A stock price-based model for the
optimal timing of a merger and
acquisition event
By:
Stefan Damen (54.47.48)
B.Sc. Tilburg University
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Science in Quantitative Finance and Actuarial Science.
Tilburg School of Economics and Management
Tilburg University
Supervised by:
Dr. R.J. Mahieu
Second reader:
Dr. R. van den Akker
Date:
January 31, 2012
ABSTRACT
This paper investigates the optimal timing to announce a merger or acquisition based on the
stock market valuations of the merging firms. We compare the actual timing to the optimal
timing as originally presented in a model by McDonald and Siegel (1986) and investigated by
Dixit and Pindyck (1994). One of the main inputs in the model is the firm value of the bidding,
target and the combined firm. To determine these firm values (and the whole processes) we use
the Merton (1974) model. The paper’s results are based on financial and trading data of 82
mergers and acquisitions announced between 2000 until and including 2004. We conclude that
half of these takeovers revenues are lower than the investment cost, suggesting it would be
optimal to refrain from making an announcement. The quality, in terms of timing, of the other
half increases value and may, hence, be called ‘quite well’. 27 of the remaining 42
announcements are optimally timed. For another 6 deals, the paper shows it is optimal to wait
‘forever’ with announcing the takeover. For the remaining 9 the project revenue is lower than
the minimum required revenue. These takeovers have been timed too early.
Keywords: merger and acquisition (M&A), firm valuation, Merton’s model, optimal timing, real
option, contingent claims.
[2]
ACKNOWLEDGEMENT
This is the start of the final part of my study period; an optimal timing to thank several persons.
First of all I would like to thank my university supervisors dr. R.J. Mahieu and dr. R. van den
Akker for their great support. Dr. R.J. Mahieu, I greatly admire your tremendously broad interest
in everyday topics. I liked the many discussions we have had during my studies about, for
example the creditworthiness of companies, electronic batteries, pensions, etc. Dr. R. van den
Akker, I admire your enthusiasm about Econometric applications. I remember the many email
conversations about the mathematics behind some quantitative finance theorems. You are
always willing to help students and to show the beauty Econometrics has to offer.
I would like to thank my family as well. In particular, I thank my parents. I would like to thank
them for their mental support, confidence and the freedom they gave me in succeeding my
studies. I do not forget about the “Sunday morning’’ discussions about, for example, the Dutch
pension system, derivatives and the many other things I can’t think of right now. Truly, I loved
these conversations and hope that many will follow in the future. Those conversations made me
aware of the beauty and the broad range of applications of my studies.
Then, I would like to thank my lovely friends from my birthplace Wageningen. You are so
important in my life. I am proud of it!
To conclude I would like to mention my best Tilburg friend, study mate and sparring partner
Emile van Elen. I am aware of the fact that we two together were the best study couple that I can
imagine. From the start of our studies, we have complemented each other perfectly. Our
collaboration has confirmed that the power of a team is larger than the sum of the two powers
separately.
[3]
TABLE OF CONTENTS
1
INTRODUCTION .......................................................................................................................................................... 5
2
PROBLEM DEFINITION ............................................................................................................................................ 8
3
MERGERS AND ACQUISITIONS .............................................................................................................................. 9
4
TRADITIONAL VALUATION METHODS ........................................................................................................... 11
5
FIRM VALUATION: MERTON’S OPTION PRICING MODEL ......................................................................... 13
5.1
5.2
5.3
5.4
5.5
5.6
CAPITAL STRUCTURE ............................................................................................................................................................. 17
EXERCISE PRICE...................................................................................................................................................................... 18
TIME TO EXPIRATION ............................................................................................................................................................ 19
DIVIDEND PAYMENTS ............................................................................................................................................................ 19
VOLATILITY............................................................................................................................................................................. 19
COUPON PAYMENTS ............................................................................................................................................................... 20
6
REAL OPTIONS ......................................................................................................................................................... 21
7
THE DYNAMICS AROUND A MERGER AND ACQUISITION ......................................................................... 25
7.1
7.2
8
ASSUMPTIONS ASSOCIATED WITH THE FIRM VALUE ........................................................................................................ 25
SYNERGY.................................................................................................................................................................................. 26
DATA ........................................................................................................................................................................... 29
8.1
8.2
8.3
8.4
9
SECURITIES DATA COMPANY (SDC) .................................................................................................................................. 29
DATASTREAM......................................................................................................................................................................... 29
WHARTON RESEARCH DATA SERVICES (WRDS) ........................................................................................................... 30
ASSUMPTIONS WITH RESPECT TO THE DATA ..................................................................................................................... 30
EXAMPLE TAKEOVER: PATINA OIL & GAS CORP. BY NOBLE ENERGY INC. ........................................ 32
10
10.1
10.2
11
11.1
11.2
RESULTS ................................................................................................................................................................ 37
GENERAL DESCRIPTIVE STATISTICS DATA.......................................................................................................................... 37
THE INVESTMENT VALUE AND PROJECT REVENUE ........................................................................................................... 42
CONCLUSION ........................................................................................................................................................ 51
SUMMARY ................................................................................................................................................................................ 51
RECOMMENDATIONS FOR FUTURE RESEARCH .................................................................................................................. 52
REFERENCES ...................................................................................................................................................................... 54
APPENDIX ........................................................................................................................................................................... 57
[4]
1 INTRODUCTION
A merger or an acquisition is a highly important strategic issue for the management of a
company. This is emphasized by the fact that management of a publicly traded company has
fiduciary duties towards the company’s shareholders, the owners of the firm. A merger of an
acquisition is potentially value increasing and is, hence, an act in the interest of the company’s
shareholders. In particular, if expected synergies materialize, it generally creates additional
value. Because of the strategic and financial importance of a takeover, it is not surprising that
academics have thoroughly looked into this subject. Despite the rich literature on this subject, it
remains unclear when a takeover is optimally timed in terms of value maximization.
This paper aims to take away this unclarity; it investigates the optimal timing in a merger and
acquisition event based on a real option approach. In the world of finance, an option gives the
holder of the option the right but not the obligation to buy (call option) or sell (put option) the
underlying for a given price (the strike price) at or before a predefined time (the maturity).
Therefore, a call option gives the holder the upside potential without the downside risk (except
for the option’s premium). A breakthrough in option pricing occurred when Black and Scholes
(1973) proposed an explicit pricing function for the valuation of options.
While financial option theory was still under development, Myers (1977) and thereafter,
amongst others, McDonald and Siegel (1986) and Dixit and Pindyck (1994) emphasized the
importance of the real option theory. Real options are, to some extent, similar to the financial
option as discussed above. For real options as well, the holder has the possibility to undertake
some decision (i.e., to exercise or not to exercise the option). But instead of a purely financial
decision, like buying the underlying asset, real options may be applied to a much broader
horizon of subjects. These kinds of options can be used for almost all daily decision problems
that are subject to uncertainty. For example, a high school scholar has the option to go to
university or can decide to find a fulltime job. If we take into account only the current and future
expected (uncertain) wages of this individual, we can solve the problem by the use of a real
option. Based on this method, the high school student chooses to look for a job immediately in
case the net present value of the sum of all future (lower) wages is higher than the net present
value of all future (higher) wages minus the net present value of the total cost of going to
university. Business related examples are, for instance, the option to make, abandon, expand or
contract a capital investment. A classic example of a business related real option is the option to
undertake a Research & Development (R&D) investment.1.
More specifically, this paper uses the real option approach to determine the optimal timing to
announce a merger or acquisition event of a publicly traded company. Margrabe (1978) is the
first to apply real options to takeovers. His paper introduces an equation to value the possibility
to exchange one risky asset for another risky asset. Although Margrabe (1978) touches upon a
very interesting topic, this paper focuses on the optimal timing to exercise an option. Since the
Also referred to as an exploratory investment since it can resolve cost uncertainty and then results in
additional value.
1
[5]
moment of exercising the option may be anytime, we are dealing with an American type of
option.2 In this context, the option of the bidding firm is as follows:
1. announce to take over the target firm (i.e., exercise option);
2. wait for a better moment in time (if that moment exists) to take over the target firm (i.e.,
do not exercise option).
The real option approach is characterized by uncertainty surrounding the benefits and the fact
that the investment decision is at least partially irreversible. This results in the value of waiting:
by choosing to wait, the investor can make a more informed decision. Since the value of waiting
is taken into account in the real option approach, the acquiring firm should decide to acquire the
target firm if the net benefits are higher than a certain threshold. This threshold, the optimal
timing, is, in general, higher than the threshold of a Net Present Value (NPV) decision which is
based on the assumption that either the investment is reversible or, if the investment is
irreversible, it is a now or never proposition. In fact, one may argue whether or not one is
dealing with a reversible investment. From a technical point of view, the investment is reversible
since all acquired shares can be sold again anytime. If, for instance, business is going worse than
expected, the firm may consider this option. But due to the difficulties of a merger or acquisition
process, it takes a long time between the moment of announcing this decision and the actual
moment of execution. And if the shares are sold, the firm receives probably much less than the
original purchase value. As a result of both the duration of the process and the loss the company
suffers when it decides to sell the shares, the investment of a publicly traded firm can be seen as
an irreversible project.
This paper uses Merton’s (1974) contingent claims analysis for corporate bond valuation
method to infer the value of the acquiring, target and combined firm. The values of these
(publicly traded) firms are the main input variables for the real option model. Merton (1974)
assumes the market value of equity as a residual claim on a company after paying the debt
holders. Hence, the market value of equity can be interpreted as a European type call option,
where the (adjusted) book value of debt represents the strike price and the market value of the
firm the underlying. Both the strike price and the market value of equity (price of the call option)
are observable. By backward calculation, the market value of the firm can be calculated as well.
Merton’s model is generally accepted in the academic literature. For instance, Eberhart (2005)
concludes that Merton’s (1974) model provides more accurate estimates of corporate debt than
simply the book valuation of debt. Hull, Nelken and White (2004) argue, based on the
performance study of Eom, Helwege and Huang (2004), that
“a number of authors such as Black and Cox (1976), Geske (1977), Longstaff and Schwartz (1995),
Leland and Toft (1996), and Collin-Dufresne and Goldstein (2001) have developed interesting
extensions of Merton’s model, but none has emerged as clearly superior”.
Moreover, Merton’s valuation method has been implemented and extended in the famous
commercial Moody’s KMV model, proposed by Kealhofer, Mc Quown and Vasicek (KMV) for
As opposed to a European option, which allows the holder of the option to exercise his or her option only
at a predefined moment in the future.
2
[6]
forecasting default probabilities of companies and countries. This model is used for practical
purposes to rate the creditworthiness of companies and countries.
In this paper we analyze a total of 82 mergers or acquisitions of listed entities. For all these
takeovers we analyze financial data, for example, the debt and equity positions of these firms.
Results are obtained in three steps. First, using Merton’s method (1974), the firm value process
is estimated. In the second step we determine, using the firm value process obtained in step 1
and McDonald and Siegel’s (1986) (and extended by Dixit and Pindyck (1994)) real option
approach, the optimal investment threshold. Finally, we compare the empirical results with the
optimal theoretic results.
We conclude that in 40 of the 82 cases the announcement is value destroying for the
shareholders, implying it is optimal to refrain from making an announcement. As a result of this,
the cost of the investment is larger than the revenues. Synergies, defined as the difference
between the value of the combined firm and the values of the two firms separately, are, in fact,
negative. This mainly results from the change in risk profile. Due to this, the announcement
results, on average, in a loss of shareholder value for both the acquirer’s and target’s
shareholders. For the remaining 42 announced takeovers we conclude that the project value is
at least equal to the investment cost. Therefore, we are able to compare the actual
announcement timings with the optimal timings. For this group it holds that in 27 of these cases
the takeover could have been announced earlier than the moment the deal was announced in
practice. That is, based on the real option framework, the value of exercising the option is higher
than the value of waiting. For these cases it holds that the actual investment level is higher than
the optimal investment threshold. Based on the real option theory we label these cases as ‘well
timed mergers or acquisitions’. For the other 15 of the 42 cases it holds that either the actual
investment level is lower than the optimal investment threshold (9 cases) or there is simply no
optimal timing possible since the expected growth rate of the investment revenues is too large
(6 cases). For the cases for which it holds that the revenues are larger than the threshold value
to invest (also called the optimally timed announcements) we conclude that the mean
investment level equals 1.25 times the investment cost while the optimal investment level is
equal to 1.07 times the investment cost.
The remainder of this paper is structured as follows. In section 2, the main topic of investigation
is formally described. In section 3, we touch upon the main definitions and most important
theories in relation to mergers and acquisitions that are of relevance to this paper. Section 4
describes different firm valuation methods. Section 5 dives into one of these methods, Merton’s
(1974) method. The section aims to elaborate on how to price corporate debt. Section 6
describes the real option model which determines the optimal timings. In section 7, we discuss
some dynamics of the investigated processes, like the capturing of the synergies. A detailed
description of the data is given in section 8 and in section 9 we show, using an example, our
research method. To see how the research method works in practice, we apply the method to the
Patina Oil & Gas Corp. by Noble Energy Inc. merger. The empirical findings are discussed in
section 10. Section 11 concludes the paper.
[7]
2 PROBLEM DEFINITION
This paper investigates the optimal timing of announcing a merger or acquisition event based on
the evolution of stock prices of the associated firms. In practice, a takeover of a publicly traded
firm is often announced months prior to the actual takeover date. Rather than on the actual date
of the takeover itself, financial markets respond to the announced takeover at the date of
announcement. On the day of announcement it can be concluded, based on the stock price
movement of both the bidding firm and the target firm, if the information about the announced
takeover has been received positive (positive announcement returns, hence, synergy gains) or
negative (negative announcement returns, hence, synergy losses) by the market. Existing
literature often chooses the date of announcement as the event analysis date.3 Therefore, we
investigate the optimal timings of the announcement date in a merger or acquisition event.
Based on Merton’s (1974) method to price corporate debt, we calculate, for both the acquiring
firm and the target firm, the firm value starting one year before the announcement date. These
computed values are denoted by
and
, respectively. The most important input
variables in the pricing model are the equity value and its accompanying characteristics and the
data from the balance sheet.4 From the firm characteristics of
and
, we are able to
define the value of the combined firm, which will be denoted by
. One of the main
characteristics of
is that the capital structure is identical with the sum of capital structure
of the bidding and target firm. The same is true for the equity value process. This new equity
value process results in new values of the drift and volatility term.
Synergy gains or losses associated with the takeover can be captured around the date of
announcement.5 As a direct result of the specific deal conditions, the resulting synergies for the
bidding and target firm may vary. This paper does not aim to judge whether a deal is good or bad
for either the bidding or the target firm. Therefore, we sum all synergies to one item.
The characteristics of the processes of
,
and
, such as the drift and volatility of the
process, enables us to empirically investigate the timing of the announcement of the takeover.
By assuming that the firm value can be modeled by a geometric Brownian Motion we are able to
compare the optimal timing of the announcement resulting from the real option framework with
the empirical timing (i.e., the timing as occurred in practice).6 In the real option framework, we
use the optimal timing rule of McDonald and Siegel’s (1986) and Dixit and Pindyck (1994).
Summarizing, this paper aims at answering the following two questions:


What is the optimal timing of announcing a merger and acquisition event if both the
evolution of the stock price of the acquiring and the target company (excluding the specific
deal terms) are observed?
How does the actual implementation date of a merger and acquisition correspond to the
optimal timing resulting from the real option model?
See, for instance, Bowman (1983).
See section 5, Firm valuation: Merton’s option pricing model for a detailed description.
5 See section 3, Mergers and Acquisitions, for a more detailed description of the notion
6 Characteristics of the Brownian motion are:
,
is independent of the past,
( ), the sample paths
are continuous.
3
4
[8]
3 MERGERS AND ACQUISITIONS
This section touches upon the basic definitions of mergers and acquisitions.7 We explain the
different types of takeovers that exist and the key driver of takeovers: synergy.8 All corporate
acquisitions can be ascribed to one of the following three forms:



merger or consolidation;
acquisition of stock;
acquisition of assets.
In case of a merger or a consolidation, all assets and liabilities of one firm (the target) are
absorbed completely by another firm (the acquirer). The difference between a merger and a
consolidation is that after a merger, the acquiring firm ceases to exist as a separate business
entity, whereas in the case of consolidation a new entity is created. In most cases, a merger or
consolidation requires a vote of approval by the shareholders.9
If the acquisition is in the form of stock, the target firm’s voting stock is purchased in exchange
for cash, shares of stock of the acquiring firm or other securities. In this form, a shareholders
meeting need not to be held and a vote is not required. Acquisition of stocks often occurs
through a so-called tender offer. This is a public offer to buy shares of the target firm. The
management of the company may or may not have endorsed the tender offer proposal. The
shareholders of the target firm are not obliged to sell their shares to the acquiring firm.
However, to get the shareholders aboard, a premium over the current stock price is often
offered. If some stock holders are unwilling to sell their shares, the target firm cannot be
absorbed completely. If all stocks of the target firm are aborted, we are legally speaking about a
merger.
If the acquiring firm buys all assets of the target firm, then we are dealing with an acquisition of
assets. The target’s stockholders have to vote about this type of acquisition. If the target firm is
acquired, all shareholders renounce their shares.
The typical investor is keen on his return on a per share basis. Therefore, in the event of a
merger or acquisition of publicly traded firms it is preferred to structure the deal such that
earnings per share (EPS) will increase. The change in EPS may be computed with a so-called
Accretion/Dilution analysis. Without going into too much detail, a deal is called accretive when
EPS increases on a pro forma basis and is called dilutive when EPS is expected to decrease. The
Accretion/Dilution analysis is highly sensitive to gains in synergy. The notion of synergy is
beneficial to the stockholder since it creates additional firm value. Synergy may be defined as:
(
)
(
)
In part, inspired by Ross, Westerfield and Jaffe (2010).
In case of a strategic buyer. Financial sponsors may be driven by different reasons to pursue an
acquisition. Examples include growth opportunities, entrance of a certain market, etc. This paper merely
focuses on strategic buyers and hence, synergy is the main driver indeed.
9 The specific percentage of the shareholders needed to approve a merger or consolidation differs per
company.
7
8
[9]
where
,
and
denote the value of the combined, acquiring and target firm
respectively. That is, synergy equals the difference between the value of the combined firm and
the value of two firms separately. Synergies can be realized through e.g., revenue enhancement,
cost reduction, lower taxes or lower capital requirements. If the premium offered by the
acquiring party is lower than the synergy gains, then the takeover is attractive for the
shareholders of the acquiring company.
The fiduciary duties of the management of a publicly traded firm towards the company’s
shareholders, obliges management by law to act in the interest of the company’s shareholders.
However, Roll (1986) argues that managerial hubris could be a motive to initiate a takeover of
another firm. A similar argument is put forward by Brown (2007), who identifies overconfidence
of a CEO as a driver of corporate acquisitions. This overconfidence may result in an
overestimation of the potential synergy gains which can subsequently lead to an unjustifiable
premium. Hence, it is possible that in principal a potential takeover can result in additional
shareholders’ value, but due to the unjustified high premium the deal as whole (i.e., including
synergies) is value destroying for the shareholders of the acquiring firm.
By diversifying its business model, a firm aims to eliminate its unsystematic risk. A general
misconception, however, is that diversification is a driver for a merger or an acquisition. Ross,
Westerfield and Jaffe (2010) argue that diversification in itself cannot be a reason for a publicly
traded firm to consider a takeover. To see this, consider the following. Stockholders of a publicly
traded firm have a residual claim on the company’s assets after debt holders are paid.10 Hence,
the equity holders’ benefit is zero in case the debt claim is higher than the company value;
otherwise the equity holders’ benefit equals the difference between the firm value and the debt
claim. Due to the bounded downside risk and the upside potential, equity holders prefer higher
risks. Note that, by definition, diversification results in a decrease of the total risk exposure.
Therefore, diversification is beneficial to debt holders (since the probability of a default
declines) and detrimental to equity holders. This phenomenon is referred as coinsurance effect.
Mergers and acquisitions have been extensively investigated from many different angles in the
existing literature. However, the application of the real option framework to takeovers is
relatively new. A first start was made by Margrabe (1978), who analyzes takeovers as exchange
options. Grenadier (2002) investigates the timing and terms of takeovers through an option
exercise game between the bidding and the target firm. Lambrecht (2004) analyzes takeovers in
a real option setting with endogenous timing. He assumes a strong form of market efficiency
which excludes abnormal stock returns surrounding the announcement of the takeover.
Morellec and Zhdanov (2005) develop a dynamic real option model that determines the timing
and terms of the takeover. The model incorporates imperfect information, learning and
competition. More recently, Hackbarth and Morellec (2008) investigate the impact of the
announcement of mergers and acquisitions on the change of, amongst others, the sensitivity of
stock changes relative to the market (also known as beta).11 In our real option model we do not
consider the deal terms for the bidding and target firm separately. Instead, we sum the
acquirer’s and target’s synergies and revenues resulting from the announcement into one
number that may be attributed to the combined entity.
10
11
see Section 4, Firm Valuation.
See Section 7, The dynamics around a merger and acquisition.
[10]
4 TRADITIONAL VALUATION METHODS
This section describes the concept of ‘firm value’ and it explains some common used valuation
methods like Discounted Cash Flow and multiple analyses. Subsequently, we discuss our
valuation method, which is based on Merton’s (1974) valuation method.12
The value of the firm is often described as the value of its business as a going concern. Future
prospects and profitability of the firm’s business, its risks, and its standing relative to other
investment opportunities existing in the economy are important parameters to determine a
minimal bandwidth of the firm’s value.
The building blocks of the firm’s business are the assets. The assets can be valued at the market
price at which the total firm’s liabilities can be bought or sold. These liabilities are claims on the
assets. The difference between the value of the firm as an ongoing business and the book value
(which can be found at the balance sheet) is usually accounted for as ‘goodwill’.
A straightforward way of determining the size of a publicly traded company is simply by
multiplying the number of outstanding shares with the price of the stock. This results in the
equity market value of the company and is known as market capitalization. This method only
reflects the equity value of a company.
An often-used method to determine a firm’s value is the Discounted Cash Flow method, which
requires calculations of the net present value (NPV) of a company’s future expected free cash
flows. These cash flows are discounted with a discount rate to correct for time and risk and are
called the Weigthed Average Cost of Capital (WACC). The WACC is composed by the required
return on equity and debt.
Another method looks at so-called multiples of comparable companies or of precedent
transactions (multiple analyses). A frequently used multiple, for instance, is the EBITDA/EV
multiple. Here, EBITDA denotes Earnings Before Interest, Taxes Depreciation and Amortization
and EV represent Enterprise Value.13 The advantage of this specific multiple over other multiples
lies in the fact that the multiple is capital structure-neutral.. That is, it considers the company’s
earnings that are attributable to both debt and equity holders. In other words, the EBITDA/EV
multiple allows one to compare companies with different capital structures. In practice, specific
multiples apply to certain sectors. For instance, the multiple EV / Regulated Asset Base applies
to the valuation of Transmission System Operations (e.g., TenneT or Gasunie).
The different methods described above all result in different outcomes, but give a clear
interpretation of a ‘fair’ i.e., justifiable value. We emphasize that there is no such a thing as one
correct value. A simple argumentation for this is that all stakeholders have different future
perspectives of the company. Therefore, all these stakeholders value a firm differently. For
example, an acquirer values the company as low as possible whereas the seller has grounded
reasons to overestimate the value of the very same company.
Please refer to the website of Damodaran, pages.stern.nyu/~adamodar/, for a more detailed description
of the valuation methods.
13 Enterprise value = market capitalization + debt + preferred stock + minority interest – cash.
12
[11]
For our real option approach it is important that one method is consistently applied such that
we are able to observe the evolution of the firm value. The valuation method that is applied
throughout this paper is an extension to the market capitalization in the sense that besides
equity, also debt is taken into account. The guideline of our model, discussed in the next section,
is based on Merton’s (1974) structural bond valuation model, which is a well-accepted approach
to determine a fair firm value.
[12]
5 FIRM VALUATION: MERTON’S OPTION PRICING MODEL
This section discusses the most important input variable of our model: the valuation of the
assets of a publicly traded firm. The bulk of the method is based on Merton’s (1974) structural
bond valuation model. We extend this approach with scientific enhancements of Eberhart
(2005) and with Moody’s KMV model for determining the risk of default.
Merton’s (1974) contingent claim analysis of corporate debt assumes that a firm consists of
equity and has only one, single, debt liability. Moreover, there are no other obligations. The value
of corporate debt is computed as the firm value minus the market value of equity. Put differently,
we can determine the value of the firm using the value of corporate debt ( ) and the market
value of equity ( ). The value of corporate debt is calculated by making use of the face value of
debt, . In turn, the face value of debt can be calculated by adjusting the book value of debt for all
interest payments.14 The market value of equity can be observed from trading data.15 The
market value of equity and Merton’s debt value sums up to the market value of the assets ( ):
(
)
The market value of assets is a good measure of the firm value since it takes into account the
present value of the future cash flows produced by the firm’s assets. In the remainder of this
paper we interchangeably use the sentences ‘value of the firm’ and ‘value of the assets’.
Investigating the liability side of the balance sheet of a publicly traded company, one identifies
two parts: the current and long-term liabilities, both consisting of debt (senior) and the residual
stockholders equity part (junior). Note that this book value of equity can differ significantly from
the market value of equity, ( ) as observed in the market. Merton (1974) uses the following
argumentation to determine the market value of equity. In case the market value of the firm’s
assets falls below the outstanding liabilities to debt holder at a given moment in time, the firm is
in default. Otherwise, the loan is paid.16 In case of default, the debt holders are the first in line to
receive their loans.17 The residual part of the assets may be claimed by the equity holders i.e.,
they are subordinated. Therefore, owning equity may be interpreted as owning a European type
call option on the firm’s assets with a strike price equal to the face value of the firm’s liabilities.
At maturity, the payoff to the equity holders (market value of equity) is equal to
(
{
)
}
(
)
where is the time to maturity.18
Figure 5.1 shows the equity value as a function of the firm value at maturity. Here, the facevalue
of debt is equal to 50.
The debt’s book value is to be found at the liability side of the balance sheet and equals the amount of
money the company pays to a lender. Note that no adjustments have been made for debt-like items, like
leasing contracts and pension deficits.
15 More on data in Section 9, Data.
16 It is in the interest of stockholders to pay the loan, since otherwise the lenders would force the firm into
bankruptcy i.e., the stockholders would lose control of the firm. Moreover, stockholders are only entitled
to the residual claim in case of bankruptcy.
17 Hence, they are called senior.
18 To be defined and explained in this section at a later stage.
14
[13]
Figure 5.1: equity value as a function of firm value
) depends on the value of
Equation ( ) shows that the market value of equity at maturity (
the firm ( ) and the time to maturity ( ). Namely, the market value of equity is equal to the
maximum of the value of the firm minus the face value of debt, and zero. So, is zero in
) at maturity equals
case
. Note that the value of corporate debt (
(
Figure 5.2 shows
)
as a function of
. Again,
{
}
(
)
(
)
equals 50.
Figure 5.2: market value of debt at maturity as a function of firm value
Equation (
) can be rewritten in a formula with a more intuitive interpretation:
(
{
)
[14]
}
Here, , denotes the debt claim (including interest payments as a default-free zero-coupon bond
{
}, represents
maturing at time with value ). The second term,
“the put debt holders sell implicitly to shareholders when they agree to buy debt in a firm with
limited liability for its shareholders. That is, in the event of default, shareholders have the right to
sell the firm’s assets back to the bondholders at the face value of debt, and walk away from the
difference between the firm value and face value of debt” , Eberhart (2005).
In conclusion, the value of corporate debt is equal to the face value of debt minus the value of the
put. Figure 5.3 shows a graphical representation of this transformation at maturity.
Figure 5.3: breakdown of the market value of debt (left) into the face value of debt (dashed line) and a short
position in a put option (solid line)
To price the risky corporate debt, Merton (1974) assumes the value of the firm can be described
by a diffusion-type of stochastic process:
(
)
Here,
denotes the firm’s asset value drift per unit of time,
the volatility of the return on
the firm per unit of time and represents a standard Brownian motion. It can be shown that
follows a lognormal distribution.
Other common assumptions in contingent claims analysis are (see e.g., Ingersoll (1976, 1977)
and the Black-Scholes pricing model assumptions of Black and Scholes (1973):


A perfect capital market. This includes the following:
 no transaction costs;
 no taxes;
 no informational asymmetries;
 investors are price takers;
continuous trading;
[15]





a non-stochastic term-structure. The instantaneous interest rate ( ) is a known function
of time;
Management acts to maximize shareholder wealth;
Perfect bankruptcy protection: firms cannot file for protection from creditors except
when they are unable to make required cash payments;
perfect liquidity: firms can buy and sell assets as much as they want to make cash payouts;
short positions are allowed.
Merton (1974) assumes the following boundary condition with respect to the value of debt and
equity:
(
(
)
)
(
)
.
(
)
(
)
Equation ( ) states that the market value of debt is lower than or equal to the firm value. From
( ) one can conclude that the market value of debt and the market value of equity are zero in
case the value of the firm is zero.
Because the boundary conditions ( ) and ( )are exact the same that can be found in the
Black-Scholes model and because the firm value evolves over time according to a Geometric
Brownian Motion, we are dealing with a Black-Scholes type of problem. Therefore, Merton’s
(1974) method to price equity is identical to the equations to price a European call option on a
non-dividend paying common stock.19 Hence, Merton (1974) defines the closed form solution for
the market value of equity on a given moment in time as
(
)
(
)
(
)
(
)
where
( )
(
)
√
√
and
Here, ( ) represents the cumulative standard normal distribution function and
denotes the
instantaneous variance of the return on the firm. The term
gives the present value of the
promised debt payments. Note that, as a result of the risk neutrality conditions, the drift term of
the firm value, , does not appear in the Black-Scholes pricing formula. This does not take
away, however, the fact that we are interest in the value of . The reason for this being that this
term enables one to simulate the future development of the firm value.
19
More precisely, Merton (1974) shows that the partial differential equation corresponding to the equity
value equals
. With boundary conditions (
), (
) and (
partial differential equation is identical to the one that corresponds to a European call option.
[16]
) this
Merton (1974) calculates the value of corporate debt by subtracting the market value of equity
from the firm value. We are dealing with a slightly different situation, however. That is, in our
case, the firm value is the only unknown since both the book value of debt and the market value
of equity are observable. Therefore, this paper follows the approach of Eberhart (2005) to value
a firm.20
In order to determine the firm value one needs to compute the volatility of the firm’s return.
Because of Merton’s (1974) assumption that the equity value is a function of the value of the
firm and time, Jones, Mason and Rosefeld (1984) shows using Ito’s lemma the following volatility
relation:21
(
)
(
)
Note that, because ( ) also depends on the firm value, we actually have a problem of two
equations (i.e., ( ) and ( )) and two unknowns,
and . We can solve the implied
market value of the firm and the volatility of the firm backwards. Please refer to the appendix for
a detailed discussion of this method.
It is common practice in finance to use Merton’s (1974) method in reverse to determine a firm’s
value. For example, Moody’s KMV uses the same methodology to estimate the value of a firm
needed for modeling default risks in the Vasicek-Kealhofer model. See Kealhofer (2003) and
Vasicek (1984), and Crosbie and Bohn (2003) and Dwyer and Qu (2007) for practical purposes.
This paper applies Merton’s model as described into the real option framework. Unfortunately,
this also means we have to deal with some weaknesses inherent to Merton’s model. For example,
Merton (1974) makes the simplified assumption of a capital structure with just one type of debt
and equity.
The remainder of this section extensively elaborates on the details of the model as implemented.
We discuss the inherent weaknesses and find solutions to tackle them. We extend the model
using Moody’s KMV model and results from Eberhart (2005). Note that our goal is to develop a
model that reflects the real world as well as possible. We would like to reemphasize the fact that
our aim is to plot the evolution of the firm value rather than to given an accurate estimation of
the firm value.
5.1 CAPITAL STRUCTURE
Merton (1974) assumes a rather simplistic capital structure with only one type of debt (zero
coupon bonds) and equity. To connect the more complex capital structure of more realistic firms
with more than one type of debt with the intuitions of Merton’s approach, one can either
simplify the complex capital structure of firms into a structure that fits Merton’s structure or one
can extend Merton’s model such that it fits with the more complex capital structures. This
section justifies our choice to simplify the capital structure, rather than extending the model.
Eberhart’s (2005) approach is based on Merton’s (1974) method, which is, in fact, equivalent to
Merton’s method in reverse order.
21 See the Appendix for the proof of equation [5.9].
20
[17]
According to the Modigliani-Miller proposition (Modigliani and Miller, 1958), the market value
of a firm depends on its capital structure. Hence, changing the various types of debt into one
single type of debt, such that the total repayment of the initial amount plus the interest
payments to the lender is equal to the sum of the different debt types, does not influence the
total market value of the firm. Nevertheless, the KMV model applies the more detailed capital
structure. The reason for this being that Moody’s KMV is not primarily interested in the value of
the firm, but more in its creditworthiness. In general, a company defaults in case it is unable to
fulfill its liabilities. By changing the different debt claims into one zero coupon bond, all default
moments are neglected, which might result in a misinterpretation of a company’s credit risk.
In case of default, senior debt holders retrieve their money prior to the more junior debt holders.
Since all debt holders are ranked according to their seniority, each lender has a different risk
profile. The relevant differentiation is between claims that prevail over the lender’s claim, claims
that are at par, and claims that are subordinated to the lenders claim (Vasicek, 1984). Therefore,
the riskiness of an investment depends on the rank of all other investors. A model that takes
different lenders into account, but which we do not investigate in this paper, is proposed by
Geske (1977). Geske’s model is somewhat similar to Merton’s model in the sense that equity is
considered as an option as well. More specifically, equity is considered as a compound option.
Geske (1977) states that:
“at every coupon date, until the final payments, the stockholders have the opportunity of buying the
next option by paying the coupon or forfeiting the firm to the bondholders. The final stockholder
option is to repurchase the claims on the firm from the bondholders by paying off the principal at
maturity.”
In this paper, we use Merton’s model to determine the firm value process rather than the firm’s
creditworthiness. Therefore, it is preferred to simplify the capital structure by changing all
different debt claims to one zero coupon bond (see subsection [5.2], Exercise price for details).
In case of a default, the common shareholders are the last in line that may claim any
compensation. Therefore, we classify all investors that hold assets with more rights than the
common equity holders as a debt holder/item. The capital structure for the liability side of the
balance that we assume then becomes:
Assets
Assets
Liabilities
Debt
Total debt
Total liabilities minus total debt
Shareholders’ equity – common equity
Equity
Common equity
Table 5.1: assumed capital structure
5.2 EXERCISE PRICE
In Merton’s model, the exercise price of the call option (the face value of debt), is equivalent to
one zero coupon bond. This is a direct result of the ‘one type of debt’ assumption. Since, in
practice, most companies issue more than one type of coupon paying bond, we consequently
have to deal with all types of bonds such that our debt valuation is consistent with Merton’s debt
[18]
valuation method. Therefore, we adjust all debt items, such that it can be replaced by just debt
item; we follow the procedure of Eberhart (2005). Eberharts’s model of debt valuation, changes
all debt claims into one zero coupon claim. Therefore, the following formula applies to
determine the face value of debt number , :
(
)
(
)
Here,
denotes the book value of debt as filed, the coupon rate and the time to maturity of
the contract. The coupon rate can simply be estimated using the interest expense divided by the
total amount of interest-bearing debt.
5.3 TIME TO EXPIRATION
The time to expiration can be estimated by computing a weighted average of the duration of the
firm’s outstanding debt. That is,
∑
( )
(
)
where and denote the adjusted face value of outstanding debt item and its corresponding
duration, respectively. Note that the sum of all
yields the adjusted face value of debt, . This
method of estimation is in line with Eberhart (2005). The difference being, however, that instead
of just one item of short-term debt and one item of long-term debt we take into account all
different durations belonging to the different debt claims. Using now the adjusted time to
expiration we are able to interpret the maturity structure of a company as if the firm issued just
one zero-coupon bond.
5.4 DIVIDEND PAYMENTS
Merton’s option pricing formula is based on a non-dividend paying firm. Nevertheless, we do not
need to incorporate these dividend payments into the pricing formula. This can be seen as
follows. In case of a plain vanilla European call option on the firm’s stock, one need to adjust the
value of the underlying for dividend payments, since the holder of the option cannot claim these
payments. The argumentation for an option written on the value of the firm is slightly different.
The dividend payments made by the firm are directly deposited on the account of the equity
holders. Because the equity holders themselves are the holders of the option, the price of the
option should not be adjusted. This implies that dividend payments are not necessarily a
disadvantage for the holder of the option.
5.5 VOLATILITY
Equation ( ) is a transformation formula to determine
. However, Moody’s KMV uses
another method to find an expression for
, because the relation between
and
as stated in ( ), holds only instantaneously (Dwyer and Qu, 2007). One of the main reasons for
this is that the market leverage, defined as the debt equity ratio, fluctuates too heavily to provide
accurate results (Crosbie and Bohn, 2003).
[19]
To see this, consider the following. If, for example, the market leverage increases quickly, then,
according to ( ), the volatility of the firm will be underestimated. The opposite holds true
when market leverage decreases.
Let us look at a numerical application.
,
,
and
. Then,
[Moody’s KMV] model returns a firm value of 12.51 and a firm volatility of 0.096. Now suppose
that on a given day the equity value increases to 3.5 from 3. This will cause the leverage ratio to
decline. The firm volatility as a result of this change now becomes 0.108, implying an increase in
volatility of circa 12.4%. Note that, as a result of this quick change of the equity value, the new
firm volatility overestimates the actual asset volatility.
In contrast with the above method, Moody’s KMV introduces a more sustainable method to
determine the volatility of the firm. That is, Moody’s KMV links the firm’s volatility on a given
day to the volatility within a certain period. As a result of this construction, Moody’s KMV
eliminates high fluctuations in volatility value.22 This paper uses equation (5.9) as its main basis
but for the sake of completeness we investigate the results using Moody’s KMV method as well.
5.6 COUPON PAYMENTS
The coupon payments of the outstanding debt are, as discussed in subsection 5.2, Exercise Price,
included in the adjusted face value of debt. Because of this re-allocation, the outstanding debt
may now be interpreted as a single zero coupon paying bond.
22
See Appendix C for the basic intuitions.
[20]
6 REAL OPTIONS
This section explains the main characteristics of the real option approach we use to determine
the optimal timing of merger or acquisition event. We will start with explaining why the
standard NPV method does not work in case of announcing the acquisition of a publicly traded
firm. Second, we describe the method used to determine the optimal timing, which is based on
McDonald and Siegel (1986) and Dixit and Pindyck (1994).
For projects for which it holds that 1. there is uncertainty surrounding the cost or revenues of
the investment, 2. the investment is at least partly irreversible and 3. for projects with a
possibility to delay, investing according to the NPV rule often leads to the wrong decision. 23 This
is because the NPV ignores the value inherent to waiting for additional information. In
particular, if an investor opts to wait (i.e., delay his investment decision) the investor is enabled
to make a better informed decision. For example, some uncertainties will become certainties on
a given moment in time, or the probability of an unprofitable investment declines as a result of a
higher expected revenue flow. The NPV method works well for investments that are reversible
or, when irreversible, if it is a now or never decision. One may argue that in case a publicly
traded firm announces to acquire another publicly traded firm, the investment is partly
irreversible. This may be attributed to the fact that the acquiring firm is able to sell the shares of
the acquired firm if the investment turns out to be unprofitable. However, it is reasonable to
assume that, due to the poor performance of the acquired firm and the overflow of the supply of
shares, the market price of the acquired shares is likely to decline. In case the acquiring firm
decides to sell the acquired stocks, it should take a lower selling price into consideration. That is,
a selling price which will likely be too low to repay the debt claim. And last, the market of selling
such an amount of shares is illiquid. Therefore, it probably takes a lot of time from the moment
of announcing the supply of shares and the actual moment. Hence, the investment is at least
partly irreversible.
For investment under uncertainty, the NPV rule should be replaced by a rule which takes into
account the characteristics of the investment. In general, a firm should announce a takeover in
case the expected revenues are at least equal to a certain threshold, consisting of the investment
cost times a certain factor > 1. This threshold is referred to as the optimal timing. Time in this
context is, therefore, not equal to a calendar date, but to a condition for which it is, from a
financial point of view, attractive to invest in. McDonald and Siegel (1986) and Dixit and Pindyck
(1994) investigate the optimal stopping of investments with uncertainty. Using dynamic
programming, the remainder of this section describes the optimal moment of an
announcement.24 We present the continuous time model of the dynamic programming approach
of McDonald and Siegel’s (1986) and Dixit and Pindyck (1994) with an infinite horizon.
In this paper we assume that there exists one publicly traded firm that has the opportunity to
take over another publicly traded company. Therefore, the bidding firm has, on each moment of
time, the following two possibilities:
Put shortly, the NPV rule states to invest in a project when the present value of its expected cash flows is
at least as large as its costs.
24 Referred to as optimal stopping in the existing literature.
23
[21]
1. announce to take over the target firm (stopping);
2. wait for a better moment in time to announce the takeover, if that moment exists
(continuation).
The word ‘better’ is actually quite vague in this context. Therefore, let us define a better moment
as: “a moment in time for which holds that the financial conditions are better”. Better financials
conditions may mean, for instance, that either the investment cost is lower or that the value of
the project is higher. However, the moment of undertaking a merger or acquisition may be
defined as better as well if the decline in investment costs is much more than the decline in the
project value, or, if the increase in project value is much more than the increase in the
investment costs.
The investor makes, on each moment of time a binary decision, which can be captured in a
decision model, , as follows:
(
{
)
(
)
An investor chooses these control variables in such a way that the continuation value is
maximized. The continuation value ( ) is defined as the expected net present value when the
firm makes all decisions optimally from this point onwards (Dixit and Pindyck (1994)). This can
be written as
( )
{
(
)
(
(
))}
(
)
Here, is the state of the firm at time . That is, the information about the current situation
) represents the immediate
which is needed to make a correct decision. The first term, (
profit flow, whereas the second term denotes the continuation value. All optimal decisions after
(
). Since this is a random variable, we take the
time are summarized in the
expectation of it and discount it back with
to time to observe the value of waiting. Bellman
(1957), one of the founding fathers of dynamic programming, argues that the described
decomposition in Bellman’s Principle of Optimality is as follows:
“An optimal policy has the property that, whatever the initial action, the remaining choices
constitute an optimal policy with respect to the sub problem starting at the state that result from
the initial actions”.
As a result of this, the optimality of the remaining actions
,
., is subsumed in the
continuation value. Therefore, only has to be chosen in an optimal way. Since we are dealing
with an infinite horizon for the decision problem, there is no known final value from which we
could work backwards. Therefore, we transform the problem into a recursive structure. Since
the problem one period further looks exactly the same as the problem now but only the starting
state differs, Dixit and Pindyck (1994) conclude that the value function is common to all periods.
Equation ( ) can, therefore, be generalized by the following Bellman equation:
[22]
( )
{ (
)
( ( )
)}
(
)
Here, denotes the current state, and is the state of the firm in the subsequent period. The
expectation is taken over all future states conditioned on the information available in the current
period’s
.
When in continuous time, i.e., when infinitesimal time steps are considered, (
rewritten to
( )
{ (
)
(
)}
) can be
(
)
(
)
⇔
( )
{ (
)
(
) ( )
(
)}
To obtain the equation for optimal stopping, take the maximum of the Bellman equation for
continuation and value of stopping, ( ):
( )
{ ( )
(
)
(
) ( )
(
)}
(
)
(
)
(
) ( )
( ), ( ) results in
For those for which it holds that ( )
stopping. If the opposite holds true, the maximum will be achieved through continuation. Note
(
)
(
) ( )
( ). Dixit and
also, that at the boundary point
, ( )
Pindyck (1994) refer to this as value matching condition. Another necessary condition for
optimal timing concerns smooth pasting condition. This means that the first derivatives of both
the stopping and continuation value at the boundary point
are equal.
We now apply this basic real option model to our investment opportunity, in part based on
McDonald and Siegel (1986) and Dixit and Pindyck (1994). In their models, the cost of
investment, is known and fixed and the value of the investment, follows a geometric
Brownian Motion. In order to obtain a finite solution, one needs to assume that the drift term of
the adjusted project value, ̂ , is smaller than the discount rate, .
The value of the investment opportunity i.e., the value of the option to invest is defined by
{(
( )
)
}
(
)
Here, is the (unknown) future investment time. We are looking for the value
for which it
holds that the firm is indifferent between investing (stopping) and not investing (continuation).
The value of the continuation region (values for for which it is not optimal to invest) can be
determined using the Bellman equation described in ( ). Since there is no payoff as long as one
does not invest, ( ) can be simplified to:
( )
Ito’s lemma enables us to introduce
changes to
(
)
(
)
into the equation. As a result, the Bellman equation
[23]
(
( ))
( )
( )
(
)
In order to observe a value for ( ), we must solve ( ) with respect to the value matching and
the smooth pasting criteria and the boundary criterion ( )
.25 McDonald and Siegel (1986)
try the solution ( )
. After substituting this function and the corresponding derivatives
with respect to into ( ), equation( ) is obtained:
√(
)
√(
)
(
)
Because of the boundary condition ( )
, the value function ( )
becomes
( )
. Substituting this result into the value matching and smooth pasting criteria
yields, after some tedious manipulation, the optimal investment rule:
(
Because
, it holds that
and
(invest if
) is incorrect. Put differently:
. This constitutes the proof that the NPV rule
“uncertainty and irreversibility drive a wedge between the critical value
wedge is the factor
)
and . The size of the
”, Dixit and Pindyck (1994) .
In this paper we compare the actual investment timing with the optimal investment timing
In section 9 we show the application of this framework with an example.
The latter condition is also referred to as the absorbing boundary: when
project value is not possible.
25
[24]
, an increase in the
7 THE DYNAMICS AROUND A MERGER AND ACQUISITION
This section first discusses the assumptions associated with the value of a firm. Then, it touches
upon the assumptions related to changes in the firm’s value resulting from the announcement of
the takeover and the input variable of the real option model.
7.1 ASSUMPTIONS ASSOCIATED WITH THE FIRM VALUE
In this paper we simply compute the equity value of the combined firm by adding the equity
values of the bidding and the target firms. The liability claim of the combined entity is
constructed in such that the total liability claim equals the sum of the two different liability
claims. We apply the Eberhart’s (2005) methodology once more to determine the duration and
interest rate of the composed debt claim from the two separate debt claims. More specifically,
we use the following formula:
(
)
(
)
The dynamics of the equity value processes of the acquirer and target are subject to changes
around the date of announcement of a merger or acquisition. Since we investigate mergers and
acquisitions, irrespective of the deal conditions, we investigate whether an acquisition is
possible by assuming that there is no premium and all synergy gains benefit the acquiring firm.
We investigate this case since it is empirically shown that many bidding firms suffer significantly
negative abnormal returns surrounding the announcement date.26 These negative abnormal
returns indicate that the paid premium to acquire the stocks of the target firm is higher than the
total synergy gains. This suggests bad deal conditions and hence there might be no optimal
timing to make an announcement.
To define the project revenues


of the investment we split the time into two periods:
the period before the announcement;
the period at and after the announcement.
On the date of announcement, synergies, included in the different value processes, as observed
by the market become visible. We are able to simulate the investment revenues and the
investment costs backwards. and are defined as follows:
26
{
(
)
{
(
)
See for example Argawal, Jaffe and Mandelker (1992).
[25]
Here
denotes the moment in time at which the merger of acquisition is announced.
Equations (7.3) and (7.5) may be interpreted as follows. equals the value of the target firm
corrected for changes in firm value from synergies on the announcement date. Note that this is
equal to the investment cost a firm should pay to acquire the target’s firm assets without the
knowledge of a merger. is equal to the value of the combined firm minus the value of the
bidding firm (this equals the ‘new’ value of the bidding firm as a result of the change in capital
structure) corrected for the synergy gains or losses. This project revenue can be seen as the
increase/decrease in firm value resulting from the announced takeover.
For the real option framework we need a deterministic investment cost Therefore, allow us to
slightly adjust the processes such that investment uncertainty is removed by taking as a
numéraire. By so doing, one finds the following adjusted project value ̂ and the riskless
investment cost ̂:
̂
̂
(
)
Assume ̂ evolves as a geometric Brownian motion over time with the following characteristics:
̂
̂
̂
̂
̂
(
)
Here, ̂ denotes the adjusted firm’s asset value drift per unit of time, ̂ the instantaneous
variance of the adjusted firm return per unit of time and a standard Brownian motion.
7.2 SYNERGY
Recall that synergy can be defined as
(
)
Andrade, Mitchell and Stafford (2001) argue that, for publicly traded firms, the synergy gains
are observable in the period around the announcement day, the so called event date. The
abnormal stock market reaction of a merger’s announcement is used as a gauge of value creation
or destruction. One important assumption here is that the capital market is efficient. Put shortly,
this means that all available information is taken into account in the prices at which stocks
currently trade. Specifically, this is realized by quick responds from investors to new
information. As a result, the market’s response to an announcement of a merger or acquisition is
directly observable and measurable.
) time window surrounding the
Mulherin and Boone (2000) use a three day (
announcement date to isolate the specific market reaction to an announcement of a merger of
acquisition. This is measured using abnormal returns ( ). This method is useful in case both
the market is efficient and the information is ‘pure’, in the sense that the abnormal reaction of
the stock price of the bidding or target firm is not influenced by other information (e.g., the
presentation of the annual report). It is also possible that the takeover has been leaked before
the official date of announcement. This may well cause a pre-anticipation of the equity value on
the upcoming announcement. The opposite can hold as well: in the days after the announcement
the market reacts after announcing new deal information. Therefore we apply, inspired by
) event window as well.
Mulherin and Boone (2000), a (
[26]
Abnormal returns ( ) are defined as the difference of the actual return of asset and the
expected return of asset :
(
The cumulative abnormal returns,
)
(
)
(
)
, are defined as the sum of the abnormal returns:
∑
Actual returns surrounding the announcement date are observable from trading data. We
calculate the expected return using the CAPM , resulting from the Sharpe-Lintner model of
Sharpe (1964) and Lintner (1965). The CAPM model builds on the model of portfolio choice
developed by Markowitz (1959). This model induces that investors choose a mean variance
efficient portfolio. That is to say, investors minimize the variance of a portfolio with a given
expected return or maximize the return of a portfolio given a certain variance. For both the
Markowitz optimal portfolio model and the CAPM model, the following is assumed:





there are numerous of investors, all of which are price takers;
all risky assets are publicly traded;
all investors are risk-averse and mean-variance optimizers;
all investors have access to the same information and interpret it in a similar way
(homogeneous expectations);
the market is assumed to be perfect i.e.,:
 no taxes, transaction costs and information costs;
 there are no frictions;
 stocks can be bought and sold in any quantity;27
Sharpe (1964) and Lintner (1965) make two additional important assumptions to the CAPM
model:


investors agree on the joint distribution of asset returns. It is assumed that this
distribution is the true one;
there is one risk-free asset and all investors can borrow or lend at the risk free
rate of that asset.
Under these assumptions the (unconditional) CAPM
is defined as:
(
)
(
(
)
)
can be interpreted as a measure of an asset’s return to the variation in the market return. By
use of the expected return of asset can be calculated as follows:
(
27
)
((
I.e., short selling is allowed.
[27]
)
)
(
)
Note that the expected return of asset is composed of the risk-free rate plus a risk premium.
This risk premium is defined as the of the asset times the premium per unit of beta risk. We
use the data of the website of Kenneth R. French to retrieve the Center for Research Security
prices (CRSP) equally-weighted index returns. 28 To retrieve the total synergy gains in terms of
firm value, we execute the following procedure:
) the abnormal returns of the acquirer and
1. calculate, using ( ), ( ) and (
target,
and
, respectively;
2. calculate using ( ) the cumulative abnormal returns of the acquirer and the target,
and
, respectively;
3. multiply the
with the equity value to obtain the dollar value
;
4. subtract from the original the
to obtain the announcement adjusted
;29
5. calculate, for both the acquiring and the target firm, the adjusted value of the firm,
,
using
. The total synergistic gains or losses resulting from the announcement are
now defined as
This paper assumes that the synergy gains or losses are constant over time. To calculate the
value of the combined firm for the period prior to announcement, adjust the value of the
combined entity by adding the synergy gains or losses (in terms of firm value).
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
Note that this corresponds to the actual equity value on the announcement date minus the abnormal
equity value.
28
29
[28]
8 DATA
In this section we discuss the three different databases we use, Securities Data Company (SDC),
DataStream and Wharton Research Data Services (WRDS), and the different filters we apply to
obtain our final dataset. Our primary information about mergers & acquisitions is available from
SDC.
8.1 SECURITIES DATA COMPANY (SDC)
Within SDC, we apply the following filters:








Location target and acquirer: United States;
announcement date of takeover: January 1, 2000 - December 31, 2004;
target and acquirer are public listed firms on the DataStream database;
all deals have a disclosed dollar value;
tender offers only;
deals with one bidder only;
deal value > US$500 million;
focus on completely control transactions. I.e. the percent of shares sought, acquired and
owned in the deal is 100%;
 all regulated (SICs 4900—4999) and financial (SICs 6000—6999) firms are removed
from the sample to avoid restructuring governed by regulatory requirements.
The above criteria yield a total of 183 mergers and acquisitions.
8.2 DATASTREAM
Using DataStream and WorldScope we search for different kinds of companies and market
information of the firms resulting from our SDC results. In case the execution for a certain data
item results in an error for a particular firm or the data of a certain company is not available on
January 1, 1999 (e.g., in case the registration date of the publicly listed company on an exchange
is after January 1, 1999), we remove the complete merger and acquisition from our sample.30
After removing all incomplete financial information of firms, we are left with 82 of the 183 initial
observations.
For each transaction we obtain the following information:
 market capitalization*;
 book value total liabilities and shareholders’ equity**;
 book value total shareholders’ equity**;
- book value common equity**;
- book value other equity (like treasury stocks and convertible
securities)**;
 book value total liabilities**;
- book value other liabilities**;
We make an exception for the debt items with a maturity longer over 10 years since most firms do not
have this information available.
30
[29]
-

book value total debt**;
1. book value short term debt and current portion of long term
debt**;
2. book value long term debt**;
a. book value debt greater than 2 year and less than 6
years**;
b. book value debt greater than 6 years and less than 10**;
c. book value debt greater than 10 years**.
interest expense on debt**;
*stands for time-series data and **stands for static data.
With respect to the category ‘book value long term debt’, WorldScope also defines the category
‘book value debt with a maturity longer than 10 years’. Searching in Datastream for these
financial data results in many errors. Therefore we remove this criterion and we assume that
debt with a maturity longer than 10 years is equal to the post ‘book value total debt’ minus book
value short term debt and current portion of long term debt minus book value debt greater than
1 and less than 5 years and book value debt greater than 5 and less than 10 years.
With respect to the duration, we assume that the duration of short term debt and current
portion of long term debt is equal to 1 year, the duration of debt with a maturity between 2 and
6 years is equal to 4 years, the duration of debt with a maturity between 6 and 10 years is equal
to 8 years and debt with a maturity over 10 years is equal to 15 years. As introduced in section
5.1 and shown in Table 5.1, we define a debt item as the sum of all liabilities (consisting of debt
and other liabilities) and shareholders’ equity less common equity. We assume that the duration
of the liabilities other than debt and shareholders’ equity minus common equity is equal to 0.5.
8.3 WHARTON RESEARCH DATA SERVICES (WRDS)
From WRDS, we obtain the following:


return on market portfolio (time-series data);
risk-free interest rate (time-series data).
Besides data we obtain from DataStream, we retrieve the CAPM factor market minus risk-free
rate and the risk-free rate website Kenneth French.28 This data can also be found in the Fama
French Portfolios and Factors database from WRDS. The market portfolio, on which the factor
market rate is based, is constructed as the annually weighted average of all NYSE, AMEX and
NASDAQ stocks (from CRSP). The risk free rate corresponds to the one-month Treasury bill rate
(from Ibbotson Associates).
8.4 ASSUMPTIONS WITH RESPECT TO THE DATA
Note that balance sheet data is mainly static data. Naturally, only at one, or occasionally at a few
moments in a fiscal year, data is updated. Inspired by Feltham and Ohlson (1995), we assume
that persistent accounting data changes linearly over time between two data points. A similar
assumption is made for the duration of debt and the interest rate.
[30]
In regards to calculating the drift and the noise (volatility) terms we use a rolling window of 250
days. The parameter , as part of the CAPM model, is estimated 10 days prior to the
announcement of the takeover over a period during the 250 days before.
In our standard model we use a discount rate, , of
consider the cases in which
and
.
[31]
. For the sake of completeness we also
9 EXAMPLE TAKEOVER: PATINA OIL & GAS CORP. BY NOBLE
ENERGY INC.31
This section shows the used method to determine the abnormal returns of both the bidding and
the target firm and then to obtain ̂ . As a working example, we investigate the announced
takeover (100% of the target’s shares) of Patina Oil & Gas Corporation by Noble Energy
Incorporate, which was announced on December 16, 2004.
Table 9.1 states financial characteristics of both companies on the announcement date. Values
are rounded to units of US$1,000,000.
Noble Energy Incorporate
(bidding firm)
1974
6.77
0.89
2.55%
0.24
0.15
Patina Oil & Gas Corporation
(target firm)
1012
4.60
1.03
2.55%
0.35
0.25
Table 9.1: firm characteristics of the bidding and the target firm
Using Newton-Raphson algorithm as presented in appendix B and Merton’s method in reverse
order, we are able to calculate the value of both firms as well as the value of the combined firm
(see Figure 9.1).
Figure 9.1: plot of the values of the bidding (dotted line), target (marked dotted line) and combined (blue
solid line) firm. Left: the period January 2004 until and including December 2004. Right: the period
surrounding the announcement date.
From Figure 9.1, it can be observed that the value of the bidding firm slightly decreases around
the announcement date whereas the value of the target firm increases. The value of the
combined firm, composed by adding the equity values and the debt claims of both firms, and
using equations ( ) and ( ) for calculating the duration and coupon rate respectively,
This section merely aims to clarify the discussed methods and hence the section should not be
considered as an integral and essential part of the thesis.
31
[32]
increases during the days surrounding the announcement. Note that the value of the combined
firm is unequal to the sum of the firm value of the bidding and target firm separately. The reason
being that the risk profile changes. A decent explanation is given at a later stage in this section.
) day event window.
Next, allow us to calculate the abnormal returns within the (
Therefore, we consider the change of equity value of both firms on these days (Table 9.2) and
the characteristics of the market portfolio and the one-month Treasury bill rate on a daily basis
(Table 9.3).
Noble Energy Incorporate
(bidding firm)
3554
3620
3492
3538
Table 9.2:
and
Return
Patina Oil & Gas Corporation
(target firm)
2206
2254
2586
2602
1.8%
-3.5%
1.3%
Return
2.2%
14.7%
0.6%
of the bidding and the target firm around the announcement date
0.37%
-0.33%
-0.44%
0.0071%
0.0071%
0.0071%
Table 9.3: the CAPM input variable
and
(daily basis)
Using the given parameter values, we are able to calculate the
Noble Energy Incorporate
(bidding firm)
-5
Table 9.4:
Since we capture
more in order to obtain
as
.
adjusted firm value).
of both firms:
Patina Oil & Gas Corporation
(target firm)
407
(dollar value)
of both the acquirer and target firm, we apply Merton’s method once
. We calculate the firm value using ( ), but now with ̂ defined
̂ (i.e., the original firm value minus the
is then defined as
Noble Energy Incorporate
(bidding firm)
-5
Table 9.5
Patina Oil & Gas Corporation
(target firm)
409
(dollar value)
From Table 9.5 we conclude that the sum of the bidder’s and target’s
is equal to 404.
Since this number is larger than zero, one may conclude that the financial markets positively
receive the announced acquisition. Indeed, it can be stated that the market observes synergy
possibilities.
Zooming in on
of the two firms separately, we conclude that the bidding
and
are negative. This means that the market reacts negatively to the announcement of the
takeover. Apparently, the market observes a too high premium compared to potential synergy
gains for the bidding firm.
[33]
Besides the increase as a result of the announcement returns,
also increases as due to the
change in risk profile for the combined firm. In this particular example, it holds that
is equal to 5577+3535= 9112, which is smaller than
, equal to 9113. There are two main
reasons for this change in value:
1. changes in volatility;
2. changes in duration.
These two parameters are important input variables in Merton’s firm valuation method. Table
9.6 summarizes the changing characteristics of the capital structure and the equity value process
on the announcement date. We indeed observe that the duration of the combined firm is almost
10% lower than the duration of the bidder and 33% higher than the duration of the target firm.
Based on this new duration and the intuitions of Merton’s method, we conclude that the new
debt claim of the combined firm expires, on average after approximately 6.11 years. The
volatility of the newly combined firm equals 0.17. This implies a 10% increase relative to the
volatility of the bidder’s firm and a 31% decrease relative to the target’s firm volatility.
Noble Energy Incorporate
(bidding firm)
2480
6.77
2.55%
3492
0.24
0.15
Patina Oil & Gas Corporation
(target firm)
1070
4.60
2.55%
2586
0.35
0.25
Combined firms
3551
6.11
2.55%
6078
0.25
0.17
Table 9.6: firm characteristics of the bidder, the target and the combined firm
Figure 9.2 shows the value of the combined firm as a function of
and
to observe the
sensitivity of the firm value. From this Figure one may conclude that, ceteris paribus, the lower
the duration, the higher the value of the firm. A similar relation holds for the volatility of the
firm: the lower the volatility of the firm the higher the firm value.
Figure 9.2: value of the combined firm as a function of the duration and the volatility
[34]
Given the duration of 6.11, a volatility of at most 0.185 results in a higher value of the combined
firm. Given the firm volatility of 0.17 a duration of at most 6.12 results in a higher value of the
combined firm. All in all, we can conclude that the volatility and the duration are important
sources for the value of a company and therefore for the possible benefits of a merger and
acquisition as well.
Because of the cumulative abnormal returns and a change in firm value due to the new capital
structure, we calculate all changes in firm value as a result of the announcement of the takeover
summarized into one item. We will refer to this as the total synergistic gains:
(
)
(
)
Based on the firm values one day after the announcement date, we conclude that the
announcement of the takeover results in an increase of the firm value of 405.
Because of the value accretion we can determine the optimal timing using the real option model.
For this takeover it holds that the dynamics of the revenue process, as defined by equation ( )
are as follows:
̂
-0.030
0.027
Table 9.7: drift and volatility
̂
In order to calculate the accompanying we need the discount rate
let us present the results in case =
.
as well. In this example,
The quadratic equation, as stated in section 6 Real Options, is equal to:
(
When
)
⇒
, this equation can depicted as shown in Figure 9.3
Figure 9.3: The Fundamental Quadratic equation (
[35]
)
As can be observed from Figure 9.3 (and solved from the corresponding equation),
-1.2 and equals 86.1.
̂ Can now be calculated using (
is equal to
) and the numéraire condition of equation 7.5:
̂
̂
Hence, it is optimal to invest in case
. That is, in case the real project revenue is at
least equal to 1.01 times the investment cost. 32 The actual investment value on the
announcement date is equal to 1.13 times the investment cost. From a real option point of view
̂ . The same results
this particular announcement can be considered as well timed, since ̂
are obtained if we apply the alternative volatility method, based on Moody’s KMV.
In summary, we conclude that the bidding’s equity holders and the target’s equity holders jointly
gain after announcing the takeover. This becomes visible by both the positive sum of
and
the additional firm value resulting from a change in capital structure. Whereas the NPV rule
̂), based on the real
states that an investment is optimal in case the NPV is positive (i.e., if ̂
̂ Because of the characteristics of ̂ as
option model it is optimal to invest whenever ̂
given by equation ( ), we conclude that it is optimal to invest if the project value is larger
than or equal to
times the investment costs .
In reality, on the announcement date revenues of this takeover are much higher, namely 1.13
times the investment costs. Therefore, we conclude that the announcement of the takeover has
been timed optimally.
32
For
and
the optimal investment threshold is equal to
[36]
̂ as well.
10 RESULTS
This section discusses the empirical results. First, we explain the data’s descriptive statistics.
Second, we answer, using these results, the research questions as formulated in section 2,
Problem Definition:


“What is the optimal timing of announcing a merger and acquisition event if both the
evolution of the stock price of the acquiring and the target company (excluding the specific
deal terms) are observed?”
“How does the actual implementation date of a merger and acquisition correspond to the
optimal timing resulting from the real option model?”
10.1 GENERAL DESCRIPTIVE STATISTICS DATA
For 82 takeover announcements we investigate the financial characteristics from January 1,
1999 onwards. In particular, we investigate the period surrounding the announcement. In this
section we discuss the implication on both the firm and equity values for these 82 deals.
Appendix D shows a list containing the names of the 82 investigated takeovers, the
announcement date and the transaction value. All values in this section are in units of US$
1.000.000.
10.1.1 GENERAL CHARACTERISTICS OF THE DEAL AND THE BIDDING AND TARGET FIRM
Table 10.1 describes general characteristics of the bidding and target firm as well as the
transaction itself. The transaction values are collected from SDC and are defined as
Total value of consideration paid by the acquirer, excluding fees and expenses. This value includes,
amongst others, the amount paid for all type of equity, debt and all other types of liabilities.
From the table we conclude that the mean of the 82 transaction values is more than twice as
large as the median. This implies that the distribution of transaction values is skewed to the
right. This implies that there are some deals with an extremely large transaction value. This
observation is confirmed by Figure A.1 in the appendix. From the data and the Figure we
observe that 76 of the 82 deals have a transaction value lower than 10.000 From the 6 largest
transactions we conclude that the average of these transactions is equal to 21.600. The largest
transaction in terms of value, the acquisition of Pharmacia Corp by Pfizer Inc. in 2002, is more
than twice the transaction value of the second most expensive transaction.
The diversity of the size of the transactions becomes clear from Table 10.1. For example, the
largest transaction value, 59.515 (the Pfizer Inc. - Pharmacia Corp deal), is almost 110 times as
large as the smallest transaction value (the Belden Inc. - Cable Design Technologies Corp deal).
General Characteristics
Transaction value
Mean
Median
minimum
maximum
3952
1808
542
59515
(
25458 4076
7896 1791
993
532
290930 56483
/
)
12.30
3.85
0.54
253.02
Table 10.1: general characteristics of the deal and the bidding and target firm
[37]
A similar pattern can be observed for the value of the bidder and the target firms. A few
extremely large firms ensure that the average of the firm values is above the median. From the
column “Ratio (
/
)” in Table 10.1 we observe that the average of the ratio ‘bidder value
divided by target value’ is approximately equal to 12.30. Dividing the average value of the bidder
by the average value of the target results in a value of 6.24. Therefore, we conclude that there
are some smaller deals with a relatively high ratio. Since the median of this ratio is 3.85, we
conclude that in 50% of the cases the bidder is at least 3.85 times as large as the target. There
are two announced takeovers for which it holds that the target firm is larger than the bidding
firm (a so called reverse takeover).
10.1.2 DEBT AND EQUITY
Table 10.2 and Table 10.3 state the characteristics of (as defined as in Table 5.1) and . These
tables confirm that we have a diverse data sample in terms of value: both for the bidding and the
target firm the mean of and is at least two times as large as the median. From
we
conclude that, both for the bidding and target firm, in 50% of the cases the book value of debt is
at most one half of .
Recall that , according to Merton’s model (1974), equals the value of the call option. Therefore,
we conclude that in these cases the option is far in-the-money. We observe one exceptional
outcome in the target’s sample.
Debt and equity characteristics bidder
/
Mean
4913
19398 0.71
Median
2279
4815
0.47
minimum 31
506
0.01
maximum 27165
31623 3.97
Table 10.2: debt and equity characteristics bidding firm
Debt and equity characteristics target
Mean
Median
minimum
maximum
1401
436
6
12263
2966
1321
81
50755
/
0.68
0.42
0.01
9.40
Table 10.3: debt and equity characteristics target firm
Furthermore, we conclude that the mean of the acquirer’s equity volatility is 0.50, versus a mean
of the target’s equity volatility of 0.65. As stated above, Ross, Westerfield and Jaffe (2010) argue
that common shareholders prefer high risks, since they have a residual claim on the firm.
Therefore, the expected payoff to the equity holders will be, ceteris paribus, higher when the
level of risk increases. Moreover, we conclude that in 77 of the 82 cases
, resulting from
adding the equity processes of the bidding and target firms, is lower than
declines with 0.04 to 0.46 after combining the processes.
[38]
. On average,
10.1.3
For the period surrounding the announcement dates, Table 10.4 presents
as a dollar
value and
as a percentage of . It is remarkable that the average of the acquirers’
is negative. In particular, comparing with the median, the mean is more than five
times more negative than the median value. This implies that the sample contains deals that
have a highly negative
.
For the target’s
, the opposite holds true: both the mean and the median of the
are positive. Moreover, the mean is higher than the median. Because of the different
signs of the
for the bidding and target firm, it seems the saying
“one man's meat is another man's poison”
holds in this case. For each individual takeover announcement, we conclude that the mean of the
sum of both the bidder’s and target’s
is negative. This implies that, on average, the
market reacts negatively to the announcement of the merger or acquisition. In our sample, 43 of
the 82 takeover announcements result in a negative sum of
. More specifically, in 58
out of the 82 cases the bidder’s
is negative while only 8 of the 82 target’s
are negative. Here, we conclude that the premium paid for the takeover is in 58 of the cases too
high (compared with the potential synergistic gains).
The columns with respect to
(%) in Table 10.4 correct the values of the dollar value of
for the size of the firm. The table shows that per dollar equity the shareholders of the
acquiring firm loses, on average, $0.045, while the target’s shareholders gain on average $0.196
per dollar.
Dollar
Mean
median
minimum
maximum
Acquirer
-806
-148
-22047
8990
Target
402
147
-3115
10146
Percentage
Mean
median
minimum
maximum
Acquirer
-4,47%
-3,81%
-27,96%
25,55%
Target
19,60%
16,94%
-23,87%
129,01%
Per announcement
-404
-33
-12455
9323
Per announcement
-0,01%
-0,03%
-24,16%
19,16%
Table 10.4: equity
dollar value (above) and
as a percentage of equity value (below)
In Figure 10.1, the dollar value
of the bidding and target firm for each announcement
are added and sorted from small to large. This figure is in line with our findings presented in
Table 10.4. A small number of deals results in a very high or low
.
[39]
Figure 10.1: sum bidding and target
sorted from small to large
Figure 10.2 shows that 65 of the 82 investigated announcements results in a ‘sum bidding and
target
per dollar equity’ between -10% and +10%.
Figure 10.2 sum bidding and target
divided by the sum of
and
sorted from small to large
Figure 10.3 shows the mean of the best takeovers. We conclude that, by removing the worst 4
sums of the bidding and target
s, the mean of the remaining 78
are positive.
[40]
Figure 10.3: mean best
10.1.4
Table 10.5 presents the numerical values for
. Comparing the dollar value
with
the dollar value
, we observe that the numbers are of the same magnitude. The value of
and
per takeover does not differ significantly. We can explain this
observation using the option intuition (Merton’s option method). We conclude that all options
are in-the-money, since an out-of-the money option implies that the liability claims are higher
than the value of the firm (this induces a default). Options which are (far) in the money have a
delta of about 1. This means that in case increases with one, the value of the option (and hence
the value of ) increases with one as well. In our case, we follow a similar argumentation, but in
reversed order: if the option is (far) in-the-money, an increase in option value (and hence an
increase in ) results in an increase in of, approximately, the same size.
Dollar
Mean
median
minimum
maximum
Acquirer
-811
-151
-22047
8990
Percentage Acquirer
Mean
-3,47%
median
-2,40%
minimum
-27,85%
maximum
13,81%
Target
410
156
-3119
10150
Per announcement
-400
-31
-12569
9323
Target
12,99%
9,76%
-23,73%
66,90%
Per announcement
-1.32%
-0.17%
-29.96%
10.99%
Table 10.5: firm
dollar value (above) and
as a percentage of the firm value (below)
[41]
10.2 THE INVESTMENT VALUE AND PROJECT REVENUE
When taking a closer look at
and
, we observe a twofold movement of and
, respectively for the general sample. While the target’s
is often positive, the acquirer’s
more often assumes a negative value than a positive value: in 43 of the 82 cases a negative
value occurs. Based on these outcomes we conclude that approximately 50% of the announced
takeover result in value destruction for the target’s and acquirer’s shareholders taken
altogether.
Besides the change of with respect to the
, also changes due to the new capital structure.
For example, by combining the two firms, both the duration and the volatility changes. Section
7.2 showed that the combined firm value of the Patina Oil & Gas Corp./Noble Energy Inc. deal is
higher than the value of the sum of the two firms separately. Hence, one could argue that the
announcement of the merger or acquisition causes two effects:
1. the effect on
2. the effect on
and based on the
;
based on the new capital structure.
These two effects together influence the project value ̂ and the investment value ̂. Using the
characteristics of these processes (e.g., the drift and volatility term) we are able to construct an
answer to the research questions.
We observe the following results for ̂ (defined as the ratio of the project value and the
investment costs) on the announcement date:
Criterion
̂
̂ [ )
̂
#
6
34
42
Table 10.6: distribution ̂
Based on the changes in firm value as a result of the changes of the capital structure and the
synergy gains or losses, we conclude that in 40 of the 82 cases ̂
. In particular, this means
that the project revenue on that day is lower than the investment cost. In turn, we conclude that,
even for the NPV method, the announcement of the takeover is considered a bad decision. In 6
deals we find that ̂
. For all of these cases it holds that the decline in
is larger than
the decline in
. Hence, including all synergy gains or losses, combining the two firms causes
a destruction of firm value of an order of magnitude equal to the value of the target firm.
On the contrary, however, in 42 deals we find that ̂
. This implies that
and, therefore,
based on the NPV methodology, the announcement of the takeover is justifiable. For the sake of
interpretation, the remainder of the section is divided into three categories:



deals for which it holds that ̂
deals for which it holds that ̂
deals for which it holds that ̂
;
[
);
.
[42]
10.2.1 DEALS FOR WHICH IT HOLDS THAT ̂
Irrespective of the premium paid for the takeover, we conclude that, in case ̂
, announcing
the takeover results in a negative project revenue. When comparing this with ( ), one may
argue that the synergy losses of the acquirer and the target firm altogether are larger than the
value of the target firm. Hence, announcing the takeover is value destroying. Therefore, we
conclude that there is no optimal timing to announce a takeover in this particular case. More
precisely, based on the project value the takeover should not have been announced.
Based on backward simulations, we come to a similar conclusion: there exists no optimal
moment of time in the past to make the announcement either.
10.2.2 DEALS FOR WHICH IT HOLDS THAT ̂
[
)
For this sample of deals, it also holds that
on the day of announcement. Compared with the
Net Present Value method, a deal should be announced in case
. In this scenario, however,
revenues are lower than the investment costs. Therefore, we may conclude once more that it
would be optimal that for these 34 acquisitions for which
the deal should not have been
announced (yet).
In 13 of these 34 acquisitions ̂ has a negative drift term. As a result, the project revenue ̂ is
expected to decline. Therefore, we conclude that in expectation there exists no optimal moment
to invest (i.e., to engage in a merger or acquisition) for this group.
In 13 of the remaining 21 cases, the drift term is significantly higher than the chosen discount
value of 0.025. This implies that no optimal timing exists. Ceteris paribus, it is optimal to wait
forever with announcing the takeover. Table 10.7 states the optimal timing to invest (mean and
median) for the other 8 cases (for
,
and
).
0.025
0.035
0.045
̂ (mean)
5.01
1.90
1.58
̂ (median)
2.17
1.67
1.48
Table 10.7: mean and median ̂ for
,
and
̂(
From Table 10.7 we conclude that , ̂ is, on average, equal to
). This means
that, disregarding the determination of the premium, it is on average optimal to announce a
̂ for the sample as a whole. For a lower or higher discount rate, the
takeover in case ̂
threshold value will either increase or decrease, respectively. This results from the fact that the
) with respect to the discount rate is negative. That is, waiting
derivative of equation (
becomes more expensive in case the discount rate increases. Comparing ̂ with ̂ we conclude
̂ for all deals on the
that none of the 8 takeovers in this group is announced optimally i.e., ̂
day of announcement.
Furthermore, we observe that the threshold values resulting from the standard volatility method
differs from the threshold value resulting from the Moody’s KMV volatility method. This may be
explained by the fact that the threshold value is highly sensitive to changes in the drift term (e.g.,
the closer the drift term to the discount rate the higher the threshold value).
[43]
Comparing the optimal investment values with the actual investment values we conclude that
there is a wide gap between the empirical timing and the optimal timing.
10.2.3 DEALS FOR WHICH IT HOLDS THAT ̂
For the 42 deals for which ̂
it holds that the project revenue is higher than the investment
cost. Based on the NPV method, there is no reason not to announce the takeover. However, since
we are not dealing with a so-called “now-or-never decision” and because the investment is not
reversible, we are able to verify the optimal timing based on the real option approach of
McDonald and Siegel’s (1986) and Dixit and Pindyck (1994).
It turns out that the drift term of the adjusted project value is negative in 32 cases. Ceteris
paribus, this implies that, on average, the takeover conditions are more favorable now than they
will be in the future. Or, reasoned the other way around: the conditions on average for this group
of takeovers were, ceteris paribus, better in the past than the current conditions.
Let us now look at the characteristics of the 42 deals considered in this subsection. Recall that
the real option model as specified in section 6 only holds in case ̂
. Therefore, we analyze
̂ with respect to three different values of : 0.025, 0.035 and 0.045. If
0.025, it holds that
35 of the 42 samples satisfy the criterion ̂
. For
0.035 and
0.045, 36 and 37 cases
satisfy the criterion, respectively. Ceteris paribus, based on the discount rate we conclude that, it
is optimal for the remainder of the deals to wait forever with announcing the deal.
Table 10.8 and Figure 10.4 show both ̂ and ̂ for those takeovers for which it holds that ̂
.33 We conclude that the number of optimally timed takeovers is equal to 27. Furthermore,
observe that (Figure 10.4) there are some takeovers with a relatively high optimal threshold in
our sample. 34 The reason for this being the high volatility of the adjusted project value. Note
that, in particular it holds that
⇒
⇒ ̂
.
̂
̂
27 out of 35
27 out of 36
27 out of 37
Table 10.8: number of optimally timed takeovers ( ̂
for
̂ )
Table 10.9 summarizes the general statistics of this group for the deals for which ̂
. From
this table we observe that the average optimal timing is higher than or equal to the average of
the empirical timing for all scenarios. On average, we may conclude that the takeovers have been
announced too early. However, we do remark that there are some extreme outcomes in the
To compare the results for the different values of , we only present the takeovers that are in all three
samples. As a result, we remove one takeover from the figure for
and two for
. These
takeovers are included in the results in the table, however.
34 For example, observation number 3 (equal to takeover number 14) and 7 (equal to takeover number
21). For example, when
we observe that the optimal timing of observation number 7 is equal to
. The actual timing of this observation is lower i.e., 1.53. Based on the real option approach, the
timing is not optimal. Based on the NPV method, however, one may conclude that the announcement can
be considered highly optimal, since the project revenue is equal to 1.53 times the investment cost.
33
[44]
Figure 10.4 the optimal (lines) and actual timing (bars) of the 36 takeovers with
( and hence ̂
) and with
.
(blue solid line),
,
(green dashed line) and
(brown solid dotted line). The x-axis represents the individual observations. The y-axes corresponds to the adjusted investment
threshold values ̂ and ̂ .
[45]
optimal timing. As a result, the mean optimal timing is skewed to the right. Therefore, we prefer
to use the median as a scale. Based on the characteristics of both the investment value process
and the project value process , we conclude that the optimal timing of half of the
announcements is in case the adjusted project value is lower than 1.04. Needless to say, the
other half takes place in case the project value is higher than 1.04.
Timing announcement
Mean
Median
Min
Max
̂
̂
̂
̂
̂
̂
1.22
1.15
1.00
2.02
1.64
1.04
1.00
13.93
1.22
1.15
1.01
2.02
1.92
1.04
1.00
26.26
1.56
1.15
1.01
13.96
2.93
1.04
1.00
63.70
Table 10.9: characteristics of both the actual ( ̂ ) and the optimal timing ( ̂ ) for the group
̂
and,
,
and
.
In general, the mean investment threshold decreases whenever
. Because increases,
however, there is one more takeover in the sample
compared to the sample
. Similarly, there is one more takeover in the sample
compared to the sample
. These additional takeovers have an extremely high threshold value. This is not too
surprising, since the drift term of the project revenue of the additional takeovers is at least 0.025
and therefore close to .
Figure 10.5 depicts a scatterplot of the scenario
, where the -axis represents the
optimal timing and the -axis the corresponding actual timing.35 From this figure we conclude
once again that most timings of the announcements of the group ̂
are optimal in the sense
that investment values are higher than the optimal threshold value.
Figure 10.5: optimal timing (horizontal) vs. actual timing (vertical)
One observation is out of the scope of the figure. This is deal number 56 with ̂ equal to 26.26 and ̂
equals 1.26.
35
[46]
Table 10.10 gives the results of the 21 outcomes for which it holds that ̂
that these criteria correspond to those deals that are optimally timed.
̂ and
̂
. Note
Timing announcement
̂
Mean
Median
Min
Max
1.25
1.17
1.02
2.02
̂
1.07
1.03
1.00
1.52
̂
1.25
1.17
1.02
2.02
̂
1.07
1.03
1.00
1.47
̂
1.25
1.17
1.02
2.02
̂
1.07
1.03
1.00
1.44
Table 10.10: characteristics of both the actual ( ̂) and the optimal timing ( ̂ ) for the group
̂
̂ and
,
and,
.
From Table 10.10 we conclude that, based on the optimal timing approach, the takeovers could
have been announced earlier. For
, we observe that the mean optimal timing equals
1.07, while the mean of the actual timing is significant higher, namely 1.25.36
10.2.4 SENSITIVITY ANALYSIS TO THE DURATION AND FIRM VOLATILITY
This subsection investigates the sensitivity of the optimal timing results with respect to
,
.
Figure 9.2 showed the relation between the value of the combined firm as a function of the
duration and the firm volatility (deal number 82). Based on that result, we conclude that, ceteris
paribus:
if
.
Due to the call option characteristics of Merton’s firm valuation model, we conclude that this
relationship holds in general.37. Because of the changes in the firm value as a result of changes in
and
, the optimal timing may be affected as well. We start with explaining the
importance of this sensitivity analysis.
As a result of the new capital structure
may change significantly. For example, in case of a
takeover, the acquiring firm is likely to refinance the target firm’s debt claims. As a result, the
duration is expected to change accordingly. In conclusion, it is useful to investigate the
sensitivity of the optimal timing characteristics with respect to
.
Recall that we assumed that the equity process of the combined firm is simply defined as the
sum of the equity processes of the bidding and target firm. Based on these processes we
calculate the volatility (one of the input variables in Merton’s model). It is questionable whether
the characteristics of the newly defined process are in line with the actual characteristics of the
Under the standard student t-test assumptions, we observe that on a two sided 95% confidence interval,
).
the true mean optimal timing lies within the interval (
37 The derivative of the call option formula with respect to both the volatility (known as vega) and the
duration (theta) are positive. This means that a higher volatility or duration of the underlying implies, in
case of a fixed firm value, a higher price of the call option. Or, put the other way around: a higher
volatility/duration of the underlying implies, in case of a fixed call price, a lower price of the underlying.
36
[47]
combined process. Therefore, we investigate the sensitivity of the optimal timing framework to
changes of
.
In our sensitivity analysis we take the firm characteristics resulting from the combined firm as a
starting point. For both the duration and the volatility we investigate the scenarios:
{
{
From Tables 10.11 and 10.12, we observe that the higher the volatility or the duration the
smaller the number of deals with ̂
(and the larger the number of badly timed deals
(̂
). This movement is best visible for changes in the duration. In other words, the project
revenue is more sensitive to changes in the duration than to changes in the volatility. This effect
̂ . Increasing or
is also visible in the number of deals satisfying the optimality condition ̂
decreasing by, say, 10% of its original value does not affect the number of optimally timed
takeovers (it remains 27). However, a decrease of by 10% results in one additional optimally
timed announcement. An increase of from to
results in a decrease of the number
of optimally timed deals of 2.
criterion
̂
̂ [ )
̂
5
35
42
6
34
42
7
34
41
Table 10.11: number of deals within the category.
(
)
criterion
̂
̂ [ )
̂
5
33
44
6
34
42
7
38
37
Table 10.12: number of deals within the category.
(
)
Tables 10.13 and 10.14 present the characteristics of the announced takeovers satisfying the
̂ and ̂
two criteria ̂
for and , respectively. From these tables we conclude
that the level of the optimal timing seems not too sensitive to changes in and . For the
sensitivity analysis with respect to it holds that the mean is around 1.07 in all cases.
We argue that the insensitivity of the optimal timing as follows. Given the fixed equity price
(price of the option), the entire firm value process of the combined firm moves upwards (in case
of a decrease in ) or downwards (in case of an increase in ). Because in most cases the firm
value is much larger than the value of debt, we are dealing with a so called deep in-the-money
[48]
option. These options are less sensitive to changes in volatility38. Due to the small changes of firm
value into one direction, the project revenue process ̂ shifts in the same direction as well. The
higher the volatility the lower the value of
and, because of ( ), the lower the value of
the project revenue process ̂ .
Timing announcement
̂
Mean
Median
Min
Max
1.25
1.18
1.00
2.02
̂
1.07
1.03
1.00
1.47
̂
1.25
1.17
1.02
2.02
̂
1.07
1.03
1.00
1.47
̂
1.23
1.16
1.02
2.02
̂
1.06
1.03
1.00
1.47
Table 10.13: characteristics of both the actual ( ̂ ) and the optimal timing ( ̂ ) for the group
̂
̂ and ̂
for
,
and
.
Timing announcement
̂
Mean
Median
Min
Max
1.23
1.16
1.03
2.06
̂
1.07
1.04
1.00
1.34
̂
1.25
1.17
1.02
2.02
̂
1.07
1.03
1.00
1.47
̂
1.24
1.17
1.02
1.98
̂
1.09
1.04
1.00
1.84
Table 10.14: characteristics of both the actual ( ̂ ) and the optimal timing ( ̂ ) for the group
̂
̂ and ̂
for
,
and
.
In general it holds that, given the fixed equity price (price of the option), the lower the duration
the higher the value of the underlying to obtain the same price of the option. This phenomenon
is called the time decay of an option: in case the value of the underlying remains the same, the
value of the option declines if
. Put differently, the value of the combined firm is expected
to decrease in case the duration increases and therefore the project value is expected to
decrease as well. From Table 10.14 we observe that this does not occur in our sample. The
̂ and ̂
reason for this being that the number of deals fulfilling the criteria ̂
changes whenever changes.
10.2.5 SENSITIVITY ANALYSIS TO THE LENGTH OF THE EVENT WINDOW AND THE
ALTERNATIVE VOLATILITY METHOD
We investigate the sensitivity with respect to the length of the event window for calculating the
and the effect of the alternative volatility calculation method as used by Moody’s KMV as
39
well.
) days, ensures us that we capture changes in
The longer event window, i.e., a window of (
the equity price resulting from leaked information concerning the deal that is at hand. On the
This can easily be seen as follows. If an option is deep in-the-money, an increase in volatility increases
the probability of both higher and lower outcomes. These two effects cancel out which means that a small
change in volatility does not affect the price of the option. Therefore, the deeper the option is in-themoney the less sensitive the option will be to changes in volatility.
39 as discussed in section 5.5
38
[49]
days after the announcement we are able to catch market movements based on additional
information. The disadvantage of this larger event window is the fact that the equity price is
affected by information that is unrelated to the deal. That is to say, the longer the event window
the more difficult it will be in general to catch the abnormal returns resulting from the
announcement.
). This means that we calculated the
Our analysis thus far is based on an event window of (
, an input variable for the determination of synergy, from the equity return one day before,
on, and one day after the announcement date. Table 10.15 presents the results in case we
). We conclude that the group of takeovers with ̂
expand the event window to (
̂ , remains the same i.e.,
increases to 43. Nevertheless, the group of optimally timed deals, ̂
27 deals.
Criterion
̂
̂ [ )
̂
(
6
34
42
)
(
)
9
30
43
Table 10.15: number of deals within the category.
(
) and
(
)
for
Using Moody’s KMV volatility method we analyze the optimal investment problem as well. The
corresponding results are summarized in Table 10.16.
Criterion
̂
̂ [ )
̂
#
5
36
41
Table 10.16: distribution ̂ by use of
Moody’s KMV volatility method
Comparing Table 10.16 with Table 10.6 we observe that the number of announcements fulfilling
the criterion slightly differs. These are the takeovers for which it holds that the actual
investment threshold is close to one of our chosen boundaries. Nevertheless, the number of
̂ ) equals 27 for both methods.
optimally timed announcements (i.e., ̂
[50]
11 CONCLUSION
11.1 SUMMARY
In this paper we focus on the timing of 82 takeovers announced from 2000 up until and
including 2004. We aim to answer the research questions:


“What is the optimal timing of announcing a merger and acquisition event if both the
evolution of the stock price of the acquiring and the target company (excluding the specific
deal terms) are observed?”
”How does the actual implementation date of a merger and acquisition correspond to the
optimal timing resulting from the real option model”?
For our analysis we use Merton’s corporate bond valuation method (1974) to infer the firm
value process of the acquiring, target and combined firm. Merton (1974) argues the market
value of equity is, in fact, a residual claim on a company after paying the debt holders (zerocoupon debt) at a future moment in time. This is equivalent with the European call option
construction with the firm value as underlying, the debt claim as strike price and the market
value of equity as the price of the call option. The firm defaults if the market value of its assets
(firm value) is less than the promised debt repayments.
We apply the real option approach of McDonald and Siegel (1986) and lately extensively
investigated by Dixit and Pindyck (1994) to determine the optimal timing of the announcement
of a merger or acquisition. This approach states that one should decide to invest in a (partly)
irreversible project in case the net benefit (project value) is higher than a certain threshold
value. This threshold value is related to the investment cost and is dependent amongst others of
uncertainty: the more uncertain a project the higher the threshold value. The real option
framework incorporates the value of waiting: by waiting the investor is capable of making a
more informed decision. We assume that the net benefits follow a geometric Brownian motion.
From our analysis we conclude that in 43 of the 82 cases the sum of the bidding and target firm’s
returns around the announcement of the deal is negative. This means that for these takeovers
shareholder value is lost as a result of the announcement. More specifically, in 58 of the 82 cases
the bidding firm’s shareholders lose value on the days around the announcement day. This
implies that the premium paid by the bidding firm to the target firm’s shareholders is too high
relative to the synergy gains. For the target firm’s shareholders we observe that in only in 8 of
the 82 cases equity value declines. Excluding the premium paid and from a shareholders point of
view, we conclude that, based on the 43 negative sums of announcement returns, more than half
of the deals should not have been announced.
The change in firm value stems from both the change in equity value and the capital structure.
Using the optimal timing framework we conclude that in half of the cases the project revenue is
higher than the investment cost. This means that, based on the NPV criterion, the
announcements of the takeovers are justified.
Zooming in on this group of takeovers we observe that only 27 are optimally timed. This means
that the optimal timing approach suggests that the project revenue on the announcement date is
higher than the minimum required project revenue for an optimal investment. For the sake of
[51]
completeness, we consider three different discount rates (
,
and
).
It turns out that the actual project revenue on average equals 1.25 times the investment cost
while the average optimal investment threshold is equal to 1.07 times the investment cost.
Therefore, we conclude that the actual revenues resulting from the announcement are for the
optimally timed takeovers substantially higher than the theoretical optimal revenues.
We investigate the sensitivity of the results with respect to changes in duration of the
outstanding debt, volatility of the firm value process, the event window and the effect of using
Moody’s KMV volatility method.
For the duration and the volatility we conclude that an increase in the duration or volatility
yields a decrease in the number of deals that have a project revenue of at least the investment
cost. However characteristics of the optimal investment threshold remain approximately the
same. The change in volatility does not affect the number of optimally timed deals (i.e., remains
27), while the change in duration does. Therefore, we conclude that the results are more
sensitive to changes in duration.
) to (
) days, or using Moody’s KMV’s method to
Extending the event window from (
determine the firm volatility, changes the number of deals that have a project revenue of at least
the investment cost. However, the number of optimally timed deals stays put at 27.
All in all, one may conclude that approximately 1/3 of the takeovers in our sample are optimally
timed. For this group it holds that on average the investment was announced when expected
revenues were equal to 1.25 times the investment cost. This is substantially higher than the
minimum required investment level of 1.07 times the investment cost.
11.2 RECOMMENDATIONS FOR FUTURE RESEARCH
This paper builds on two frameworks. First, it heavily leans on the findings of Merton (1974).
We use this framework to determine the firm value processes needed for our real option
approach. Wrong inputs in Merton’s model results in an erroneous firm value process and
therefore in incorrect optimal timing results. Hence, it is important that the fundamental
building block, Merton’s model (1974), represents the real firm value process as well as possible.
Fisher emphasize in the paper of Jones, Mason and Rosefeld (1984) some weaknesses in
Merton’s model
“It seems to me that there are three crucial assumptions at the heart of Merton’s contingent claims
analysis. Three assumptions that may be required to make the model more tactable but which may
not be sufficient true for the model to provide useful estimates of security prices. These are: the
perfectly liquidity, the irrelevance of taxes and the non-stochastic interest rates”.
For the sake of the right projection of the firm value process it is interesting to investigate the
research question based on more realistic assumptions, such as a term structure.
Another possible direction for future research is concerns the way volatility is calculated. In this
paper we apply two different methods to determine the equity volatility/firm volatility. The
volatility is one of the input variables in Merton’s method as well. Hull, Nelken and White (2004)
use another method to calibrate the volatility. In their model, they use two implied volatilities
(e.g., resulting from the Credit Default Swap Data) to solve and
and then . They write
[52]
“it is a potentially attractive alternative to the traditional implementation based on equation 1
[equation ( ) in this paper] and 2 [equation ( )]. because it avoids the need to estimate the
instantaneous equity volatility and the need to map the company’s liability structure (some of
which may be off balance sheet) on to a single zero-coupon bond’. And then ‘the used implied
volatilities are of the form observed in practice where an increase in the strike price leads to a
reduction in the implied volatility.”
In this paper we quantitatively answer the question around the optimal timing of a merger and
acquisition. We conclude that half of the announcements results in negative equity returns,
implying that the announcement is destroying shareholders value. Therefore, another topic for
further research might focus on the underlying reason for this failure. Do these companies have
certain factors in common?
[53]
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[56]
APPENDIX
A.
Conversion equity volatility to firm volatility
In section 5 we assume that the evolution of the value of the firm follows a Geometric Brownian
Motion. Merton (1973) argues that the dynamics of the market value of equity ( ) can be
written in stochastic differential equation form as
(
)
( ). We showed that this function is, in
is a function of the value of the firm. That is,
(
) there is an explicit
fact a Black-Scholes option price function. Provided that
functional relationship between , and , . Using Ito’s lemma we can write the dynamics
of as
=
(
[
)
= [
]
(
]
)
Comparing the terms (A.1) with (A.2) we know that the volatility part must be equal. That is to
say,
(
)
The derivative of the option price formula to the underlying ( ) is called the delta and is equal to
(
). If we substitute (
) for
we can write the volatility of the firm,
as
( )
(
)
In this case, the instantaneous returns on equity and the firm are perfectly correlated.
B.
Firm valuation: standard volatility method
As discussed in this thesis we have a problem consisting of two equations, ( ) and ( ), and
two unknowns,
and . Since the market value of equity (equal to the price of a call option)
is given, we can solve backwards the implied market value of the firm. One of the input variables
for this formula is the volatility of the stock. We cannot observe this, but we can estimate it using
( ). Unfortunately, this formula depends on the (unknown) firm value. A more important
problem is that we are not able to solve these equations analytically. Therefore, we left no choice
but to refer to alternative methods. A method that comes in handy is Newton-Raphson method,
which enables us to solve nonlinear equations. Newton-Raphson’s method iteratively constructs
approximations to a solution of the equation ( )
, starting from an initial guess , by the
rule
[57]
(
)
(
(
)
)
This method holds for problems of one equation and one unknown. For problems of two
equations and two unknowns (as in our case), we have to solve for the unknown parameters
such that:
(
(
)
(
)
)
(
(
)
)
(
)
(
)
Note that this is similar to ( )
in the one equation problem. The ( ) in the case of one
unknown can be replaced by the jacobian for the multi unknown problem. Here is a matrix
and is defined as
(
[
)
]
is the first derivative of the call option formula with respect to the underlying. This is also
called the delta and is equal to
The derivative of
equal to
(
).
only depends on
with respect to
through
and
.
is also called the vega of a call option and is
)√ . The derivative of
And the last one,
(
(
to is solved as follows:
(
)
(
)
(
)
(
)
(
)
(
)
(
(
)
√
(
√ )
)
√
, can be solved by making use of the chain rule:
)
(
)
(
)
(
)
(
)
(
)
(
√ (
√
)
(
( ) (
) )
√ )
The general formula of Newton-Raphson method for the multi unknown case then becomes:
[
]
[
]
[58]
[
(
(
)
]
)
(
)
C.
Firm valuation: Moody’s KMV volatility method
As an alternative to the volatility estimation as given by equation ( ), Moody’s KMV introduces
another method. This method is based on the volatility of the firm value within a certain period.
Therefore, Moody’s KMV introduces an iterative procedure. This procedure works as follows.
Via an initial guess of the volatility of the firm, the value of the firm can be determined. By
making use of this value, we can calculate the firm’s volatility for a given period. This volatility is
compared with the initial guess. If the difference between these two is too large, we recalculate
the value of the firm by making use of the new volatility.
Here, we make use of Newton-Raphson’s method as well.
[59]
D.
Announcement data and transaction value takeovers
Deal
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Date
Announced
2-22-2000
3-7-2000
3-13-2000
3-22-2000
3-22-2000
5-8-2000
5-25-2000
6-21-2000
6-23-2000
6-26-2000
6-28-2000
7-2-2000
7-10-2000
7-13-2000
7-26-2000
8-14-2000
9-11-2000
18
19
20
21
22
23
24
25
9-25-2000
10-16-2000
10-26-2000
11-13-2000
12-4-2000
12-4-2000
12-21-2000
12-21-2000
26
27
28
29
30
31
32
33
34
35
36
1-29-2001
2-4-2001
2-5-2001
3-12-2001
3-16-2001
3-19-2001
3-22-2001
3-27-2001
4-2-2001
4-5-2001
4-29-2001
37
38
39
5-4-2001
5-23-2001
5-30-2001
Acquirer
MGM Grand Inc.
VeriSign Inc.
i2 Technologies Inc.
PSINet Inc.
Tuboscope Inc.
QLogic Corp.
Watson Pharmaceuticals Inc.
Texas Instruments Inc.
ConAgra Inc.
Valspar Corp.
Gannett Co Inc.
EGL Inc.
Forest Oil Corp.
King Pharmaceuticals Inc.
Symbol Technologies Inc.
Chiron Corp.
Genzyme Corp.
International Flavors &
Fragrances Inc.
United Technologies Corp.
Kellogg Co
FEDEX Corp.
Cardinal Health Inc.
PepsiCo Inc.
Microsoft Corp.
Northrop Grumman Corp.
Maxim Integrated Products
Inc.
Phillips Petroleum Co Inc.
Patterson Energy Inc.
SPX Corp.
AmeriSource Health Corp.
Interpublic Group
Avnet Inc.
Johnson & Johnson
Vishay Intertechnology Inc.
Suiza Foods Corp.
Vertex Pharmaceuticals Inc.
Target
Mirage Resorts Inc.
Network Solutions Inc.
Aspect Development Inc.
Metamor Worldwide Inc.
Varco International Inc.
Ancor Communication Inc.
Schein Pharmaceutical Inc.
Burr-Brown Corp.
International Home Foods Inc.
Lilly Industries Inc.
Central Newspapers Inc.
Circle International Group Inc.
Forcenergy Inc.
Jones Pharmaceutical Inc.
Telxon Corp.
PathoGenesis Corp.
GelTex Pharmaceuticals Inc.
Transaction
value
(US $ mil)
6483
21101
7974
1835
804
1780
916
6956
3036
955
2446
559
646
3523
571
700
1052
Bush Boake Allen(Union Camp)
Specialty Equipment Cos Inc.
Keebler Foods Co
American Freightways Corp.
Bindley Western Industries Inc.
Quaker Oats Co
Great Plains Software Inc.
Litton Industries Inc.
964
724
4652
1226
1751
14392
940
5158
Dallas-Semiconductor Corp.
Tosco Corp.
UTI Energy Corp.
United Dominion Industries Ltd
Bergen Brunswig Corp.
True North Communications Inc.
Kent Electronics Corp.
ALZA Corp.
General Semiconductor Inc.
Dean Foods Co
Aurora Biosciences Corp.
Ultramar Diamond Shamrock
Valero Energy Corp.
Corp.
Electronic Data Systems Corp. Structural Dynamics Research
Medtronic Inc.
MiniMed Inc.
[60]
1621
9388
1408
1839
4479
2133
689
11070
890
2455
554
6215
984
3304
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
6-29-2001
7-2-2001
7-9-2001
8-21-2001
8-29-2001
9-4-2001
11-19-2001
12-3-2001
Barr Laboratories Inc.
Sara Lee Corp.
International Game Technology
Roadway Express Inc.
Mead Corp.
Hewlett-Packard Co
Mohawk Industries Inc.
Synopsys Inc.
Millennium Pharmaceuticals
12-6-2001 Inc.
1-30-2002 Beazer Homes USA Inc.
2-22-2002 Northrop Grumman Corp.
4-29-2002 Fair Isaac & Co Inc.
5-29-2002 Newfield Exploration Co
6-12-2002 Univision Communications Inc.
6-14-2002 Cardinal Health Inc.
7-15-2002 Pfizer Inc.
8-7-2002
Penn National Gaming Inc.
Laboratory Corp. of America
11-8-2002 Holdings
2-10-2003 Johnson & Johnson
2-24-2003 Devon Energy Corp.
6-2-2003
PeopleSoft Inc.
6-6-2003
Oracle Corp.
6-20-2003 IDEC Pharmaceuticals Corp.
7-7-2003
VF Corp.
7-14-2003 Boise Cascade Corp.
8-4-2003
Genzyme Corp.
8-18-2003 Precision Castparts Corp.
9-2-2003
Caremark Rx Inc.
10-14-2003 EMC Corp.
12-9-2003 SunGard Data Systems Inc.
2-4-2004
Belden Inc.
2-26-2004 Genzyme Corp.
Fisher Scientific International
3-17-2004 Inc.
3-29-2004 Lyondell Chemical Co
5-4-2004
Pioneer Natural Resources Co
5-19-2004 Cardinal Health Inc.
6-4-2004
MGM Mirage Inc.
7-15-2004 Harrah's Entertainment Inc.
7-27-2004 The Cooper Cos Inc.
8-12-2004 National-Oilwell Inc.
10-19-2004 Constellation Brands Inc.
11-3-2004 Penn National Gaming Inc.
12-16-2004 Noble Energy Inc.
[61]
Duramed Pharmaceuticals Inc.
Earthgrains Co
Anchor Gaming Inc.
Arnold Industries Inc.
Westvaco Corp.
Compaq Computer Corp.
Dal-Tile International Inc.
Avant! Corp.
594
2906
1327
554
2961
25263
2024
827
COR Therapeutics Inc.
Crossmann Communities Inc.
TRW Inc.
HNC Software Inc.
EEX Corp. (ENSERCH Corp. )
Hispanic Broadcasting Corp.
Syncor International Corp.
Pharmacia Corp.
Hollywood Casino Corp.
2417
619
6678
826
621
3537
998
59515
917
Dianon Systems Inc.
Scios Inc.
Ocean Energy Inc.
JD Edwards & Co
PeopleSoft Inc.
Biogen Inc.
Nautica Enterprises Inc.
OfficeMax Inc.
SangStat Medical Corp.
SPS Technologies Inc.
AdvancePCS
Documentum Inc.
Systems & Computer Technology
Cable Design Technologies Corp.
ILEX Oncology Inc.
601
2323
5442
1776
10467
6830
590
1366
614
586
5548
1953
580
542
1050
Apogent Technologies Inc.
Millennium Chemicals Inc.
Evergreen Resources Inc.
ALARIS Medical Systems Inc.
Mandalay Resort Group
Caesars Entertainment Inc.
Ocular Sciences Inc.
Varco International Inc.
Robert Mondavi Corp.
Argosy Gaming Co
Patina Oil & Gas Corp.
2720
2546
1898
1744
7811
6332
1178
2570
1029
2213
2954
Figure D1: deals sorted from low transaction value to high transaction value
[62]