Question 1 (b)
Purchase of a machine: NPV with depreciation and tax
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 1 (b) · 10 marksA machine, available for ₹2,88,000, is likely to yield following our earnings over the next 5 years, as below:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Earnings | 1,26000 | 115200 | 1,08,000 | 86,400 | 93,600 |
The machine will be depreciated by the straight line method, and its salvage value is ₹36,000 the machine is subject to tax, at a 40% rate. If the cost of capital is 12%, should the machine be purchased.
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
- should theEnd with a one-line decision that follows from your figures.
What the paper leaves open
- The yearly figures are called "earnings" ("following our earnings" is printed); whether they are before or after depreciation and tax is not said. The answer reads them as earnings before depreciation and tax, since depreciation and the 40% tax are given separately, and shows the other reading's result.
- The first year's figure is printed "1,26000", read as 1,26,000 (the Hindi version prints the figure with the usual commas); it is kept as printed.
- The salvage value is read as received at the end of year 5.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Depreciation on the straight-line basis, net of salvage 1 mark 2 min
- 2 Tax and cash inflows after tax for each year 4 marks 7 min
- 3 Salvage at the end of year 5; present values at 12% 3 marks 5 min
- 4 NPV and decision 2 marks 4 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.
Method. The net present value technique discounts each year's cash flow at the required rate of return (here the 12% cost of capital) and compares the total with the outlay. The yearly earnings are taken before depreciation and tax (paper note 1). Depreciation is a non-cash item: it is deducted to find the tax, and added back, so that only its tax saving counts as a cash inflow.
Depreciation (straight line) = (2,88,000 − salvage 36,000) ÷ 5 = ₹50,400 a year.
| Year | Earnings before dep. and tax | Depreciation | Earnings before tax | Tax @ 40% | Earnings after tax | Add: depreciation | Cash inflow after tax |
|---|---|---|---|---|---|---|---|
| 1 | 1,26,000 | 50,400 | 75,600 | 30,240 | 45,360 | 50,400 | 95,760 |
| 2 | 1,15,200 | 50,400 | 64,800 | 25,920 | 38,880 | 50,400 | 89,280 |
| 3 | 1,08,000 | 50,400 | 57,600 | 23,040 | 34,560 | 50,400 | 84,960 |
| 4 | 86,400 | 50,400 | 36,000 | 14,400 | 21,600 | 50,400 | 72,000 |
| 5 | 93,600 | 50,400 | 43,200 | 17,280 | 25,920 | 50,400 | 76,320 |
| Year | Cash inflow | PV factor @ 12% | Present value |
|---|---|---|---|
| 1 | 95,760 | 0.893 | 85,513.68 |
| 2 | 89,280 | 0.797 | 71,156.16 |
| 3 | 84,960 | 0.712 | 60,491.52 |
| 4 | 72,000 | 0.636 | 45,792 |
| 5 (76,320 + salvage 36,000) | 1,12,320 | 0.567 | 63,685.44 |
| Total present value of inflows | 3,26,638.80 | ||
| Less: cost of the machine | 2,88,000 | ||
| Net present value | 38,638.80 |
Decision. A project is accepted if its NPV is positive. The NPV is ₹38,638.80, positive, so the machine should be purchased.
The other reading. If the printed earnings are taken as already after depreciation and tax, each year's cash inflow is the earnings plus ₹50,400 depreciation, and the NPV is ₹3,03,354; the machine is worth buying either way.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Depreciation on the straight-line basis, net of salvage | 1 |
| 2 | Tax and cash inflows after tax for each year | 4 |
| 3 | Salvage at the end of year 5; present values at 12% | 3 |
| 4 | NPV and decision | 2 |
| Total | 10 |
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