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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?