Question

A company just paid a dividend of $1.95 per share, and that dividend is expected to grow at a constant rate of 4.50% per year in the future. The company's beta is 1.65, the market risk premium is 8.5%, and the risk-free rate is 6.50%. What is the company's current stock price?

Answer 1

To find out the current stock price, first we have to find out the required rate of return (cost of equity). The required rate of return can be computed with help of CAPM equation.

CAPM equation -

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

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

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

Here,

Company's beta = 1.65

Market risk premium = 8.5%

Risk-free rate = 6.50%

Putting all these in CAPM equation-

Required rate of return = 6.50 + (8.5) * 1.65

= 6.5 + 14.025

= 20.525 %

Hence, required rate of return/cost of equity = 20.525 %

Now, constant dividend growth model can be used to find the current stock price of the security.

According to this, current stock price can be computed as under-

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

Here,

D0 = 1.95 $

g = 4.50%

Ke = 20.525 %

Putting all these in the equation -

Po = 12.72 $ (approx)

Current stock price = 12.72 $ (approx)

Hope it helps!