Question

Aluminum maker Alcoa has a beta of about 1.97​, whereas Hormel Foods has a beta of 0.38 If the expected excess return of the market portfolio is 4​%, which of these firms has a higher equity cost of​ capital, and how much higher is​ it?

Answer 1

Aluminum maker Alcoa beta = 1.97​

Hormel Foods beta = 0.38

Capital asset pricing model describes the relation between expected return on a security and the systematic risk (beta) of the market.

According to capital asset pricing model -

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

E(Rm) - Rf ) is nothing but excess market risk premium. Here, market price is given as 4 %.

( E(Rm) - Rf ) * beta of the security is risk premium on the security i.e return undertaken for taking extra risk.)

Aluminum maker Alcoa required rate of return will be -

E(r) = Rf + 4 * 1.97

= Rf + 7.88

Hormel Foods required rate of return will be -

E(r) = Rf + 4 * 0.38

= Rf + 1.52

--> As the beta of Aluminum maker Alcoa is more, the risk premium will be more, hence the required rate will be more.

--> Required rate of Aluminum maker Alcoa will be 6.36 % higher than the Hormel Foods. ( Rf + 7.88 - (rf + 1.52)) = 6.36 %

Hope it helps!