31.A firm's free cash flow to the firm (FCFF) in the most recent year is $80M and is expected to grow at 3 percent per year forever. If the firm has $100M in debt financing and its weighted average cost of capital is 10 percent. The value of the firm's equity using the single-stage FCFF model is:

A)   $1,077M.

B)   $1,043M.

C)   $1,143M.

D)   $1,177M.

32.A firm has projected free cash flow to equity next year of $1.25 per share, $1.55 in two years, and a terminal value of $90.00 two years from now, as well. Given the firm’s cost of equity of 12 percent, a weighted average cost of capital of 14 percent, and total outstanding debt of $30.00 per share, what is the current value of equity?

A)   $71.74.

B)   $90.00.

C)   $41.54.

D)   $74.10.

33.Industrial Light currently has:

§ Expected free cash flow to the firm in one year = $4.0 million.

§ Cost of equity = 12 percent.

§ Weighted average cost of capital = 10 percent.

§ Total debt = $30.0 million.

§ Long-term expected growth rate = 5 percent. 

What is the value of equity?

A)   $80,000,000.

B)   $44,440,000.

C)   $50,000,000.

D)   $14,440,000.

34.Burcar-Eckhardt, a firm specializing in value investments, has been approached by the management of Overhaul Trucking, Inc., to explore the possibility of taking the firm private via a management buyout. Overhaul’s stock has stumbled recently, in large part due to a sudden increase in oil prices. Management considers this an opportune time to take the company private. Burcar would be a minority investor in a group of friendly buyers.

Jaimie Carson, CFA, is a private equity portfolio manager with Burcar. He has been asked by Thelma Eckhardt, CFA, one of the firm’s founding partners, to take a look at Overhaul and come up with a strategy for valuing the firm. After analyzing Overhaul’s financial statements as of the most recent fiscal year-end (presented below), he determines that a valuation using Free Cash Flow to Equity (FCFE) is most appropriate.

Eckhardt agrees with Carson ’s choice of valuation method, but her concern is Overhaul’s debt ratio. Considerably higher than the industry average, Eckhardt worries that the firm’s heavy leverage poses a risk to equity investors. Overhaul Trucking uses a weighted average cost of capital of 12 percent for capital budgeting, and Eckhardt wonders if that’s realistic.

Eckhardt asks Carson to do a valuation of Overhaul in a high-growth scenario to see if optimistic estimates of the firm’s near-term growth rate can justify the required return to equity. For the high-growth scenario, she asks him to start with his 2006 estimate of FCFE, grow it at 30 percent per year for three years and then decrease the growth rate in FCFE in equal increments for another three years until it hits the long-run growth rate of 3 percent in 2012. Eckhardt tells Carson that the returns to equity Burcar-Eckhardt would require are 20 percent until the completion of the high-growth phase, 15 percent during the three years of declining growth, and 10 percent thereafter. Eckhardt wants to know what Burcar could afford to pay for a 15 percent stake in Overhaul in this high-growth scenario.

Carson assembles a few spreadsheets and tells Eckhardt, “We could make a bid of just under $16 million for the stake in Overhaul if the high-growth scenario plays out.” Eckhardt worries, though, that the value of their bid is extremely sensitive to the assumption for terminal growth, since in that scenario, the terminal value of the firm accounts for slightly more than two-thirds of the total value.

Carson agrees, and proposes doing a valuation under a “sustained growth” scenario. His estimates show Overhaul growing FCFE by the following amounts:

In this scenario, he would project sustained growth of 6 percent per year in 2012 and beyond. With the more stable growth pattern in cash flow, Eckhardt and Carson agree that the required return to equity could be cut to a more moderate 12 percent.

Carson also decides to try valuing the firm on Free Cash Flow to the Firm (FCFF) using this same 12 percent required return. Using a single-stage model on the estimated 2006 figures presented in the financial statements above, he comes up with a valuation of $1.08 billion.

One of the differences between FCFE and FCFF is that FCFF includes adjustments to revenue for all of the following EXCEPT:

A)   interest payments to bondholders.

B)   operating expenses.

C)   fixed capital investment.

D)   working capital investment.

答案和详解如下：

31.A firm's free cash flow to the firm (FCFF) in the most recent year is $80M and is expected to grow at 3 percent per year forever. If the firm has $100M in debt financing and its weighted average cost of capital is 10 percent. The value of the firm's equity using the single-stage FCFF model is:

A)   $1,077M.

B)   $1,043M.

C)   $1,143M.

D)   $1,177M.

The correct answer was A)

The value of the firm's equity is equal to the value of the firm minus the value of the debt. Firm value = $80M x 1.03/(0.10 - 0.03) = $1,177M, so equity value is $1,177M - $100M = $1,077M.

32.A firm has projected free cash flow to equity next year of $1.25 per share, $1.55 in two years, and a terminal value of $90.00 two years from now, as well. Given the firm’s cost of equity of 12 percent, a weighted average cost of capital of 14 percent, and total outstanding debt of $30.00 per share, what is the current value of equity?

A)   $71.74.

B)   $90.00.

C)   $41.54.

D)   $74.10.

The correct answer was D)

Value of equity = $1.25/(1.12)¹ + $1.55/(1.12)² + $90.00/(1.12)² = $74.10

33.Industrial Light currently has:

§ Expected free cash flow to the firm in one year = $4.0 million.

§ Cost of equity = 12 percent.

§ Weighted average cost of capital = 10 percent.

§ Total debt = $30.0 million.

§ Long-term expected growth rate = 5 percent. 

What is the value of equity?

A)   $80,000,000.

B)   $44,440,000.

C)   $50,000,000.

D)   $14,440,000.

The correct answer was C)

The overall value of the firm is $4,000,000 / (0.10 – 0.05) = $80,000,000. Thus, the value of equity is $80,000,000 – $30,000,000 = $50,000,000.

34.Burcar-Eckhardt, a firm specializing in value investments, has been approached by the management of Overhaul Trucking, Inc., to explore the possibility of taking the firm private via a management buyout. Overhaul’s stock has stumbled recently, in large part due to a sudden increase in oil prices. Management considers this an opportune time to take the company private. Burcar would be a minority investor in a group of friendly buyers.

Jaimie Carson, CFA, is a private equity portfolio manager with Burcar. He has been asked by Thelma Eckhardt, CFA, one of the firm’s founding partners, to take a look at Overhaul and come up with a strategy for valuing the firm. After analyzing Overhaul’s financial statements as of the most recent fiscal year-end (presented below), he determines that a valuation using Free Cash Flow to Equity (FCFE) is most appropriate.

Overhaul Trucking, Inc. Income Statement April 30, 2005 (Millions of dollars)
	2005	2006E
Sales	300.0	320.0
Gross Profit	200.0	190.0
SG&A	50.0	50.0
Depreciation	70.0	80.0
EBIT	80.0	60.0
Interest Expense	30.0	34.0
Taxes (at 35 percent)	17.5	9.1
Net Income	32.5	16.9

Overhaul Trucking, Inc. Balance Sheet April 30, 2005 (Millions of dollars)
	2005	2006E
Cash	10.0	15.0
Current Assets	50.0	55.0
Gross Property, Plant & Equip.	400.0	480.0
Accumulated Depreciation	(160.0)	(240.0)
Total Assets	300.0	310.0
Accounts Payable	50.0	70.0
Long-Term Debt	140.0	113.1
Common Stock	80.0	80.0
Retained Earnings	30.0	46.9
Total Liabilities & Equity	300.0	310.0

Eckhardt agrees with Carson ’s choice of valuation method, but her concern is Overhaul’s debt ratio. Considerably higher than the industry average, Eckhardt worries that the firm’s heavy leverage poses a risk to equity investors. Overhaul Trucking uses a weighted average cost of capital of 12 percent for capital budgeting, and Eckhardt wonders if that’s realistic.

Eckhardt asks Carson to do a valuation of Overhaul in a high-growth scenario to see if optimistic estimates of the firm’s near-term growth rate can justify the required return to equity. For the high-growth scenario, she asks him to start with his 2006 estimate of FCFE, grow it at 30 percent per year for three years and then decrease the growth rate in FCFE in equal increments for another three years until it hits the long-run growth rate of 3 percent in 2012. Eckhardt tells Carson that the returns to equity Burcar-Eckhardt would require are 20 percent until the completion of the high-growth phase, 15 percent during the three years of declining growth, and 10 percent thereafter. Eckhardt wants to know what Burcar could afford to pay for a 15 percent stake in Overhaul in this high-growth scenario.

Carson assembles a few spreadsheets and tells Eckhardt, “We could make a bid of just under $16 million for the stake in Overhaul if the high-growth scenario plays out.” Eckhardt worries, though, that the value of their bid is extremely sensitive to the assumption for terminal growth, since in that scenario, the terminal value of the firm accounts for slightly more than two-thirds of the total value.

Carson agrees, and proposes doing a valuation under a “sustained growth” scenario. His estimates show Overhaul growing FCFE by the following amounts:

	2007	2008	2009	2010	2011
Growth in FCFE	40.0%	15.7%	8.6%	9.1%	8.3%

In this scenario, he would project sustained growth of 6 percent per year in 2012 and beyond. With the more stable growth pattern in cash flow, Eckhardt and Carson agree that the required return to equity could be cut to a more moderate 12 percent.

Carson also decides to try valuing the firm on Free Cash Flow to the Firm (FCFF) using this same 12 percent required return. Using a single-stage model on the estimated 2006 figures presented in the financial statements above, he comes up with a valuation of $1.08 billion.

One of the differences between FCFE and FCFF is that FCFF includes adjustments to revenue for all of the following EXCEPT:

A)   interest payments to bondholders.

B)   operating expenses.

C)   fixed capital investment.

D)   working capital investment.

The correct answer was A)

FCFF includes the cash available to all of the firm’s investors, including bondholders. Therefore, interest payments to bondholders are not removed from revenues to derive FCFF. FCFE is FCFF minus interest payments to bondholders plus net borrowings from bondholders.