Question 1 (b)
Replacement decision: NPV over ten years
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 1 (b) · 10 marksSterling Ltd. now has a manually operated machine, bought ten years ago. Its book value is Rs. 1,20,000, and its remaining life ten years. The company is thinking of replacing the old machine with a fully automated one costing Rs. 3,12,000, with an expected ten-year life and an expected salvage value of Rs. 24,000. The new machine is estimated to save Rs. 72,000 of cost per year. The company has an offer of Rs. 96,000 for the old machine if it is sold now. Its tax rate is 40%, and it uses the Straight line method of depreciation. On its investments, the company expects a minimum return of 12% per annum. Should the machine be replaced? (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
- Should the machine…?A yes-or-no question: answer it in your first line, then explain why.
- replacingCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
The old machine is depreciated straight line over its remaining ten years to nil; it is sold now for less than book value, and the loss on sale is taken with its tax effect (C7). The new machine's salvage value is received at the end of year 10.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Net cash outlay, with the tax saved on the loss 2 marks 4 min
- 2 Incremental depreciation 2 marks 4 min
- 3 Annual cash inflow after tax 3 marks 5 min
- 4 PV of inflows and salvage; NPV 2 marks 4 min
- 5 Decision 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 5'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.
Net cash outlay. The old machine (book value ₹1,20,000) is sold for ₹96,000; the loss of ₹24,000 saves tax of 40% = ₹9,600 (paper note). For a replacement, the outflow is the new cost less the net proceeds of the old asset, adjusted for tax on its sale.
| Particulars | ₹ |
|---|---|
| Cost of the new machine | 3,12,000 |
| Less: sale of the old machine | 96,000 |
| Less: tax saved on the loss on sale | 9,600 |
| Net cash outlay | 2,06,400 |
Incremental depreciation. New: (3,12,000 − 24,000) ÷ 10 = 28,800; old: 1,20,000 ÷ 10 = 12,000 (lost on replacement); incremental = ₹16,800. Only its tax saving is a cash flow.
Annual cash inflow (years 1–10): saving 72,000 − incremental depreciation 16,800 = 55,200 before tax; tax @ 40% = 22,080.
| Particulars | ₹ |
|---|---|
| Increase in profit after tax | 33,120 |
| Add: incremental depreciation | 16,800 |
| Annual cash inflow after tax | 49,920 |
NPV at 12%. PV of the annual inflows = 49,920 × 5.650 (annuity factor, 10 years) = 2,82,048; PV of the salvage at the end of year 10 = 24,000 × 0.322 = 7,728; total = ₹2,89,776. NPV = 2,89,776 − 2,06,400 = ₹83,376.
Decision. The NPV is positive, so the machine should be replaced.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net cash outlay, with the tax saved on the loss | 2 |
| 2 | Incremental depreciation | 2 |
| 3 | Annual cash inflow after tax | 3 |
| 4 | PV of inflows and salvage; NPV | 2 |
| 5 | Decision | 1 |
| Total | 10 |
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