Would I be right? Using the P/E ratio approach to valuation, calculate the value

Question

Would I be right?

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 $8, the firm follows a policy of retaining 60 percent of its earnings, the return on equity {ROE) is 13 percent, and similar shares of stock sell at multiples of 7.693 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 $ 61.54 b. The stock price using the dividend discount model is $ 23.33.

Explanation / Answer

ANSWER A:

P/E = 7.693 times Earnings per share (EPS)= $ 8 Market Price per Share (MPS)= ?

P/e = MPS / EPS

MPS = P/E * EPS = 7.693 * 8

MPS = $ 61.544

ANSWER B:

Price as per dividend discount model = Dividend per Share / ( Ke - g)

Ke = Cost of equity/ Expected Rate of Return = 13%

g=?

Dividend = earnings*payout ratio = 8 * 0.40 = $ 3.20

Step1: calculate value of " g"

g = ROE * ( 1 - payout ratio) payout ratio = 1 - retention ratio = 1- 0.60 = 0.40

g = 0.13 * (1 - 0.40)

g = 0.13*0.60

g = 7.8%

Step 2: Applying value of g in dividend discount model

Value of Stock = 3.20/ (0.13 - 0.078) = $ 61.538 or $ 61.54

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