Question 2 OR (a)
Why NPV and IRR can rank projects differently, and which is preferable
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 2 OR (a) · 8 marksDiscuss why NPV head IRR techniques can give conflicting ranking. Which method is preferable, and why?
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
- Discuss…Which…?Two asks in one question: answer both. Where it asks why, give reasons, not a description.
- NPVCash flows year by year in one table, then discount, then a one-line decision.
- Which method is preferableEnd with a clear choice and the reason for it.
What the paper leaves open
"NPV head IRR" is read as NPV and IRR; it is kept as printed.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Agreement for a single project and conflict for mutually exclusive projects 1 mark 2 min
- 2 Size disparity, with example 2 marks 4 min
- 3 Time disparity, with example, and unequal lives 2 marks 3 min
- 4 Reason and which is preferable 3 marks 5 min
- Check: every ask answered, key terms underlined 1 min
Short on time? Trim steps 2–4 evenly rather than skip one: each is capped at its own marks.
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.
No conflict for a single project. For an independent, conventional project NPV and IRR give the same accept/reject signal: if NPV > 0 at the cost of capital k, the IRR exceeds k, and vice versa. Conflict arises when mutually exclusive projects are ranked: the project with the highest IRR may not be the most profitable, the one that maximises shareholders' wealth.
- Size (scale) disparity. NPV is an absolute measure and IRR a relative one, so where the outlays differ the methods can disagree. Example (k = 10%): Project A costs ₹1,00,000 and returns ₹1,25,000 after a year: IRR 25%, NPV = 1,25,000 × 0.909 − 1,00,000 = ₹13,625. Project B costs ₹5,00,000 and returns ₹6,00,000 after a year: IRR 20%, NPV = ₹45,400. IRR ranks A first; NPV ranks B first.
- Time disparity (pattern of cash flows). When one project's inflows come early and the other's late, the ranking depends on the discount rate. Example (k = 10%): X costs ₹1,00,000 and returns ₹1,20,000 after one year: IRR 20%, NPV ₹9,080. Y costs ₹1,00,000 and returns ₹1,60,000 after three years: IRR 16.96%, NPV = 1,60,000 × 0.751 − 1,00,000 = ₹20,160. IRR prefers X; NPV prefers Y.
- Unequal lives. A longer-lived project may have a higher NPV but a lower IRR than a shorter one.
Why they conflict: the reinvestment assumption. The IRR method assumes intermediate cash flows are reinvested at the IRR itself, whereas NPV assumes reinvestment at the cost of capital, a more realistic rate. At discount rates below the "crossover" rate (where the two projects' NPV profiles intersect) the rankings differ.
Which to follow. NPV, because it measures the absolute addition to shareholders' wealth and uses a realistic reinvestment rate; IRR can also give multiple rates when cash flows change sign more than once.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Agreement for a single project and conflict for mutually exclusive projects | 1 |
| 2 | Size disparity, with example | 2 |
| 3 | Time disparity, with example, and unequal lives | 2 |
| 4 | Reason and which is preferable | 3 |
| Total | 8 |
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