Question 5
Modernisation decision: equal-profit output, indifference point and comparative profit
18 marks
- Time to write
- About 36 minutes
Question
Question 5 · 18 marksTara Ltd. gives the following details of its present operations:
Selling price (Rs.) 24
Variable Cost per unit (Rs.) 18
Fixed Cost (Rs.) 60,000
Actual Output and Sales (units) 26,000
Management is considering a proposal to modernise its production operations.
Under this proposal, the estimated cost structure is:
Selling price (Rs.) 24
Variable Cost per unit (Rs.) 12
Fixed Cost (Rs.) 1,80,000
As the company's management accountant, give the following calculations and advice for management to consider:
The level of output under the proposed alternative at which the company will earn the same profit as it earns at the existing level of sales operations.
The range of sales over which the existing operations, and over which the proposed modernization, will be more profitable. Whether, at the existing level of sales operations, the company should consider modernizing its production facility.
If the company plans to produce and sell 32,000 units, prepare a statement comparing the profit under the two alternatives.
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- (i)–(iii)3 items, each marked on its own: give each its share.
- prepare a statementDraw the format first (heading, columns, dates), then fill in the figures from your working.
- estimatedFormula first, then the working, then the answer with its unit (₹, %, units).
- adviceEnd with a one-line decision that follows from your figures.
What the paper leaves open
No marks are printed against Q5; it is reckoned at 18 (its alternative carries 6 + 12).
Write it in this order
- Read the data; tick every adjustment as you plan it 2 min
- 1 Present profit and output for the same profit under the proposal 5 marks 9 min
- 2 Indifference point, ranges and advice 7 marks 12 min
- 3 Comparative statement units 6 marks 11 min
- Check: every adjustment used, both sides agree, dates in 2 min
Try it first. About 36 minutes for 18 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
| Particulars | Existing | Proposed |
|---|---|---|
| Selling price per unit (₹) | 24 | 24 |
| Variable cost per unit (₹) | 18 | 12 |
| Contribution per unit (₹) | 6 | 12 |
| Fixed cost (₹) | 60,000 | 1,80,000 |
| Break-even point (units) | 10,000 | 15,000 |
Present profit at 26,000 units = 26,000 × ₹6 − ₹60,000 = ₹1,56,000 − ₹60,000 = ₹96,000.
(i) Output under the proposal for the same profit
Units = (Fixed cost + Profit) ÷ Contribution per unit = (₹1,80,000 + ₹96,000) ÷ ₹12 = 23,000 units.
(ii) Range of sales and advice
Cost indifference point (where both give the same profit):
Units = Difference in fixed cost ÷ Difference in contribution per unit = (₹1,80,000 − ₹60,000) ÷ (₹12 − ₹6) = 20,000 units (sales of ₹4,80,000). At 20,000 units both give a profit of ₹60,000.
- Below 20,000 units the existing operation is more profitable (it has lower fixed costs). Below 15,000 units the proposal would even make a loss, while the existing operation breaks even at 10,000 units.
- Above 20,000 units the proposed modernisation is more profitable (it has the higher contribution per unit).
At the existing level of 26,000 units, which is above the indifference point, the proposal earns 26,000 × ₹12 − ₹1,80,000 = ₹1,32,000 against ₹96,000 now. The company should consider modernisation, provided sales are expected to stay above 20,000 units; the higher fixed cost does make profit more sensitive to a fall in sales.
(iii) Comparative statement at 32,000 units
| Particulars | Existing (₹) | Proposed (₹) |
|---|---|---|
| Sales (32,000 × ₹24) | 7,68,000 | 7,68,000 |
| Less: Variable cost | 5,76,000 | 3,84,000 |
| Contribution | 1,92,000 | 3,84,000 |
| Less: Fixed cost | 60,000 | 1,80,000 |
| Profit | 1,32,000 | 2,04,000 |
At 32,000 units the proposed modernisation gives ₹72,000 more profit.
Where the 18 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present profit and output for the same profit under the proposal | 5 |
| 2 | Indifference point, ranges and advice | 7 |
| 3 | Comparative statement at 32,000 units | 6 |
| Total | 18 |
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