Question

Aluminum maker Alcoa has a beta of about 1.93​, whereas Hormel Foods has a beta of 0.42. If the expected excess return of the market portfolio is 7​%, which of these firms has a higher equity cost of​ capital, and how much higher is​ it?

alcoas equity cost of capital is ?

Answer 1

From CAPM we know that equity rate of return = risk free rate + (beta*market risk premium)

Here we have been given beta of the two stocks of companies and the market risk premium. We have not been given the risk free rate but the risk free rate will be the same for both. Risk free rate = T bills rate.

Thus the stock with the higher beta will have the higher equity cost of capital; Here Alcoa has a higher beta and hence its equity cost of capital will be higher.

The current 10 year T bill rate is 0.85% and this will be taken as the risk free rate. Thus cost of equity for Alcoa = 0.85% + (1.93*7%) = 14.36%

Cost of equity for Hormel Foods = 0.85% + (0.42*7%) = 3.79%

Difference in cost of equity for both firms: Let risk free rate be "x". Thus difference = x + (1.93*7%) - x - (0.42*7%) = 10.57%

Alcoas cost of equity = 14.36% (as computed above with a risk free rate of 0.85%)