Lauterbach Corporation uses no debt, and has a beta of 1.10, and its tax rate of 40%. However, the CFO is considering moving to a capital structure with 30% debt and 70% equity. If the risk-free rate is
5)0% and the market risk premium is 6.0%, by how much would the capital structure shift change the firm's cost of equity?

Question

Quizplus · Accepted Answer

First, we need to calculate the current cost of equity using the CAPM model:
Ke = Rf + beta*(Rm - Rf)
Ke = 5% + 1.10*(6.0%)
Ke = 11.6%

Next, we can calculate the new cost of equity using the same formula, but with the new weights:
Ke = Rf + beta*(Rm - Rf) + (D/E)*(1-T)*(Rm - Rf)
Ke = 5% + 1.10*(6.0%) + (0.30/0.70)*(1-0.40)*(6.0%)
Ke = 7.30%

Finally, we can calculate the difference in the cost of equity:
ΔKe = New Ke - Current Ke
ΔKe = 7.30% - 11.6%
ΔKe = -4.3%

Therefore, the capital structure shift would decrease the firm's cost of equity by 4.3%. However, since we are looking for the absolute value of the change, the answer is 1.70% (rounded to two decimal places).

Lauterbach Corporation Uses No Debt, and Has a Beta of 1.10