Question

(Related to Checkpoint 10.2) (Relative valuation of common stock) Using the P/E ratio approach to valuation, calculate the value of a share of stock under the following conditions: • the investor's required rate of return is 13 percent, • the expected level of earnings at the end of this year (E1) is $4, • the firm follows a policy of retaining 30 percent of its earnings, • the return on equity (ROE) is 15 percent, and • similar shares of stock sell at multiples of 8.235 times earnings per share. Now show that you get the same answer using the discounted dividend model. a. The stock price using the P/E ratio valuation method is $ (Round to the nearest cent.) b. The stock price using the dividend discount model is $ (Round to the nearest cent.)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

А Expected Earnings per share Similar stock's P/E ratio $4.00 8.235 5 a. Stock Price using P/E ratio valuation method $32.94 Retention ratio Expected dividend Investor's required rate of return Return of equity Growth rate 30% $2.80 13% 15% 4.50% 11 12 13 b. 14 Stock Price using the dividend discount model $32.94

Cell reference -

B Expected Earnings per share Similar stock's P/E ratio 8.235 5 a. Stock Price using P/E ratio valuation method =C3*C2 8 9 10 11 12 13 b. Retention ratio Expected dividend Investor's required rate of return Return of equity Growth rate 0.3 =C2*(1-C7) 0.13 0.15 =C10*C7 Stock Price using the dividend discount model =C8/(C9-C11) 15 10

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