Question 2
Replacement decision with tax on the loss on sale
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 · 15 marksXYZ Limited has a machine, with a further life of 5 years, which costs Rs. 12,00,000 and has a book value of Rs. 4,80,000. A new machine costing Rs. 24,00,000 is available. Though its capacity is the same as the old machine's, it will save variable cost to the extent of Rs. 8,40,000 per annum. The machine's life will be 5 years, at the end of which its scrap value will be Rs. 2,40,000. The income tax rate is 40%, and as a policy the firm makes no investment yielding less than 12% p.a. If sold today, the old machine will realize Rs. 1,20,000; if sold at the end of 5 years, it will have no salvage value. The company follows the straight line method of depreciation. Capital gain on the sale of the old machine is also taxed at the rate of 40%. Advise XYZ Limited whether or not to replace the old machine. 15
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
"Capital gain on sale of old machine" is applied to the sale today: it sells below book value, so the loss on sale gives a tax saving at 40%, stated in the answer (C7).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Net cash outlay, with the tax on the loss on sale 4 marks 7 min
- 2 Incremental depreciation 2 marks 3 min
- 3 Annual cash inflow after tax 4 marks 7 min
- 4 NPV and advice 5 marks 9 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 30 minutes for 15 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.
1. Net cash outlay (year 0). For a replacement, the outflow is the new cost less the net proceeds of the old machine. The old machine sells for ₹1,20,000 against a book value of ₹4,80,000: a loss of ₹3,60,000, which saves tax of 40% × 3,60,000 = ₹1,44,000 (paper note).
| Particulars | ₹ |
|---|---|
| Cost of new machine | 24,00,000 |
| Less: sale of old machine | 1,20,000 |
| Less: tax saved on the loss on sale | 1,44,000 |
| Net cash outlay | 21,36,000 |
2. Incremental depreciation. New: (24,00,000 − 2,40,000) ÷ 5 = 4,32,000. Old: 4,80,000 ÷ 5 = 96,000 (lost on replacement). Increment = ₹3,36,000; its tax saving is a cash inflow.
3. Annual incremental cash inflow (years 1–5). EBT = saving 8,40,000 − 3,36,000 = 5,04,000; tax @ 40% = 2,01,600.
| Particulars | ₹ |
|---|---|
| Increase in profit after tax | 3,02,400 |
| Add: incremental depreciation | 3,36,000 |
| Annual cash inflow after tax | 6,38,400 |
| Particulars | ₹ |
|---|---|
| PV of annual inflows (6,38,400 × 3.605) | 23,01,432 |
| PV of scrap of new machine (2,40,000 × 0.567) | 1,36,080 |
| Total PV of inflows | 24,37,512 |
NPV = 24,37,512 − 21,36,000 = ₹3,01,512. (The scrap equals the new machine's book value at the end, so no tax arises on it; the old machine would have had no salvage.)
Advice. NPV is positive, so XYZ Limited should replace the old machine.
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net cash outlay, with the tax on the loss on sale | 4 |
| 2 | Incremental depreciation | 2 |
| 3 | Annual cash inflow after tax | 4 |
| 4 | NPV and advice | 5 |
| Total | 15 |
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