Question

A firm's stock recently earned $5 per share and the firm distributed sixteen percent of its earnings as cash dividends. Its dividends grow annually at 4 percent.
a. What is the stock's price if the required rate of return is 9 percent?b. The firm borrows funds and, as a result, its per-share earnings and dividends increase by 20 percent. What happens to the stock's price if the growth rate and the required return are unaffected? What will the stock's price be if after using financial leverage and increasing the dividend to $1, the required return rises to 10 percent? What may cause this required return to rise?

Answer 1

Solution :

Given :

a). Value of stock earned per share =  $5

Percentage of dividends distributed = 16%

Growth of dividend annually = 4%

Calculating the value of the common stock :

$D_0$ = 16% of $5

    = 0.16 x 5

    = 0.8

k = 0.09

g = 0.04

Therefore, the stock's value is give by,

$=\frac{D_0(1+g)}{k-g}$

$=\frac{0.8(1+0.04)}{0.09-0.04}$

=$16.64

b). Therefore, the value of the common stock when the growth rate increases is,

$D_0$ = 0.8+20% of 0.8

     = 0.96

k = 0.09

g = 0.04

Value of stock   $=\frac{D_0(1+g)}{k-g}$

                          $=\frac{0.96(1+0.04)}{0.09-0.04}$

                          =$19.96