Private Equity puzzles, solved step by step

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  1. 087Two identical office buildings. A is let for 10 more years to a strong tenant at a net income of Rs 8 crore a year. B earns Rs 10 crore, but its lease ends in 2 years; the market rent is Rs 8 crore and re-letting takes a year. At a 10% discount rate and a 7.5% exit cap rate, which is worth more?Valuation riddlesHardApollo Global ManagementWilliamsport · 2022

    Try it first

    Which building is worth more?

    Show the worked solution

    A is worth more, by about Rs 2.5 crore. From year 4 the buildings earn the same 8, so only the first three years differ. B earns 2 more in years 1 and 2, worth 3.47 today, and 8 less in year 3, worth 6.01. Valued on three years plus a sale at a 7.5% cap, A is about 100.0 and B about 97.5.

    If the buildings are identical, what is actually different?

    Two identical flats on the same floor can sell at different prices if one has a tenant paying above market on a lease about to end and the other a reliable tenant at market. Buildings are valued on the certainty and timing of their income, not their bricks. A has eight crore a year from a strong tenant for ten years. B has ten crore for two years, then a vacancy, then whatever the market pays, which is eight.

    Same bricks, different income: only the first three years differBuilding ARs crore888888Building BRs crore1010void888Yr 1Yr 2Yr 3Yr 4Yr 5Yr 6identical from year 4: cancelsB minus A, todayYr 1: +2+1.82Yr 2: +2+1.65Yr 3: -8-6.01B worth less by2.54The wrong shortcut: cap B's in-place 10 at 7.5% = 133.3, against A at 8 / 7.5% = 106.7It pays for rent B is about to lose and a void it is about to suffer.
    Building B earns 2 more than A in years 1 and 2 but nothing in year 3, and from year 4 the two are identical; the differences are worth +1.82, +1.65 and -6.01 today, so B is worth about Rs 2.54 crore less than A.

    How do you value them so the comparison is fair?

    Use the same method for both: three years of cash, then a sale at the end of year 3 at a 7.5% cap rateNet operating income divided by property value. A building earning 8 a year at a 7.5% cap rate is worth 8 divided by 0.075, about 106.7. on the 8 a year both will earn from then, which is 106.7. Discount at 10%. A comes to 100.0 and B to 97.5, and the gap of 2.54 is just the present value of the three years in which they differ.

    The relationship
    VB−VA=+21.1++21.12+−81.13=1.82+1.65−6.01=−2.54V_B - V_A = \frac{+2}{1.1} + \frac{+2}{1.1^2} + \frac{-8}{1.1^3} = 1.82 + 1.65 - 6.01 = -2.54
    +2B's extra rent over A in years 1 and 2
    -8the year 3 void, when B earns nothing and A earns 8
    1.1one plus the 10% discount rate
    What it says in wordsOnly the years in which the buildings differ matter, and the void in year 3 outweighs two years of higher rent.

    Say the limitation. The absolute values shift with the exit year you pick, because a 10% discount rate against a 7.5% cap implies rents that grow, while this question holds rent flat. The gap does not shift, because after year 3 the buildings are the same. In practice B's discount is also larger: re-letting costs agents' fees and incentives, and the market rent of 8 is a forecast while A's is a contract.

    Where candidates lose it

    The classic error is capping B's in-place rent: 10 divided by 7.5% is 133.3, a quarter more than A at 106.7. That pays full value for rent that disappears in two years and ignores the empty year.

    The second is calling them equal because the bricks are the same. The interviewer chose identical buildings to strip out everything except the lease, so the lease is the answer.

    What the interviewer asks next

    • How long can B's void last before the gap reaches Rs 10 crore?
    • B's tenant offers to renew at 9 for five years. What is that worth?
    • Why might a buyer still prefer B despite the lower value?

    Asked at Apollo Global Management, Generalist, Williamsport, 2022 (Wall Street Oasis): Comparing two identical buildings, how would you value them?

  2. 098A PIK note of 200 accrues 12% a year, compounded annually, for 5 years, with nothing paid until maturity. How much is owed at maturity, and how much more is that than five years of the same 12% paid in cash?Credit and PIK mathsWarm upAres ManagementNew York · 2026

    Try it first

    Roughly how much is owed after five years?

    Show the worked solution

    About 352.5 is owed, about 32.5 more than a cash-pay note's 320. PIK interest is added to the balance each year: 224, 250.9, 281.0, 314.7, then 352.5. A cash-pay note returns 24 a year plus 200 at the end, 320 in all. The extra 32.5 is interest on interest, which is why a PIK claim grows faster than its coupon suggests.

    What does paid in kind actually mean for the balance?

    A PIKPayment in kind: interest that is not paid in cash but added to the amount owed, so the loan balance grows instead. note pays its interest with more debt. It is like a credit card where you pay nothing and the interest is added to the bill each month, so next month's interest is charged on the bigger bill. Because each year's interest joins the balance, the 12% is earned on a growing base, and the claim compounds. After one year the balance is 224, after two 250.9.

    PIK interest earns interest, so the claim outruns the coupon200Yr 0224.0Yr 1250.9Yr 2281.0Yr 3314.7Yr 4352.5Yr 5At year 5PIK owed 352.5Cash-pay total 320PIK extra+32.5Bars: PIK balanceDashed: principal pluscash interest received
    A 200 PIK note at 12% compounds to 224, 250.9, 281.0, 314.7 and 352.5 over five years, while a cash-pay note's principal plus interest received rises in a straight line to 320, so the PIK claim ends 32.5 higher.
    The relationship
    200×1.125=352.5200+5×24=320352.5−320=32.5200 \times 1.12^5 = 352.5 \qquad 200 + 5 \times 24 = 320 \qquad 352.5 - 320 = 32.5
    1.12^5five years of 12% compounding, about 1.762
    24the yearly cash interest on 200 at 12%
    What it says in wordsPIK compounds the balance; cash-pay adds the same interest each year without compounding, and the gap is the interest on interest.

    Why does a private credit lender or a sponsor care?

    The borrower keeps its cash today, which helps a company that is growing or stretched. The price is a claim that grows every year, so at exit the sponsor's equity sits behind a bigger debt than the original 200. For the lender, PIK means more risk: nothing is received for five years, and if the company fails the larger balance may not be recovered. Lenders usually charge a higher rate for PIK than for the same loan paid in cash.

    Where candidates lose it

    The common slip is 320: adding five years of simple interest. That treats PIK as if the interest were paid in cash, missing that it compounds on the balance.

    The other is calling the 32.5 free money for the lender. It is compensation for waiting five years with nothing in hand, and for the risk that the balance is never paid.

    What the interviewer asks next

    • What is owed after 5 years if the PIK compounds semi-annually at 6% a half-year?
    • If the cash-pay interest could be reinvested at 12%, how do the two compare?
    • How does a PIK toggle option change who bears the risk?

    Asked at Ares Management, Generalist, New York, 2026 (Wall Street Oasis): Asked me basic behaviorals as well as some technicals around accounting as well as PIK interest.