Question 2 OR (b)

When NPV and IRR give conflicting rankings

7 marks

Time to write
About 14 minutes

From an older CBCS paper

Question

Question 2 OR (b) · 7 marks

In capital budgeting, when do NPV and IRR give conflicting rankings? Explain, with examples. 7

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

14 minfor 7 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

  1. Read; underline the asks; jot your points 1 min
  2. 1 Agreement for a single project; conflict for mutually exclusive projects 1 mark 2 min
  3. 2 Size disparity, with example 2 marks 4 min
  4. 3 Time disparity, with example, and unequal lives 2 marks 3 min
  5. 4 Reason (reinvestment assumption) and which to follow 2 marks 3 min
  6. 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 14 minutes for 7 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.

When rankings conflict

  1. 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.
  2. 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.
  3. 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 7 marks sit

#ComponentMarks
1Agreement for a single project; conflict for mutually exclusive projects1
2Size disparity, with example2
3Time disparity, with example, and unequal lives2
4Reason (reinvestment assumption) and which to follow2
Total7
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