Reading 41: Free Cash Flow Valuation-LOS k 习题精选 2010, face, currently, company, center

土豆妮

Session 12: Equity Investments: Valuation Models
Reading 41: Free Cash Flow Valuation

LOS k: Calculate the value of a company using the stable-growth, two-stage, and three-stage FCFF and FCFE models.

 

 

 

 

Industrial Light currently has:

• Free cash flow to equity = $4.0 million.
• Cost of equity = 12%.
• Weighted average cost of capital = 10%.
• Total debt = $30.0 million.
• Long-term expected growth rate = 5%. 

What is the value of equity?> >

 

A) $57,142,857.

B) $60,000,000.

C) $27,142,857.

---

 

The value of equity is [($4,000,000)(1.05) / (0.12 – 0.05)] = $60,000,000.

土豆妮

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%, a weighted average cost of capital of 14%, and total outstanding debt of $30.00 per share, what is the current value of equity?

A) $41.54.

B) $71.74.

C) $74.10.

---

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

土豆妮

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

A) $1,177M.

B) $1,043M.

C) $1,077M.

---

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

土豆妮

Which of the following is the least likely reason for Carson’s decision to use FCFE in valuing Overhaul rather than FCFF?

A) Overhaul’s capital structure is stable.

B) FCFE is an easier and more straightforward calculation than FCFF.

C) Overhaul’s debt ratio is significantly higher than the industry average.

---

The difference between FCFF and FCFE is related to capital structure and resulting interest expense. When the company’s capital structure is relatively stable, FCFE is easier and more straightforward to use. FCFF is generally the best choice when FCFE is negative or the firm is highly leveraged. The fact that Overhaul’s debt ratio is significantly higher than the industry average would argue against the use of FCFE. Hence, this is the least likely reason to favor FCFE. (Study Session 12, LOS 42.b, n)

---

Assuming that Carson is using May 1, 2005 as his date of valuation, what is the estimated value of the firm’s equity under the scenario most suited to using the two-stage FCFE method?

A) $173.3 million.

B) $125.2 million.

C) $129.5 million.

---

The “sustained-growth” scenario is the only scenario suitable for using the two-stage method, in part because the “high-growth” scenario uses three different required rates of return.

First, we need to calculate estimated FCFE in 2006.

FCFF = NI + NCC + [Int × (1 ? tax rate)] ? FCInv ? WCInv
= 16.9 + 80 + [34 × (1 - 0.35)] – [(480 - 240) - (400 - 160) + 80] – [(55 - 70) - (50 - 50)]
= 16.9 + 80 + 22.1 – 80 – (?15)
= 54

FCFE = FCFF – [Int × (1 - tax rate)] + Net Borrowing
= 54 – [34 × (1 - .35)] + (?26.9)
= 54 – 22.1 – 26.9
= $5 million in 2006

Having calculated FCFE in 2006, we can calculate FCFE for 2007 through 2011 using the growth rates provided:

	2007	2008	2009	2010	2011
Growth in FCFE	40.0%	15.7%	8.6%	9.1%	8.3%
Implied level of FCFE (in millions)	$7.0	$8.1	$8.8	$9.6	$10.4

Now that we know FCFE, we can discount future FCFE back to the present at the cost of equity.

In the first stage of the two-stage model, we determine the terminal value at the start of the constant growth period as follows:

Terminal Value = (10.4 × 1.06)/(0.12 - 0.06) = $183.733 million.

In the second stage, we discount FCFE for the first six years and the terminal value to the present.

Equity Value = [5.0 / (1.12)¹] + [7.0 / (1.12)²] + [8.1 / (1.12)³] + [8.8 / (1.12)⁴] + [9.6 / (1.12)⁵] + [(10.4 + 183.7333) / (1.12)⁶]
Equity Value = 4.46 + 5.58 + 5.77 + 5.59 + 5.45 + 98.35
Equity Value = $125.20 million

(Study Session 12, LOS 42.k)

---

土豆妮

 

Industrial Light currently has:

• Expected free cash flow to the firm in one year = $4.0 million.
• Cost of equity = 12%.
• Weighted average cost of capital = 10%.
• Total debt = $30.0 million.
• Long-term expected growth rate = 5%. 

What is the value of equity?> >

A) $80,000,000.

B) $50,000,000.

C) $44,440,000.

---

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.

土豆妮

 

The following information was collected from the financial statements of Bankers Industrial Corp. for the year ended December 31, 2000.

• Earnings before interest and taxes (EBIT) = $6 million.

• Capital expenditures = $1.25 million.

• Depreciation expense = $0.63 million.

• Working capital additions = $0.59 million.

• Cost of debt = 10.5%.

• Cost of equity = 16%.

• Growth rate = 7%.

Bankers is currently operating at their target debt ratio of 40%. The firm’s tax rate is 40%.

The free cash flow to the firm (FCFF) for the current year is:

A) $3.57 million.

B) $2.39 million.

C) $2.31 million.

---

The FCFF for the current year is $2.39m = [$6.0m(1 ? 0.40)] + $0.63m ? $1.25m ? $0.59m.

---

The appropriate discount rate used in valuing Bankers using FCFF will be:

A) 16.00%.

B) 12.12%.

C) 6.30%.

---

The appropriate discount rate to be used is the weighted average cost of capital (WACC), and this is 12.12% = (0.60 × 0.16) + [0.40 × 0.105 × (1 ? 0.40)].

---

The estimated value of the firm is:

A) $37.61 million.

B) $46.68 million.

C) $49.95 million.

---

The value of Bankers using stable-growth FCFF model is $49.95 million, calculated as:

FCFF = $2.39m = [$6.0m(1 ? 0.40)] + $0.63m ? $1.25m ? $0.59m.

WACC = 12.12% = (0.60 × 0.16) + [0.40 × 0.105 × (1 × 0.40)].

Estimated value = $49.95 million = ($2.39m × 1.07) / (0.1212 ? 0.07)

土豆妮

The following table provides background information on a per share basis for TOY, Inc., in the year 0:

Current Information	Year 0
Earnings	$5.00
Capital Expenditures	$2.40
Depreciation	$1.80
Change in Working Capital	$1.70

TOY, Inc.'s, target debt ratio is 30% and has a required rate of return of 12%. Earnings, capital expenditures, depreciation, and working capital are all expected to grow by 5% a year in the future.

In year 1, what is the forecasted free cash flow to equity (FCFE) for TOY, Inc.?

A) $4.53.

B) $3.56.

C) $4.31.

---

Earnings = 5 × 1.05 = 5.25, capital expenditures = 2.4 × 1.05 = 2.52, deprecation = 1.8 × 1.05 = 1.89, change in working capital = 1.7 × 1.05 = 1.785, FCFE = Earnings per share ? (Capital Expenditures ? Depreciation)(1 ? Debt Ratio) ? (Change in working capital)(1 ? Debt Ratio) = 5.25 ? (2.52 ? 1.89)(1 ? 0.3) ? (1.785)(1 ? 0.3) = 3.56.

---

What is the value of TOY, Inc.'s, stock given the above assumptions?

A) $50.86.

B) $61.57.

C) $64.71.

---

The value of the stock = FCFE₁ / (r ? g_n) = 3.56 / (0.12 ? 0.05) = 50.86.

土豆妮

The following information was collected from the financial statements of the Hiller Corp. for the year ending December 31, 2000: 

• Earnings per share = $4.50.

• Capital Expenditures per share = $3.00.

• Depreciation per share = $2.75.

• Increase in working capital per share = $0.75.

• Debt financing ratio = 30%.

• Cost of equity = 12%.

The financial leverage for the firm is expected to be stable.

The FCFE for the base-year will be:

A) $3.00.

B) $4.85.

C) $3.80.

---

Base-year FCFE = EPS ? (capital expenditures ? depreciation) × (1 ? debt ratio) ? increase in working capital × (1 ? debt ratio) = $ 4.50 ? ($3.00 ? $2.75)(1 ? 0.30) ? $0.75(1 ? 0.30) = $3.80.

---

 If earnings, capital expenditures, depreciation and working capital are all expected to grow constantly at 5%, the value per share using stable-growth FCFE model will be:

A) $57.00.

B) $72.75.

C) $54.29.

---

Value per share = $57.00 = ($3.80 × 1.05) / (0.12 ? 0.05).

土豆妮

The value of stock under the two-stage FCFE model will be equal to:

A) present value (PV) of FCFE during the extraordinary growth period plus the PV of terminal value.

B) present value (PV) of FCFE during the extraordinary growth period plus the terminal value.

C) present value (PV) of FCFE during the extraordinary growth and transitional periods plus the PV of terminal value.

---

The value of stock under the two-stage FCFE model will be equal to the present value of FCFE during the extraordinary growth period plus the present value of the terminal value at the end of this period.

土豆妮

A firm's free cash flow to equity (FCFE) in the most recent year is $50M and is expected to grow at 5% per year forever. If its shareholders require a return of 12%, the value of the firm's equity using the single-stage FCFE model is:

A) $417M.

B) $750M.

C) $714M.

---

The value of the firm's equity is: $50M × 1.05 / (0.12 ? 0.05) = $750M