Question

NEED ANSWERS TO (e) and (f ) only:

(Common stock​ valuation)  Assume the​ following:   

the​ investor's required rate of return is ​13.5percent,   

the expected level of earnings at the end of this year ​(E1​) is ​$​8   

the retention ratio is 45 ​percent,   

the return on equity ​(ROE​) is 15 percent​ (that is, it can earn 15 percent on reinvested​ earnings), and   similar shares of stock sell at multiples of 8.149 times earnings per share.

​Questions:

a.  Determine the expected growth rate for dividends.

b.  Determine the price earnings ratio ​(P​/​).

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​/​) and stock price if the company increased its retention rate to 60 percent​ (holding all else​ constant)? What would happen to the ​P/E ratio ​(P​/​) and stock price if the company paid out all its earnings in the form of​ dividends?

f.  What have you learned about the relationship between the retention rate and the ​P/E​ ratios?

Answer 1

E If the company increased it retention rate to = 60%

The payout ratio = (1- retention rate %)

= 1-0.60 = 0.4 or 40% is the payout ratio

Earnings per share = 8

Dividend per share = 8*.40 = 3.2

G = ROE *Retention ratio = 0.15*0.60 = 0.09 or 9%

So

The Price of the stock

Ke- g = D1 / Po

0.135- 0.09 = 3.20 / Po

Or Po = 3.2/ 0.045 = 71.11

So

P/E ratio = 71.11 / 8 = 8.89

If paid all earnings as dividends

If the company retention rate to = 0%

The payout ratio = (1- retention rate %)

=100% is the payout ratio

Earnings per share = 8

Dividend per share = 8*1= 8

G = ROE *Retention ratio = 0.15*0 = 0

So

The Price of the stock

Ke- g = D1 / Po

0.135- 0 = 8 / Po

Or Po =8/0.135 = 59.26

P/E ratio = 59.26 / 8 =7.407

f.

With the increasing retention rate , the PE ratio of the company also increases as per the DDM model as both the Dividends per share and the the Price of the share changes with the changes in the retention