Question 1 OR (b)
NPV of a machine with working capital
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 1 OR (b) · 10 marksA company is considering buying a machine costing Rs.6,00,000, whose life is 5 years, after which it can be sold for Rs. 1,20,000. An initial investment of Rs.24,000 in working capital will be needed, and Additional working capital of Rs 24,000 at the end of the first year. The company's tax rate is 40 %, and it uses the straight line method of depreciation. Its cost of capital is 12%. Using the NPV method, advise the company on the project's profitability. The profits before depreciation and tax are expected to be:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| PBDT (Rs.) | 1,80,000 | 2,40,000 | 2,40,000 | 1,80,000 | 1,20,000 |
(5,10)
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
- NPVCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
Working capital (both instalments) is recovered at the end of year 5. The machine's sale at the end of year 5 is at its book value, so no tax arises on it.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Depreciation and cash inflows after tax 4 marks 7 min
- 2 Working capital invested and recovered; sale value 3 marks 6 min
- 3 Present values and NPV 2 marks 4 min
- 4 Advice 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 20 minutes for 10 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.
Approach. Depreciation (straight line) = (6,00,000 − 1,20,000) ÷ 5 = ₹96,000; it is non-cash and counts only through its tax saving. Working capital of ₹24,000 is invested now and ₹24,000 more at the end of year 1; increases in working capital are outflows and the full amount is recovered at the end of the project (paper note). The machine sells at its book value, so no tax arises on the sale.
| Year | PBDT | Depreciation | EBT | Tax @ 40% | EAT | Add: depreciation | Cash inflow after tax |
|---|---|---|---|---|---|---|---|
| 1 | 1,80,000 | 96,000 | 84,000 | 33,600 | 50,400 | 96,000 | 1,46,400 |
| 2 | 2,40,000 | 96,000 | 1,44,000 | 57,600 | 86,400 | 96,000 | 1,82,400 |
| 3 | 2,40,000 | 96,000 | 1,44,000 | 57,600 | 86,400 | 96,000 | 1,82,400 |
| 4 | 1,80,000 | 96,000 | 84,000 | 33,600 | 50,400 | 96,000 | 1,46,400 |
| 5 | 1,20,000 | 96,000 | 24,000 | 9,600 | 14,400 | 96,000 | 1,10,400 |
| Year | Net cash flow | PV factor @ 12% | Present value |
|---|---|---|---|
| 1 (1,46,400 − additional working capital 24,000) | 1,22,400 | 0.893 | 1,09,303.20 |
| 2 | 1,82,400 | 0.797 | 1,45,372.80 |
| 3 | 1,82,400 | 0.712 | 1,29,868.80 |
| 4 | 1,46,400 | 0.636 | 93,110.40 |
| 5 (1,10,400 + sale 1,20,000 + working capital 48,000) | 2,78,400 | 0.567 | 1,57,852.80 |
| Total present value | 6,35,508 | ||
| Less: initial outlay (machine 6,00,000 + working capital 24,000) | 6,24,000 | ||
| NPV | 11,508 |
Advice. The NPV is positive (₹11,508), so the project is profitable and should be taken up, though by a small margin.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Depreciation and cash inflows after tax | 4 |
| 2 | Working capital invested and recovered; sale value | 3 |
| 3 | Present values and NPV | 2 |
| 4 | Advice | 1 |
| Total | 10 |
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