current policy & JIT

Particulars Current Policy JIT Rs Rs

Purchasing cost 18,20,000 18,20,260

- 10 -

Ordering cost

Opportunity carrying cost

Other carrying cost(Insurance, material handling etc)

Stock out cost

(13,000 × 140) 26 (2×13 orders) 10,500.00 (1/2×1000×140×15%)

1,550.00 (1/2×1000×3.10)

(13,000 × 140.02) 260 (2×130 orders) 1,050.15 (1/2×100×140.02×15%)

155

200 (4 × 50)

Total relevant cost 18,32,076 18,21,925.15 Comments: As may be seen from above, the relevant cost under the JIT purchasing policy is lower than the cost incurred under the existing system. Hence, a JIT purchasing policy should be adopted by the company. (ii) Statement of cost for purchasing from Z Co Ltd.

Particulars Purchasing cost

Ordering Cost

Opportunity Carrying Cost Other Carrying Cost

Stock out Cost

Inspection Cost

Customer Return Cost

Rs. 1,76,800

(13,000x13.60) 260

(2x130 orders) 102

(1/2×100×13.60× 15%) 150

(1/2×100×3.00) 2,880

(8x360) 650

(13,000 x .05)

6,500.00 ( 13,000 x 2% x 25)

1,87,342 Total Relevant Cost Comments : The comparative costs are as follows, Under current policy Rs 18,32,076.00 Under purchase under JIT Rs 18,21,925.10 Under purchase from Z Co Ltd Rs 1,87,342.00 Packages should be bought from Z Co as it is the cheapest.

Costing in Service Sector Ans. 8. Total Room days =No of rooms x Days in a year = 300 rooms x 365 days

= 10,95,000 Rooms days = Rs. 50-Rs.10 = Rs.40

(Rs.) 600000 400000

10,00,000 7,50,000

17,50,000 = Rs.17,50,000 / Rs.40 = 43.750 Room days

= Rs.7,50,000 / Rs.40 = 18.750 Room days

Dally contribution required per room Desired profit after tax Add Income Tax (Rs.6,00,000X40/60) Desired profit before tax Add: Fixed cost Total Revenue to be earned No. of room days to be rented No. of rooms to be rented to attain break- even

Ans 9: Room Occupancy days per annum Single rooms (180 rooms X 365days X85/100) Double rooms (60 rooms X 365 days X 85/100)

Variable and Fixed cost p.a. Particulars Room occupancy days Variable cost per day Total Variable cost Fixed cost per room day Total Fixed cost

55845 18615

Single rooms 55845 300 16753500 500 27922500

Double rooms 18615 500 9307500 780 14519700

Total

26061000

42442200

Margin of Safety desired at 20% of total revenue. Therefore, Break even should be at 80% of total revenue. Revenue at break even level = Variable cost + Fixed cost = 26061000+42442200 = Rs. 68503200 Desired total revenue to be = Rs. 68503200 X 100/80 = Rs. 85629000

(i) Computation of tariff per room day Single room days occupancy Double room days occupancy equivalent to single room day (18615X160/100) Total single room days

Rent per single room day = Rs. 85620000/85629 room days = Rs. 1000 Rent per double room day = Rs. 1000 X 160/100 = Rs. 1600 Tariff per room for single room = Rs. 1000 X 100/80 = Rs. 1250 Tariff per room for double room = Rs. 1600 X 100/80 = Rs. 2000

(ii) Computation of increase in occupancy of the remaining single rooms days loss arising from the discount. Number of single rooms intends to reserve for corporate customers = 12 Occupancy days for reserved rooms = 12 rooms X 365 days X 85/100 Discount given on room rent per day = Rs. 1000 X 10/100 Amount of revenue lost due to discounting = 3723 room days X 100 Contribution per day on a single room = Rs. 1000- Rs. 300 Increase in occupancy days required in single rooms = Rs. 372300/Rs. 700

Ans. 10 Working Name: Calculation of occupancy (a) Single room occupancy p. a.

55845 29784 85629

required to compensate the

= 3723 = Rs. 100 = Rs.372300 = Rs. 700 = 532 days

( 100 rooms X 365 days X 75/100) 27,375

Solutions of service sector

(b) Double room occupancy p. a. ( 20 rooms X 365 X 75/1000) = 5475 Conversion of double room to single room occupancy ( 5,475 X 1.20)

Total

Statement of Rent chargeable to single room and double room per day Particulars Single Room No. of occupancy days (a) 27,375 Costs per day Rs. Variable cost 400 Fixed cost 200

(b) 600 Total (Rs.) (a) X (b) 1,64,25,000

6,570 33,945

Double room 5,475

Rs. 500 250 750

41,06,250

(Rs.) Total Cost Add: 20% Margin safety on hire of room Total rental charges to be received

Room rent per day to be collected (Rs.)

(a) Single Room (b) Double Room

Profitability statement of restaurant Sales Revenue Contribution Less: Fixed cost p. a. Profit

Profitability statement of sports centre (Rs.)

Contribution p. a. Less: Fixed Cost p. a. Profit

(50 persons X Rs.50X 365 days) 9,12,500 5,00,000 4,12,500

(Rs.2,56,64,062 / 33,945) (Rs.756 X 1.20)

(Rs.) (Rs.1,00,000 X 365 days)

(30% of Rs.365 Lakhs) 3,65,00,000 1,09,50,000

10,00,000 99,50,000

756 907

(Rs.1,64,25,000 + Rs.41,06,250) (Rs.25% 0n cost)

2,05,31,250 51,32,812

2,56,64,062

Profitability statement of shopping arcade (Rs.)

Contribution p. a. Less: Fixed Cost p. a. Profit

Ans. 11 (i) Income Statement of Kangan Resort for the next year

Rs.

Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 200 × 85%) Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×85%) Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 85%)

13,60,000

(Rs.50,000 X 12 months) 6,00,000 6,00,000

Nil

6,80,000

10,88,000

Total Sales Revenue Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%) Shopping Arcade (50% of Rs. 6,80,000) Restaurant (60% of Rs. 10,88 ,000) Total Variable Cost Contribution (Total Sales Revenue – Total Variable Cost) Less: Fixed Cost Profit (Estimated)

31,28,000

2,04,000

3,40,000 6,52,800

11,96,800 19,31,200 10,00,000 9,31,200

(ii) Income Statement on the basis of reduced room rent Rs.

Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 150 × 95%) Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×95%) Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 95%) Total Sales Revenue Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%) Shopping Arcade (50% of Rs. 7,60,000) Restaurant (60% of Rs. 12,16 ,000) Total Variable Cost Contribution (Total Sales Revenue – Total Variable Cost) Less: Fixed Cost

2,28,000

3,80,000 7,29,600

13,37,600 17,78,400 10,00,000

11,40,000

7,60,000

12,16,000

31,16,000

Profit 7,78,400 The profitability decreases by 9,31,200 – 7,78,400 = Rs. 1,52,800. Hence reducing room rent proposal may not be accepted.

Ans. 12 Estimated Income Statement for the coming year Revenue Hotel Room Rent (100 rooms X 250 days X Rs.150 X 75/100) Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 75/100) Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 75/100)

(a) Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 75/100) Shops (Rs.11,25,000 X 50/100) Restaurant (Rs.22,50,000 X 55/100)

(b)

(Rs.)

28,12,500 11,25,000 22,50,000 61,87,500

4,68,750 5,62,500

12,37,500 22,68,750

Contribution Less: Fixed Costs Estimated Profit

(a) - (b) 39,18,750 19,50,000 19,68,750

(a) Revised estimated income statement or the coming year ( if room rent reduced to Rs.125 per day to enhance occupancy to 90%) (Rs.) Revenue

28,12,500 Hotel Room Rent (100 rooms X 250 days X Rs.125 X 90/100) 13,50,000 Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 90/100)

Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 90/100) 27,00,000 (a) 68,62,500

Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 90/100) 5,62,500 Shops (Rs.13,50,000 X 50/100) 6,75,000 Restaurant (Rs.27,00,000 X 55/100) 14,85,000

(b) 27,22,500 Contribution (a) - (b) 41,40,000 Less: Fixed Costs 19,50,000 Estimated Profit 21,90,000 (b) Analysis: With the reduction in room rent from Rs.150 per day to Rs.125 the occupancy will increase to 90% which will result in increase of profit by Rs.2,21,250 (i.e, Rs.21,90,000- Rs.19,68,750).

Ans. 13

(i) Occupancy: Single rooms 100 X 365 X 80/100=29,200 Double rooms 20 X 365 X 80/100 = 5,840

Variable costs: Single rooms (29,200 X 220) Double rooms (5,840 X 350) Fixed Costs: Single rooms (29,200 X 120) Double rooms (5,840 X 250) Total costs:

Margin of safety 20%, Break- even point 80% Sales at BEP = Total Costs Total revenue = 1,34,32,000 X 100

80

Single rooms (29,200 X 1) Double rooms (5,840 X 1.25) National single rooms/days

Rent per day per Single room = 1,67,90,000 36,500

=Rs.460 X 1.25

64,24,000 20,44,000

35,04,000 14,60,000

84,68,000

49,64,000 1,34,32,000

=Rs.1,34,32,000

=Rs.1,67,90,000 (Rs.)

29,200 7,300

36,500

= Rs.460

= Rs.575 Rent per day per Double room

(ii) Restaurant (a) Sales /day Rs.25,000 Contribution 30% Total contribution 25,000 X 30/100 = Rs.7,500 per day

Contribution p. a. Fixed cost p. a.

(7,500 X 365) (Rs.)

27,37,500 8,00,000

Profit

(b) Sports centre No. of persons /days Average contribution per person / day Total contribution/day

19,37,500

(Rs.) 50 15

750

(Rs.) 2,73,750 4,00,000 1,26,250

(Rs.) 4,20,000 4,00,000

20,000 (Rs.)

1,67,90,000 1,34,32,00 33,58,000

19,37,500 (1,26,250)

20,000 51,89,250

(50X 15)

Total contribution/p. a. (750X 365) Fixed Overheads Loss

(c) Shopping arcade Average contribution p.m. Rs.35,000

Average contribution p. a. (Rs.35,000 X 12) Fixed expenses Profit

Profit Statement Hotel accommodation Rentals Less: Costs Restaurant Sports centre Shopping arcade Total (III) Reservation = 10 rooms X 365 X 80 /100 Rent = 2,920 X 460 Discount 10%

Total contribution of remaining rooms Single 90 X 365 X 80/100 X (460-220) Double 20 X 365 X 80/100 X (575-350) Total Increase in contribution required 76,21,200 + 1,34,320 = Rs.77,55,520

% occupancy

Alternatively, % Increase in contribution required = 134320 × 100 = 1.76%

7621200

= 2,920 =Rs.13,43,200

=Rs. 1,34,320

(Rs.) 63,07,200 13,14,000 76,21,200

= 7755520 × 80 (i.e. Current Occupancy level) = 81.41 7621200

= Say 81.5%

Current occupancy level = 80 Revised occupancy level = 101.76% of 80 = 81.41% = Say 81.5%

(IV) Total profit per annum = Rs.51, 89,250

Capital recovery factor Discounted income for 5 years Lease rent Hence lease not acceptable

3.79 Rs.1, 96, 67,257

Rs.1, 75, 00,000

Ans 14: Calculation of variable cost Distance

X Distance

Y

One side distance Round trip Variable cost @ 0.80 per km

Calculation of fixed cost

24 km 48 km

Rs. 38.40

16 km 32 km

Rs. 25.60

Distance X

Actual running time for round trip distance at the Speed of 24 km per hour Filling time Empty time Total time

Fixed cost @ Rs. 7.50 per hour Calculation of ton km Capacity Full load Tons km

Cost per ton km 38.40 + 25

= Rs. 0.33 192

Distance Y

80 Min 30 Min 40 Min

150 Min

Rs. 18.75

8 tones 16 km

128

25.60 + 18.75 = Rs. 0.347

128

120 Min 40 Min 40 Min

200 Min

Rs. 25

8 tones 24 km

192

Ans.15 Working notes:

(1) Total distance travelled (in 25 days) = 60 km.(two sides ) X 6 trips per day X 25 days = 9,000 km. (2) Total passenger km. = 9,000 km. X 20 seats = 1,80,000 passenger km. (3) Depreciation p.a.

=Rs.78,000 = (Rs.4,00,000-Rs.10,000) = Purchase price – Scrap value 5 Years 5 Years

Statement suggesting fare per passenger – km (Rs.) Fixed Expenses Cost per annum Cost per annum Insurance 15,000 Garage rent 9,000 Road Tax 3,000 Administrative charges 5,000 Depreciation 78,000

10,000 Interest on Loan 1,20,000 10,000

Running Expenses 1,250 Repair and maintenance

300 Replacement of tyre-tube 45,000 Diesel and oil cost (9,000 km. X Rs.5

5,000 Driver and conductor’s salary 61,550.00 Total cost (per month) 15,387.50 Add: Profit (20% of total revenue or 25% of total cost

Total Revenue Rate per passenger – km

76,937.50 =Rs.76,937.50/1,80,000 passenger km.=0.4274305 or 0.43 Paise

Ans.16 (i) Comparative cost sheet Particulars

Total trips per day No. of days per month Total trips per month Tonnes carried per truck Capacity to be handed p.m. tones No .of trucks required No. of drivers (including relievers) Total km. run per truck per month (120 X 12) Total km. run by all trucks per month Km. per litre of diesel Diesel required ( Litres)

Monthly Sheet No. of Trucks

(a) Variable with km run Diesel @ Rs.10 per litre Oil and sundries Rs.10 per 100 km. Total

(b) Variable with No. of trucks run Repairs & Maintenance Road Tax Drivers Salary Depreciation Total

© Fixed Supervisor Mechanic Fitter Miscellaneous Expenses Total

Grand Total Tonnage hauled Cost / Tonne

Cost/Tonne:

10 Tonne Capacity Trucks

5 24

120 1,200

24,000 20 22

1,440 28,800

3 9,600

8 Tonne Capacity Trucks

5 24

120 960

24,000 25 27

1,440 36,000

4 9,000

10 Tonne Capacity 20 10 Tonne Capacity 25

90,000 3,600

93,600

96,000 2,880

98,880

78,500 4,000

35,200 1,16,000 2,33,700

80,000 5,000

43,200 1,50,000 2,78,200

3,200 2,000 1,600 3,000 9,800

3,42,380 24,000

14.27 Rs.14.27 Rs.15.90 Rs.18.00

3,200 2,000 1,600 3,000 9,800

3,81,600 24,000

15.90 10 Tonne Trucks

8 Tonne Trucks Hire charges

Hence buy 10 tonne trucks. (iii) Before taking final decision on purchase of trucks, on factor that may have to be given weight age

is that we have assumed consistent operation of all the 20 trucks for 24 days in a month, transporting 24,000 tonnes without default for a period of five years. This aspect must be considered on the basis of past recorded of hiring trucks on day to day basis over a three y3ear period so that optimum calculations on saving get properly weighed down. Second issue that an immediate investment of Rs.86 lakhs in purchase of 20 tracks has to be made. This could be totally from own resources or totally out to borrowings or could be partly either way. For own investment technique of discounted cash flow is to be applied while is case of borrowings, recurrent interest cost as also initial cost of procuring the same has to be provided out of saving from year to year apart from meeting normal schedule of loan repayment. Net

saving works out to Rs.10.74 lakhs per annum on hauling of 24,000 tonnes for 12 months in comparison to hiring of trucks. Third issue is to compare return on investment of own funds made for procurement of trucks either fully or in part vis-à-vis return in alternate outlets. This is opportunity cost of capital will have to be given consideration. Decision will be made after considering all the above factors.

Ans. 17: Costs specific to booking operations: Direct person’s salary

Mobile expenses Conveyance

Share of other overheads: Office space General Telephone Security/Maintenance Miscellaneous Expenses

Total Cost allocated to the service

Average demand per month= 2500×3+1000×2+700×7 =1200

12

20,000 3,000 4,000

4,000 2,400 1,600 1,000 9,000

36,000

27,000

Total cost per booking= Total cost per month 36000 = =`30

average booking per month 1200

Revenue per ticket = Rs. 30 Total revenue less total cost = 30 - 30 = 0

Assuming that other overheads will anyway exist even of the service is not provided, the manager can hope to achieve a profit of Rs. 30x 1,200 - 27,000 is Rs. 9,000 for the full year. Minimum average volume to set up the service will be the amount needed to recover the specific costs of this service, is 27,000 per month.

Minimum average bookings = 27,000 = 900 bookings

30

Ans.18 Working Notes:

(1) Calculation of requirement of trucks: No. of Trips X No. of working days in a month X No. of tones 10 tonne = 5 X 24 X 10 = 1,200 tonnes 8 tonne = 5 X 24 x 8 = 960 tonnes

No. of trucks required to handle 24,000 tonnes

10 tonne trucks 8 tonne trucks

=24,000 tonnes/1200 tonnes =24,000 tonnes/960 tonnes

= 20 trucks =25 trucks

(2) No. of drivers required: 10 tonne =20 trucks X 2 drivers =40 Drivers

8 tonne =25 trucks X 2drivers =50 Drivers

(3) Total monthly depreciation:

10 tonne = 20 trucks X Rs.10,00,000 5 years

= 25 trucks X Rs.8,50,000 5 years

X 1 =Rs.3,33,333 12

X 1 =Rs.3,54,167 12

8 tonne

(4) Diesel Required: (No. of km. X No. of trips X No. of days in month X No. of trucks) Diesel required =(6 km. X 10 trips X 24 days x 20 trucks )/No. km. per litre of diesel 10 tonne =(6 km. X 10 trips X 24 days x 20 trucks )/3. km. per litre 8 tonne =(6 km. X 10 trips X 24 days x 25 trucks )/4. km. per litre

Comparative Cost Sheet Particulars Fixed charges (p.m.) Drivers salary(@ Rs.3,000 p.m) Staff Expenses Other fixed expenses

(i) Operating and Maintenance charges Depreciation Diesel Cost Lubricants & Sundries Repairs & Maintenance

=9,600 litres =9,000 litres

(Rs.) 10 tonne

1,20,000 9,000 5,000

1,34,000

8 tonne

1,50,000 9,000 3,000

1,62,000

3,33,333 3,54,167 1,44,000 1,35,000

5,760 7,200 1,00,000 1,00,000

(ii) Total 5,83,093 5,96,367 Operating Cost (i) + (ii)

7,17,093 7,58,367 Tonnage carried (tonnes) 24,000 24,000 Cost per tonne

Rs.29.88 Rs.31.60 Analysis : From the above analysis it is observed that cost per tonne is lowest if 10 tonne trucks are used, and the cost of Rs.50 per tonne presently incurring is highest and it can be reduced to Rs.29.88 by using 10 tonne trucks.

Ans.19 (a) Statement of operating income of Modern Airways

operating between EXETOWN and WYETOWN (on each one way flight) Rs.

Fare received (per flight): (A) 10,00,000 200 passenger × Rs. 5,000

Variable costs (per flight) Commission paid Rs. 10,00,000 × 8% Food services 200 passengers × Rs. 200 Fuel costs Total variable costs: (B) Contribution (per flight): (C): {(A) – (B)}

Fixed costs (per flight): Fixed annual lease costs Baggage handling (Fixed ground services) costs Fixed salaries of flight crew

80,000

40,000 1,40,000 2,60,000 7,40,000

5,30,000 70,000

___40,000

Total fixed costs: (D) Operating income (per flight): {(C) – (D)}

6,40,000 1,00,000

Rs. 10,17,600 (b) Fare received (per flight): (X)

212 passenger × Rs. 4,800

Variable costs: Commission paid Rs. 10,17,600 × 8% Food services 212 passenger × Rs. 200 Fuel costs Total variable cost: (Y) Contribution per flight: (Z): {(X) – (Y)} Excess contribution due to lowering of fare: {(Z) – (C)} [Refer to (a) part] (Rs. 7,53,792 – Rs. 7,40,000)

81,408

42,400 1,40,000 2,63,808 7,53,792

13,792

Modern Airways should lower its fare as it would increase it contribution towards profit by Rs. 13,792 per flight.

(C) Financial consideration of Modern Airways to Charter its plane to Zed Tours and Travel should use option (b) and not (a).

Rs. Under option (b) Modern Airways Receives contribution (per flight): 7,53,792 Modern Airways would get (per flight) 7,50,000 If it charters the plane

A comparison of the above data clearly shows that the Modern Airways would be financially better off by not chartering the plane.

Other consideration with regard to chartering a plane to Zed Tours and Travels

1. The loss of contribution involved in chartering a plane is Rs. 3,792 (per flight). This loss is on a lower side as compared with uncertainties about the number of passengers on scheduled fights.

modern Airways passengers may be inconvenienced when a plane is chartered to zed Tour and Travel. They may go other airlines.

The relationship between the two parties is important. If it is not a long term arrangement. Modern Airways may lose.

2.

3.

Ans.20 Working Notes: Calculation operating capacity of a single aircraft =160 seats X 60/100 (i) Calculation of net operating income per flight Fare collection (96 X 7000) Variable costs: Fuel Food (96 X 130) Commission @ 5% Total Variable costs Contribution per flight Fixed Costs: Lease 3,50,000

=96 passengers per flight (Rs.)

6,72,000

95,000 12,480 33,600

1,41,080 5,30,920

Crew Net Income per flight

72,000 4,22,000 1,08,920

(ii) Evaluation of proposal if Occupancy increases to 108 passengers per flight and the fare reduced to Rs.6,720 (Rs.)

Fare collection Variable costs: Fuel Food Commission @ 5%

(108 X 6720) 7,25,760

95,000 (108 X 130) 14,040

36,288 1,45,328

Contribution 5,80,432 Analysis: The contribution will increase by Rs.49,512 (i.e Rs.5,80,432-Rs.5,30,920). Hence, it is suggested to accept the proposal (iii) Evaluation of proposal to charter the aircraft Current contribution 5,30,920 Less: Fixed charge 5,00,000 Loss: 30,920

Analysis: if the aircraft is given on charter, it will cause loss of contribution by Rs.30,920. Hence the proposal is not suggested.

Ans. 21: (i) With respect to the passenger,

10% Commission on fare Food Total variable cost/passenger

the only variable costs are : Rs. 500 Rs. 300 Rs. 800

Revenue per passenger = gross fare = 5000 Contribution = 5000 – 800 = Rs. 4200 Total Contribution Less: Costs/flight

Fuel Lease Baggage Flight Crew

(ii)

90,000 2,00,000

40,000 48,000 3,78,000

6,30,000

4200 x 240 10,08,000

Profit per flight Cost per flight Rs. 3,78,000 are fixed in relation to the number of passengers.

B.E.= 378000 =90 passengers

4200

Effect of Mid Air’s offer A to D Fare

Rs 2000

200 1800

Less: Comm.

Less:Snacks Contribution per passenger 1500

300

Additional Cost ( Rs)

Additional Revenue

(Rs) 1,25,000

45,000 19,000

53,000 90,000

1,05,000 2,22,000 2,15,000

50 seats x 2500 ( D to B ) Fuel Baggage Snacks @ Rs 200 for passenger ( 240 -25+ 50): 200 x [ 240 – 25 + 50 ] Additional Contribution (A to D) 60 x 1500

Contribution lost (A to B) : 25 x 4200 ( opportunity cost)

Aero will loose Rs. 7,000 per flight if it accepts Mid Air’s offer.

Decision : Reject Mid Air’s offer.

Ans.22

Calculation of variable cost per student of last year Revenue 1. Students tuition-75% (Rs.3,600 X 12,000 students) 2. Endowment & contribution-25% (Rs.432 lakhs X 25/75) Total revenue Less: Fixed cost Variable cost

Variable cost per student

(Rs.lakhs)

432 144 576 300 276

=Rs.2,76,00,000 12,000 students =Rs.2,300 per student

(i) Calculation of amount available in the first year for capital improvements and building (Rs.lalhs)

Revenue 1. Tuition Fee (Rs.4,200 X 11,200 students) 2. Endowment & contribution 3. Grant Total revenue Less: Variable cost (2,300 X 1.10 X 11200 students) Contribution Less: Fixed cost (Rs.300 lakhs + Rs.30 lakhs) Balance available for capital improvements and building

470.40 144.00

50.00 664.40 283.36 381.04 330.00

51.04 Calculation of break-even if the grant is received and costs increases as predicted for the coming year

(Rs.lakhs) Variable cost (Rs.2,300 X 1.10 X 12,000 students) 303.60 Fixed Cost (Rs.300 lakhs + Rs. 30 lakhs) 330.00 Capital improvement 40.40 Total cost 674.00 Less: Endowment and contribution 144.00

Grant 50.00 Balance amount to be collected as tuition fee Tuition fee to be collected per student = Rs.4,80,00,000

12,000 students

Ans.23 Working Notes: (i) Expected Variable cost this year Variable cost last year Add: Expected increase this year (25% of Re.0.80) Expected variable cost this year

(ii) Expected fixed costs this year Fixed cost last year Add: Expected increase this year (10% of Rs.32,00,000) Expected variable cost this year

(1) Rides which DD Amusement park sell last year

(No. of rides DD sell last year) = Total Sales of rides last year Charges per ride last year

194.00 480.00

=Rs.4,000 per student

(Re.per ride) 0.80 0.20 1.00

(Rs.) 32,00,000

3,20,000 35,20,000

=Rs.48,00,000 =12,00,000 rides Rs.4

(Rs.) 4 1 3

12,00,000 36,00,000 35,20,000

80,000

(2) Expected net income for the year if price increase if not implemented Charges per ride Less: Expected Variable cost per ride Contribution per ride No. of rides Total expected contribution Less: Expected fixed costs Expected net income

(3)Price indifference point for the new ride Price indifference point is a point at which the expected profits remains the same irrespective of sales price and costs. (Rs.)

New ride price Less: Variable cost Contribution per ride Fixed Costs of this year Net Income of last year Contribution require

5.00 1.00 4.00

35,20,000 6,40,000

41,60,000

Price- Indifference point = Rs.41,60,000 =10,40,000 rides Rs.4

(4) Break –even point for this year using the old price and the new price

Break-even point = Fixed costs Contribution per ride

At old price = Rs.35,20,000 Rs.4-Re.1

= Rs.35,20,000

=11,73,334 rides

At New price =8,80,000 rides

Rs.5-Re.1

(5) Expected net income if the price increase will reduce ride volume by 10% from the last year’s levels (Rs.)

Charges per ride 5.00 Less: Variable cost 1.00 Contribution per ride: (a) 4.00 No. of rides (12,00,000-1,20,000): (b) 10,80,000 Total contribution for all rides: (a) X (b) 43,20,000 Less: fixed costs 35,20,000 Expected net income 80,000

Justification: Since the increase in price of a ride will increase the net income by Rs.1,60,000(Rs.8,00,000- Rs.6,40,000) the management should raise the price of a ride.

Ans 24: (1) Total number of patients attended Number of patients attended per day by a physician: 20 Number of physicians employed 6 Number of days in week 6 Number of weeks in a year 52 Total number of patients attended = 20×6 ×6×52 = 37,440.

(2) Patient Mix: Adults (50%) Children (40%) Senior Citizens (10%)

37,440 ×50/100 = 37,440 ×40/100 = 37,440 ×10/100 =

18,720 14,976

__3,744 37,440

(3) Patient Appointments: No treatment required (70%) 37,440 ×70/100 = Minor treatment (20%) 37,440×20/100 = Major treatment (10%) 37,440 ×10/100 =

Income from Insurance Companies: Number of patients

(A) No treatment patients 26,208 Minor treatment patients 7,488 Major treatment patients 3,744

Total

26,208 7,488

___3,744 37,440

Rs.

(B) 60

250 500

Rs.

(A×B) 15,72,480 18,72,000 18,72,000 53,16,480

(4)

(5) Co-payment from adult patients: Number of Patients

Payment Rs.

Total Payment

(Rs.) Total number of adult patients No treatment patients (70%) Minor treatment (20%) Major treatment (10%)

Total

18,720 13,104

3,744 1,872

60 250 500

7,86,240 9,36,000 9,36,000

26,58,240

(6) Net income: Rs.

53,16,480 26,58,240 79,74,720

2,25,280

Rs. Payment from Insurance companies Co-payment from adult patients Total Other Income (fixed) Total Income (A)

Less: Expenditure Variable expenses: Material and consumables Fixed expenses:

Physician’s salary (6 ×4,50,000) Assistants salary (7 ×1,50,000)

Administrative staff’s salary (2 ×90,000) Establishment and other operating costs Total Expenditure (B) Net Income (A – B)

(ii) 1. Contribution Analysis:

82,00,000

22,32,000

27,00,000 10,50,000

1,80,000 16,00,000 55,30,000

77,62,000 __4,38,000

Total Fees from Insurance Companies and adult patients Less: Variable costs Contribution Average contribution per patient (57,42,720÷37,440)

2. Break-even patients:

(Rs.) 79,74,720 22,32,000 57,42,720

153.38

Fixed costs Less: Fixed income Net Fixed costs

Break-even patients = (Net fixed costs÷ Contribution per patient) = (53,04,720÷ 34,585)

(Rs.) 55,30,000

2,25,280 53,04,720

153.38

3. Percentage of maximum capacity required to be utilized in order to break-even

Present utilization = 20 patients = 83.33% = 37,440

24 patients

100% patient capacity is 37,440 ÷0.8333 =44,930 patients

Percentage of maximum capacity required to be utilized in order to break-even Break Even patients ÷100% patients capacity ×100

= {(34,585÷ 44,930)×100 } = 76.98% say 77%.

Assumption: Patient mix and mix of patient appointments will be same in the next year.

Ans 25 (a) Statement of Total Cost

Total cost

Salary of Supervisor , Nurses, Ward boys Repairs and Maintenance Salary of doctors Food supplied to patients Laundry charges for their bed linens Medicines supplied Cost of oxygen, X ray etc, other than directly borne for treatment of patients General administration charges Building rent

Additional building rent on takings Hire charges extra beds Fees to heart specialists Total cost

Profit Total takings

Total taking(assuming X to be the rent per day) Rent to be charged 1,05,000 × X = 23,49,000 +25% (1,05,000 × X) = 78750 X = 23,49,000 or X = 29.83(Rounded Off) No of beds with Equivalent Rent Nature of wards

General ward

Additional general ward

Occupancy

100 × 360 × 100%

Weight of rent

36,000 × 1

600 × 1

Ward Days

36,000

600

(3 × 15,000)

Amount (Rs)

4,25,000

90,000 13,50,000

40,000 80,500 74,000 49,500

63,000 (10 ×

12,000)

Rs 21,72,000 Rs 1,20,000

5% on Total Taking Rs 12,000 Rs 45,000 Rs 23,49,000 + 5% on Total Taking 20% on Total Taking Rs 23,49,000 + 25% of Total Taking 1,05,000 × X

12,000 20

50 × 360 × 80% 50 × 360 × 60%

Cottage ward Deluxe ward Total Rent to be charged Particulars General ward

14,400 × 2.5 6,480 × 5

36,000 32,400

1,05,000

Basic 29.83

Service tax 2.39

Total 32.22

Cottage ward Deluxe ward

74.58 149.15

5.97 11.93

80.55 161.08

Note : You may assume Total Taking to include Service Tax also. Rent = 23,49,000 + 25% × (1,05,000 X × 1.08) + 0.08 × (1,05,000X ) = 1,05,000X × 1.08 = 23,49,000 + 28350X + 8400X = 1,13,400X Therefore X = Rs 30.65 Rent to be charged Particulars General ward Cottage ward Deluxe ward

Basic 30.65 76.63

153.25

Service tax 2.45 6.13

12.26

Total 33.10 82.76

165.51

solutions of activity based costing -...

Documents