Question 2 OR (a)
NPV and IRR of two mutually exclusive projects
12 marks
- Time to write
- About 24 minutes
Question
Question 2 OR (a) · 12 marksVidya Ltd is evaluating investment opportunities in two mutually exclusive projects which involve different cash outflows. The details are given below:
| Year | X | Y |
|---|---|---|
| 0 | (-) ₹3,84,000 | (-) ₹11,52,000 |
| 1 | 2,49,600 | 6,72,000 |
| 2 | 2,88,000 | 8,64,000 |
The firm uses a discount rate of 10% in assessing its investment decisions. Evaluate the projects using the Net Present Value (NPV) and Internal Rate of Return (IRR) methods, and comment on the selection of the project.
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
- EvaluateBoth sides: the strengths, the limits, then your own view.
- and comment onThe comment carries marks too: say what the figures show, in two or three lines.
- Net Present ValueCash 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 2 min
- 1 NPV of both projects 4 marks 7 min
- 2 IRR of both projects 4 marks 7 min
- 3 Comment on the conflict and selection 4 marks 6 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 24 minutes for 12 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 present value at 10% (table factors 0.909 and 0.826)
| ₹ | Project X | Project Y |
|---|---|---|
| PV of year-1 inflow | 2,49,600 × 0.909 = 2,26,886.40 | 6,72,000 × 0.909 = 6,10,848 |
| PV of year-2 inflow | 2,88,000 × 0.826 = 2,37,888 | 8,64,000 × 0.826 = 7,13,664 |
| PV of inflows | 4,64,774.40 | 13,24,512 |
| Less: initial outlay | 3,84,000 | 11,52,000 |
| NPV | 80,774.40 | 1,72,512 |
2. Internal rate of return. The IRR is the rate at which the PV of the inflows equals the outlay; a project is acceptable if its IRR exceeds the cut-off rate. With two annual inflows the IRR can be solved exactly, writing x = 1 + IRR:
- X: 3,84,000x² − 2,49,600x − 2,88,000 = 0 gives x = 1.25, so IRR = 25.00%. Check: 2,49,600 ÷ 1.25 + 2,88,000 ÷ 1.5625 = 1,99,680 + 1,84,320 = 3,84,000.
- Y: 11,52,000x² − 6,72,000x − 8,64,000 = 0, i.e. 12x² − 7x − 9 = 0, gives x = (7 + √481) ÷ 24 = 1.2055, so IRR = 20.55%.
| Project X | Project Y | Preferred | |
|---|---|---|---|
| NPV at 10% (₹) | 80,774.40 | 1,72,512 | Y |
| IRR | 25.00% | 20.55% | X |
Both projects are acceptable on their own (NPV > 0; IRR > 10%), but they are mutually exclusive and the two methods rank them differently. The conflict arises because Y needs a much larger outlay: IRR picks the higher rate, while a project with a larger outlay but lower IRR can add more in absolute NPV to shareholders' wealth. The incremental investment in Y over X (outlay ₹7,68,000; inflows ₹4,22,400 and ₹5,76,000) itself earns about 18.4%, more than the 10% cost of capital. Project Y should be selected, as it adds ₹1,72,512 to the firm's value against ₹80,774.40 for X.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | NPV of both projects | 4 |
| 2 | IRR of both projects | 4 |
| 3 | Comment on the conflict and selection | 4 |
| Total | 12 |
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