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