Question

Given that a​ firm's return on equity is 15 percent and management plans to retain 44 percent of earnings for investment​ purposes, what will be the​ firm's growth​ rate? If the firm decides to increase its retention​ rate, what will happen to the value of its common​ stock?

a. The​ firm's growth rate will be________% (Round to two decimal​ places.)

b. If the firm decides to increase its retention​ ratio, what will happen to the value of its common​ stock? ​(Select from the​ drop-down menus.)

An increase in the retention rate will (increase/decrease) the rate of growth in​ dividends, which in turn will (increase/decrease) the value of the common stock.

Answer 1

Answer-

Given

return on equity ( ROE ) = 15 %
retention rate (b) = 44 % = 0.44

a )

The firm's growth rate (g)
= retention rate (b) x ROE
= 0.44 x 15 %
= 6.6 %

b)

An increase in the retention rate will decrease the rate of growth in​ dividends, which in turn will decrease the value of the common stock.

When the retention rate increases the dividend growth will decrease as

retention rate = 1 - payout ratio ( dividend payout) [ both are inversely related ]

As the dividends decrease the stock price will decrease and  when the dividends are higher, one can expect an increase in the stock price.

Therefore an increase in retention rate will decrease the value of the stock price