Question

A firm expects to increase its annual dividend by 20 percent per year for the next two years and by 15 percent per year for the following two years. After that, the company plans to pay a constant annual dividend of $3 a share. The last dividend paid was $1.00 a share. What is the current value of this stock if the required rate of return is 12 percent?

Answer 1

Answer:

Current price = $20.50

Explanation:

Data provided in the question;

Growth rate, g = 20% = 0.2 for the 2 years

Growth rate, g' = 15% = 0.15 for the following 2 years

after 4 years annual dividend = $3

Last dividend paid, D0 = $1

Required rate of return, r = 12% = 0.12

Now,

D1 = D0 × (1 + g)

= $1 × (1 + 0.2)

= $1.2

D2 = $1 × (1 + 0.2)²

D3 = $1 × (1 + 0.2)² × (1 + 0.15)

D4 = $1 × (1 + 0.2)²  × (1 + 0.15)²

D5 = 3

Therefore,

Current price = $\frac{1.2}{(1 + 0.12)}$ + $\frac{\ 1\times(1 + 0.2)^2}{(1 + 0.12)^2}$ + $\frac{\ 1\times(1 + 0.2)^2\times(1 + 0.15)}{(1 + 0.12)^3}$ + $\frac{\ 1\times(1 + 0.2)^2\times(1 + 0.15)^2}{(1 + 0.12)^4}$ + $\frac{\frac{\ 3}{0.12}}{(1+0.12)^4}$

⇒ Current price = $20.50