Using the P/E ratio approach to valuation, calculate the value of a share of sto

Question

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 (E_1) is $4, the firm follows a policy of retaining 20 percent of its earnings, the return on equity (ROE) is 15 percent, and similar shares of stock sell at multiples of 8.000 times earnings per share. Now show that you get the same answer using the discounted dividend model.

Explanation / Answer

Answer:

EPS = $4

Market Price per SHare = 8 times of EPS = 8 x 4 = $32

P/E Ratio = Market Price Per Share / Earnings Price Per Share i.e. MPS/EPS

P/E Ratio = MPS / EPS = $32 / $4 = 8

(a) Market Price Per Share as per P/E Ratio valuation method = EPS x P/E Ratio = $4 x 8 = $32

(b) Market Price per Hsare using dividend discount model

As per Dividend Growth Model,

Market Price per Share = EPS (1-Retention Ratio) / (Investor's Required Rate of Return – growth rate)

MPS = $4 (1 - 0.20) / (0.13 - 0.03) = ($4 x 0.80) / 0.10 = $3.20 / 0.10 = $32

Growth Rate = Retaintion Ratio x Ke = 0.20 x 0.15 = 0.03

Growth Rate is calculated by taking Retention Ration ie.e those portion of earning which company retain for future investment and Cost of Capital which a company expect to earn from its investment..

Market Price is calculated based on Investor's Point of View that is the reason of taking Investor's Required Rate of Return in calculating Stock price....

Hope the above solution works for you....

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