Question 2 OR (a)
When NPV and IRR rank projects differently
6 marks
- Time to write
- About 12 minutes
Question
Question 2 OR (a) · 6 marksIn capital budgeting, when do NPV and IRR give conflicting rankings? Explain with examples.
Reworded from the university paper; 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
- When…?Explain…Two asks in one question: answer both.
- with examplesExamples are asked for: one short example with each point.
- NPVCash flows year by year in one table, then discount, then a one-line decision.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Scale difference, with example 2 marks 3 min
- 2 Timing difference and reinvestment assumption, with example 2 marks 3 min
- 3 Different lives or patterns; which method to follow 2 marks 3 min
- Check: every ask answered, key terms underlined 2 min
Short on time? Trim steps 1–3 evenly rather than skip one: each is capped at its own marks.
Try it first. About 12 minutes for 6 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.
For a single conventional project, NPV and IRR always give the same accept-or-reject decision. They can rank mutually exclusive projects differently in three situations.
1. Projects of different size (scale). IRR is a percentage and ignores size; a larger project with a lower IRR may add more wealth.
Example (cost of capital 10%, one-year projects): Project A costs ₹10,000 and returns ₹12,000; Project B costs ₹50,000 and returns ₹57,500.
| Project A | Project B | |
|---|---|---|
| IRR | 20% | 15% |
| NPV at 10% (factor 0.909) | 12,000 × 0.909 − 10,000 = ₹908 | 57,500 × 0.909 − 50,000 = ₹2,267.50 |
IRR prefers A; NPV prefers B.
2. Different timing of cash flows. IRR assumes the cash flows are reinvested at the project's own IRR, NPV at the cost of capital, so IRR favours projects with heavy early cash flows.
Example (cost of capital 8%): Project P costs ₹10,000 and returns ₹13,000 after one year; Project Q costs ₹10,000 and returns ₹20,000 after three years.
| Project P | Project Q | |
|---|---|---|
| IRR | 30.00% | 2^(1/3) − 1 = 25.99% |
| NPV at 8% | 13,000 ÷ 1.08 − 10,000 = ₹2,037.04 | 20,000 ÷ 1.08³ − 10,000 = ₹5,876.64 |
IRR prefers P; NPV prefers Q.
3. Different lives or unconventional cash flows. Projects with different lives or inflow/outflow patterns can be ranked differently, and flows that change sign more than once can give several IRRs.
Which to follow. NPV, because it measures the absolute increase in shareholders' wealth and assumes the more realistic reinvestment at the cost of capital; the project with the highest IRR may not be the most profitable.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Scale difference, with example | 2 |
| 2 | Timing difference and reinvestment assumption, with example | 2 |
| 3 | Different lives or patterns; which method to follow | 2 |
| Total | 6 |
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