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  1. 097A stock trades at 20x next year's earnings, pays out 60% of earnings as dividends, and its dividends are expected to grow at 7% a year forever. What cost of equity is the market implying?Valuation riddlesCoreElite boutique IBBulge bracket IB

    Try it first

    What return is a buyer at this price implicitly expecting?

    Show the worked solution

    About 10%. The Gordon growth model says price equals next year's dividend over (cost of equity minus growth). Rearranged, cost of equity equals dividend yield plus growth. The dividend yield is payout over P/E, 0.6 / 20, which is 3%. Adding 7% growth gives 10%. If the 20x were on trailing earnings, the answer would be slightly higher, about 10.2%.

    How does a price turn into a return?

    If a flat costs Rs 1 crore and rents for Rs 3 lakh a year, rising 7% a year, a buyer is earning 3% in rent now and 7% a year from the rent growing, about 10% in total. A buyer of a growing income stream earns its current yield plus its growth, so a price plus a growth assumption tells you the return the buyer must be expecting. For a share, the income is the dividend.

    Rearrange the Gordon model and a price becomes a returnP/E 20earnings yield 1/20= 5%x payout 60%dividend yield 0.6 / 20= 3%+ growth 7%cost of equity= 10%Return thebuyer expects3% paid as dividends7% from the dividend growing10% cost of equity implied by the priceIf the 20x is on trailing earnings, next year's dividend is 7% bigger: 3% x 1.07 + 7% = 10.21%.Growth is the soft input: at 6% growth the same price implies 9%.
    A P/E of 20 and a 60% payout give a dividend yield of 3%, and adding 7% expected dividend growth implies that buyers at this price expect a 10% return on equity.

    Why is the dividend yield payout over P/E?

    The relationship
    P=D1ke−g  ⇒  ke=D1P+g=0.6×E20×E+0.07=3%+7%=10%P = \frac{D_1}{k_e - g} \;\Rightarrow\; k_e = \frac{D_1}{P} + g = \frac{0.6 \times E}{20 \times E} + 0.07 = 3\% + 7\% = 10\%
    Pshare price, 20 times next year's earnings E
    D_1next year's dividend, 60% of E
    k_ecost of equity implied by the price
    gperpetual dividend growth, 7%
    What it says in wordsThe return implied by a price is next year's dividend yield plus the dividend's growth rate.

    Dividend over price is (payout x earnings) over (P/E x earnings), and earnings cancel, leaving 0.6 / 20 = 3%. You never need the share price or the earnings per share, only the two ratios. That is the trick the interviewer is looking for: spotting that the units cancel.

    How much should you trust the 10%?

    Only as far as the growth input. The dividend yield is observable; the 7% perpetual growth is an opinion. Drop it to 6% and the same price implies 9%. Check consistency too: growth of 7% with 40% of earnings retained implies a return on retained equity of about 17.5%, since growth equals retention times return on equity. If the company cannot earn that, the 7% is too high.

    Where candidates lose it

    The fast wrong answer is 5%, the earnings yield, which treats all earnings as paid out and ignores growth. A close second is answering 7%, quoting the growth rate as if it were the return.

    The quieter slip is mixing trailing and forward. Say which earnings the 20x is on; if trailing, grow the dividend one year before dividing.

    What the interviewer asks next

    • What P/E would the stock trade on if the cost of equity were 12% with the same payout and growth?
    • Check the 7% growth against retention and return on equity: is it consistent?
    • Why might the implied cost of equity differ from a CAPM estimate for the same company?