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  1. 023A stock trades at 40 times forward earnings, pays out half its earnings as dividends, and investors want a 12% return. What long-run growth rate is the price implying?Valuation, accounting and macro riddlesHardLong-short equity fundsGlobal macro funds

    Try it first

    What growth does the price imply?

    Show the worked solution

    About 10.75% a year, for ever. In a constant-growth model the forward P/E equals the payout ratio divided by (required return minus growth). With a P/E of 40 and a payout of 0.5, r minus g must be 0.5/40 = 1.25%, so g = 12% - 1.25% = 10.75%. Retaining half its earnings, the company would need a return on equity of 21.5% for ever to fund that growth.

    How does a P/E hide a growth assumption?

    A flat that rents for Rs 30,000 a month and sells for Rs 1.2 crore is priced at 400 months of rent; a buyer paying that is quietly assuming the rent will grow. A price multiple is a compressed forecast: fix the return investors want and the share of earnings paid out, and the multiple pins down the growth the price needs. The constant-growth model, price equals next year's dividend over (r minus g), divided through by earnings, gives P/E = payout/(r - g).

    Rearrange the multiple and the growth assumption falls outThe modelP/E = payout / (r - g)Plug in40 = 0.5 / (0.12 - g)Solve the gapr - g = 0.5 / 40 = 1.25%The answerg = 12% - 1.25% = 10.75%r = 12%10.75%dividend yield0.5 / 40 = 1.25%growth the priceneeds, for everNeeds ROE of10.75% / 0.5 = 21.5%
    Rearranging P/E = payout/(r - g) with a P/E of 40, a 50% payout and a 12% required return leaves a dividend yield of 1.25% and implied growth of 10.75% a year for ever, which needs a return on equity of 21.5%.
    The relationship
    PE1=payoutr−g  ⇒  g=r−payoutP/E=12%−0.540=10.75%\frac{P}{E_1} = \frac{\text{payout}}{r - g} \;\Rightarrow\; g = r - \frac{\text{payout}}{P/E} = 12\% - \frac{0.5}{40} = 10.75\%
    E_1next year's earnings, so the P/E is forward
    payoutthe share of earnings paid as dividends, 0.5
    rthe return investors require, 12%
    gthe constant growth rate the price implies
    What it says in wordsThe required return is the dividend yield plus growth, so growth is whatever is left after the yield.

    Is 10.75% for ever plausible?

    Test it against the business. Growth funded by retained earnings is return on equity times the share retained, so 10.75% growth with half the earnings kept needs a return on equity of 21.5%, held for ever. Few businesses hold returns like that for decades, and no company can outgrow the economy it sells into indefinitely, so compare the figure with the nominal growth you expect for that economy and say it as your assumption. The price is not wrong by arithmetic; it is demanding by assumption.

    How sensitive is the answer?

    Very. Because r - g is only 1.25%, every point on the required return moves the implied growth by a full point: at 11% the price implies 9.75%, at 13% it implies 11.75%. Using trailing rather than forward earnings shifts it too: 40 = 0.5(1 + g)/(0.12 - g) gives 10.62%. A high multiple rests on a thin gap between two large numbers, so small changes in either swing the value.

    Where candidates lose it

    Candidates treat the P/E as if it were price over dividend and forget the payout, which gives r - g = 2.5% and growth of 9.5%. The payout ratio is what turns earnings into the dividends the model actually discounts.

    The other miss is stopping at 10.75% without judging it. The question asks what the price implies; the strong answer adds the return on equity it needs and whether that is believable.

    What the interviewer asks next

    • What P/E would 6% growth for ever justify at the same payout and required return?
    • How does a rise in the required return to 13% change the implied growth?
    • Why is a constant-growth model a poor fit for a young, fast-growing company?