Question 2
Replacement decision: incremental cash flows and NPV
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 · 15 marksLMN Limited is considering buying a machine to replace an existing one, which has a book value of rupees 57600 and can be sold for Rs. 28800. The old machine's salvage value in 4 years is zero; it is being depreciated on a straight-line basis. The proposed machine will do the same job as the old one; however, improved technology will let the firm reap cash benefits before depreciation and taxes of Rs. 144000 a year in materials and labour. With a four-year life, the new machine costs Rs. 300000, and is expected to be saleable for rupees 38880 at the end of the fourth year. It will also need an installation cost of Rs. 60000 at the beginning, and will be depreciated on the WDV method at a rate of 25% per annum. Assuming a 40% tax rate, compute the cash flows associated with the replacement, and advise the company whether or not it should go for the replacement if its cost of capital is 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
- Assuming a 40% tax rate, compute…The paper fixes this: use it as given, and say so in your answer.
- computeFormula first, then the working, then the answer with its unit (₹, %, units).
- adviseEnd with a one-line decision that follows from your figures.
What the paper leaves open
- No tax is charged on the sale of the old machine or the terminal sale of the new one unless it is stated; the answer states its reading.
- The old machine's straight-line depreciation runs over its remaining 4 years to a zero salvage.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Initial cash outflow 2 marks 4 min
- 2 Depreciation: new on WDV, old on straight line, incremental 3 marks 5 min
- 3 Incremental cash flows after tax 5 marks 9 min
- 4 Terminal inflow and present values at 10% 3 marks 5 min
- 5 NPV and advice 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 5'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.
Initial cash outflow. For a replacement, it is the cost of the new asset plus installation, less the net proceeds from selling the old asset, adjusted for any tax on that sale. No tax on the sale is stated, so none is charged (paper note 1).
| Particulars | ₹ |
|---|---|
| Cost of the new machine | 3,00,000 |
| Add: installation cost | 60,000 |
| Cost of the new machine, installed | 3,60,000 |
| Less: sale of the old machine | 28,800 |
| Initial cash outflow | 3,31,200 |
Depreciation. Old machine: straight line, 57,600 ÷ 4 = ₹14,400 a year (paper note 2), which is lost on replacement. New machine: 25% WDV on ₹3,60,000. Only the incremental depreciation affects the cash flows, through its tax saving.
| Year | Opening WDV | Depreciation, new (25%) | Depreciation, old | Incremental depreciation |
|---|---|---|---|---|
| 1 | 3,60,000 | 90,000 | 14,400 | 75,600 |
| 2 | 2,70,000 | 67,500 | 14,400 | 53,100 |
| 3 | 2,02,500 | 50,625 | 14,400 | 36,225 |
| 4 | 1,51,875 | 37,968.75 | 14,400 | 23,568.75 |
Incremental cash flows after tax (₹)
| Year | Saving before dep. and tax | Incremental depreciation | EBT | Tax @ 40% | EAT | Add: incremental depreciation | Cash inflow after tax |
|---|---|---|---|---|---|---|---|
| 1 | 1,44,000 | 75,600 | 68,400 | 27,360 | 41,040 | 75,600 | 1,16,640 |
| 2 | 1,44,000 | 53,100 | 90,900 | 36,360 | 54,540 | 53,100 | 1,07,640 |
| 3 | 1,44,000 | 36,225 | 1,07,775 | 43,110 | 64,665 | 36,225 | 1,00,890 |
| 4 | 1,44,000 | 23,568.75 | 1,20,431.25 | 48,172.50 | 72,258.75 | 23,568.75 | 95,827.50 |
| Year | Cash inflow | PV factor @ 10% | Present value |
|---|---|---|---|
| 1 | 1,16,640 | 0.909 | 1,06,025.76 |
| 2 | 1,07,640 | 0.826 | 88,910.64 |
| 3 | 1,00,890 | 0.751 | 75,768.39 |
| 4 (95,827.50 + sale of new machine 38,880) | 1,34,707.50 | 0.683 | 92,005.22 |
| Total present value | 3,62,710.01 | ||
| Less: initial cash outflow | 3,31,200 | ||
| NPV | 31,510.01 |
Advice. A project is accepted when its NPV is positive. The replacement has an NPV of ₹31,510.01, so LMN Limited should replace the machine. (The new machine's book value of ₹1,13,906.25 at the end of year 4 exceeds its sale price of ₹38,880; the paper says nothing about taxing the sale or allowing the loss, so neither is taken, paper note 1.)
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Initial cash outflow | 2 |
| 2 | Depreciation: new on WDV, old on straight line, incremental | 3 |
| 3 | Incremental cash flows after tax | 5 |
| 4 | Terminal inflow and present values at 10% | 3 |
| 5 | NPV and advice | 2 |
| Total | 15 |
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