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  1. 059Why should I buy your college, and how much would you sell it for? Suppose it earns an operating surplus of Rs 40 crore this year, the surplus grows 5% a year for the foreseeable future, and a buyer wants a 12% return.Valuation riddlesCoreWellington ManagementBoston · 2024

    Try it first

    What price does the growing surplus support, before land?

    Show the worked solution

    About Rs 600 crore for the operating business, before any value in the land. Next year's surplus is Rs 40 crore grown 5%, or Rs 42 crore. A surplus that grows forever at 5% and is valued at 12% is worth next year's amount divided by the 7-point gap: 42 over 0.07 is Rs 600 crore. The reason to buy is the durability of that surplus: steady demand for seats and fees that can rise with costs.

    What is the question really asking?

    It is a stock pitch in disguise. The interviewer wants two things in order: why this asset produces reliable cash, and what that cash is worth. Answer the why with the quality of the surplus, and the how much with a valuation you can do out loud. For a college the why is simple to say: students keep applying every year, fees are paid in advance, and a college with a good name can raise fees roughly in line with its costs. Those are the reasons the surplus can be treated as growing and durable.

    Why divide by 12% less 5%?

    Think of a rented flat whose rent rises every year. A buyer asking for a 12% return on a rent that grows 5% needs only 7% from the current rent; the other 5% arrives through growth. A cash flow growing at g forever, valued at a required return r, is worth next year's cash flow divided by r minus g. Here that is Rs 42 crore over 0.07, which is Rs 600 crore. Dividing this year's Rs 40 crore instead gives Rs 571 crore, a common small slip: the buyer receives next year's surplus, not this year's.

    The relationship
    V=S1r−g=40×1.050.12−0.05=420.07=600V = \frac{S_1}{r - g} = \frac{40 \times 1.05}{0.12 - 0.05} = \frac{42}{0.07} = 600
    S_1next year's surplus, Rs crore
    rthe buyer's required return
    gthe permanent growth rate of the surplus
    What it says in wordsA growing perpetuity is worth next year's payment divided by the gap between the required return and the growth rate.
    Value of a growing surplus: the gap between return and growth does the work05001,0001,50012%: Rs 600 crore11%: Rs 700 crore13%: Rs 525 croreat 8%: Rs 1,400 croreone point either side of 12%moves value by Rs 100 and Rs 75 crore8%10%12%14%16%Buyer's required return, growth fixed at 5%Rs crore
    With growth fixed at 5%, the college is worth Rs 600 crore at a 12% required return, but Rs 700 crore at 11% and Rs 525 crore at 13%, because value depends on the gap between return and growth and that gap is small.

    Now say what the number is sensitive to. One point on the required return moves the value by Rs 100 crore up or Rs 75 crore down, because a 7-point gap becoming 6 or 8 is a large change in proportion. The land and buildings may be worth more than the operating surplus, so a seller would also ask what the campus fetches as property. And check the structure before promising anyone the surplus: many colleges, in India among other places, are run by trusts or societies, and whether an owner can take surplus out at all is a legal question to confirm.

    Where candidates lose it

    The trap is diving into a formula without answering why. The question starts with why should I buy, and a candidate who opens with a number has skipped the half the interviewer cares about most.

    The arithmetic trap is dividing Rs 40 crore by 12%, which treats a growing surplus as flat and values it at Rs 333 crore. Name the growth, use next year's surplus, and divide by the gap.

    What the interviewer asks next

    • What growth rate is the seller implicitly assuming if he asks Rs 800 crore?
    • How would you value the land separately, and when would it exceed the value of the operating business?
    • What would make you use a higher required return for this college than for a listed education company?

    Asked at Wellington Management, Investment Research, Boston, 2024 (Wall Street Oasis): Why should I buy your College and how much would you sell it for?