Question

A firm will pay a dividend of $0 one year from today and $5.00 two years from today (that is, D1 = $0 and D2 = 5.00). Thereafter, the dividend is expected to grow at a constant rate forever. The price of this stock today is $100 and the required rate of return on the stock is 10%. What is the expected constant growth rate of the dividend stream from year 2 to infinity? For this problem, you must compute the growth rate to 2 decimal places (i.e., as a percent rounded to 2 decimal places; for example, record 0.034824 = 3.4824% as 3.48).

Answer 1

value of stock = Present value of dividends + Horizontal value

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

Horizontal value = dividend next year/(Required return - growth rate)

Horizontal value = 5*(1+g)/(10%-g)

=>

Value of stock = 100

=>

0/1.1 + 5/1.1^2 + 5*(1+g)/(0.1-g)/1.1^2 = 100

=>

5* (1+g)/(0.1-g) = (100 - 5/1.1^2) * 1.1^2 = 116

=>

(1+g)/0.1-g = 116/5 = 23.2

=>

1+g = 2.32 - 23.2g

=>

23.2g +g = 2.32 -1

=>

g = 1.32/24.2

=>

growth rate g = 5.46%