Question

Assume the following: the investor's required rate of return is 17 percent, the expected level of earnings at the end of this year (Upper E 1) is $5, the retention ratio is 45 percent, the return on equity (ROE) is 19 percent (that is, it can earn 19 percent on reinvested earnings), and similar shares of stock sell at multiples of 6.508 times earnings per share. Questions: a. Determine the expected growth rate for dividends. b. Determine the price earnings ratio (P/Upper E 1). c. What is the stock price using the P/E ratio valuation method? d. What is the stock price using the dividend discount model? e. What would happen to the P/E ratio (P/Upper E 1) and stock price if the firm could earn 24 percent on reinvested earnings (ROE)? f. What does this tell you about the relationship between the rate the firm can earn on reinvested earnings and P/E ratios?

Round to the nearest cent or three decimal places

Answer #1

**1. Answer to Part (A)**

Calculation of Growth Rate (g)

g = b x r

Where

g = Growth Rate of Dividend

b = Retention Ratio

r = ROE

g = 45% x 19%

g = 8.55%

**4. Answer to Part (B)**

P/E Ration = 6.508

Since Similar stock has the same P/E Ration.

**3. Answer to Part (C)**

Stock Price under P/E Valuation = EPS X P/E Ration

Stock Price under P/E Valuation = $ 5 X 6.508

Stock Price under P/E Valuation = $ 32.54

**4. Answer to Part (D)**

Stock Price under the Dividend Discount Model:

Po = D1/ Ke - g

Where

Po = Current Market Price of Share

D1 = Expected Dividend

Ke = Cost of Equity

g = Growth rate

Now, Po = $ (5*55%) / 17.00% - 8.55%

Po = $ 32.54

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