Question

Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e., years 2 through 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%?

Answer 1

At 10 percent capitalization rate the price of the stock is $104.49

At 7 percent capitalization rate the price of the stock is $156.48

Step-by-step explanation:

D1 = 5

D2 = 5 x 1.2 = 6

D3 = 5 x 1.2^2= 7.2

D4 = 5 x 1.2^3 = 8.64

D5 = 5 x 1.2^4 = 10.37

D6 = 5 x 1.2^5 = 12.44

At 10 percent capitalization rate the price of the stock can be computed by first calculating the present value of the dividends computed above

5/1.1 = 4.54

6/1.1^2 = 4.96

7.2/1.1^3 = 5.41

8.64/1.1^4 = 5.90

10.37/1.1^5 = 6.44

12.44/1.1^6 = 7.02

Price after six years when the stock will experience zero growth should be

P = 12.44/0.1 = 124.4

The present value of the price six years after should be

124.4 / 1.1^6 = 70.22

Adding up all the p[resent values gives us the price of the stock today

4.54 + 4.96 + 5.41 + 5.90 + 6.44 + 7.02 + 70.22 = $104.49

At 7 percent capitalization rate the price of the stock can be computed by first calculating the present value of the dividends computed above

5/1.07 = 4.67

6/1.07^2 = 5.24

7.2/1.07^3 = 5.88

8.64/1.07^4 = 6.59

10.37/1.07^5 = 7.39

12.44/1.07^6 = 8.29

Price after six years when the stock will experience zero growth should be

P = 12.44/0.07 = 177.71

The present value of the price six years after should be

177.71 / 1.07^6 = 118.42

Adding up all the p[resent values gives us the price of the stock today

4.67 + 5.24 + 5.88 + 6.59 + 7.39 + 8.29 + 118.42 = 156.48