Question

You are trying to evaluate a private firm’s potential as a good investment opportunity. Your mentor at the investment bank you interned during the summer told you to collect information on comparable firms, which will help you find the WACC of the private firm. The private firm has ND/E ratio of 2. The risk free rate is 2%. Market risk premium is 5%. Cost of debt for the private firm is assumed is 6%. The tax rate is 50%. The following table lists the information you have gathered:

Firm	Beta Equity	Equity (Million)	Debt (Million)	Cash (Million)
A	1.3	20	11	6
B	1.1	15	8	2
C	0.9	10	6	3
D	0.8	5	7	2

What is the net debt for firm A?

Q2. Calculate the asset beta for firm D.

Q3. What is the average asset beta you should use combining all the comparable firms?

Q4. What is the equity beta for the private firm?

Q5. What is the cost of equity for the private firm? 0.0/1.0 point (graded) Input the cost of equity for the private firm. （use the result from problem 3） ______ %(keep two decimal points)

Answer 1

(1) Firm A:

Debt = $ 11 million, Cash = $ 6 million

Net Debt = Debt - Cash = 11 - 6 = $ 5 million

(2) For Firm D:

Tax Rate = 50 %, Gross Debt = $ 7 million, Cash = $ 2 million

Net Debt = Gross Debt - Cash = 7 - 2 = $ 5 million

Equity = $ 5 million

Debt to Equity Ratio = DE(D) = 5/5 = 1

Equity Beta = 0.8

Asset Beta (D) = 0.8 / [1+(1-0.5) x 1] = 0.4

(3) Firm B:

Tax Rate = 50 %, Gross Debt = $ 8 million, Cash = $ 2 million

Net Debt = Gross Debt - Cash = 8 - 2 = $ 6 million

Equity = $ 15 million

Debt to Equity Ratio = DE(B) = 6/15 = 2/5 = 0.4

Equity Beta = 1.1

Asset Beta (D) = 1.1 / [1+(1-0.5) x (0.4)] = 0.9167

Firm C:

Tax Rate = 50 %, Gross Debt = $ 6 million, Cash = $ 3 million

Net Debt = Gross Debt - Cash = 6 - 3 = $ 3 million

Equity = $ 10 million

Debt to Equity Ratio = DE(C) = 3/10 = 0.3

Equity Beta = 0.9

Asset Beta (D) = 0.9 / [1+(1-0.5) x (0.3)] = 0.78261

Firm A:

Net Debt = $ 5 million and Equity = $ 20 million

DE(A) = 5/20 = 1/4 = 0.25

Equity Beta = 1.3

Asset Beta = 1.3 / [1+(1-0.5) x (0.25)] = 1.156

Average Asset Beta = [1.156 + 0.4 + 0.9167 + 0.78261] / 4 = 0.81371

(4) Private FIrm:

DE = 2

Asset Beta = Average Asset Beta = 0.81371

Equity Beta = 0.81371 x [1+(1-0.5) x (2)] = 1.62742 ~ 1.63

(5) RIsk-Free Rate = Rf = 2% and Market Risk Premium = MRP = 5 %

Cost of Equity = Rf + Equity Beta x MRP = 2 + 1.63 x 5 = 10.1371 % ~ 10.14 %