Table 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 share price unchanged?

Question

Quizplus · Accepted Answer

Firstly, we need to determine the new beta of the firm after the asset sale and purchase:
New Beta = (0.9 x 1.25) + (0.1 x 1.1) = 1.235

Next, we can use the capital asset pricing model (CAPM) to calculate the new overall required rate of return:
rE = rRF + (rM - rRF) x beta
rE = 7% + (14% - 7%) x 1.235
rE = 15.645%

Finally, we need to calculate the rate of return the new assets must produce in order to leave the share price unchanged. We can use the following equation to do this:
rE = (Earnings after asset sale) / (Market value of equity)

Since the firm sells and purchases 10% of its assets, we can assume that the earnings will also decrease by 10%. Therefore:
New earnings = 0.9 x Old earnings
New Market value of equity = Old Market value of equity

We can rearrange the equation above to solve for the required rate of return:
rE = (0.9 x Old earnings) / Old Market value of equity
rE = (0.9 x Earnings after asset sale) / Old Market value of equity
rE x Old Market value of equity = 0.9 x Earnings after asset sale
Earnings after asset sale = Old earnings - (0.1 x Old earnings) = 0.9 x Old earnings

Substituting the values we have:
15.645% = (0.9 x Old earnings) / Old Market value of equity
Old earnings / Old Market value of equity = 15.645% / 0.9
Old earnings / Old Market value of equity = 17.383%

The new assets must produce this same rate of return in order to leave the share price unchanged:
17.383% x 0.1 + 14% x 0.9 = 14.7%

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