Question

The Jameson Company just paid a dividend of $0.75 per share, and that dividend is expected to grow at a constant rate of 5.00% per year in the future. The company's beta is 1.75, the market risk premium is 5.00%, and the risk-free rate is 4.00%. What is Jameson's current stock price, P0?

Answer 1

First we will calculate the required rate of return on stock with help of CAPM equation, and after that use that to find out the current stock price.

CAPM equation -

E(Ri) = Rf + ( E(Rm) - Rf ) * beta of security

where,
E(Ri) = Expected/ required return on security i
rf = risk free return
E(Rm) = Expected market return

( E(Rm) - Rf ) is nothing but market risk premium.

Here,

Beta = 1.75

market risk premium = 5 %

Risk free return = 4 %

Required return on the stock = 4 + ( 5) * 1.75

= 4 + 8.75

= 12.75 %

Now, we will use this required rate of return to find of current stock price. Current stock price can be calculated with help of below equation-

where, Po is the current market price.
D0= Dividend just paid by company.
g = Growth rate
Ke = required rate of return on equity

here,

D0 = 0.75 $

g = 5 %

and as calculated Ke = 12.75 %

Po = $ 10.16 (approx)

Current stock price, P0 = $ 10.16

Hope it clarifies!