You are trying to value a private company. The company has 5 million of debt and

Question

You are trying to value a private company. The company has 5 million of debt and 4 million of book equity. The ratio of market value to book value for similar firms is 2. You decide to use this ratio to estimate the market value of equity as the input for the weights in WACC calculation. The average beta for publicly traded firms in the same industry is 2, and the average debt-to-equity ratio for public firms in this industry is 0.4. The corporate tax rate is 40%. The risk free rate is 6% and the market risk premium is 5.5%. The interest rate for debt is 10%. Here is the FCFF model for valuing the business:

Year 1 2 3 4 5 6
EBIT (EBIT grows at 15% for the first $2.30 $2.65 $3.04 $3.50 $4.02 $4.22
five years and 5% thereafter.)
EBIT (1-Tax Rate) $1.38 $1.59 $1.82 $2.10 $2.41 $2.53
Less
(Cap. Expenditures-Depreciation) grows $.115 $.132 $.152 $.175 $.201 $0.00
at same 15% annual rate as revenue for 5 years and are offsetting thereafter)
Equals FCF Assuming after 5 years, the growth rate is 5% forever.

1. What is the unlevered Beta for publicly traded firms in the same industry?
2. What is levered beta for the private firm?

3. What is the cost of equity for the private firm (in percentage)?

4. What is the WACC for the private firm (in percentage)?

Explanation / Answer

Unlevered Beta = Levered Beta / (1 + ((1 - Tax Rate) * (Total Debt/Equity)))

Levered Beta = Unlevered Beta * (1 + ((1 - Tax Rate) * (Total Debt/Equity)))

1)

Unlevered Beta = 2 / (1 + ((1 - 40%) * (0.4))) = 1.6129

2)

Equity = 2*4 = 8

Debt = 5

Levered Beta = 1.6129 * (1 + ((1 - 40%) * (5/8))) = 2.2177

3)

Re = 6% + 2.2177*5.5% = 18.20%

4)

WACC = (5/13)*10%*(1-40%) + (8/13)*18.20% = 13.51%

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