上一主题:Reading 41: Free Cash Flow Valuation-LOS l 习题精选
下一主题:Reading 41: Free Cash Flow Valuation-LOS j 习题精选
返回列表 发帖

Reading 41: Free Cash Flow Valuation-LOS k 习题精选

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.

Ashley Winters, CFA, has been hired to value Goliath Communications, a company that is currently undergoing rapid growth and expansion. Ashley is an expert in the communications industry and has had extensive experience in valuing similar firms. She is convinced that a value for the equity of Goliath can be reliably obtained through the use of a three-stage free cash flow to equity (FCFE) model with declining growth in the second stage. Based on up-to-date financial statements, she has determined that the current FCFE per share is $0.90. Ashley has prepared a forecast of expected growth rates in FCFE as follows:

Stage 1: 10.5% for years 1 through 3
Stage 2: 8.5% in year 4, 6.5% in year 5, 5% in year 6
Stage 3: 3% in year 7 and thereafter
Moreover, she has determined that the company has a beta of 1.8, the current risk-free rate is 3%, and the equity risk premium is 5%.

The required return and terminal value in year 6 are closest to:

Required return

Terminal value in year 6

A)

12%

$16.867

B)

9%

$16.867

C)

12%

$12.650




Based on the CAPM we can estimate a required return on equity as:

Required return = 3% + 1.8(5%) = 12%



Estimates for the future FCFE based on supplied growth rates are:
Year

1

2

3

4

5

6

7

Growth rate

10.5%

10.5%

10.5%

8.5%

6.5%

5%

3%

FCFE/share

$0.995

$1.099

$1.214

$1.318

$1.403

$1.473

$1.518

R$ = 1.518/(12% × 3%) = 16.867


The per-share value Winters should assign to Goliath’s equity is closest to:

A)
$20.24.
B)
$13.55.
C)
$16.87.



We find the value of the equity/share by discounting all future FCFE/share by the required rate of return on equity.

Using the calculator, enter CF0 = 0; C01 = 0.995; C02 = 1.099; C03 = 1.214; C04 = 1.318; C05 = 1.403; C06 = 1.473 + 16.867 = 18.34; I = 12; Compute →?NPV = 13.55.

TOP

Starshah Industries competes in a high-growth, emerging technology sector that is facing increasing competitive pressures. So far, the firm has been performing well, earning $4.55 per share in 2004. Investment requirements were high, with capital expenditures of $1.75 per share, depreciation expense of $1.05, and a net investment in working capital that year of $1.00 per share. However, despite Starshah’s high growth rate and impressive profitability, Starshah’s Chairman, Lorenzo di Stefano, has become concerned about the impact that a slowdown in expected growth may have on the firm’s valuation.

Di Stefano asked Starshah’s Director of Strategic Planning, Keisha Simmons, to make a presentation to Starshah’s board at the end of 2004 about the future growth of the firm. The news was sobering. Simmons told the board members that Starshah could expect two more years of rapid growth, during which time earnings per share could be expected to rise 45% per year with 30% annual increases in capital spending and depreciation. During this high-growth period, Simmons estimates that the required return on equity for Starshah will be 25%. Starshah consistently maintains a target debt ratio of 0.25.

After the near-term spurt of high growth, however, she and her group expect Starshah to move eventually to a stable growth period. During the stable growth period, free cash flow to equity (FCFE) will rise only 5% per year and the annual return to shareholders will decline to 10%.

The strategy group expects the transitional period between high-growth and mature growth to last five years. During that time, capital expenditures will rise only 8% per year, with depreciation rising 13% per year. The growth in earnings should drop by eight percentage points per year, hitting 5% in the fifth year. During this transition, the expected return to shareholders will be 15% per year.

Throughout the high-growth and transitional growth periods, Simmons expects Starshah to be able to limit increases in the investment in working capital to 20 cents per year. In her analysis, the investment in working capital will peak in 2010, declining a dime to $2.10 per share in 2011.

After Simmons’ presentation, the board debated what to do about the incipient slowdown in Starshah’s growth. A majority of the board argued in favor of moving to offset this slowdown in organic growth through a new emphasis on growth by acquisition.

One potential target is TPX. TPX's current and expected FCFE: $425,000 in 2004, $500,000 in 2005, $600,000 the following year, and $700,000 in 2007. After that, Starshah expects FCFE at TPX to grow 3% per year indefinitely. Starshah would require a return on its equity investment of 20% per year in the high-growth stage and 12% per year in the stable growth stage.

Di Stefano and Simmons had a somber meeting the day after the board presentation. But despite the bleak news about future years, di Stefano had convinced himself it was worth staying around through the high-growth and transitional periods. He pointed out to Simmons that, if Simmons’ projections were correct, the value of Starshah’s stock would be in excess of $450 per share by the time the company hit the stable-growth phase. Di Stefano was very pleased with what that implied for the value of his stock options.

Simmons had done the same calculations herself, but she also realized that if required rates of return in 2012 rose from the very modest 10% she used in her board projections to only 15%, that would cut the terminal value of Starshah’s stock in 2011 to only half the level di Stefano was counting on. She considered that valuation too small to make the wait worthwhile. Simmons said nothing to di Stefano, but planned to look for another job.

Which of the following FCFE models is best suited to analyzing TPX?

A)
Stable growth FCFE model.
B)
Three-stage FCFE model.
C)
Two-stage FCFE model.



The two-stage FCFE model is most suited to analyzing TPX because we have specific forecasts for the first several years and then a stable growth pattern into the indefinite future. (Study Session 12, LOS 42.n)


TOP

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.

TOP

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

TOP

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 ? gn) = 3.56 / (0.12 ? 0.05) = 50.86.

TOP

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).

TOP

 

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)

TOP

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)


TOP

 

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.

TOP

返回列表
上一主题:Reading 41: Free Cash Flow Valuation-LOS l 习题精选
下一主题:Reading 41: Free Cash Flow Valuation-LOS j 习题精选