Assignment 6
Q1-Q6 are based on the following information:
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 of the debt is 10%.
Here is the FCFF model for valuing the business:
Year
EBIT (EBIT grows at 15% for the first
five years and 5% thereafter.)
1
2
3
4
5
6
$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 $.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?
2.00 / (1 + .6 x .4) = 1.61, where 2.00 is the levered beta, .6 is (1-tax rate), and .4 is the average debt
ratio for firms in this industry.
2.
What is levered beta for the private firm?
Debt/Equity ratio for the private firm = 5 / (2 x 4) = .625 where 5, 4, and 2 are the private firm’s debt,
book value of equity, and the ratio of market value to book value for similar firms.
Levered beta for the private firm = 1.61 x (1 + .6 x .625) = 2.21
3.
What is the cost of equity for the private firm (in percentage)?
6 + 2.21 x 5.5 = 18.16
4.
What is the WACC for the private firm (in percentage)?
After-tax cost of debt = .10 x (1 - .4) = 6.0
WACC for the private firm = 18.16 x 2x4 + 6.00 x 5__
2x4+5
2x4+5
= 18.16 x. 615 + 6.00 x. 385
= 13.48
5.
What is the terminal value of the firm at the end of year 5 (in millions)?
Valuing the business using the FCFF model:
Year
1
EBIT (EBIT grows at 15% for the first
five years and 5% thereafter.)
2
3
4
5
6
$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 $.115 $.132 $.152 $.175 $.201 $0.00
at same 15% annual rate as revenue
for 5 years and are offsetting
thereafter)
Equals
Free Cash Flow to the Firm
$1.26 $1.46 $1.67 $1.93 $2.21 $2.53
Terminal value = $2.53 / (.1348 - .05) = $29.83
6.
What is the equity value of the firm right now (in millions)? (Note the question is not asking for firm
value)
Present Value of FCFF = $1.26 + $1.46 + $1.67 + $1.93 + $2.21 + $29.83
1.1348 1.13482 1.13483 1.13484 1.13485 1.13485
= $1.11 + $1.13 + $1.14 + $1.16 + $1.17 + $15.85
= $21.56
Value of Equity = $21.56 (MV of the firm) - $5 (MV of debt) = $16.56
Q7-Q10 are based on the following information:
Y, Inc. has no debt right now. You project that this company can generate EBIT of 8
million per year for the next few years. There is no depreciation. You plan to attempt a
leveraged buyout of this company. Your plan is to operate the company for three years and
sell the company then. You think the company can be sold at price to EBIT ratio of 9.5
three years from now. You plan to borrow 60 million in three-year interest only loan and
putting 10 millions of your own equity to buy the company. (Note that the loan is interest
only and you do not plan to retire any debt before you sell the company. Your interest
payment will remain the same for the three years.) The interest rate on the loan is 10% and
the tax rate is 40%.
7.
What will be the selling price of the company in three years (in millions)?
8 * 9.5 = 76
8.
What is the cash flow to the equity investor in the first year (in millions)?
Interest expense = 60 * 10% = 6
CF = (8 – 6)*(1-0.4) = 1.2
9. What is the cash flow to the equity investor in the third year in millions (the final year of the
project, including sale proceeds and loan repayment)?
CF from operation = 1.2
CF from selling and loan repayment = 76 – 60 = 16
Total CF = 1.2 + 16 = 17.2
10. What is the rate of return to you as the equity investor (in percentage)?
All cash flows for the equity investor
0
1
2
3
-10
1.2
1.2
17.2
IRR = 27.4%