Canine Crates just paid an annual dividend of $.45 per share but plans to double that amount each year for three years. After that, the firm expects to maintain a constant dividend. What is the value of this stock today if the required return is 13 percent?a. $24.48b. $26.45c. $23.46d. $19.91e. $23.89

e) $23.89

Explanation:

The question is to determine the value of Canine Crates stock today  based on a return rate of 13%

The first step is to determine the yearly value based on the dividend for three years as follows

D1= The annual dividend x 2 ( since Canine Crates plans to double the amount each year for three years

D1= $0.45 x 2 = $0.9

D2= $0.90 x 2 = $1.80

D3= $1.80 x 2 = $3.60

Based on these calculations, we calculate the value of the stock by adding the present values of the dividend of each year.

This is based on the following formula

Dividend per year / (1+r)∧n

= Dividend per year

r = required rate

n= period

Value of the stock = $0.9 / (1.13) + $1.80 / (1.13)∧2 + $3.60/ (1.13)∧3

The value of the stock = $23.89

The correct answer is E ,$23.89

Explanation:

The value of the stock today can be calculated by discounting all future dividends payable by the stock with $0.9 in year 1, $1.8 in year 2,$3.6 in year 3 and in perpetuity.

In knowing the dividends in perpetuity, the $3.6 is divided by 13% cost of capital.

It is also important to know that the discounting factor in perpetuity is the same as year 3 discounting factor.

Years  Dividends           DCF=(1+r)^n                PV

1             0.9                        0.885                  0.80  

2              1.8                         0.783                    1.41  

3             3.6                         0.693                   2.49  

4             27.69                           0.693                  19.19  

     total of present values                                    23.89  

Since $0.45 is just been paid, next year dividend will be doubled and so on.