Question 2

NPV and IRR rankings; choosing between two machines

18.75 marks

Time to write
About 38 minutes

From an older CBCS paper

Question

Question 2 · 18.75 marks

Can the NPV and IRR methods result in different rankings of investment proposals? Why?

The management of LMN Ltd. may buy either Machine A or Machine B. Machine A, at a cost of Rs. 1,08,000, has an expected life of 6 years with no salvage value at the end, and would generate net cash flows of Rs. 30,000 per year. Machine B, by contrast, would cost Rs. 72,000, with an expected life of 6 years and no salvage value at the end, and would generate net cash flow of Rs. 21,600 per year. Assuming LMN Ltd.'s cost of capital to be 10%, you are required to calculate:

  1. The Net Present Value of each machine

  2. The Internal rate of return of each machine

  3. Which machine should be recommended, and why?

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

38 minfor 18.8 marks

Read from the question

  • Can…?Which…?Two asks in one question: answer both. Where it asks why, give reasons, not a description.
  • Can the NPV…?A yes-or-no question: answer it in your first line, then explain why.
  • Assuming LMN LtdThe paper fixes this: use it as given, and say so in your answer.
  • NPVCash flows year by year in one table, then discount, then a one-line decision.

What the paper leaves open

No mark is printed for the question; the paper asks for any four of six, equal marks.

Write it in this order

  1. Read the data; note exactly what is asked 2 min
  2. 1 Why NPV and IRR can rank differently 6 marks 11 min
  3. 2 NPV of each machine 4 marks 7 min
  4. 3 IRR of each machine 5 marks 9 min
  5. 4 Recommendation with reasons 3.8 marks 7 min
  6. Check: arithmetic, units (₹, %), final answer underlined 2 min

Short on time? End with step 4's one-line decision, whatever happens: never leave the figures without it.

Try it first. About 38 minutes for 18.75 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.

Can NPV and IRR rank proposals differently? Why?

Yes, for mutually exclusive proposals. For a single conventional project the two methods always agree on accept or reject. But when projects compete, the one with the highest IRR may not be the one that adds most to shareholders' wealth. The rankings can differ because of:

  1. Size disparity: NPV is an absolute measure, IRR a relative one; a larger project may have a higher NPV but a lower IRR.
  2. Time disparity: projects whose cash flows come at different times rank differently at different discount rates.
  3. Unequal lives: a longer-lived project may have the higher NPV but the lower IRR.
  4. The reinvestment assumption: IRR assumes intermediate cash flows are reinvested at the IRR itself; NPV assumes reinvestment at the cost of capital, which is more realistic.

When they conflict, NPV is preferred: it measures the absolute increase in wealth. The machines below illustrate the size disparity.

Machines A and B (cost of capital 10%)

Annuity factor, 6 years at 10% = 4.355.

(i) Net present value

Particulars (₹)Machine AMachine B
Annual cash flow30,00021,600
PV of cash flows (× 4.355)1,30,65094,068
Less: cost1,08,00072,000
NPV22,65022,068
Profitability index1.20971.3065

(ii) Internal rate of return. With equal annual flows, the IRR is the rate at which the annuity factor equals cost ÷ annual cash flow.

  • A: factor = 1,08,000 ÷ 30,000 = 3.600, between 16% (3.685) and 17% (3.589): IRR = 16% + (3.685 − 3.600) ÷ (3.685 − 3.589) × 1% = 16.89%.
  • B: factor = 72,000 ÷ 21,600 = 3.333, between 19% (3.410) and 20% (3.326): IRR = 19% + (3.410 − 3.333) ÷ (3.410 − 3.326) × 1% = 19.91%.

(iii) Recommendation. The methods conflict: NPV favours A (by ₹582), IRR and PI favour B. The conflict comes from the difference in size: A needs ₹36,000 more. Machine A is recommended, because it adds slightly more to the shareholders' wealth, and NPV is the reliable criterion when mutually exclusive projects conflict. The margin is very small, however: if the ₹36,000 saved by choosing B could be invested elsewhere at an NPV above ₹582 (a return above 10%), B together with that investment would be better; and under capital rationing B, with the higher PI, would be chosen.

Where the 18.75 marks sit

#ComponentMarks
1Why NPV and IRR can rank differently6
2NPV of each machine4
3IRR of each machine5
4Recommendation with reasons3.75
Total18.75
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