Question 2 (a)
NPV and IRR of two proposals
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 2 (a) · 8 marksM Ltd is considering two proposals, I and II, whose details are below:
| Items | Year | Proposal I | Proposal II |
|---|---|---|---|
| Investment | ₹ 22,800 | ₹ 48,000 | |
| Cash Inflows | Year 1 | ₹ 9,600 | ₹ 19,200 |
| Year 2 | ₹ 9,600 | ₹ 19,200 | |
| Year 3 | ₹ 10,800 | ₹ 28,800 |
Future incomes being discounted at 12%, you are required to suggest the most attractive proposal on the basis of the NPV method. Also, find the IRR of the two proposals.
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
- NPVCash flows year by year in one table, then discount, then a one-line decision.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Present values and NPV of each proposal 4 marks 7 min
- 2 Choice on NPV 1 mark 2 min
- 3 IRR of each proposal 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? Step 1 carries 4 of the 8 marks: guard its minutes.
Try it first. About 16 minutes for 8 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.
| Year | PVF @ 12% | Proposal I cash flow | PV (I) | Proposal II cash flow | PV (II) |
|---|---|---|---|---|---|
| 1 | 0.893 | 9,600 | 8,572.80 | 19,200 | 17,145.60 |
| 2 | 0.797 | 9,600 | 7,651.20 | 19,200 | 15,302.40 |
| 3 | 0.712 | 10,800 | 7,689.60 | 28,800 | 20,505.60 |
| Total PV | 23,913.60 | 52,953.60 |
| Particulars (₹) | Proposal I | Proposal II |
|---|---|---|
| PV of inflows | 23,913.60 | 52,953.60 |
| Less: investment | 22,800 | 48,000 |
| NPV | 1,113.60 | 4,953.60 |
On the NPV method, Proposal II is the more attractive: it adds ₹4,953.60 to the firm's value against ₹1,113.60.
IRR. The IRR is the rate at which the present value of the inflows equals the investment; it is found by trial and interpolation (3-decimal table factors).
- Proposal I: at 14% (factors 0.877, 0.769, 0.675) NPV = +₹291.60; at 15% (0.870, 0.756, 0.658) NPV = −₹84.00. IRR = 14% + 291.60 ÷ (291.60 + 84.00) × 1% = 14.78%.
- Proposal II: at 17% (0.855, 0.731, 0.624) NPV = +₹422.40; at 18% (0.847, 0.718, 0.609) NPV = −₹412.80. IRR = 17% + 422.40 ÷ (422.40 + 412.80) × 1% = 17.51%.
Both IRRs exceed the 12% cost of capital; Proposal II is preferred on both NPV and IRR.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present values and NPV of each proposal | 4 |
| 2 | Choice on NPV | 1 |
| 3 | IRR of each proposal | 3 |
| Total | 8 |
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