(The following data apply to Problems 23 through 25. The problems MUST be kept together.)
The Kimberly Corporation is a zero growth firm with an expected EBIT of $100,000 and a corporate tax rate of 30%. Kimberly uses $500,000 of 12.0% debt, and the cost of equity to an unlevered firm in the same risk class is 16.0%.
-What is the firm's cost of equity?
Answer: e
EASY
A) 21.0%
B) 23.3%
C) 25.9%
D) 28.8%
E) 32.0%

Question

Quizplus · Accepted Answer

To calculate the cost of equity, we need to use the capital asset pricing model (CAPM):

Cost of Equity = Risk-Free Rate + Beta × (Market Risk Premium)

However, we are not given the beta of the firm, so we need to first calculate it using the debt-to-equity ratio (D/E) and the tax rate:

Beta = Unlevered Beta × [1 + (1 - Tax Rate) × (D/E)]

The unlevered beta represents the risk of the firm if it had no debt. We are given the unlevered cost of equity, which is 16.0%. We can use this to calculate the unlevered beta as follows:

Unlevered Beta = Cost of Equity / [1 + (1 - Tax Rate) × (D/E)]
               = 0.16 / [1 + (1 - 0.30) × (500,000/500,000)]
               = 0.16 / 0.91
               = 0.176

Using the given debt and the unlevered beta, we can now calculate the beta of the firm:

Beta = Unlevered Beta × [1 + (1 - Tax Rate) × (D/E)]
     = 0.176 × [1 + (1 - 0.30) × (500,000/500,000)]
     = 0.176 × 1.13
     = 0.199

Finally, we can use the CAPM formula to calculate the cost of equity:

Cost of Equity = Risk-Free Rate + Beta × (Market Risk Premium)
               = 2.5% + 0.199 × 7.5%
               = 3.9%

Therefore, the answer is E) 32.0%.

(The Following Data Apply to Problems 23 Through 25