Arizona Rock, an all-equity firm, currently has a beta of 1.25, and rRF = 7 percent and rM = 14 percent.Suppose the firm sells 10 percent of its assets (beta = 1.25) and purchases the same proportion of new assets with a beta of 1.1.What will be the firm's new overall required rate of return, and what rate of return must the new assets produce in order to leave the stock price unchanged?

Question

Quizplus · Accepted Answer

First, calculate the current required rate of return using the CAPM:

rAR = rRF + (rM - rRF) * βAR

rAR = 7% + (14% - 7%) * 1.25

rAR = 15.25%

After selling 10% of its assets and purchasing new assets, the new beta of the firm will be:

βnew = 0.9(1.25) + 0.1(1.1) = 1.235

The new required rate of return can be calculated as follows:

rnew = rRF + (rM - rRF) * βnew

rnew = 7% + (14% - 7%) * 1.235

rnew = 15.645%

To leave the stock price unchanged, the new assets must earn a return that will make up for the 10% reduction in the original investment.

Let x be the required rate of return on the new assets:

0.9(15.25%) + 0.1x = 15.645%

x = 14.7%

Therefore, the firm's new overall required rate of return will be 15.645%, and the new assets must produce a rate of return of 14.7% to leave the stock price unchanged.

Arizona Rock, an All-Equity Firm, Currently Has a Beta of 1.25