Question

The risk-free rate is 1.15% and the market risk premium is 6.74%. A stock with a β of 1.31 just paid a dividend of $1.40. The dividend is expected to grow at 22.68% for three years and then grow at 4.35% forever. What is the value of the stock?

Answer 1

HI,

here risk free rate rf = 1.15%

market risk premium rm = 6.74%

beta =1.31

according to CAPM

required rate r = rf+ beta*market risk premium

r = 1.15 + 1.31*6,74

r = 9.979%

now dividend now D0 = $1.40

growth rate g for 3 years =22.68%

so Dividend after 1 years D1 = 1.4*(1+22.68%) = 1.72

D2 = 1.72*(1+22.68%) = $2.11

D3 = 2.11*(1+22.68%) = $2.59

and then terminal growth rate g = 4.35%

As per dividend discount model current value of stock will be present value all future dividends.

so value of stock P = 1.72/(1+9.979%) +2.11/(1+9.979%)^2 +2.59/(1+9.979%)^3

+ 2.59*(1+4.35%)/(9.979%-4.35%)(1+9.979%)^3

Value of stock P = $41.27

Thanks