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Chapter 7: Merger and Acquisition Cash Flow Valuation Basics
Answers to End of Chapter Discussion Questions
7.1 What is the significance of the weighted average cost of capital? How is it calculated? Do the weights
reflect the firm’s actual or target debt to total capital ratio? Why?
Answer: The weighted average cost of capital (WACC) is a broader measure than the cost of equity and
represents the return a firm must earn in order to induce investors to buy its stock and bonds. The WACC
7.2 What does a firm’s ß measure? What is the difference between an unlevered and levered ß? Why is this
distinction significant?
Answer: A beta coefficient () is a measure of nondiversifiable risk or the extent to which a firm’s (or
asset’s) return changes due to a change in the market’s return. It is a measure of the risk of a stock’s
7.3 Under what circumstances is it important to adjust the Capital Asset Pricing Model for firm size? Why?
7.4 What are the primary differences between FCFE and FCFF?
Answer: Free cash flow to the firm represents cash available to satisfy all investors holding claims against
the firm’s resources. In the FCFF formulation, there is no effort to adjust for payments of interest or
7.5 Explain the conditions under which it makes most sense to use the zero growth and constant growth DCF
models. Be specific.
Answer: While often overly simplistic, the zero-growth model may be used because it is the most easily
7.6 Which discounted cash flow valuation methods require the estimation of a terminal value? Why?
Answer: The variable growth model, which consists of the present value of the annual cash flows projected
7.7 Do small changes in the assumptions pertaining to the estimation of the terminal value have a significant
impact on the calculation of the total value of the target firm? If so, why?
Answer: Yes, small changes in the discount rate or terminal period growth rate can have dramatic changes
7.8 How would you estimate the equity value of a firm if you knew its enterprise value and the present value of
all non-operating assets, non-operating liabilities, and long-term debt?
7.9 Why is it important to distinguish between operating and on-operating assets and liabilities when valuing a
firm? Be specific.
Answer: Operating assets and liabilities are directly associated with generating a firm’s free cash flow.
Free cash flow is subsequently projected and discounted at the firm’s cost of capital to estimate the firm’s
7.10 Explain how you would value a patent under the following situations: a patent without any current
application, a patent linked to an existing product, and a patent portfolio.
Answer: Many firms have patents for which no current application within the firm has yet been identified.
However, the patent may have value to an external party. Prior to closing, the buyer and seller may
Answers to End of Chapter Practice Problems
7.11 ABC Incorporated shares are currently trading for $32 per share. The firm has 1.13 billion shares
outstanding. In addition, the market value of the firm’s outstanding debt is $2 billion. The 10-year
Treasury bond rate is 6.25%. ABC has an outstanding credit record and has earned an AAA rating from the
major credit rating agencies. The current interest rate on AAA corporate bonds is 6.45%. The historical
risk premium for stocks over the risk-free rate of return is 5.5 percentage points. The firm’s beta is
estimated to be 1.1 and its marginal tax rate, including federal, state, and local taxes is 40%.
a. What is the cost of equity?
b. What is the after-tax cost of debt?
c. What is the cost of capital?
Answers:
a. 12.3%
7.12 HiFlyer Corporation does not currently have any debt. Its tax rate is .4 and its unlevered beta is estimated
by examining comparable companies to be 2.0. The 10-year Treasury bond rate is 6.25% and the historical
risk premium over the risk free rate is 5.5%. Next year, HiFlyer expects to borrow up to 75% of its equity
value to fund future growth.
a. Calculate the firm’s current cost of equity.
b. Estimate the firm’s cost of equity after it increases its leverage to 75% of equity?
Answers:
7.13 Abbreviated financial statements are given for Fletcher Corporation in the following table:
2010
2011
Revenues
$600.0
$690.0
Operating expenses
520.0
600.0
Depreciation
16.0
18.0
Earnings before
interest and taxes
64.0
72.0
Less Interest Expense
5.0
5.0
Less: Taxes
23.6
26.8
Equals: Net income
35.4
40.2
Addendum:
Yearend working
capital
150
200
Principal repayment
25.0
25.0
Capital expenditures
20
10
Yearend working capital in 2009 was $160 million and the firm’s marginal tax rate is 40% in both 2010
and 2011. Estimate the following for 2010 and 2011:
a. Free cash flow to equity.
b. Free cash flow to the firm.
Answers:
a. $16.4 million in 2010 and $(26.8) million in 2011
b. $44.4 million in 2010 and $1.2 million in 2011
7.14 No Growth Incorporated had operating income before interest and taxes in 2011 of $220 million. The firm
was expected to generate this level of operating income indefinitely. The firm had depreciation expense of
$10 million that same year. Capital spending totaled $20 million during 2011. At the end of 2010 and
2011, working capital totaled $70 and $80 million, respectively. The firm’s combined marginal state, local,
and federal tax rate was 40% and its debt outstanding had a market value of $1.2 billion. The 10-year
Treasury bond rate is 5% and the borrowing rate for companies exhibiting levels of creditworthiness similar
to No Growth is 7%. The historical risk premium for stocks over the risk free rate of return is 5.5%. No
Growth’s beta was estimated to be 1.0. The firm had 2,500,000 common shares outstanding at the end of
2011. No Growth’s target debt to total capital ratio is 30%.
a. Estimate free cash flow to the firm in 2011.
b. Estimate the firm’s cost of capital.
c. Estimate the value of the firm (i.e., includes the value of equity and debt) at the end of 2011,
assuming that it will generate the value of free cash flow estimated in (a) indefinitely.
d. Estimate the value of the equity of the firm at the end of 2011.
e. Estimate the value per share at the end of 2011.
Answers:
a. $112 million
7.15 Carlisle Enterprises, a specialty pharmaceutical manufacturer, has been losing market share for three years
since several key patents have expired. The free cash flow to the firm in 2002 was $10 million. This figure
is expected to decline rapidly as more competitive generic drugs enter the market. Projected cash flows for
the next five years are $8.5 million, $7.0 million, $5 million, $2.0 million, and $.5 million. Cash flow after
the fifth year is expected to be negligible. The firm’s board has decided to sell the firm to a larger
pharmaceutical company interested in using Carlisle’s product offering to fill gaps in its own product
offering until it can develop similar drugs. Carlisle’s cost of capital is 15%. What purchase price must
Carlisle obtain to earn its cost of capital?
Answer: $17.4 million
7.16 Ergo Unlimited’s current year’s free cash flow is $10 million. It is projected to grow at 20% per year for
the next five years. It is expected to grow at a more modest 5% beyond the fifth year. The firm estimates
that its cost of capital is 12% during the next five years and then will drop to 10% beyond the fifth year as
the business matures. Estimate the firm’s current market value.
Answer: $358.30
PV1-5 = 10(1.2)/1.12 + 10(1.2)2/1.122 + 10(1.2)3/1.123 + 10(1.2)4/1.124 + 10(1.2)5/1.125
7.17 In the year in which it intends to go public, a firm has revenues of $20 million and net income after taxes of
$2 million. The firm has no debt, and revenue is expected to grow at 20% annually for the next five years
and 5% annually thereafter. Net profit margins are expected remain constant throughout. Capital
expenditures are expected to grow in line with depreciation and working capital requirements are minimal.
The average beta of a publicly traded company in this industry is 1.50 and the average debt/equity ratio is
20%. The firm is managed very conservatively and does not intend to borrow through the foreseeable
future. The Treasury bond rate is 6% and the tax rate is 40%. The normal spread between the return on
stocks and the risk free rate of return is believed to be 5.5%. Reflecting the slower growth rate in the sixth
year and beyond, the firm’s discount rate is expected to decline to the industry average cost of capital of
10.4%. Estimate the value of the firm’s equity.
a. u (unlevered beta) for comparable firms = ____l_____ = ___1.5___ = 1.5 = 1.34
(1 + D/E (1-t)) (1 + .2 x .6) 1.12
7.18 The following information is available for two different common stocks: company A and Company B.
Company A
Company B
Free cash flow per share
in the current year
$1.00
$5.00
Growth rate in cash flow
per share
8%
4%
Beta
1.3
.8
Risk-free return
7%
7%
Expected return on all
stocks
13.5%
13.5%
a. Estimate the cost of equity for each firm.
b. Assume that the companies’ growth rates will continue at the same rate indefinitely. Estimate the
per share value of each companies common stock.
Answer:
a. 15.45%
Answer:
a. Company A: 7 + 1.3 (13.5-7) = 7+8.45=15.45%
7.19 You have been asked to estimate the beta of a high-technology firm, which has three divisions with the
following characteristics.
Division
Beta
Market Value
Personal Computers
1.6
$100 million
Software
2.00
$150 million
Computer Mainframes
1.2
$250 million
a. What is the beta of the equity of the firm?
b. If the risk free return is 5% and the spread between the return on all stocks is 5.5%, estimate the
cost of equity for the software division?
c. What is the cost of equity for the entire firm?
d. Free cash flow to equity investors in the current year (FCFE) for the entire firm is $7.4 million
and for the software division is $3.1 million. If the total firm and the software division are
expected to grow at the same 8% rate into the foreseeable future, estimate the market value of the
firm and of the software division.
Answer:
a. 1.52
Answer:
a. Beta = 1.6 x 100/500 + 2.00 x 150/500 + 1.2 x 250/500 =1.52
7.20 Financial Corporation wants to acquire Great Western Inc. Financial has estimated the enterprise value of
Great Western at $104 million. The market value of Great Western’s long-term debt is $15 million, and
cash balances in excess of the firm’s normal working capital requirements are $3 million. Financial
estimates the present value of certain licenses that Great Western is not currently using to be $4 million.
Great Western is the defendant in several outstanding lawsuits. Financial Corporation’s legal department
estimates the potential future cost of this litigation to be $3 million, with an estimated present value of $2.5
million. Great Western has 2 million common shares outstanding. What is the value of Great Western per
common share?
End of Chapter Case Study
Did United Technologies Overpay for Rockwell Collins?
Discussion Questions and Solutions:
1. Estimate the firm's cost of equity and after tax cost of debt.
Answer: Using the capital asset pricing model (ke = Rf +
(Rm – Rf)), Rockwell Collins' cost of equity is
2. Estimate the firm's weighted average cost of capital. (Hint: Recall that the debt-to-total capital ratio is
equal to the debt-to-equity ratio divided by one plus the debt-to-equity ratio.)
Answer: Debt-to-total capital ratio = 1.39 / (1 + 1.39) = 1.39 / 2.39 = .5816 x 100 = 58.2%
3. What is the WAAC beyond 2022?
4. Use the discounted cash flow method to determine the standalone value for Rockwell Collins. Show your
work.
Year
FCFF
($Millions)
Present Value
Interest Factor
Present Value
($Millions)
2017
750
2018
802.5
.9509
763.10
2020
918.7
.8599
789.99
2022
1051.9
.7776
817.96
5. Assuming the free cash flows from synergy will remain level in perpetuity, estimate the after-tax present
value of anticipated synergy?
6. What is the maximum purchase price United Technologies should pay for Rockwell Collins? Did United
Technologies overpay?
7. How might your answer to Question 5 change if the discount rate during the first five years and during the
terminal period is the same as estimated in Question 2?
Terminal Value = $817.96 x (1.02) / (.0516 - .02) = $26,402.51 = $20,530.72
8. What are the limitations of the discounted cash flow method employed in this case study?
Answer: The valuation is heavily dependent on the choice of assumptions concerning growth rates during
Examination Questions and Answers
True and False Questions: Answer true or false to the following questions: (Circle True or False)
1. In calculating the weighted average cost of capital, the weights should be estimated using the market value of
the target firm’s debt and equity. True or False
2. A beta coefficient is a measure of a firm’s diversifiable risk. True or False
3. In the absence of debt, the unlevered beta measures the volatility of the firm’s financial return to changes in the
general stock market’s overall return. True or False
4. Free cash flow to the firm is calculated before debt and taxes. True or False
5. Free cash flow to equity is calculated using operating income. True or False
6. If free cash flow to the firm is expected to remain at $10 million indefinitely and the firm’s cost of equity is .10,
the present value of the firm is $100 million. True or False
7. The constant growth valuation model is primarily applicable to firms in mature markets. True or False
8. The estimation of present value using the constant growth model involves the calculation of a terminal value.
True or False
9. It is possible to determine the equity value of the firm if you know the present value of free cash flow to the
firm and the book value of the firm’s outstanding shares. True or False
10. The discounted cash flow method for valuing a firm adjusts for differences in the magnitude and timing of cash
flows and for risk.
True or False
11. The cost of equity is the minimum financial return required by investors to invest in stocks of comparable risk.
True or False
12. The capital asset pricing model is commonly used to estimate the cost of equity. True or False
13. Interest payments are tax deductible to firms in the U.S. True or False
14. A firm’s beta is affected by the amount of debt a firm maintains relative to its equity. True or False
15. Free cash flow to the firm is also called enterprise cash flow. True or False
16. A risk-free rate of return is one for which the expected return is certain. True or False
17. If an investor anticipates a future cash flow stream of five or ten years, she needs to use either a five- or ten-
year Treasury bond rate as the risk-free rate. True or False
18. Studies show that it is generally unnecessary to adjust the capital asset pricing model for the size of the firm
. True or False
19. The size factor used to adjust the capital asset pricing model serves as a proxy for factors such as smaller firms
being subject to higher default risk and generally being less liquid than large capitalization firms. True or
False
20. Preferred stock exhibits some of the characteristics of long-term debt in that its dividend is generally constant
and preferred stockholders are paid before common shareholders in the event the firm is liquidated. True or
False
21. Viewing preferred dividends as paid in perpetuity, the cost of preferred stock can be calculated as dividends
per share of preferred stock divided by the market value of the preferred stock. True or False
22. The weighted average cost of capital consists only of debt and equity. True or False
23. The after-tax cost of borrowed funds to the firm is estimated by multiplying the pretax interest rate, i, by (1 –
t), where t is the marginal tax rate for the firm. True or False
24. The weights used to calculate the weighted average cost of capital for a firm with common equity and debt
only represent the book value of equity and debt. True or False
25. The cost of capital formula can be generalized to include hybrid sources of funds available to firms such as
convertible preferred and debt. True or False
26. According to the capital asset pricing model, risk consists of both diversifiable and non-diversifiable
components. True or False
27. Both public and private firms are subject to non-diversifiable risk. True or False
28. In the absence of debt, measures the volatility of a firm’s financial return to changes in the general
market’s overall financial return. True or False
29. Net debt is defined as all of the firm’s interest bearing debt less the value of cash and marketable securities.
True or False
30. When the firm increases its debt in direct proportion to the market value of its equity, the level of the debt is
perfectly correlated with the firm’s market value. True or False
31. Beta is a measure of non-diversifiable risk. True or False
32. Free cash flow to the firm is often called enterprise cash flow. True or False
33. The enterprise or free cash flow to the firm approach to valuation discounts the after-tax free cash flow
available to the firm from operations at the weighted average cost of capital to obtain the enterprise value.
True or False
34. The constant growth model is most applicable to firms in mature markets. True or False
35. The variable growth model would be most appropriate for valuing firms in the growth phase of their
product life cycle. True or False
36. Growth rates can be calculated based on the historical experience of the firm or industry. True or False
37. Intuition suggests that the length of the high-growth period when applying the variable growth model
should be shorter the greater the current growth rate of the firm’s cash flow. True or False
38. When cash flow is temporarily depressed due to strikes, litigation, warranty claims, or other one-time
events, it is generally safe to assume that cash flow will recover in the near term. True or False
39. The projected cash flow of firms in highly cyclical industries can be distorted depending on where the firm
is in the business cycle. True or False
40. The constant growth model may be used to estimate the risk premium component of the cost of equity as an
alternative to relying on historical information as is done in the capital asset pricing model. True or False
41. Discounted cash flow and the asset-oriented valuation methods necessarily provide identical results. True
or False
42. Investors require a minimum rate of return on an investment to compensate them for the level of perceived
risk associated with that investment. True or False
43. The cost of equity can also be viewed as an opportunity cost. True or False
44. For a return to be considered risk-free over some future time period it must be free of default risk and there
must not be any uncertainty about the reinvestment rate (i.e., the rate of return that can be earned at the end
of the investor’s holding period).
True or False
45. Whether an analyst should use a short or long-term interest rate for the risk free rate in calculating the
CAPM depends on when the investor receives their future cash flows. True or False
46. A three-month Treasury bill rate is not free of risk for a five- or ten-year period, since interest and principal
received at maturity must be reinvested at three month intervals. True or False
47. The market risk or equity premium refers to the additional rate of return in excess of the weighted average
cost of capital that investors require to purchase a firm’s equity. True or False
48. Betas do not vary over time and are quite insensitive to the time period and methodology employed in their
estimation. True or False
49. Studies show that the market risk premium is unstable, lower during periods of prosperity and higher
during periods of economic slowdowns. True or False
50. For firms whose market value is less than $50 million, the adjustment to the CAPM in estimating the cost
of equity can be as large as 2 percentage points. True or False
51. Assume the firm size premium for a firm with a market value of $20 million is 7.2%. Also, assume the risk-
free rate of return, equity premium, and are 5.0%, 5.5%, and 1.75 respectively. The firm’s cost of equity
using the CAPM method adjusted for firm size is 21.8%. True or False
52. A firm’s credit rating is a poor measure of a firm’s default risk. True or False
53. For non-rated firms, the analyst may estimate the pretax cost of debt for an individual firm by comparing
debt-to-equity or total capital ratios, interest coverage ratios, and operating margins with those of similar
rated firms. True or False
54. Preferred dividends are tax deductible to U.S. corporations. True or False
55. The weighted average cost of capital (WACC) is the broadest measure of the firm’s cost of funds and
represents the return that a firm must earn to induce investors to buy its common stock. True or False
56. The relationship between the overall market and a specific firm’s beta may change significantly if a large
sector of stocks that make up the overall index increase or decrease substantially. True or False
57. The reduction in the firm’s tax liability due to the tax deductibility of interest is often referred as a tax
shield. True or False
58. When the firm increases its debt in direct proportion to the market value of its equity, the level of the debt
is perfectly correlated with the firm’s market value. Consequently, the risk associated with the tax shield
(resulting from interest paid on outstanding debt) is the same as that associated with the firm. True or False
59. The effective tax rate is calculated from actual taxes paid based on accounting statements prepared for tax
reporting purposes. True or False
60. Whatever the analyst chooses to do with respect to the selection of a tax rate, it is critical to use the
marginal rate in calculating after-tax operating income in perpetuity. Otherwise, the implicit assumption is
that taxes can be deferred indefinitely. True or False
61. The levered beta reflects the firm’s degree of cyclicality, operating and financial leverage. True or False
62. The unlevered beta reflects the firm’s degree of cyclicality and operating leverage but not financial
leverage. True or False
Multiple Choice Questions (Circle only one alternative)
1. Which one of the following factors is not considered in calculating the firm’s cost of equity?
a. risk free rate of return
b. beta
c. interest rate on corporate debt
d. expected return on equities
e. difference between expected return on stocks and the risk free rate of return
2. Which one of the following factors is not considered in calculating the firm’s cost of capital?
a. cost of equity
b. interest rate on debt
c. the firm’s marginal tax rate
d. book value of debt and equity
e. the firm’s target debt to equity ratio
3. A firm’s leveraged beta reflects all of the following except for
a. unleveraged beta
b. the firm’s debt
c. marginal tax rate
d. the firm’s cost of equity
e. the firm’s equity
4. Which of the following factors is excluded from the calculation of free cash flow to the firm?
a. Principal repayments
b. Operating income
c. Depreciation
d. The change in working capital
e. Gross plant and equipment spending
5. Which of the following is not true about the constant growth valuation model?
a. The firm’s free cash flow is assumed to be unchanged in perpetuity
b. The firm’s free cash flow is assumed to grow at a constant rate in perpetuity
c. Free cash flow is discounted by the difference between the appropriate discount rate and the
expected growth rate of cash flow.
d. The constant growth model is sometimes referred to as the Gordon Growth Model.
e. If the analyst were using free cash flow to the firm, cash flow would be discounted by the firm’s
cost of capital less the expected growth rate in cash flow.
6. Which of the following is not true about the variable growth valuation model?
a. Assumes a high growth period followed by a stable growth period.
b. Assumes that the discount rate during the high and stable growth periods is the same.
c. Is used primarily to evaluate firms in high growth industries.
d. Involves the calculation of a terminal value.
e. The terminal value often comprises a substantial percentage of the total present value of the firm.
7. The cost of capital reflects all of the following except for
a. Cost of equity
b. The firm’s beta
c. The book value of the firm’s debt
d. The after-tax cost of interest paid by the firm
e. The risk free rate of return
8. The calculation of free cash flow to the firm includes all of the following except for
a. Net income
b. Marginal tax rate
c. Change in working capital
d. Gross plant and equipment spending
e. Depreciation
9. The calculation of free cash flow to equity includes all of the following except for
a. Operating income
b. Preferred dividends
c. Change in working capital
d. Gross plant and equipment spending
e. Principal repayments
10. All of the following are true about the marginal tax rate for the firm except for
a. The marginal tax rate in the U.S. is usually about 40%.
b. The effective tax rate is usually less than the marginal tax rate.
c. Once tax credits have been used and the ability to further defer taxes exhausted, the effective rate
can exceed the marginal rate at some point in the future.
d. It is critical to use the effective tax rate in calculating after-tax operating income in perpetuity.
e. It is critical to use the marginal rate in calculating after-tax operating income in perpetuity.
11. For a firm having common and preferred equity as well as debt, common equity value can be estimated in
which of the following ways?
a. By subtracting the book value of debt and preferred equity from the enterprise value of the firm
b. By subtracting the market value of debt from the enterprise value of the firm
c. By subtracting the market value of debt and the market value of preferred equity from the
enterprise value of the firm
d. By adding the market value of debt and preferred equity to the enterprise value of the firm
e. By adding the market value of debt and book value of preferred equity to the enterprise value of
the firm
12. The zero growth model is a special case of what valuation model?
a. Variable growth model
b. Constant growth model
c. Delta growth model
d. Perpetuity valuation model
e. None of the above
13. Which of the following is true of the enterprise valuation model?
a. Discounts free cash flow to the firm by the cost of equity
b. Discounts free cash flow to the firm by the weighted average cost of capital
c. Discounts free cash flow to equity by the cost of equity
