Question

4

(4) An issue of common stock pays a dividend which grows at a rate of 8%. (a) At a stock price of $10 and expected rate of return of 16%, what dividend must it pay at the end of the first year? (b) How long will it take for the stock price to double?

Answer 1

a) This question requires application of constant growth dividend discount model, according to which

Po - Divi -9 Po = Price of Stock Divi = Estimated Dividends for Next Period r = Required Rate of Return 9 = Growth Rate

$10 = \frac{Div_1}{0.16 - 0.08}$

$10 = \frac{Div_1}{0.08}$

Div1 = $0.80

b) This requires application of basic time value of money formula, according to which

FV = PV * (1 + r)ⁿ

FV = 2* PV

2 * PV = PV * (1 + r)ⁿ

2 = (1 + 0.16)ⁿ

Taking log of both sides,

LN(2) = n * LN(1.16)

0.6931 = n * 0.14842

n = 4.67 years