Business has been good for keystone control systems, as indicated by the four-year growth in earnings per share. the earnings have grown from $1.00 to $3.51.

a.
determine the compound annual rate of growth in earnings (n = 4). (do not round intermediate calculations. input your answer as a percent rounded to 2 decimal places.)

compound annual rate of growth ? %

b.
based on the growth rate determined in part a, project earnings for next year (e1). (do not round intermediate calculations. round your answer to 2 decimal places.)

e1 $ ?

c.
assume the dividend payout ratio is 45 percent. compute d1. (do not round intermediate calculations. round your answer to 2 decimal places.)

d1 $ ?

d.
the current price of the stock is $20. using the growth rate (g) from part a and d1 from part c, compute ke. (do not round intermediate calculations. input your answer as a percent rounded to 2 decimal

ke ? %

e.
if the flotation cost is $3.00, compute the cost of new common stock (kn) using growth rate (g) from part a and dividend (d1) from part c. (do not round intermediate calculations. input your answer as a percent rounded to 2 decimal places.)

kn ? %

a. E4 = Eo(1 + g)4

$3.51 = $1.00(1 + g)4

$3.51  = (1 + g)4                                                                                                                                                              

$1.00                                                                                                                                                                                                                                                                                                                      

3.51 = (1 + g)4

4√3.51 - 1 = g

1.3688 - 1 = g

g = 0.3688 = 36.88%

b. Earnings for next year (E1)

E1 = Eo(1 + g)1

E1 = $1.00(1 + 0.3688)1  

E1 = $1.37 per share

c. D1 = 45% of E1

D1 = 0.45 x $1.37 = $0.62 per share

d. Ke = D1 + g

            Po  

Ke = $0.62 + 0.3688

         $20

Ke = 0.3998 = 39.98%

e. Kn =     D1           + g

           Po(1 - FC)

  Kn   = $0.62        + 0.3688

             $20 - $3

  Kn = $0.62 + 0.3688

           $17

   Kn = 0.4053 = 40.53%

Explanation:

The compound annual rate of growth is calculated as E4 = Eo(1 + g)4

Where E4 is earnings per share at the end of year 4, Eo is the current earnings per share and g refers to growth in earnings. Since E4 and Eo have been provided, g becomes the subject of the formula.

E1 is calculated as Eo(1 + g)1 where E1 refers to earnings per share at the end of year 1.  

Since dividend payout ratio is 45%, D1 will be 45% of E1. D1 denotes dividend at the end of year 1.

Cost of equity equals dividend at the end of year 1 divided by the current market price plus the annual rate of growth.