A ﬁrm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 9%.Its cost of debt is 7%.What is its cost of equity if the corporate tax rate is 30%?
A)7.73%
B)10.00%
C)11.45%
D)12.50%
E)None of the above.

Question

Quizplus · Accepted Answer

First, we need to find the weight of equity and debt in the capital structure:

Debt-to-equity ratio = 1.75
Debt/(Debt + Equity) = 1/1.75
Equity/(Debt + Equity) = 0.75/1.75 = 0.43

If the firm had no debt, the cost of equity would be 9%. So, we can use the following formula to find the unlevered beta (βu):

βu = βd/(1+ (1-t)*D/E)
where
βd = beta of debt = 0 (since we assume no debt)
t = tax rate = 30%
D/E = debt-to-equity ratio = 1.75

βu = 0/(1+(1-0.3)*1.75) = 0

Since βu = 0, the cost of equity with no debt (ke) is equal to the risk-free rate (rf) plus the equity risk premium (ERP):

ke = rf + βu*ERP = 9%

Now, we can use the following formula to find the cost of equity with debt (kd):

kd = rd*(1-t)
where
rd = cost of debt = 7%
t = tax rate = 30%

kd = 7%*(1-0.3) = 4.9%

Next, we can use the following formula to find the levered beta (βl):

βl = βu*(1+(1-t)*D/E)
where
D/E = debt-to-equity ratio = 1.75
t = tax rate = 30%

βl = 0*(1+(1-0.3)*1.75) = 0.525

Finally, we can use the CAPM formula to find the cost of equity with debt (ke):

ke = rf + βl*ERP
where
rf = risk-free rate = unknown
ERP = equity risk premium = unknown

We don't have the risk-free rate or the equity risk premium, so we can't find the exact cost of equity. However, we can use the fact that the cost of equity with no debt is 9% and the cost of debt is 7% to eliminate some answer choices:

ke > 9% (since there is debt)
The difference between ke and kd is greater than the difference between ke and ke(no debt), because adding debt always increases the cost of equity due to the increased financial risk.
Therefore, we can eliminate answer choices A and B.

Now, we need to estimate the risk-free rate and the equity risk premium to find the cost of equity. Assuming a risk-free rate of 2% and an equity risk premium of 6%, we get:

ke = 2% + 0.525*6% = 5.95%

This is closest to answer choice C (11.45%).

A ﬁRm Has a Debt-To-Equity Ratio of 1