Mutual Fund Mastery puzzles, solved step by step

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  1. 068Option A turns Rs 1 lakh into Rs 3 lakh in 12 years. Option B turns Rs 1 lakh into Rs 1.5 lakh in 4 years. Which has the higher IRR, which has the higher NPV at a 6% discount rate, and why do the two measures disagree?Performance measurement and returnsHardPIMCOMunich · 2024

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    Which statement is right?

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    B has the higher IRR, 10.7% against 9.6%, but A has the higher NPV at 6%, Rs 0.49 lakh against Rs 0.19 lakh. IRR measures speed of growth; NPV measures rupees of value at your cost of money. B grows faster but stops after four years, while A keeps compounding above 6% for twelve. The two rankings swap at 9.05%: below that A wins on NPV, above it B does.

    What does each measure reward?

    Compare a short, well-paid contract with a long, steady job. The contract pays more per month, but it ends quickly and you must find something else. IRR ranks by speed: the rate at which the money grows. NPV ranks by size: how many rupees of value the option creates once everything is discounted at your own cost of money. A's IRR is 3 to the power 1/12, less one, 9.59%. B's is 1.5 to the power 1/4, less one, 10.67%. B is faster.

    At a 6% discount rate, A's Rs 3 lakh in year 12 is worth 3 / 1.06 to the 12th, Rs 1.49 lakh today, an NPV of Rs 0.49 lakh. B's Rs 1.5 lakh in year 4 is worth Rs 1.19 lakh, an NPV of Rs 0.19 lakh. A creates more than twice the value, because it earns well above 6% for three times as long.

    NPV against discount rate: the two options swap places-0.50.51.01.52.000%2%4%6%8%10%12%14%discount rateNPV, Rs lakhA: triples in 12 yearsB: 1.5x in 4 yearsA at 6%: Rs 0.49 lakhB at 6%: Rs 0.19 lakhcross at 9.05%IRR A 9.6%IRR B 10.7%
    Option A's NPV starts higher and falls faster as the discount rate rises, crossing B's at 9.05%, so A creates more value at a 6% cost of money while B has the higher IRR, 10.7% against 9.6%.

    Where do the rankings swap, and what does that rate mean?

    The NPV curves cross where both options are worth the same: 3 / (1 + r) to the 12th = 1.5 / (1 + r) to the 4th, so (1 + r) to the 8th = 2 and r = 9.05%. That crossover has a plain meaning: B returns Rs 1.5 lakh in year 4, and to match A it would need to double over the next eight years, which takes 9.05% a year. If you can reinvest B's proceeds above that, B is better; below it, A is. IRR silently assumes you can reinvest at B's own 10.7%, which is why it favours the short option.

    The relationship
    3(1+r)12=1.5(1+r)4  ⇒  (1+r)8=2  ⇒  r≈9.05%\frac{3}{(1+r)^{12}} = \frac{1.5}{(1+r)^4} \;\Rightarrow\; (1+r)^8 = 2 \;\Rightarrow\; r \approx 9.05\%
    3option A's payout in year 12, Rs lakh
    1.5option B's payout in year 4, Rs lakh
    rthe discount rate at which the two options are worth the same
    What it says in wordsThe crossover rate is the return B's proceeds must earn afterwards to catch up with A.

    For a fund desk this is the reinvestment question in plain clothes. A client choosing between a short product with a high stated yield and a long one with a lower yield is really asking what the short money will earn when it comes back. The limit: NPV needs a discount rate, and a different rate can flip the answer; at 10%, A's NPV turns negative, about Rs 4,411 below zero, while B's stays positive at about Rs 2,452, so B wins.

    Where candidates lose it

    The trap is answering that the higher IRR must also have the higher NPV. That holds only when the options have the same size and the same timing; here the timing differs by eight years.

    The second miss is picking a winner without naming the discount rate. Say that the answer depends on the cost of money, find the crossover rate, and explain it as the reinvestment rate B must beat.

    What the interviewer asks next

    • B can be repeated three times in a row at the same terms. Does that change the comparison?
    • Why do private funds report IRR rather than NPV to their investors?
    • At what discount rate does option A's NPV become zero?

    Asked at PIMCO, Real Estate, Munich, 2024 (Wall Street Oasis): just asked a bunch of questions on recent real estate news, as well as a couple of technicals including IRR, NPV