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
DELAWARE SUPREME COURT RULES ON THE ROLE OF VALUATION METHODS
IN APPRAISAL RIGHTS
____________________________________________________________________________
KEY POINTS
• The most reliable indicator of firm value is the merger price negotiated by the parties to the deal none of
whom is under duress or subject to conflicts of interest.
• Alternative valuation methods are employed to estimate fair value when the negotiated purchase price is
problematic.
• These alternative valuation methods are derived from a logical process but often are applied subjectively.
• Dissenting shareholders may have their shares valued by an independent appraiser according to the
appraisal rights described in state statutes.
____________________________________________________________________________
Some argue that a firm’s current publicly traded share price reflects all relevant information about the firm’s future
earnings stream and its associated risk; and, new information will cause the share price to adjust quickly. Others
believe that over long time periods public markets are efficient but that at any moment in time a firm’s share price
can be above or below its true value. In the absence of an efficient market (i.e., one in which current share prices
reflect all available information), fair value is a term that applies to a rational and unbiased estimate of the potential
value of a firm’s share price.
On August 1, 2017, the Delaware Supreme Court reversed the Delaware Court of Chancery’s3 appraisal decision
involving the acquisition of DFC Global Corp. (DFC), a publicly traded pay-day lending firm4 by private equity firm
Lone Star. As a result, the case was returned to the Chancery court for further consideration. The Chancery court
had determined that the sales process was competitive but concluded that because of the potential overhaul of pay-
day industry regulations, DFC’s publicly traded share price was an unreliable estimate of fair value. The Chancery
court therefore decided to use a weighted average of the merger price, DCF estimates, and comparable sales
analyses to determine fair value. Each of the three factors was given a one-third weight. The resulting estimate of
fair value was 8.4% above the $1.3 billion merger price.
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
appropriate discount rate. In practice, buyers and sellers estimate the value of a firm using an array of valuation
methodologies discussed in Chapters 7 and 8 of this text. The actual price paid by the buyer to selling firm
shareholders is determined when the parties to the negotiation reach an agreement on what is a mutually acceptable
price. Assuming neither party was under duress to accept the price, the price paid by the buyer and accepted by the
seller is said to represent the “fair market value” of the firm.
Vice Chancellor Travis Laster of the Delaware Court of Chancery exercised his legal right to determine what is
fair on June 16, 2016 in ruling that public shareholders were undercompensated for their shares in the 2013 $24.9
billion management buyout of Dell Corporation. The judge ruled that the price paid to such shareholders was
undervalued by 22% and should have been $17.62 per share, even though he found no wrongdoing with the process
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.
The judge’s conclusion ignored the absence of strategic bidders showing an interest in buying Dell. Thus, the
auction process included only private equity firms. The deal was widely contested in public by the likes of such
activist investors as Carl Icahn who argued relentlessly that the price offered by Michael Dell and Silver Lake
Partners undervalued the stock held by public shareholders. If the judge’s conclusion was correct, Dell’s public
shareholders acting rationally should have chosen to vote against the deal, as they did have access to Icahn’s
arguments. Instead, they voted for the transaction in large numbers.
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.
Will the ruling accelerate the trend toward “appraisal arbitrage” in which hedge funds buy a firm’s shares after
takeover announcements intent upon suing the bidder claiming the price was too low? The number of appraisal
rights petitions has indeed increased from a trickle of cases in early 2000s to over 20 a year in recent years, or close
to one-quarter of all transactions where appraisal rights were available to target firm shareholders.10 Also, will deals
be more difficult to negotiate because of the additional uncertainty posed by the potential adverse impact from
appraisal arbitrage?
Critics of the Delaware Court of Chancery’s decision expressed concern over the broad implications for the future
them to walk away if, as a result of appraisal litigation, the agreed upon price is increased above the cap by a court
ruling. Selling company boards might find such caps onerous, making closing deals that much more difficult.
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
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
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.
Answer: Yes. A freely determined price is one in which buyers and sellers agree to a price without
duress and is reflective of information available to the parties involved at that time. For the process to be
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
sale price was too low. Acquirers also may use fairness opinions if the board and management are sued over having
allegedly paid too much for a target firm.
If subsequent to closing, minority shareholders dispute the accuracy of the price offered for their shares, they can
exercise their “appraisal rights” specified in the statutes of the state in which the target is incorporated. Appraisal
rights represent the statutory option of a firm’s minority shareholders to have the fair market value of their stock
price determined by an independent appraiser and the obligation of the acquiring firm to buy back shares at that
price. While alternative valuation methodologies often are used to estimate the fair market value of shares in dispute,
courts often defer to the merger price or actual price paid as long as the process used to determine the price was fair.
A recent court case illustrates this point.
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.
_________________________________________________________________________
On September 2, 2010, a little more than two weeks after Dell’s initial bid for 3PAR, Dell Computer withdrew
from a bidding war with Hewlett-Packard when HP announced that it had raised its previous offer by 10% to $33 a
share. Dell’s last bid had been $32 per share, which had trumped HP’s previous bid the day before of $30 per share.
The final HP bid valued 3PAR at $2.1 billion versus Dell’s original offer of $1.1 billion.
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
tax rate is used rather than 3PAR’s much lower effective tax rate, to reflect potential tax savings to HP from 3PAR’s
cumulative operating losses. Given HP’s $10 billion–plus pretax profit, HP is expected to utilize 3PARs deferred tax
Table 7.1
3PAR Valuation Assumptions and Selected Historical Data
History
Projections
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Assumptions
Sales Growth Rate %
0.508
0.450
0.400
0.400
.400
0.350
0.300
0.250
0.200
0.100
0.100
–
–
Working Capital % of Sale
0.104
0.114
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
Gross P&E % of Sales
0.087
0.050
0.080
0.080
0.080
0.080
0.080
0.070
0.070
0.060
0.060
WACC (2010–2019) %
0.093
WACC (Terminal Period) %
0.085
Terminal Period Growth Rate %
0.050
Working Capital ($ 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
Operating Margin % of Sales
0.010
0.010
0.020
0.040
0.080
0.100
0.120
0.150
0.150
0.150
Depreciation Expense % of
Sales
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
24
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?
Answer: The length of the annual forecast period depends on how long the analyst believes it will take the firm’s cash
3. What portion of the purchase price can be financed by 3PAR’s nonoperating assets?
Answer: 3PAR’s primary nonoperating assets include excess cash balances of $98.55 million and deferred tax assets of
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.
Answer: No, because the equity value per share falls to $29.90, less than the $33 per share purchase price. The choice of
Table 7.2
Hewlett-Packard’s Valuation of 3PAR
(See Excel Spreadsheet Titled 3Par Valuation in Instructors’
Test Bank & Solutions Folder)
Projections
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Assumptions:
Sales Growth Rate %
0.508
0.450
0.400
0.400
0.400
0.350
0.300
0.250
0.200
0.150
0.100
Operating Margin % of Sales
-0.01
0.12
0.15
0.15
0.15
Depreciation Exp. % of Sales
0.036
0.034
0.06
0.07
0.07
0.07
0.06
Marginal Tax Rate %1
Net Working Capital % of Sales2
0.104
0.114
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.087
0.050
0.080
0.080
0.080
0.080
0.080
0.070
0.070
0.060
0.060
WACC (2010 – 2019) %4
9.31
WACC (Terminal Period) %5
8.50
Terminal Period Growth Rate %
0.05
Working Capital ($Mil)
112.8
126.4
Cash/Short-Term Investments
103.7
111.2
Minimum Cash (5% of Sales)
12.65
W Cap Excl. Excess cash
27.85
Selected Financial Data ($Mil.)
Sales
168
Depreciation Expense & Amort.
25
Valuation:
Sales
168.4
244.2
341.9
478.7
670.2
904.7
1176.2
1470.2
1764.3
2028.9
2231.8
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
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
1.9
19.9
76.5
129.4
176.4
180.6
PV (2010 – 2019)
0.4
Terminal Value
2889.1
Total Operating Value
2889.5
10.4
6.3
13.7
19.1
23.5
27.1
29.4
29.4
26.5
20.3
Plus:
Excess Cash
98.6
Net Deferred Tax Assets
73.1
Equals: Enterprise Value
3060.7
Less:
Capitalized Operating Leases
Equals: Equity Value
3038.7
Number of Shares
61.8
Equity Value Per Share
49.2
22.0
Explanatory Notes:
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
Deferred Tax Assets
73.1
22.0
Number of Shares Outstanding
61.8
26
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
Investment banks, J.P. Morgan and Morgan Stanley, were hired by Verizon Communications to certify that the $130 billion offered for
the Vodafone ownership position was reasonable. So–called “fairness opinions” represent third-party assertions about the suitability of
proposed deals. The two investment banks employed generally accepted valuation methods to arrive at their opinions as to the
appropriateness of the price to be paid to Vodafone.
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
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
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 Immuncor’s board of directors with the usual caveats, that is, the estimates of fair
27
The Importance of Distinguishing Between Operating and Nonoperating Assets
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
dividend, the $1.4 billion in cash would have transferred automatically to Verizon as a result of the purchase of MCI’s stock. Verizon
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
combined the search engine capabilities of one of the best-known brands (at that time) on the Internet, Excite, with @Home’s agreements
with 21 cable companies worldwide. @Home gains access to the nearly 17 million households that are regular users of Excite. At the
time, this transaction constituted the largest merger of Internet companies ever. At the time of the transaction, the combined firms, called
Assumptions
• Excite is properly valued immediately prior to announcement of the transaction.
• Annual customer service costs equal $50 per customer.
• Annual customer revenue in the form of @Home access charges and ancillary services equals $500 per customer. This assumes that
declining access charges in this highly competitive environment will be offset by increases in revenue from the sale of ancillary
services.
• None of the current Excite user households are current @Home customers.
• New @Home customers acquired through Excite remain @Home customers in perpetuity.
• @Home converts immediately 2 percent or 340,000 of the current 17 million Excite user households.
28
Discussion Questions
2. What other assumptions might you consider in addition to those identified in the case study?
3. What are the limitations of the discounted cash flow method employed in this case?
Answers to Case Study Questions:
1. Did @Home overpay for Excite?
Answer: To answer the question of whether @Home overpaid, it is necessary to estimate the value of synergy, add this estimate
Using the variable growth model, we can calculate the present value of potential synergy (P0) as follows:
Year: FCFF Present Value Present Value
($Millions) Interest Factor ($Millions)
1 91.8 .83 76.2
3 121.4 .58 70.4
5 160.6 .40 64.2
7 212.3 .28 59.4
9 280.8 .19 53.4
$633.6
Terminal Value = $322.9 x (1.05) / (.10 – .05) = $6,780.90 = $1,095.5
(1.20)10 6.19
2. What other assumptions might you consider?
Answer: Other sources of profitable revenue such as selling additional products and services to the Excite customer base and
3. What are the limitations of the valuation methodology employed in this case?
Answer: The valuation is heavily dependent on the choice of assumptions concerning growth rates during the high growth and
stable growth periods and the discount rates for each period. Almost two-thirds of the total valuation is dependent on the
29
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.
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
value of the ongoing businesses to the acquirer is the net present value of the cash flows generated under the management