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 five years and 5% thereafter) $2.30 $2.65 $3.04 $3.50 $4.02 $4.22

EBIT (1-Tax Rate) $1.38 $1.59 $1.82 $2.10 $2.41 $2.53

Less (Cap. Expenditures-Depreciation) grows at same 15% annual rate as revenue for 5 years and are offsetting thereafter $.115 $.132 $.152 $.175 $.201 $0.00

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)?

5) What is the terminal value of the firm at the end of year 5 (in millions)?

6) What is the equity value of the firm right now (in millions)? (Note the question is not asking for firm value)

Explanation / Answer

To find out the unlevered Beta for publicly traded firms in the same industry we have been given the following information:

The average beta for publicly traded firms in the same industry is 2

Average debt to equity ratio for public firms is 0.4

Corporate tax rate is 40%

risk free rate is 6%

Market risk premium is 5.5%

Interest rate for debt is 10%

Beta unlevered= Beta levered/ (1+(1-Tc)*D/E)

= 2/ (1+(1-40%)*0.4)= 2/(1+0.6*0.4)= 2/(1.24)= 1.61

This is the unlevered beta for publicly traded firms in the same industry, be careful that all inputs should be of publicly traded firms in the same industry

Now question 2 is about levered beta for the private firm

In an ideal scenario, we would have taken average levered beta of publicly trade firms as levered beta of the private firm since they both are in the same industry. However, leverage is different for both publicly traded firms and privately trading firm

Hence, to calculate levered beta of private firm we will need to use unlevered beta of publicly traded firm and then apply leverage of privately traded firm

Beta unlevered= 1.61

Beta levered= Beta unlevered* [1+(1-Tc)*D/E]

= 1.61* [1+ (1-0.4)* D/E)]..................(1)

Now 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, therefore market value of equity is 4*2= 8 million

Therefore, Debt to equity ratio = 5 million/ 8 million= 5/8 = 0.625...........(2)

Using (2) in (1), we get

Beta levered= 1.61*[1+(1-0.4)*0.625]= 1.61*[1+0.6*0.625]=2.21....answer to question 2

Cost of equity= Risk free rate+ beta levered* Market risk premium

= 6%+2.21*5.5%= 18.15% , note that we have used levered beta of private firm calculated above since we are calculating the cost of equity for private firm , you cannot use unlevered beta in calculating the cost of equity becasue equity cost is also linked to the extent the firm is leveraged

Now WACC for the private firm is calculated using simple formula

WACC= cost of debt * proportion of debt + cost of equity* proportion of equity

= 10%*5/(5+8)+ 18.15%* 8/(8+5); note that proportion of debt= value of debt / total value of capital

= 3.85%+ 11.17%= 15.02%

Please post the remaining questions separately

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