Question 2 (b)
Should the existing machine be replaced?
9 marks
- Time to write
- About 18 minutes
Question
Question 2 (b) · 9 marksA machine is purchased six years ago for ₹1,80,000 has been depreciated to a book value of ₹1,08,000. It originally had a projected life 15 years (salvage nil). It is proposed to replace this machine. A new machine will cost ₹3,00,000 and will reduce operating cost by ₹36,000 per annum for the next nine years. The existing machine can be replaced away now for ₹84,000. The new machine, too, will be depreciated over nine years period as per the straight line Method with salvage value ₹30,000. Given that the applicable tax rate is 30% and the cost of capital is 12%, find out whether the existing machine be replaced or not. (Any profit or loss on the sale of the asset is to be ignored for tax purposes.)
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
- replaceCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
"Replaced away" is read as sold. "Whether the existing machine be replaced or not" is printed so and kept.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Depreciation of both machines and net outlay 2 marks 4 min
- 2 Incremental cash flows after tax 3 marks 6 min
- 3 Present values including salvage; NPV 3 marks 5 min
- 4 Decision 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 18 minutes for 9 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.
Existing machine. Cost ₹1,80,000, 15-year life, nil salvage: straight-line depreciation ₹12,000 a year; after six years its book value is ₹1,08,000 and nine years remain. It can be sold now for ₹84,000 ("replaced away" read as sold); profit or loss on the sale is ignored for tax, as the question says.
New machine. Cost ₹3,00,000, salvage ₹30,000 after nine years: depreciation (3,00,000 − 30,000) ÷ 9 = ₹30,000 a year.
1. Net initial outlay: 3,00,000 − 84,000 = ₹2,16,000.
2. Incremental annual cash flow (years 1–9)
| ₹ | |
|---|---|
| Saving in operating cost | 36,000 |
| Less: incremental depreciation (30,000 − 12,000) | 18,000 |
| Incremental profit before tax | 18,000 |
| Less: tax @ 30% | 5,400 |
| Incremental profit after tax | 12,600 |
| Add: incremental depreciation | 18,000 |
| Incremental cash flow after tax | 30,600 |
3. Present value at 12%. The annuity factor for 9 years is the sum of the 3-decimal yearly factors, 0.893 + 0.797 + 0.712 + 0.636 + 0.567 + 0.507 + 0.452 + 0.404 + 0.361 = 5.329.
| ₹ | |
|---|---|
| PV of annual cash flows (30,600 × 5.329) | 1,63,067.40 |
| PV of salvage of the new machine (30,000 × 0.361) | 10,830.00 |
| Total present value | 1,73,897.40 |
| Less: net initial outlay | 2,16,000.00 |
| NPV | (42,102.60) |
Decision. The NPV of replacing at 12% is negative: the savings do not justify the outlay. The existing machine should not be replaced.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Depreciation of both machines and net outlay | 2 |
| 2 | Incremental cash flows after tax | 3 |
| 3 | Present values including salvage; NPV | 3 |
| 4 | Decision | 1 |
| Total | 9 |
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