Venture Capital puzzles, solved step by step

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  1. 071Business A costs 10x earnings, grows earnings 5% a year, and still trades at 10x in ten years. Business B costs 25x earnings, grows earnings 20% a year, and trades at only 15x in ten years. Ignoring dividends, which makes you more money over the ten years, and at what annual rate?Valuation riddlesCoreCoatue ManagementNew York · 2023

    Try it first

    Which business returns more over ten years?

    Show the worked solution

    B, about 3.72x or 14% a year, against 1.63x or 5% a year for A. Your return is earnings growth times the change in multiple. A's earnings grow 1.05 to the tenth, 1.63x, and its multiple stays at 10x, so you make 1.63x. B's earnings grow 1.2 to the tenth, 6.19x, and its multiple falls from 25x to 15x, a factor of 0.6, so you make 3.72x. B's multiple could fall to 6.6x and still match A.

    How do you split a ten-year return into its parts?

    A flat bought cheap in a stagnant town can earn less than one bought dear in a fast-growing suburb, even if the suburb's prices later cool. Ignoring dividends, the return on a business is the growth in its earnings times the change in the multiple the market pays for them, so a high starting multiple only hurts if earnings growth cannot outrun the fall in that multiple. A gets 1.63 x 1.0. B gets 6.19 x 0.6. Ten years of 20% growth multiplies earnings by over six, which swamps the 40% multiple compression.

    Paying up for growth beats a bargain that barely grows0x1x2x3x4xYr 0Yr 2Yr 4Yr 6Yr 8Yr 10B: 3.72x, 14% a yearA: 1.63x, 5% a yearA: cheap, slowearnings x 1.63multiple 10x to 10x: x 1.0= 1.63xB: dear, fastearnings x 6.19multiple 25x to 15x: x 0.6= 3.72xbreak-even exit: 6.6xValue of Rs 1 invested, before dividends.
    Rs 1 in the 10x business growing 5% becomes 1.63x in ten years, while Rs 1 in the 25x business growing 20% becomes 3.72x even after its multiple falls to 15x, because earnings growth of 6.19x outruns the 0.6 multiple factor.
    The relationship
    M=(1+g)10×P/EexitP/Eentry:A=1.0510×1010=1.63,B=1.210×1525=3.72M = (1+g)^{10} \times \frac{P/E_{\text{exit}}}{P/E_{\text{entry}}}: \quad A = 1.05^{10} \times \tfrac{10}{10} = 1.63, \quad B = 1.2^{10} \times \tfrac{15}{25} = 3.72
    gannual earnings growth
    P/E entry, exitthe price-to-earnings multiple paid and received
    Mmoney multiple over ten years
    What it says in wordsMultiply how much earnings grew by how much the multiple changed; the annual rate is the tenth root of the result.

    When does the cheap business win instead?

    Three cases. If B's growth fades early, the answer flips: at 10% a year, B's earnings grow only 2.6x and 2.6 x 0.6 is about 1.55x, below A. If A pays out its earnings as dividends, a 10x multiple means a 10% earnings yield, and reinvesting that cash adds a lot that this sum leaves out; B, growing at 20%, likely reinvests everything. And if the growth never arrives, B's price has nothing to fall back on. The honest answer to a 'great price or great business' question is that it turns on how long and how surely the better business keeps growing.

    Give the interviewer a number that frames the judgement: B's exit multiple could fall all the way to 6.6x and still match A's return. That margin, not the entry multiple, is the measure of how much you are overpaying.

    Where candidates lose it

    The common error is choosing A because 10x feels safe and the 40% multiple drop on B sounds painful. Candidates react to the entry price and never multiply out the earnings growth.

    The second trap is the opposite: declaring that quality always wins. Say the condition, growth that lasts, and give the break-even multiple, so the answer reads as a judgement rather than a slogan.

    What the interviewer asks next

    • If A pays out all its earnings as dividends and you reinvest them at 10%, does the answer change?
    • At what growth rate does B only match A?
    • Which of B's numbers would you test hardest in diligence?

    Asked at Coatue Management, Technology, Media and Telecom, New York, 2023 (Wall Street Oasis): Would you rather buy a low quality business at a great price or a high quality business at an ok price?