Question

Assume the following: bullet the investor's required rate of return is 15 percent, bullet the expected level of earnings at the end of this year (Upper E 1) is $5, bullet the retention ratio is 50 percent, bullet the return on equity (ROE) is 20 percent (that is, it can earn 20 percent on reinvested earnings), and bullet similar shares of stock sell at multiples of 10.000 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 25 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?

Answer #1

Required rate of return = 15%

E1 = $5

retention ratio = 50%

Dividend ratio = 1 - 50% = 50%

So

Expected Dividend = 5 * 0.5 = $2.5

ROE = 20%

a) Expected growth rate = ROE * retention ratio

Expected growth rate = 20% * 50% = 10%

b) Price = Expected dividend / ( required return - growth rate )

Price = 2.5 / 0.15 - 0.1 = $50

So price to earning ratio = 50 / 5 = 10

c)

P/E multiple = 10

Price using P/E multiple = 10 * 5 = 50

d)

Price = Expected dividend / ( required return - growth rate )

Price = 2.5 / 0.15 - 0.1 = $50

e)

ROE = 25%

growth rate = 25% * 50% = 12.5%

Price = Dividend / ( 0.15 - 0.125 )

Price = 2.5 / ( 0.15 - 0.125 ) = $100

P/E ratio = 100 / 5 = 20

f)

As the ROE increases, it means that growth rate of company increase. This will increase the share price and in turn the P/E ratio

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