Question

Consider a stock that is planning to pay a dividend of $3 at the end of this year. After that, dividends will grow at a fixed rate of 4.5% per year indefinitely. The required return on the stock is 11%.

a. What is the value of the stock today, in 5 years, and in 8 years?

b. What are dividend yield and capital gains yield yield this year, in 5 years, and in 8 years?

Answer 1

A) D6 = D1(1+g)^n

= 3 (1+.045)^5

= 3 *1.24618

= 3.73855

Price in 5 years : D6 /(Rs-g)

= 3.73855/(.11-.045)

= 3.73855 / .065

= $ 57.52 per share

D9= D1(1+g)^n = 3 (1+.045)^8

= 3 *1.42210

= 4.2663

Price in 8 years : 4.2663/(.11-.045)

= 65.64

b)Price in 4 years : D5/(Rs-g)

= 3.57756/(.11-.045)

= 55.04

Dividend Yield: D5/ Price in year4

= 3.57756/ 55.04

= .065 or 6.5%

capital gain yield : [P5-P4]/P4

=[57.52-55.04]/55.04

= .0451 or 4.51%

Year 8)

Price in year 7: D8/(Rs-g)

= 4.08259/(.11-.045)

= 62.81

dividend yield : D8/P7

= 4.08259/62.81

= .065 or 6.5%

capital gain : [P8-P7]/P7

[65.64-62.81]/62.81

.0451 or 4.51%