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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