Question 2 (b)
Replacement with written-down-value depreciation
12 marks
- Time to write
- About 24 minutes
Question
Question 2 (b) · 12 marksK.L. & Sons Ltd. is thinking of replacing one of its existing machines, currently valued at ₹4,80,000. The machine can be sold at its book value of ₹1,08,000; its remaining useful life is 5 years, with no salvage value expected. It is depreciated at 20% per annum on the written down value method. The new machine costs ₹4,80,000 and can be sold for ₹3,00,000 after 5 years, by which time it will not be needed any more. It will be depreciated at 30% per annum, again on the written down value method. The new machine is expected to bring annual savings of ₹1,20,000 in manufacturing costs. The company is in a 30% tax bracket, and its required rate of return is 10%. Tax on any gain or loss from the sale of the asset may be ignored in this analysis. Should the existing machine be replaced by the new one?
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 the existing…?A yes-or-no question: answer it in your first line, then explain why.
- Should theEnd with a one-line decision that follows from your figures.
What the paper leaves open
The existing machine is said to be "currently valued at" the same amount as the new machine's cost, yet saleable at its book value. "Currently valued at" is read as its original cost; its book value, at which it can be sold now, is the lower figure given.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Net initial outlay 2 marks 3 min
- 2 WDV depreciation of each machine 3 marks 5 min
- 3 Incremental cash flows after tax and salvage 4 marks 7 min
- 4 Present values, NPV and decision 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 4'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.
Assumptions. "Currently valued at ₹4,80,000" is read as the existing machine's original cost; it can be sold now at its book value of ₹1,08,000 (paper note), so there is no gain or loss on sale. Each machine is depreciated on its own written-down value; tax on gain or loss on sale is ignored, as the question says. PV factors at 10% are from the table (3 decimals).
1. Net initial outlay: cost of new machine ₹4,80,000 − sale of existing machine ₹1,08,000 = ₹3,72,000.
2. Depreciation and incremental cash flows
| Year | New machine (30% WDV) | Existing machine (20% WDV) | Incremental depreciation | Saving before tax | Profit before tax | Tax @ 30% | Profit after tax | CFAT | Salvage of new machine | Net cash flow | PV factor @ 10% | Present value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1,44,000.00 | 21,600.00 | 1,22,400.00 | 1,20,000 | (2,400.00) | (720.00) | (1,680.00) | 1,20,720.00 | — | 1,20,720.00 | 0.909 | 1,09,734.48 |
| 2 | 1,00,800.00 | 17,280.00 | 83,520.00 | 1,20,000 | 36,480.00 | 10,944.00 | 25,536.00 | 1,09,056.00 | — | 1,09,056.00 | 0.826 | 90,080.26 |
| 3 | 70,560.00 | 13,824.00 | 56,736.00 | 1,20,000 | 63,264.00 | 18,979.20 | 44,284.80 | 1,01,020.80 | — | 1,01,020.80 | 0.751 | 75,866.62 |
| 4 | 49,392.00 | 11,059.20 | 38,332.80 | 1,20,000 | 81,667.20 | 24,500.16 | 57,167.04 | 95,499.84 | — | 95,499.84 | 0.683 | 65,226.39 |
| 5 | 34,574.40 | 8,847.36 | 25,727.04 | 1,20,000 | 94,272.96 | 28,281.89 | 65,991.07 | 91,718.11 | 3,00,000 | 3,91,718.11 | 0.621 | 2,43,256.95 |
| Total PV | 5,84,164.70 |
In year 1 the extra depreciation exceeds the saving, so the small loss reduces tax on the firm's other profits (a tax saving of ₹720). The new machine's sale for ₹3,00,000 after five years is added to the terminal year's net cash flow as its final salvage value. The existing machine would have no salvage.
| ₹ | |
|---|---|
| Present value of incremental inflows | 5,84,164.70 |
| Less: net initial outlay | 3,72,000.00 |
| NPV | 2,12,164.70 |
The NPV of replacing at 10% is positive. The existing machine should be replaced by the new one.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net initial outlay | 2 |
| 2 | WDV depreciation of each machine | 3 |
| 3 | Incremental cash flows after tax and salvage | 4 |
| 4 | Present values, NPV and decision | 3 |
| Total | 12 |
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