Mutual Fund Mastery puzzles, solved step by step

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  1. 055You buy an office REIT unit at Rs 300. It pays Rs 21 a year and you sell it for Rs 330 after five years. What are the equity multiple and the IRR, and why can two investments with the same multiple have very different IRRs?Performance measurement and returnsCoreInvescoNew York · 2025

    Try it first

    Which is closest to the IRR?

    Show the worked solution

    The equity multiple is 1.45x and the IRR is about 8.7%. You get back five payments of Rs 21 and Rs 330 on sale, Rs 435 in all, on Rs 300 in. The IRR is the rate at which those flows are worth exactly Rs 300 today. The multiple counts rupees and ignores time, so the same Rs 435 received in one lump at year 10 is still 1.45x but only about 3.8% a year.

    What does each measure actually count?

    Lend a friend Rs 300 and get Rs 435 back. Whether it came back in five years or fifteen, you can say you made 1.45 times your money, but you would not call the two loans equally good. The equity multipleTotal cash received divided by cash invested. It counts rupees and ignores when they arrive. counts how many rupees come back; the IRR counts how fast they come back. Here total cash is 5 x 21 plus 330, Rs 435, and 435 over 300 is 1.45x.

    Same money back, very different speedOffice REIT unitMultiple 1.45x | IRR 8.7%-30021212121351Same total, all at year 10Multiple 1.45x | IRR 3.8%-300435012345678910yearRs 21 a year, then Rs 330 on sale
    The REIT unit returns Rs 435 on Rs 300 through yearly payments and a sale at year 5, an IRR of 8.7%; the same Rs 435 in one payment at year 10 is still a 1.45x multiple but an IRR of only 3.8%.

    How do you get the IRR quickly in the room?

    Split it into income and growth. The payment of Rs 21 on Rs 300 is a 7% yield. The price rises from 300 to 330, 10% in five years, which compounds to just under 2% a year. Add them and you are near 9%; the exact answer is a little lower, 8.7%, because the price gain arrives only at the end. Then offer the check: at 8.7% the five payments and the sale discount back to Rs 300.

    The relationship
    300=∑t=1521(1+r)t+330(1+r)5  ⇒  r≈8.7%300 = \sum_{t=1}^{5} \frac{21}{(1+r)^t} + \frac{330}{(1+r)^5} \;\Rightarrow\; r \approx 8.7\%
    300the price paid for the unit
    21the yearly distribution
    330the sale price at year 5
    rthe IRR, the rate that makes both sides equal
    What it says in wordsThe IRR is the one discount rate at which everything you receive is worth exactly what you paid.

    Now the comparison the interviewer wants. The same Rs 435 in a single payment at year 5 is 7.7% a year, lower than 8.7% only because the distributions no longer arrive early. At year 10 it is 3.8%. The limit of IRR: it assumes the early cash can be reinvested at the same rate, and it says nothing about size, so a 20% IRR on Rs 1 lakh for one month is not better than 9% on Rs 1 crore for five years.

    Where candidates lose it

    The common slip is 9%: dividing the 45% total gain by five years. That treats the money as if it all came back evenly and ignores that the sale arrives last.

    The second loss is quoting only one of the two measures. Real estate and REIT desks ask for both because each hides what the other shows: the multiple hides time, the IRR hides size.

    What the interviewer asks next

    • The sale price is Rs 300 instead of Rs 330. What is the IRR?
    • Why do private real estate funds report both IRR and multiple to their investors?
    • The distribution is cut to Rs 15 in years 3 to 5. Which moves more, the multiple or the IRR?

    Asked at Invesco, Real Estate, New York, 2025 (Wall Street Oasis): Lots of basic questions asked about IRR, EM, Cap Rates etc

  2. 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

    Try it first

    Which statement is right?

    Show the worked solution

    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