Question 2 (b)
Replacement decision: incremental cash flows and NPV
12 marks
- Time to write
- About 24 minutes
Question
Question 2 (b) · 12 marksNavya Ltd. is considering replacing a machine whose written down value is ₹1,92,000 and which will be fully depreciated at the end of 2 year. The machine's remaining economic life is 4 years, after which it will have no salvage value. If sold today, however, it has a salvage value of ₹1,44,000. It will generate revenue of ₹6,24,000 per annum for 4 years and will incur expenses of ₹4,56,000 per annum. A new machine costing ₹5,76,000 can replace it. The new machine will generate revenue of ₹11,04,000 per annum and will incur annual expenses of ₹6,96,000. If the new machine is bought, additional working capital of ₹2,40,000 will be required. Depreciation of ₹96,000 per annum will be charged on the new machine so that its book value equals its salvage value of ₹1,92,000 at the end of 4th year. The company's tax rate is 30%. Advise the company if its cost of capital is 16%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| PVF at 16% | 0.862 | 0.743 | 0.641 | 0.552 |
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
- replacingCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
The paper says the existing machine will be fully depreciated at the end of "2 year" although its remaining economic life is 4 years. We read this as: its written down value is written off over the next two years, while the machine can still be used for four.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Net initial outlay new cost + working capital − sale of old machine 2 marks 3 min
- 2 Incremental EBDT and incremental depreciation old machine written off in two years 3 marks 5 min
- 3 Incremental CFAT for each year after tax 3 marks 5 min
- 4 Terminal inflows (salvage and working capital) and PV at 16% 2 marks 3 min
- 5 NPV and advice 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 3 min
Short on time? End with step 5's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 24 minutes for 12 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. In a replacement decision the relevant figures are the incremental cash flows: the initial outflow is the cost of the new machine plus the extra working capital, less the net proceeds from selling the old one. The interim cash flow is the change in operating income before tax, less tax, with depreciation (a non-cash expense) added back. Working capital put in is assumed to be released in full at the end of the project.
Assumptions (from the question and the paper note):
- the old machine's written down value of ₹1,92,000 is written off over the next two years (₹96,000 a year), although it could be used for four;
- no tax is levied on the sale of the old machine, since the question says nothing about it;
- the new machine's book value at the end of year 4 equals its salvage value, ₹5,76,000 − 4 × ₹96,000 = ₹1,92,000, so its sale then gives neither gain nor loss.
| Item | ₹ |
|---|---|
| Cost of new machine | 5,76,000 |
| Add: additional working capital | 2,40,000 |
| Less: sale value of old machine | (1,44,000) |
| Net initial outlay | 6,72,000 |
2. Incremental annual cash flows
Incremental earnings before depreciation and tax = (₹11,04,000 − ₹6,96,000) − (₹6,24,000 − ₹4,56,000) = ₹4,08,000 − ₹1,68,000 = ₹2,40,000 a year. Incremental depreciation = new ₹96,000 less old ₹96,000 in years 1–2 (nil), and ₹96,000 in years 3–4 (the old machine is then fully written off).
| ₹ | Year 1 | Year 2 | Year 3 | Year 4 |
|---|---|---|---|---|
| Incremental EBDT | 2,40,000 | 2,40,000 | 2,40,000 | 2,40,000 |
| Less: incremental depreciation | 0 | 0 | 96,000 | 96,000 |
| Incremental EBT | 2,40,000 | 2,40,000 | 1,44,000 | 1,44,000 |
| Less: tax @ 30% | 72,000 | 72,000 | 43,200 | 43,200 |
| Incremental EAT | 1,68,000 | 1,68,000 | 1,00,800 | 1,00,800 |
| Add: incremental depreciation | 0 | 0 | 96,000 | 96,000 |
| Incremental CFAT | 1,68,000 | 1,68,000 | 1,96,800 | 1,96,800 |
| Year | CFAT (₹) | Terminal inflow (₹) | Total inflow (₹) | PVF @ 16% | PV (₹) |
|---|---|---|---|---|---|
| 1 | 1,68,000 | — | 1,68,000 | 0.862 | 1,44,816.00 |
| 2 | 1,68,000 | — | 1,68,000 | 0.743 | 1,24,824.00 |
| 3 | 1,96,800 | — | 1,96,800 | 0.641 | 1,26,148.80 |
| 4 | 1,96,800 | 1,92,000 + 2,40,000 | 6,28,800 | 0.552 | 3,47,097.60 |
| Total PV of inflows | 7,42,886.40 |
The year-4 terminal inflow is the new machine's salvage value (₹1,92,000) plus the working capital released (₹2,40,000).
NPV = ₹7,42,886.40 − ₹6,72,000 = ₹70,886.40.
Advice. The NPV of replacing is positive at the 16% cost of capital, so Navya Ltd. should replace the old machine with the new one.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net initial outlay (new cost + working capital − sale of old machine) | 2 |
| 2 | Incremental EBDT and incremental depreciation (old machine written off in two years) | 3 |
| 3 | Incremental CFAT for each year after tax | 3 |
| 4 | Terminal inflows (salvage and working capital) and PV at 16% | 2 |
| 5 | NPV and advice | 2 |
| Total | 12 |
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