Question 2 (b)
Comparing two machines: NPV and profitability index
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 2 (b) · 10 marksPrakash Ltd. is considering buying new machine. Two alternative machine (X & Y) are suggested; each has initial cost of ₹ 12,00,000, and needs ₹ 60,000 of additional working capital at the end of the first year. The Net cash flows expected are:
Cash Inflows
| Year | Machine X (₹) | Machine Y (₹) |
|---|---|---|
| 1 | 1,20,000 | 3,60,000 |
| 2 | 3,60,000 | 4,80,000 |
| 3 | 4,80,000 | 6,00,000 |
| 4 | 7,20,000 | 3,60,000 |
| 5 | 4,80,000 | 2,40,000 |
The company's target return on capital is 10%; on the basis you are required to compare the machines' profitability, and state which alternative you consider financially preferable. 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
- compareCompare in a table, basis by basis.
- which alternative you consider financially preferableEnd with a one-line decision that follows from your figures.
What the paper leaves open
The additional working capital is invested at the end of year 1 and recovered at the end of year 5.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Net cash flows with working capital 3 marks 6 min
- 2 Present values 3 marks 6 min
- 3 NPV and PI 2 marks 4 min
- 4 Conclusion 2 marks 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line conclusion, 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.
Cash flows. The additional working capital of ₹60,000 is an outflow at the end of year 1 and is recovered at the end of year 5 (paper note); the inflows are discounted at the 10% target return.
| Year | PVF @ 10% | Machine X net flow | PV (X) | Machine Y net flow | PV (Y) |
|---|---|---|---|---|---|
| 1 | 0.909 | 60,000 | 54,540 | 3,00,000 | 2,72,700 |
| 2 | 0.826 | 3,60,000 | 2,97,360 | 4,80,000 | 3,96,480 |
| 3 | 0.751 | 4,80,000 | 3,60,480 | 6,00,000 | 4,50,600 |
| 4 | 0.683 | 7,20,000 | 4,91,760 | 3,60,000 | 2,45,880 |
| 5 | 0.621 | 5,40,000 | 3,35,340 | 3,00,000 | 1,86,300 |
| Total PV of net inflows | 15,39,480 | 15,51,960 |
(Year 1 net flow = inflow less ₹60,000 working capital; year 5 = inflow plus ₹60,000 released.)
| Particulars (₹) | Machine X | Machine Y |
|---|---|---|
| PV of net inflows | 15,39,480 | 15,51,960 |
| Less: initial cost | 12,00,000 | 12,00,000 |
| NPV | 3,39,480 | 3,51,960 |
Profitability index = PV of cash inflows ÷ PV of cash outflows. The working capital invested at the end of year 1 is an outflow (60,000 × 0.909 = 54,540) and its release in year 5 an inflow (60,000 × 0.621 = 37,260):
| Particulars (₹) | Machine X | Machine Y |
|---|---|---|
| PV of operating inflows | 15,56,760 | 15,69,240 |
| Add: PV of working capital released | 37,260 | 37,260 |
| PV of inflows | 15,94,020 | 16,06,500 |
| PV of outflows (12,00,000 + 54,540) | 12,54,540 | 12,54,540 |
| Profitability index | 1.2706 | 1.2805 |
The NPV is the same however the working capital is presented. The profitability index is the ratio of the present value of inflows to the outlay.
Conclusion. Both machines are acceptable (positive NPV, PI above 1). Machine Y is financially preferable: it has the higher NPV (by ₹12,480) and the higher PI, because more of its inflows come early, when they are worth more; the two methods agree, since the outlays are equal.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net cash flows with working capital | 3 |
| 2 | Present values | 3 |
| 3 | NPV and PI | 2 |
| 4 | Conclusion | 2 |
| Total | 10 |
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