Question 2
Two strategies: NPV at four rates, IRR and choice
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 2 · 18.75 marksQ2. Red Coral ltd is a marketing organisation considering the launch of a product with one of two different strategies: Strategy A and Strategy B. It must choose either of the two strategies. Each strategy has an initial outlay of Rs 24 crores, but their streams of cash inflows differ. The cash flows of the strategies over the period of 5 years are estimated as below:
(Cash Flows are in Lakhs of Rupees)
| Year | Strategy A | Strategy B |
|---|---|---|
| 0 | -2400 | -2400 |
| 1 | 600 | 1200 |
| 2 | 1020 | 1050 |
| 3 | 660 | 600 |
| 4 | 780 | 168 |
| 5 | 480 | 240 |
At discount rates between 11% and 17%, at intervals of 2%, find out the NPV of both the strategies.
Find the IRR of both strategies.
According to the NPV method, which of the strategy is to be preferred if the cost of capital is 11% and 13%? Justify your answer.
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
- Find…Which…?Justify…3 asks, each with its own marks below. Answer all 3.
- NPVCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 NPV of both strategies at the four rates 8 marks 15 min
- 2 IRR of both strategies 5 marks 9 min
- 3 Choice at 11% and 13%, with justification 5.8 marks 10 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 3's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 38 minutes for 18.75 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.
Figures in ₹ lakh; outlay ₹2,400 lakh for each strategy. Present value factors from the table (3 decimals).
1. NPV at 11%, 13%, 15% and 17%. NPV = present value of the cash inflows at the discount rate less the outlay; a project is accepted if its NPV is positive.
| Year | Cash inflow | PVF 11% | PV 11% | PVF 13% | PV 13% | PVF 15% | PV 15% | PVF 17% | PV 17% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 600 | 0.901 | 540.60 | 0.885 | 531 | 0.870 | 522 | 0.855 | 513 |
| 2 | 1,020 | 0.812 | 828.24 | 0.783 | 798.66 | 0.756 | 771.12 | 0.731 | 745.62 |
| 3 | 660 | 0.731 | 482.46 | 0.693 | 457.38 | 0.658 | 434.28 | 0.624 | 411.84 |
| 4 | 780 | 0.659 | 514.02 | 0.613 | 478.14 | 0.572 | 446.16 | 0.534 | 416.52 |
| 5 | 480 | 0.593 | 284.64 | 0.543 | 260.64 | 0.497 | 238.56 | 0.456 | 218.88 |
| Total PV | 2,649.96 | 2,525.82 | 2,412.12 | 2,305.86 | |||||
| Less: outlay | 2,400 | 2,400 | 2,400 | 2,400 | |||||
| NPV | 249.96 | 125.82 | 12.12 | −94.14 |
| Year | Cash inflow | PVF 11% | PV 11% | PVF 13% | PV 13% | PVF 15% | PV 15% | PVF 17% | PV 17% |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1,200 | 0.901 | 1,081.20 | 0.885 | 1,062 | 0.870 | 1,044 | 0.855 | 1,026 |
| 2 | 1,050 | 0.812 | 852.60 | 0.783 | 822.15 | 0.756 | 793.80 | 0.731 | 767.55 |
| 3 | 600 | 0.731 | 438.60 | 0.693 | 415.80 | 0.658 | 394.80 | 0.624 | 374.40 |
| 4 | 168 | 0.659 | 110.71 | 0.613 | 102.98 | 0.572 | 96.10 | 0.534 | 89.71 |
| 5 | 240 | 0.593 | 142.32 | 0.543 | 130.32 | 0.497 | 119.28 | 0.456 | 109.44 |
| Total PV | 2,625.43 | 2,533.25 | 2,447.98 | 2,367.10 | |||||
| Less: outlay | 2,400 | 2,400 | 2,400 | 2,400 | |||||
| NPV | 225.43 | 133.25 | 47.98 | −32.90 |
2. IRR. The IRR is the discount rate that makes the present value of the inflows equal to the outlay; it is found by interpolating between the two rates at which the NPV changes sign: IRR = LR + NPV at LR ÷ (NPV at LR − NPV at HR) × (HR − LR).
- Strategy A: 15% + 2% × 12.12 ÷ (12.12 + 94.14) = 15% + 0.23% = 15.23%.
- Strategy B: 15% + 2% × 47.98 ÷ (47.98 + 32.90) = 15% + 1.19% = 16.19%.
- At 11%: Strategy A (NPV ₹249.96 lakh against ₹225.43 lakh).
- At 13%: Strategy B (NPV ₹133.25 lakh against ₹125.82 lakh).
The ranking changes because the strategies' cash flows differ in timing: B returns most of its cash early (₹1,200 lakh in year 1), A later (₹780 lakh in year 4). Distant flows lose more value at a higher rate, so A's lead at 11% disappears by 13%. When NPV and IRR (or NPV at different rates) conflict for mutually exclusive projects, the NPV at the firm's actual cost of capital is the guide, because it measures the absolute addition to shareholders' wealth; NPV and IRR differ in the rate at which they assume the cash flows are reinvested. B has the higher IRR (16.19%), and it is preferred at any cost of capital from about 13% upwards.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | NPV of both strategies at the four rates | 8 |
| 2 | IRR of both strategies | 5 |
| 3 | Choice at 11% and 13%, with justification | 5.75 |
| Total | 18.75 |
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