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
d. Discounts free cash flow to equity by the weighted average cost of capital
e. None of the above
14. Which of the following is true of the equity valuation model?
a. Discounts free cash flow to the firm by the weighted average cost of capital
b. Discounts free cash flow to equity by the cost of equity
c. Discounts free cash flow the firm by the cost of equity
d. Discounts free cash flow to equity by the weighted average cost of capital
e. None of the above
15. Which of the following is true about the variable growth model?
a. Present value equals the discounted sum of the annual forecasts of cash flow
b. Present value equals the discounted sum of the annual forecasts of cash flow plus the discounted
value of the terminal value
c. Present value equals the discounted value of the next year’s cash flow grown at a constant rate in
perpetuity
d. Present value equals the current year’s free cash flow discounted in perpetuity
e. None of the above
16. When evaluating an acquisition, you should do which of the following:
a. Ignore market values of assets and focus on book value
b. Ignore the timing of when the cash flows will be received
c. Ignore acquisition fees and transaction costs
d. Apply the discount rate that is relevant to the incremental cash flows
e. Ignore potential losses of management talent
17. The incremental cash flows of a merger can relate to which of the following:
a. Working capital
b. Profits
c. Capital spending
d. Income taxes
e. All of the above
Additional Problems/Case Studies
COURT RULES DELL UNDERPAID PUBLIC SHAREHOLDERS
HIGHLIGHTING LEGAL DISTINCTION BETWEEN FAIR VALUE AND FAIR MARKET VALUE
______________________________________________________________________________
Case Study Objectives: To illustrate
• When “fair value” can trump “fair market value;”
• The subjectivity inherent in determining “fair value,” and
• How appraisal rights’ legal rulings could impact future deal negotiations.
_________________________________________________________________________
Financial theory postulates that the value of a firm is determined by discounting projected net cash flows at an
Despite investment banking “fairness opinions,” some target firm shareholders will argue the price offered for
their shares is inadequate, contest it in court, and choose to have their shares valued by an independent appraiser,
state statutes permitting. Historically, judges in so-called “appraisal rights” hearings have relied on experts whose
opinions rely on conventional valuation methodologies. In recent years, judges frustrated by the often contradictory
opinions expressed by experts have deferred to the merger price or actual price paid for target firm shares as long as
the process used to determine the price was deemed fair. As such “fair market value” and “fair value” are the same,
under these circumstances.1
The concept of “fair value” is applied when no active market exists for a business, accurate cash flow projections
are problematic, or it is not possible to identify the value of similar firms. “Fair value” differs from “fair market
value,” which is the cash or cash-equivalent price that a willing buyer and a willing seller would accept for a
business. “Fair value” is, by necessity, more subjective because it represents the dollar value of a business based on
an independent appraisal of the net asset value (assets less liabilities) of a firm. What follows is a discussion of a
Dell management and Silver Lake Partners employed in buying out public shareholders. With interest, investors who
sought appraisal will collect about $20.84 per share.
While finding the process fair, Vice Chancellor Laster viewed it as incomplete as he argued that the Dell board of
directors did not pay sufficient attention to all bidders (both private equity and strategic buyers). The judge also
argued that the purchase price was based on a leveraged buyout model valuation which he argued was not an actual
market determined price.
held by Dell’s public investors.
1 See the case study at the beginning of this chapter for a more detailed discussion of this point.
2 A leveraged buyout (LBO) valuation model analyzes the contribution of alternative sources of funds to the
determination of financial returns to equity investors (i.e., so-called financial buyers). The use of large amounts of
debt to finance the acquisition of a target firm improves significantly the return to equity investors, although
excessive amounts of debt add to the risk of the deal.
The judge’s conclusion ignored the absence of strategic bidders showing an interest in buying Dell. Thus, the
While the ruling applied to 5.5 million Dell shares (out of the more than 40 million purchased by Dell) costing
the firm an additional $36 million, the potential impact could have been much greater. A number of shareholders
including T. Rowe Price were excluded from the appraisal case because they had voted for the deal. To qualify for
having shares appraised in most states, a shareholder must have voted against a deal. Consequently, had other
shareholders been included as plaintiffs, the ruling could have cost Dell hundreds of millions of dollars.
appraisal arbitrage?
Critics of the Delaware Court of Chancery’s decision expressed concern over the broad implications for the future
of corporate takeovers, arguing that the judge’s ruling exceeded a reasonable interpretation of the law. Critics also
argued that seller shareholders could be hurt in the future because fewer private equity firms might participate in
auctions for fear the price agreed to by the buyer and seller can be increased postmerger by hedge funds encouraged
Supporters of the judge’s ruling argue it is a victory for shareholder rights particularly in management buyouts
which often are rife with conflicts of interest. They argue that the ruling is unlikely to discourage bidders and
contribute to an increase in appraisal litigation because it is likely to be applied primarily to management buyouts
which are relatively rare. Also, the number of shareholders affected by this specific ruling was small, even though
the impact could have been much greater as explained earlier. In addition, the ruling occurred during an appraisal
perspective.
Discussion Questions and Solutions:
1. What’s the appropriate way to determine a takeover price? (Consider the application of conventional
valuation methodology, the negotiating process in which the parties involved are not subject to duress,
and an impartial arbiter’s (i.e., a judge) determination)
Answer: DCF and relative value methodologies are commonly used to value a target firm before an initial
offer is made. Subsequent negotiations, supported by due diligence whenever possible, determine what
3 W. Jiang, 2016.
2. Do you believe this court ruling is appropriate considering the facts of the case? Explain your answer.
Answer: The court ruling was inappropriate in that its conclusion was that the LBO model valuation
employed by Dell and Silver Lake Management understated “fair value” because it involved a higher
desired rate of return (reflecting leverage of such deals) and therefore offered a lower price than a strategic
3. Should a freely negotiated purchase price always be used as the appropriate valuation of a target firm‘s
shares assuming the process was fair? Explain your answer.
4. How does this case illustrate the shortcomings of discounted cash flow (and other methodologies) in
valuing a business?
Answer: Because the outcome of any DCF calculation is heavily dependent on the underlying
assumptions pertaining to the amount and timing of future cash flows and the discount rate applied to those
The Role of Valuation Methods in Fairness Opinions and Appraisal Rights
____________________________________________________________________________
KEY POINTS
• Investment bankers often are hired to provide opinions about whether a proposed purchase price is “fair” to
shareholders.
• Alternative valuation methods often result in different estimates of value.
• Dissenting shareholders may have their shares valued by an independent appraiser according to the
appraisal rights described in state statutes.
____________________________________________________________________________
Discounted cash flow (DCF), relative valuation, recent comparable sales, and asset based valuation methods often
are used in “fairness opinions” to assess the reasonableness of an offer made to target firm shareholders. They are
designed to help protect the target firm’s board and management from future litigation in which it is argued that the
A recent court case illustrates this point.
Most U.S. companies are incorporated in Delaware and are covered by the state’s corporate law. The Delaware
Chancery Court’s opinion in Merlin Partners v Autoinfo Inc. in mid-2015 provided guidance regarding the court’s
determination of fair value in an appraisal action. Private equity company Comvest Partners completed its takeover
of Autoinfo, a supply chain logistics company, on April 13, 2013 for $1.05 per share in cash. This price constituted a
7% premium to Autoinfo’s closing share price on February 28, 2013 and a 21% premium over its average closing
price for the six months ending February 28, 2013.
In the sales process, Autoinfo, the target, with the assistance of its investment bank, contacted 164 potential
strategic and financial buyers, 70 of which entered into non-disclosure agreements. The company eventually signed
a letter of intent that provided for an acquisition of Autoinfo at $1.30 per share. After that deal fell through. Autoinfo
discounted cash flow (“DCF”) analysis prepared by Merlin’s financial expert. In its defense, AutoInfo’s management
argued that comparable companies and DCF analyses could not be reliably performed with the available data and
that the sales price represented fair value based on the integrity of the sales process and the merger price paid by
Comvest (an unrelated third party). The Chancery Court on April 30, 2015 rejected Merlin Partners’ claims,
concluding that the DCF and comparable company methods were unreliable, and the actual price paid (i.e., merger
HEWLETT PACKARD OUTBIDS DELL COMPUTER TO ACQUIRE 3PAR
Case Study Objectives: To illustrate
• The application of discounted cash flow valuation methodology;
• The importance of selecting the proper length of the forecast period, and
• How seemingly small changes in assumptions can impact valuation substantially.
3Par was sought after due to the growing acceptance of its storage product technology in the emerging “cloud
computing” market. 3PAR’s storage products enable firms to store and manage their data more efficiently at
geographically remote data centers accessible through the Internet. While 3Par has been a consistent money loser, its
revenues had been growing at more than 50% annually since it went public in 2007. The deal valued 3Par at 12.5
times 2009 sales in an industry that has rarely spent more than five times sales to acquire companies. HP’s
motivation for its rich bid seems to have been a bet on a fast–growing technology that could help energize the firm’s
growth. While impressive at $115 billion in annual revenues and $7.7 billion in net income in 2009, HP’s revenue
and earnings have slowed due to the 2008–2009 global recession and the maturing markets for its products.
Table 7.1 provides selected financial data on 3PAR and a set of valuation assumptions. Note that HP’s marginal
HP sales force in the promotion of the 3PAR technology.
Table 7.1
3PAR Valuation Assumptions and Selected Historical Data
History
Projections
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Assumptions
Sales Growth Rate %
0.508
0.450
0.400
0.400
.400
0.350
0.300
0.250
0.200
0.100
0.100
Operating Margin % of Sales
–0.020
–
0.010
–
0.010
0.020
0.040
0.080
0.100
0.120
0.150
0.150
0.150
Depreciation Expense % of
0.036
0.034
0.060
0.060
0.060
0.060
0.060
0.070
0.070
0.070
0.060
Marginal Tax Rate %
0.400
0.400
0.400
0.400
0.400
0.400
0.400
0.400
0.400
0.400
Working Capital % of Sale
0.104
0.114
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
Gross P&E % of Sales
0.087
0.050
0.080
0.080
0.080
0.080
0.080
0.070
0.070
0.060
0.060
WACC (2010–2019) %
0.093
WACC (Terminal Period) %
0.085
Terminal Period Growth Rate %
0.050
Working Capital ($ Million)
112.8
126.4
Total Cash ($ Million)
103.7
111.2
Minimum Cash (5% of Sales)
8.4
12.65
W Cap Excluding Excess Cash
17.5
27.85
Selected Financial Data ($ Million)
Sales
168
Depreciation Expense &
Amortization
6.1
Gross Plant & Equipment
14.6
Excess Cash
98.55
Deferred Tax Assets
73.1
Number of Shares Outstanding
61.8
Answers to Discussion Questions:
1. Estimate 3PAR’s equity value per share based on the assumptions and selected 3PAR data provided in Table 7.2 below?
2. Why is it appropriate to utilize at least a 10–year annual time horizon before estimating a terminal value in valuing
firm’s such as 3PAR?
3. What portion of the purchase price can be financed by 3PAR’s nonoperating assets?
4. Does the deal still make sense to HP if the terminal period growth rate is 3 percent rather than 5 percent? Explain your
answer.
Table 7.2
Hewlett-Packard’s Valuation of 3PAR
(See Excel Spreadsheet Titled 3Par Valuation in Instructors’
Test Bank & Solutions Folder)
Projections
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Assumptions:
Sales Growth Rate %
0.508
0.450
0.400
0.400
0.400
0.350
0.300
0.250
0.200
0.150
0.100
Operating Margin % of Sales
-0.02
-0.01
-0.01
0.02
0.04
0.08
0.1
0.12
0.15
0.15
0.15
Depreciation Exp. % of Sales
0.036
0.034
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.07
0.06
Marginal Tax Rate %1
0.4
0.4
0.4
0.4
0.4
0.4
Net Working Capital % of Sales2
0.104
0.114
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.087
0.050
0.080
0.080
0.080
0.080
0.070
0.070
0.060
0.060
WACC (2010 – 2019) %4
9.31
WACC (Terminal Period) %5
8.50
Terminal Period Growth Rate %
0.05
Working Capital ($Mil)
112.8
126.4
Cash/Short-Term Investments
103.7
Minimum Cash (5% of Sales)
12.65
W Cap Excl. Excess cash
17.5
27.85
Selected Financial Data ($Mil.)
Sales
Depreciation Expense & Amort.
Net Working Capital
11.2
Gross Plant & Equipment
14.6
Excess Cash
98.55
24
Deferred Tax Assets
73.1
PV of Operating Leases6
22.0
Number of Shares Outstanding
61.8
Sales
168.4
244.2
478.7
670.2
904.7
1176.2
EBIIT(1-t)
-2.0
-1.5
-2.1
5.7
16.1
43.4
70.6
105.9
158.8
182.6
200.9
Plus: Depreciation & Amort.
6.1
8.6
20.5
28.7
40.2
54.3
70.6
102.9
123.5
142.0
133.9
Minus: Δ Net Working Capital7
10.4
6.3
13.7
19.1
23.5
27.1
29.4
29.4
26.5
20.3
Minus: Gross P&E Expend.
14.6
10.1
27.4
38.3
53.6
72.4
94.1
102.9
123.5
121.7
133.9
Equals: Enterprise Cash Flow
-13.3
-15.2
-17.5
-16.5
1.9
19.9
76.5
129.4
176.4
180.6
PV (2010 – 2019)
Terminal Value
2889.1
Total Operating Value
2889.5
0.4
Plus:
Excess Cash
98.6
Net Deferred Tax Assets
Equals: Enterprise Value
3060.7
Less:
73.1
Capitalized Operating Leases
22.0
Equals: Equity Value
3038.7
Number of Shares
Equity Value Per Share
49.2
61.8
1A 40% marginal tax rate is used to reflect the full benefit of the 3PAR deferred tax assets to HP.
2Excludes 3PAR excess cash balances.
3Increases faster than depreciation through 2015 to support growth in 3PAR sales and matches depreciation through
the remainder of the forecast period.
4Cost of equity = 0.0265 + 1.21 (0.055), where 0.0265 is the 10 year Treasury bond at the time of the transacton, 1.21
is 3PAR’s beta, and 0.055 is the market premium. Note the WACC is the firm‘s cost of equity as 3PAR has no
long-term debt.
5The cost of equity for comparable firms.
6PV of annual operating lease expenses discounted at 7% the firm’s estimated cost of debt.
7Net Working Capital
17.5
27.85
34.19
47.87
67.02
90.47
117.62
147.02
176.43
202.89
223.18
25
Valuation Methodologies, Fairness Opinions, and
Verizon’s Buyout of Vodafone’s Share of Verizon Wireless
____________________________________________________________________________
Key Points
• Parties to transactions often employ investment bankers to provide opinions about whether a proposed purchase price is “fair” to
their shareholders.
• Alternative valuation methods often result in very different estimates of value, reflecting different assumptions about risk and the
amount and timing of future cash flows.
____________________________________________________________________________
Founded in 2000 as a joint venture of U.S.-based Verizon Communications Inc. and U.K.-based Vodafone, Verizon Wireless is the largest
A typical fairness opinion letter provides a range of “fair” prices, with the presumption that the actual deal price should fall within that
range. These valuation estimates were presented to the Verizon Communications board of directors with the usual caveats. That is, the
estimates of fair value should reflect an amalgam of the methods used. The investment banks also noted that in performing its analyses, it
considered industry performance, business conditions and other matters, and that the estimates of fair value are not necessarily indicative
of actual values or actual future results.
The two investment banks calculated that Vodafone’s equity interest was worth between $131 billion and $182 billion. These valuation
industry experts.
Valuation Methodologies and Fairness Opinion Letters
____________________________________________________________________________________________________________
Key Points
Parties to transactions often employ investment bankers to provide opinions about whether a proposed purchase price is “fair” to their
shareholders.
Alternative valuation methods often result in very different estimates of value, reflecting different assumptions about risk and the amount
and timing of future cash flows.
____________________________________________________________________________________________________________
In July 2011, investment bank Goldman Sachs was hired by Immucor Inc., a manufacturer of blood-testing products, to certify that the
$27 price per common share offered by well–known buyout firm TPG was fair. These “fairness opinions” represent third-party assertions
about the suitability of proposed deals. Goldman assessed Immuncor’s fair value by applying discounted cash flow (DCF) analysis to the
value should reflect an amalgam of the methods used. Goldman also noted that in performing its analyses, it considered industry
In 2006, Verizon Communications and MCI Inc. executives completed a deal in which MCI shareholders received $6.7 billion for 100%
of MCI stock. Verizon’s management argued that the deal cost their shareholders only $5.3 billion in Verizon stock, with MCI having
agreed to pay its shareholders a special dividend of $1.4 billion contingent on their approval of the transaction. The $1.4 billion special
dividend reduced MCI’s cash in excess of what was required to meet its normal operating cash requirements.
To understand the actual purchase price, it is necessary to distinguish between operating and nonoperating assets. Without the special
net acquired assets. Moreover, since the $1.4 billion represents excess cash that would have been reinvested in MCI or paid out to
shareholders anyway, the MCI shareholders were simply getting the cash earlier than they may have otherwise.
The Hunt for Elusive Synergy—@Home Acquires Excite
Background Information
Prior to @Home Network’s merger with Excite for $6.7 billion, Excite’s market value was about $3.5 billion. The new company
lackluster profit performance since their inception. @Home provided interactive services to home and business users over its proprietary
network, telephone company circuits, and through the cable companies’ infrastructure. Subscribers paid $39.95 per month for the service.
Assumptions
• Excite is properly valued immediately prior to announcement of the transaction.
• Annual customer service costs equal $50 per customer.
• @Home converts immediately 2 percent or 340,000 of the current 17 million Excite user households.
• @Home’s cost of capital is 20 percent during the growth period and drops to 10 percent during the slower, sustainable growth period;
its combined federal and state tax rate is 40 percent.
• Capital spending equals depreciation; current assets equal current liabilities.
• FCFF from synergy increases by 15 percent annually for the next 10 years and 5 percent thereafter. Its cost of capital after the high–
• The maximum purchase price @Home should pay for Excite equals Excite’s current market price plus the synergy that results from the
merger of the two businesses.
Discussion Questions
1. Use discounted cash flow (DCF) methods to determine if @Home overpaid for Excite.
2. What other assumptions might you consider in addition to those identified in the case study?
3. What are the limitations of the discounted cash flow method employed in this case?
Answers to Case Study Questions:
1. Did @Home overpay for Excite?
Answer: To answer the question of whether @Home overpaid, it is necessary to estimate the value of synergy, add this estimate
Using the variable growth model, we can calculate the present value of potential synergy (P0) as follows:
Year: FCFF Present Value Present Value
($Millions) Interest Factor ($Millions)
1 91.8 .83 76.2
2 105.6 .69 73.3
Maximum purchase price for Excite (incl. present value of synergy)
2. What other assumptions might you consider?
3. What are the limitations of the valuation methodology employed in this case?
28
Creating a Global Luxury Hotel Chain
Fairmont Hotels & Resorts Inc. announced on January 30, 2006, that it had agreed to be acquired by Kingdom Hotels and Colony Capital
in an all-cash transaction valued at $45 per share. The transaction is valued at $3.9 billion, including assumed debt. The purchase price
represents a 28% premium over Fairmont’s closing price on November 4, 2005, the last day of trading when Kingdom and Colony
expressed interest in Fairmont. The combination of Fairmont and Kingdom will create a luxury global hotel chain with 120 hotels in 24
countries. Discounted cash-flow analyses, including estimated synergies and terminal value, value the firm at $43.10 per share. The net
asset value of Fairmont’s real estate is believed to be $46.70 per share.
Discussion Questions:
1. Is it reasonable to assume that the acquirer could actually be getting the operation for “free,” since the value of the real estate per share
is worth more than the purchase price per share? Explain your answer.
2. Assume the acquirer divests all of Fairmont’s hotels and real estate properties but continues to manage the hotels and properties under
long-term management contracts. How would you estimate the net present value of the acquisition of Fairmont to the acquirer? Explain
your answer.
Answers to Case Study Questions:
1. Is it reasonable to assume that the acquirer could actually be getting the operation for “free,” since the value of the real estate per
share is worth more than the purchase price per share? Explain your answer.
Answer: The total value of the combined firms is the present value of operating cash flows including synergies and the terminal
value generated by all assets and liabilities used in the operation of the business plus the present value of non–operating
2. Assume the acquirer divests all of Fairmont’s hotels and real estate properties but continues to manage the hotels and properties
under long-term management contracts. How would you estimate the net present value of the acquisition of Fairmont to the
acquirer? Explain your answer.
Answer: If the acquirer sells the hotels and properties but continues to manage them under a long-term management contract, the