V O LU M E 2 0 | N U M B E R 2 | s p ring 2 0 0 8
Journal of
APPLIED CORPORATE FINANCE
A MO RG A N S TA N L E Y P U B L I C AT I O N
In This Issue: Valuation and Corporate Portfolio Management
Corporate Portfolio Management Roundtable
Presented by Ernst & Young
8
Panelists: Robert Bruner, University of Virginia; Robert Pozen,
MFS Investment Management; Anne Madden, Honeywell
International; Aileen Stockburger, Johnson & Johnson;
Forbes Alexander, Jabil Circuit; Steve Munger and Don Chew,
Morgan Stanley. Moderated by Jeff Greene, Ernst & Young
Liquidity, the Value of the Firm, and Corporate Finance
32
Yakov Amihud, New York University, and
Haim Mendelson, Stanford University
Real Asset Valuation: A Back-to-Basics Approach
46
David Laughton, University of Alberta; Raul Guerrero,
Asymmetric Strategy LLC; and Donald Lessard, MIT Sloan
School of Management
Expected Inflation and the Constant-Growth Valuation Model
66
Michael Bradley, Duke University, and
Gregg Jarrell, University of Rochester
Single vs. Multiple Discount Rates: How to Limit “Influence Costs”
in the Capital Allocation Process
79
The Era of Cross-Border M&A: How Current Market Dynamics are
Changing the M&A Landscape
84
Transfer Pricing for Corporate Treasury in the Multinational Enterprise
97
The Equity Market Risk Premium and Valuation of Overseas Investments
John Martin, Baylor University, and Sheridan Titman,
University of Texas at Austin
Marc Zenner, Matt Matthews, Jeff Marks, and
Nishant Mago, J.P. Morgan Chase & Co.
113
Stephen L. Curtis, Ernst & Young
Luc Soenen,Universidad Catolica del Peru, and
Robert Johnson, University of San Diego
Stock Option Expensing: The Role of Corporate Governance
122
Sanjay Deshmukh, Keith M. Howe, and
Carl Luft, DePaul University
Real Options Valuation: A Case Study of an E-commerce Company
129
Rocío Sáenz-Diez, Universidad Pontificia Comillas
de Madrid, Ricardo Gimeno, Banco de España, and
Carlos de Abajo, Morgan Stanley
Real Options Valuation: A Case Study of an E-commerce Company
by Rocío Sáenz-Diez, Universidad Pontificia Comillas de Madrid,
Ricardo Gimeno, Banco de España, and Carlos de Abajo, Morgan Stanley*
A
lthough both academics and practitioners have
accepted the basic insight of the real options
valuation method—that many corporate investment opportunities contain valuable sources of
flexibility—progress in applying the method has been disappointing. In a book published in 2001,1 Tom Copeland
and Vladimir Antikarov presented a real options approach
that attempts to expand the range of potential applications
beyond the few areas where real options appear to have had
the most success—namely, corporate investments involving
commodities such as minerals and oil and gas. In this article,
we attempt to extend their effort to narrow the gap between
real options theory and practice by applying our own modification of Copeland and Antikarov’s approach to an actual
company in the e-commerce industry.
Internet companies suffered a dramatic reversal after reaching skyrocketing valuations, raising serious doubts about the
validity of traditional valuation techniques for new economy
stocks. We believe that a real options valuation approach can
help determine the value of new economy companies in the
light of the uncertainties they face and the options they can
exercise in the future. With its limited reliance on physical
assets, Internet capital is extremely flexible. This inherent
“optionality” within many e-businesses is capable of generating
significant value in an environment of uncertainty, particularly
in the hands of a competent management team. In businesses
as new and quickly evolving as e-commerce, traditional valuation tools fail to give managers a means of capturing the
possible benefits as well as the risks that come with greater
uncertainty. A real options approach has the potential to
allow managers to incorporate strategic considerations and
contingent payoffs into their analysis and decision-making
in a rigorous way.
* The authors would especially like to thank professors Margarita Prat of Universidad
Pontificia Comillas de Madrid; Pablo Fernández of IESE Business School, Gabriel de la
Fuente of Universidad de Valladolid and Juan Manuel López Zafra and Enrique García
Pérez of Universidad Complutense de Madrid for their invaluable comments. In addition, they would like to thank Lenos Trigeorgis and the rest of the organisers of the 9th
Annual International Conference on Real Options, When Theory Meets Practice, where
this work was presented. The authors are responsible for any mistakes or ambiguities
remaining in the paper.
1. Copeland, Thomas E. and Antikarov, Vladimir (2001): Real Options: A Practitioner’s Guide. Ed. Texere. New York. See also the article in this journal: Copeland, Thomas
E. and Antikarov, Vladimir (2005): “Real Options: Meeting the Georgetown Challenge,”
Journal of Applied Corporate Finance, vol.17, no 2, pp. 32-51.
2. Both traditional valuation models and real options valuation models rely on the
assumption that markets must be complete so that the asset we are valuing does not
increase the investor’s opportunity set. Real options valuation does not need more re-
strictive assumptions than CAPM itself, which has been proved to be a useful and widely
used model. If an analyst is willing to use a discounted cash flow valuation model with a
CAPM risk-adjusted discount rate, he has implicitly accepted the underlying assumptions
for using real options techniques.
3. Cortazar and Schwartz (1998), Schwartz and Moon (2000 and 2001) or Moel
and Tufano (2000) are previous applications of real options models using Monte Carlo
simulation techniques. Some applications of simulation to Real Options valuation, such
as those by Schwartz and Moon (2000 and 2001), make the risk adjustments in the
stochastic process and perform the simulation afterwards under the risk neutral measure. Our model, by contrast, is a discrete time model to accommodate management´s
estimations. In this sense, we follow the C&A approach and perform the simulation under the objective measure, leaving the risk neutral adjustment to a later step. Thus, the
simulation results provide us with a lot of information about the probability distribution
of cash flows for the traditional present value prior to any Real Option.
Journal of Applied Corporate Finance
•
Volume 20 Number 2
The Valuation Model
In extending the valuation model presented by Copeland
and Antikarov (henceforth “C&A”), we aim to provide an
estimate of an investment’s present value that reflects both
the traditional discounted cash flows and the embedded real
options value. Our method is based on the assumption that
the “underlying asset” is the traditional DCF value of the firm
without any embedded options.
As shown in Exhibit 1, our real option approach thus
begins with the traditional PV calculated using the standard
CAPM assumptions.2 Like C&A, after identifying the uncertain variables upon which expected cash flows depend, we use
Monte Carlo simulation techniques to model future outcomes
for these variables.3
Unlike C&A, however, our model does not reduce the
simulation results to a lattice framework approach, but
instead maintains all possible outcomes during all future time
periods throughout the whole valuation process. This feature
is responsible for what we see as the main advantage of our
model over C&A in this high-uncertainty setting: given the
practical impossibility of calculating risk-neutral probabilities for all future outcomes, the risk-neutral adjustment is
carried out upon the expected cash flows using the proper
certainty-equivalent correction factor. The resulting model
is more flexible and reflects real events more accurately, since
it preserves the entire set of simulated events throughout the
valuation process and so does not require assumption of a
constant variance throughout all periods. Moreover, to keep
A Morgan Stanley Publication • Spring 2008
129
Exhibit 1 Summary of the Real Options Valuation Model
Step 1
Traditional PV
* Expected cash-flows
* Risk adjustment with
CAPM discount rate/
certainty equivalent
correction factor
* Terminal value
Monte Carlo simulation
* Identification of uncertain
variables and how they
behave
* Simulation of variables
to generate yearly cash-flows
Risk adjustment
Number of Internet users
Company´s market penetration rate (%)
Transactions per user
Average ticket per transaction (USD) Commission charged (%)
Number of company´s users = (1) x (2)
Total transactions = (6) x (3)
Gross merchandise sales = (7) x (4)
E-commerce revenues = (8) x (5)
Advertising revenues
Other revenues
Total revenues = (9) + (10) + (11) (Y1)
(Y2)
(Y3)
(Y4)
(Y5)
Case Study: Valuing an E-commerce Company
We now illustrate the application of our method with the
valuation of an e-commerce subsidiary of a publicly listed
company. The valuation was done as of December 31, 2002,
and the basis for the valuation was projections the company
provided us for the period 2002 through 2010.
On the basis of our discussions with the company’s
management, we identified 12 key variables (Y1-Y12) that are
expected to have material effects on cash flows. Five of the
variables (shown as Y1-Y5 in Exhibit 2) are important fundamental drivers of revenue and seven of the variables (Y6-Y12
shown in Exhibit 3) are drivers of expenses.
Step One: Traditional Present Value Calculation
The starting point for estimating the real options PV of this
business is its traditional PV assuming no managerial flexibility or real option value. To calculate this PV we need an
Journal of Applied Corporate Finance
•
* Identification of the main real
options
* Quantification of these real
options
* Choosing the maximum value
alternative in each point
(nearest neighbors)
* Calculation of the post option
cash-flows
Step 5
Expanded PV
* Adjustment of post option
cash-flows (Step 4) with
the certainty equivalent
correction factor (Step 3)
* Discounting with the
risk-free rate
Exhibit 3 Uncertain Variables Related to Expenses
the model as simple as possible, its information requirements
are set in the same format that corporations usually handle
their data, including their financial statements.
130
Real options
* Certainty equivalent
correction factor
for the yearly post option
cash-flows
Exhibit 2 Uncertain Variables Related to Income
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Step 4
Step 3
Step 2
Volume 20 Number 2
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
Doubtful accounts (% over e-commerce revenues)
(Y6)
Doubtful accounts = (9) x (13)
Sales and marketing fixed costs (USD)
(Y7)
Product development and technology fixed costs (USD)
(Y8)
General administration fixed costs (USD)
(Y9)
Sales and marketing variable costs (USD / transaction)
(Y10)
Product development and technology variable costs (%)
(Y11)
General administration variable costs (%)
(Y12)
Sales and marketing total costs = (15) + [(18) x (7)]
Product development and technology total costs = (16) + [(19) x (9)]
General administration total costs = (17) + [(20) x (12)]
Total operating costs = (21) + (22) + (23) estimate of the expected future cash flows (CFt), including, if
necessary, a terminal value, and the appropriate discount rate
(k) for these cash flows. The company’s forecasted financial
statements, including expected values for the aforementioned
uncertain variables, allow for the calculation of the expected
cash flows between 2002 and 2010 (shown in Exhibit 4).
The discount rate was estimated to be 21% using the
CAPM model along with the information summarized in
Exhibit 5:
k R f B – [ E ( Rm ) R f ] 14% 1.6 – (18% 14%) 21%
The data summarized in Exhibit 5 were provided by
market practitioners. The market variance and returns correspond to the Morgan Stanley Capital International (MSCI)
global index. The explanation for such a high risk-free rate
(Rf =14%) is that this company operates in Latin American
countries (mainly Brazil, Mexico, Argentina and, to a lesser
extent, Chile, Colombia, Venezuela, and Uruguay).
An alternative approach—one that, if done correctly, yields
the same answer—is to obtain estimates of future cash flows
A Morgan Stanley Publication • Spring 2008
Exhibit 4 Expected Cash-flows for the Company (2002-2010)
Expected cash-flows
2002
2003
2004
2005
2006
2007
2008
2009
2010
Uncertain variables
(expected variables)
Number of internet users
31,000,000
43,000,000
51,000,000
55,000,000
60,000,000
60,000,000
60,000,000
60,000,000
60,000,000
6.50%
4.90%
4.28%
4.11%
3.91%
4.05%
4.19%
4.34%
4.5%
0.32
0.50
0.80
1.10
1.40
1.70
2.00
2.30
2.50
Company´s market
penetration rate
Transactions per user
Average ticket per transaction
Commission charged
Doubtful accounts
Sales and marketing fixed costs
Product devel/technology
fixed costs
General administration
fixed costs
Sales and marketing
variable costs
Product devel/technology
variable costs
General administration
variable costs
Number of company´s users
Total transactions
Gross merchandise sales
115
90
80
80
80
80
80
80
80
1.50%
1.75%
2.00%
2.30%
2.50%
2.80%
3.20%
3.60%
4.00%
24.5%
19.60%
15.00%
15.00%
15.00%
15.00%
15.00%
15.00%
15.00%
250,000
250,000
250,000
250,000
250,000
250,000
250,000
250,000
250,000
420,000
420,000
420,000
420,000
420,000
420,000
420,000
420,000
420,000
1,440,000
1,440,000
1,440,000
1,440,000
1,440,000
1,440,000
1,440,000
1,440,000
1,440,000
0.40
0.40
0.40
0.45
0.45
0.45
0.50
0.55
0.55
0.33
0.30
0.30
0.30
0.25
0.22
0.20
0.18
0.15
0.220
0.200
0.180
0.150
0.130
0.100
0.080
0.075
0.075
2,015,000
2,107,000
2,182,800
2,261,600
2,346,000
2,427,000
2,514,000
2,604,000
2,700,000
639,581
1,053,500
1,746,240
2,487,760
3,284,400
4,125,900
5,028,000
5,989,200
6,750,000
73,551,806
94,815,000
139,699,200
199,020,800
262,752,000
330,072,000
402,240,000
479,136,000
540,000,000
Revenues
E-commerce revenues
Advertising revenues
Other revenues
Total revenues
1,103,277
1,659,263
2,793,984
4,577,478
6,568,800
9,242,016
12,871,680
17,248,896
21,600,000
516,991
800,000
977,500
1,124,125
1,292,744
1,486,655
1,709,654
1,966,102
2,261,017
65,362
100,000
132,000
145,200
159,720
175,692
193,261
212,587
233,846
1,685,630
2,559,263
3,903,484
5,846,803
8,021,264
10,904,363
14,774,595
19,427,585
24,094,863
Operating costs
Sales and marketing
505,832
671,400
948,496
1,369,492
1,727,980
2,106,655
2,764,000
3,544,060
3,962,500
Product development and
technology
784,081
917,779
1,258,195
1,793,244
2,062,200
2,453,244
2,994,336
3,524,801
3,660,000
General administration
1,810,839
1,951,853
2,142,627
2,317,021
2,482,764
2,530,436
2,621,968
2,897,069
3,247,115
Total operating costs
3,100,753
Doubtful accounts
3,541,032
4,349,319
5,479,757
-1,307,067
-864,933
-319,575
762,999
2,427,726
4,463,539
6,874,320
9,985,248
Depreciation and amortization
-1,418,052
-1,418,052
-1,418,052
-1,418,052
-1,418,052
-1,418,052
-1,418,052
-1,418,052
EBIT
-3,103,639
-2,725,120
-2,282,985
-1,737,627
-655,053
1,009,674
3,045,487
5,456,268
8,567,196
Post-tax EBIT
CAPEX
Cash-flow
-3,103,639
-1,685,428
Journal of Applied Corporate Finance
•
1,930,752
10,869,615
-1,418,211
Actual tax
1,386,302
9,965,931
-1,685,427
-
985,320
8,380,304
EBITDA
Theoretical tax
686,622
7,090,335
325,298
Tax-loss-carry-forward
419,098
6,272,945
270,303
2,587,334
3,240,000
-15,000,000
-15,817,536
-17,023,720
-17,220,236
-16,917,334
-16,003,688
-14,366,807
-817,536
-684,896
-521,288
-196,516
302,902
913,646
1,636,880
2,570,159
-
-
-
-
-
-
-
-
16,502,432
-2,725,120
-2,282,985
-1,737,627
-655,053
1,009,674
3,045,487
5,456,268
8,567,196
-1,000,000
-1,000,000
-1,000,000
-1,000,000
-1,500,000
-2,000,000
-2,500,000
-2,500,000
-2,307,068
-1,864,933
-1,319,575
-237,001
927,726
2,463,539
4,374,320
7,485,248
Volume 20 Number 2
A Morgan Stanley Publication • Spring 2008
131
Exhibit 5 Risk-adjusted Discount Rate According to CAPM4
Rf
E (R
14%
B
=
=
=
k
=
21%
L
=
=
8.21
0.01
)
m
Var (R m )
18%
1.6
using certainty-equivalent correction factors (κ1 = λ ⋅ cov (CFt,
Rm) ). Using such factors together with the CAPM, one then
reduces the expected cash flows to yield the certainty-equivalent (or risk-neutral expectation) future cash flows EQ (CF1):
E Q (CFt ) E P (CFt ) L – cov (CFt , Rm ),
where λ is the market price of risk defined as:
L
E (Rm ) R f
V (Rm )
These certainly-equivalent cash flows can then be discounted
at the risk-free rate to calculate the same PV as follows:
E P (CFt ) T E Q (CFt )
∑
t
t 1 (1 k )
t 1 (1 R f )
T
E P (CFt ) L – cov( CFt , Rm )
∑
(1 R f ) t
t 1
T
PV ∑
For the terminal value (TV) calculation, we used a
growing perpetuity formula with two different growth rates:
g1=12% (between 2010 and 2015) and g2= 4% (from 2010
onwards).
Using all this information, we then proceeded to calculate
the company’s traditional PV as follows:
E P (CFt ) E P (TVT ) =12.1 million USD
t
(1 k )T
t 1 (1 k )
T
PV E P (CF0 )∑
where EP(TV T) is the expected terminal value at year T.
And, as suggested, the same result can be obtained using
the following certainly-equivalent approach:
4. We follow the global CAPM approach by using the same market risk premium
for all investments around the world and reflecting the country´s risk premium in its
risk-free rate.
132
Journal of Applied Corporate Finance
•
Volume 20 Number 2
Exhibit 6 Traditional PV
K1
EP (CFt)
EQ CFt)
2002
0
2003
-137,621
2004
-215,858
2005
-222,340
2006
-51,689
2007
245,603
2008
760,240
2009
1,530,313
2010
2,908,944
Terminal Value 24,148,500
Discount rate
Present Value
-1,685,428
-2,307,068
-1,864,933
-1,319,575
-237,001
927,726
2,463,539
4,374,320
7,485,248
62,138,547
0.21
12,048,009
-1,685,428
-2,169,446
-1,649,075
-1,097,236
-185,312
682,123
1,703,299
2,844,007
4,576,305
37,990,046
0.14
12,048,009
T
PV E Q (CF0 )∑
t 1
E Q (CFt ) E Q ( TVT)
= 12.1 million USD
(1 R f ) t (1 R f )T
Exhibit 6 shows, for each year from 2002-2010, the costs of
capital (Kt), expected cash flows (EP), and certainty equivalents (EQ ) used for these calculations of traditional present
values: either the expected cash flows (including the TV)
or the certainty equivalent cash flows (including TV).
Certainty-equivalent correction factors for the expected cash
flows according to CAPM (Kt) are also included.
Exhibit 7 shows graphically both the expected cash flows
and the certainty-equivalent for the period between 2001 and
2010, including the terminal value. As can be seen clearly in
the figure, the cash flow of this company is expected to increase,
with losses that gradually fall until 2007 when expected cash
flows become positive. In such situations, most of the traditional PV comes from the cash flows situated farthest into the
future, including the terminal value. In fact, the company’s
positive traditional PV is due entirely to this terminal value,
which accounts for 114% of the total value.5
This traditional PV of the investment without flexibility
will serve as the underlying asset in the remaining steps of our
real option valuation.
Step Two: Uncertainty is Treated Explicitly Using
Monte Carlo Simulation Techniques
While continuing to work with the traditional non-flexibility
scenario, the second stage of the valuation process is to estimate the degree of uncertainty that surrounds the expected
cash flows from the investment. After identifying the uncertain variables on which these cash flows depend, we use a
Monte Carlo simulation software program to generate values
5. Since this company is an investment with systematic risk, its risk-adjusted discount
rate according to CAPM is higher than the risk-free rate, which means that the certaintyequivalent of the cash flows are higher than the expected values when the amount is
negative and lower when they are positive.
A Morgan Stanley Publication • Spring 2008
Exhibit 7 Traditional PV
Cash-Flows
Traditional PV
1
2
3
4
5
6
7
8
9
Time Period
Cert. Equiv.(TV) (LHS)
E (TV) (LHS)
Cert. Equiv.( C Ft) (RHS)
E(CFt) (RHS)
Exhibit 8 Forecast Evolution of Uncertain Variables Affecting Revenues
2002
(Y1) Number of Internet users
2003
2004
2005
2006
2007
2008
2009
2010
Expected value
31 mn 43 mn 51 mn 55 mn 60 mn 60 mn 60 mn 60 mn 60 mn
Maximum value
35 mn 50 mn 61 mn 65 mn 75 mn 75 mn 75 mn 75 mn 75 mn
Minimum value
25 mn 35 mn 41 mn 41 mn 41 mn 41 mn 41 mn 41 mn 41 mn
(Y2) Company´s market penetration rate Expected value
6.50%
4.90%
4.28%
4.11%
3.91%
4.05%
4.19%
4.34%
4.50%
Maximum value
7.42%
6.00%
5.70%
5.50%
4.50%
5.00%
5.00%
5.00%
5.00%
Minimum value
6.0%
3.5%
3.0%
2.5%
2.0%
2.0%
2.0%
2.0%
2.0%
2.50
(Y3) Transactions per user
Expected value
0.32 0.50 0.80 1.10 1.40 1.70 2.00 2.30 Maximum value
1.0 1.5 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Minimum value
0.25 0.25 0.25 0.25 0.25 0.20 0.20 0.15 0.15
(Y4) Average ticket per transaction
Expected value
115 90 80 80 80 80 80 80 80
Maximum value
130 120 120 120 120 120 120 120 120
Minimum value
50 20 20 10 10 8
8
8
8
(Y5) Commission charged
Expected value
1.50%
1.75%
2.00%
2.30%
2.50%
2.80%
3.20%
3.60%
4.00%
Maximum value
1.80%
2.00%
2.50%
3.00%
4.00%
4.50%
5.00%
5.50%
6.00%
Minimum value
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
0.50%
0.50%
0.50%
Journal of Applied Corporate Finance
•
Volume 20 Number 2
A Morgan Stanley Publication • Spring 2008
133
for these primary variables and for the cash flows (and hence
investment values) related to them. This allows us to quantify
the risk of the entire investment (as distinguished from the
risk of the individual variables).
To perform the simulation of the 12 uncertain variables
that were previously identified, we asked the company’s
management for the minimum, expected, and maximum
values they could forecast for each variable during each year of
the 2002-2010 period. Using these management forecasts (the
projected values for some of the uncertain variables are shown
in Exhibit 8), we performed 200,000 simulations6 for each of
the 12 uncertain variables Yi in each of the nine years between
2002 and 2010, resulting in 200,000 values for each yearly
cash flow during that period of time. Then, in contrast to the
C&A model, these simulation results are carried throughout
the remainder of the valuation process.7
Unlike the C&A approach, which reduces the simulation
results to a recombining event tree that follows the binomial lattice framework, we propose a fairly straightforward
and simple risk-neutral adjustment of our expected cash flow
and simulation results. In the first step of our analysis, the
expected cash flows used in the calculation of the traditional
PV were derived using investors’ probabilities (P)–that is, EP
(CFt). At the same time, we calculated certainty-equivalent
future cash flows using risk-neutral probabilities (Q) that
were discounted at R f to yield the same present value for the
underlying asset. In other words, calculation of the certaintyequivalent provides us with the risk-neutral expectation of
future cash flows, or E Q (CFt).
Expressed in equation form, EP (CFt) – κt = EQ (CFt)
Next we find the correction factors κt to calculate the
certainty-equivalents of the future cash flows.8 In a traditional
PV calculation, as mentioned earlier, we know that CAPM
can provide these correction factors:
E P CFt K t E P CFt L – cov CFt , Rm EQ FC t Using the correction factors κt for the traditional (without
6. Since the uncertain variables could only move inside a pre-determined range of
values, and since the expected value was often not symmetrically placed between the
minimum and maximum value, but closer to one or the other, we decided to use the
beta distribution for the simulation of these uncertain variables. We included in the
analysis the relationship of each variable’s value with its value in the previous year
(autocorrelation) and also the relationships among the values of some variables and
others (correlations).
7. From this point onwards, our model differs from Copeland and Antikarov’s. Their
model reduces the simulation results to a recombining event tree that follows the binomial lattice framework. This procedure simplifies greatly the simulation results and adds
some restrictions (like constant variance for every period) that distort reality considerably.
We believe our proposal reflects real-world potential events more accurately.
8. Most real options models use the risk-neutral probabilities (Q) to obtain the riskneutral expected cash flows—that is, they concentrate on the right-hand side of the
Journal of Applied Corporate Finance
t
The results of the Rm simulation will then be matched
with the new CFopt to get cov (CFopt, Rm). Using our original
market price of risk λ, we obtain the new correction factors for
the post-option cash flows (reported later in Exhibit 11):
K op L – cov CFop t , Rm t
Step Three: Risk Adjustment
134
flexibility) cash flows shown in Exhibit 6, we can obtain cov
(CFt, Rm) as reflected in Exhibit 11. We simulated 200,000
values per year for Rm to match them with the 200,000 CFt from
the second step so that these covariances are maintained.9
At a later stage in the valuation process, when we introduce the real options and obtain the cash flows that reflect
this optionality (CFopt), we will need the risk-neutral expectation EQ(CFopt). But, again, we will not work with the
risk-neutral probabilities, but instead look for the new correction factors:
E P CFop t K op E Q FCop t •
Volume 20 Number 2
Step Four: Introducing Real Options
At this stage of the valuation process, we identify and
then attempt to quantify the main real options built into
this investment. We identified two real options for our ecommerce company: the option to sell the company for a
multiple of the year’s cash flow, and the option to abandon
the investment and liquidate the company. Both options are
“American” in the sense they can be exercised any time during
the life of the investment.10 The option to sell the company
would be exercised in the more favourable events, and the
abandonment option in the least favourable circumstances,
minimizing or eliminating the possibility that both options
could be “in the money” at the same time.
First let’s examine the option to sell the company. An
investor who owns a stock of a non-listed company can sell
it at any time through an IPO or to a strategic buyer in the
corporate M&A market.11 Although the price is not easily
determined, we can assume an agreed-upon price in which
both the buyer and the seller would be happy to do the transaction, since the acquirer would be willing to pay a premium
due to the synergies arising from the combination of both
business and a more productive management of the assets.
The divergence in value between the current and prospective buyer will vary over time, but to illustrate the method
above equation. At a later stage in the valuation process, these risk-neutral probabilities
would be used with the new post-option cash flows (CFopt) to calculate the risk-neutral
expectation EQ (CFopt) which, discounted at Rf, yields the investment’s expanded PV. The
fact that we maintain all our simulation scenarios turns the calculation of risk-neutral
probabilities into an impracticable task.
9. We have used E(Rm) and V(Rm) as inputs for λ, and with this data we simulate Rm
so that cov (CTt, Rm) is maintained in every moment t.
10. Nevertheless, the fact that this is a discrete-time model using only end-of-year
data make these options behave rather like Bermuda-type options.
11. Even if the stock is already listed, such an option could exist, since the company
may be acquired by a strategic buyer through an M&A deal.
A Morgan Stanley Publication • Spring 2008
we simplify matters by using a multiple of ten times the cash
flow in a given state12 as the price for which the company
might be sold.
To quantify the value of such options, we start by choosing the maximum value alternative (abandon, sell, or continue
to operate) for each of our 200,000 simulated events at each
moment in time. We call the values of present and future cash
flows in the case of exercise the options to abandon, to sell, or
to hold (i.e., exercise no option at all) Voat , Vost , and Vnot,
respectively. The decision rule for a certain event i (i = 1,…,
200,000) can be formulated as follows:
maxi,t(Voai,t , Vosi,t , Vnoi,t)
In every state, at any moment the value of abandoning
(Voai) is assumed to be zero and the value of selling (Vosi)
is estimated to be 10 times the cash flow in the state we are
analyzing (10 ⋅ CFi). The value of continuing to operate the
company (Vnoi) is obtained by discounting future cash flows
that must be estimated without considering the simulated
cash flow linked to the event i.13 For this estimation, we had
several alternatives: the approach of Longstaff and Schwartz
(2001), which uses simple least squares regressions to establish a parametric model for the cash flows; the method of
Copeland and Antikarov (2001), which assumes a distribution
of cash flows with constant variance (due to their simplification in a recombining event tree); or, alternatively, we could
run new simulations of the cash flows linked to each event.
While the first two alternatives rely on major simplifications, the latter can be too computationally intensive. To
address these problems, we used a non-parametric method
known as “nearest neighbors” technique, which avoids the
restrictiveness of Longstaff and Schwartz and C&A, and is not
as intensive as performing a whole set of simulated cash flows
for each event. For each of the 200,000 simulated cash flows
in a given year, we took the 200 closest trajectories (simulated
events) to that number. These 200 values (the nearest neighbors) represent the simulated events closest to the event i,
and with them we can obtain an expected distribution for the
company’s cash flows. The future values (trajectories) of the
200 nearest neighbors to CFi,t are equivalent to performing a
simulation of 200 cases from event i,t.
As is often the practice in using option models, we start by
making choices at year 2010 and then work backwards toward
present values using a technique called “backward induction.”
First, we take the 200 closest trajectories to FCi in 2010,
each trajectory with its attached terminal values. The average
of these 200 terminal values (TVi*) is then used to determine
the value of continuing to operate, so that the decision rule
becomes:
max (0;10 – CFi , 2010 ; CFi , 2010 + TVi ,*2010 )
for each of the 200,000 FCi in year 2010.
Once this first set of decisions is made, we work backwards
from 2010 toward 2002. The process for years 2002-2009
requires, however, that we use risk-neutral discounting. The
real options to sell and abandon remain the same as before: the
value of selling the company is 10 ⋅ CFi,t t = 2002,…2009 and
the value of abandoning is 0. As before, the problem comes
when we determine the value of continuing to operate. Again,
we pick the 200 closest values to CFi,t and their corresponding
post-options cash flows and terminal values (CFopi,s; TVopi,T
for s = t + 1, and T = 2010). We want to discount the averages
of these 200 neighbors for the years after t (CFs, TVopT); and
since we are talking about post-option cash flows, we need to
work with the risk-neutral adjustment explained in the third
step in order to use Rf as the discount rate. For any state i at a
given moment t between 2002-2009, the value of the continuing-to-operate alternative is therefore estimated as follows: the
value of the cash flow we are analyzing CFi,t plus the value at
t of these discounted 200 elements averages:
T CFop * Kop *
TVi *,T Kopi*,T
i ,s
i ,s
CFi ,t ∑
(1 R f ) s t
(1 R f ) T t
s t 1
This results in the following decision rule:
T CFop * Kop *
¥
i ,s
i ,s
max ¦0;10 – CFi ,t ; CFi ,t ∑
st
¦
s t 1 (1 R )
§
f
TVi *,T Kop i*,T ´µ
(1 R f ) Tt µ¶
for any state i at any moment t between 2002-2009.
Once the decision is made to abandon, sell, or continue
to operate, we determine the new post-option cash flows for
each state i:
1.If we abandon the company, CFopi,t = 0, with all cash
flows after that, including the terminal value, also being zero,
since the company is closed CFopi,s = TVopi,T = TVopi,T .
2.If we sell the company, CFopi,t = 10 ⋅ CFi,t, with all cash
flows after that, including the terminal value, being zero, since
the company is being given away CFopi,s = 0, TVopi,T = 0 .
3.If we continue to operate without exercising any option,
the post-option cash flow is equal to the traditional cash flow
CFopi,t = CFi,t, and the cash flows after that remain the postoption cash flows determined before CFopi,s = CFopi,s , TVopi,T
= TVopi,T .
12. This multiple was obtained from Morgan Stanley professionals based on M&A
deals in the high tech sector that were being closed at the time of writing. Further details
on the decision of choosing this multiple are presented later in the article.
13. AUTHOR PLEASE PROVIDE
Journal of Applied Corporate Finance
•
Volume 20 Number 2
A Morgan Stanley Publication • Spring 2008
135
Exhibit 9 Post-option Cash Flows for Year 2010
Year 2010
Original Cash-flows
CF 1
CF 2
.
.
.
TV1
TV2
.
.
.
CF2
200 closest
values
.
.
.
CF200.000
Value of the
Going-on Alternative
in the Event i
CFi Nearest Neighbors
.
.
.
.
.
.
CF h
.
.
.
.
.
TVh
.
.
CF i
.
.
CF k
.
.
.
TVi
.
.
TVk
.
.
.
averages = TVi
*
CFi + TV i
*
TV200.000
Decision Among the 3 Alternatives
in Event i
Determination of the Post-option Cash-flow
(CFop) in Event i of Year 2010
Post-option Cash-flows
CFop 1
0
TVopi
=0
if abandon
TVop1
CFop 2
Max (abandon, sell, going-on) =
TVop2
.
CFop i
=
10 CF i
TVopi
=0
if sell
" = Max (0 ; 10 CFi ; CFi + TVi *) =
CF i
TVopi
.
.
.
.
.
= TVi if going-on
The optimum alternative in
event i of the period t is chosen
CFop
TVop
200.000
200.000
Exhibit 10Post-Option Cash Flows for Year 2010
Years 2002 – 2009
Original Cash-Flows in Year t
CF
1, t
CF
CFop
1, t+1
CFop
.
.
.
.
.
.
2, t
2, t+1
.
.
.
CF
200.000, t
...
...
CFop
1,T
CFop
TVop
1
TVop
.
.
.
.
.
.
CFop
200.000, t+1
.
.
.
. . . CFop
.
.
.
2
2,T
.
.
.
200.000, T
CFi,t
200 closest
values
.
.
.
TVop
+
.
.
.
.
.
.
CFop h,t+1 . . .
CFop h,T
.
.
.
.
CFop i,t+1 . . .
CFop i,T
.
.
.
.
CFop k,t+1 . . .
CFop k,T
.
.
.
.
.
.
average = CFop *i,s &TV *i
CF h,t
.
.
CF i,t
.
.
CF k,t
.
.
.
200.000
.
.
.
TVop
h
.
.
TVop
i
.
.
TVop
k
.
.
.
CFop h,s ;
COV CFop i,s ;
CFop k,s ;
TVop h ;
Rm h,T
Rm i,s COV TVop i ;
Rm i,T
TVop k ;
Rm k,T
Rm h,s
Rm k,s
COV*(CFop i,s ;Rmi,s )
Determination of the Post-option Cash-Flows
(CFop) in the Eventi,t and Afterwards
Decision Among the 3 Alternatives in Event i
Value of the going-on alternative =
T
CFop i*, s − K op i ,*s
= CFi , t + ∑
(1 + R f ) s − t
s = t +1
Obtaining the Covariances for the
Risk-Neutral Adjustment
CFi,t Nearest Neighbors
TV i* − K opi*, T
0
CFop i,s = 0
(1 + R f ) T−t
CFop i,t 10 CF i,t
Value of the option to abandon = 0
Value of the option to sell = CF i,t 10
CF i,t
CFop i,s = 0
CFop
i,s
TVop i = 0
TVop i = 0
COV*(TVi ;Rm i,T )
Post-Option Cash-Flows
if abandon
if sell
CFop1 ,t
CFop 1 ,s
...
TVop 1
CFop2 ,t
CFop 2 ,s
…
TVop 2
.
.
.
.
.
.
.
.
.
= CFopi,s TVop i = TVop i if going-on
Max (abandon, sell, going-on)
The optimum alternative in event i of the period t is chosen
136
Journal of Applied Corporate Finance
•
Volume 20 Number 2
CFop
200.000, t
CFop
200.000, s…
TVop 200.000
A Morgan Stanley Publication • Spring 2008
Exhibit 11 Computation of the Expanded Present Value
cov (CFt, Rm)
E(CFopt)
κopt = = λ ⋅ cov(CFopt, Rm)
EQ(CFopt)
2002
-
-1,685,188
0
-1,685,188
2003
-16,754
-2,301,584
-137,323
-2,164,261
2004
-26,278
-1,850,097
-213,921
-1,636,177
2005
-27,067
-1,274,491
-228,734
-1,045,757
2006
-6,293
1,602,560
-180,553
1,783,114
2007
29,899
9,182,282
1,977,182
7,205,101
2008
92,551
19,372,495
5,712,384
13,660,111
2009
186,299
26,732,779
8,835,316
17,897,463
2010
354,132
31,725,832
10,677,254
21,048,578
Terminal Value
2,939,817
303
-79
382
Present Value
20,731,030
Exhibit 12 Value Added by the Real Options to the Expanded PV
USD
25,000,000
Value due to traditional cash-flow discounting
Value due to the investment´s real options
20,731,030
19,857,103
20,000,000
8,683,021
7,809,094
14,156,239
15,000,000
2,108,229
12,048,009
10,000,000
5,000,000
0
Traditional PV
Expanded PV with both real options
Expanded PV with the
abandonment option
Expanded PV with the selling option
Real Options Contribution to the Expanded PV
These steps are summarized in Exhibits 9 and 10, and the
expected post-option cash flows resulting from this process are
summarized later in Exhibit 11.
Step Five: Expanded Present Value Calculation
The post-options cash flows (CFopt) obtained in the fourth
step are adjusted using the certainty-equivalent correction
Journal of Applied Corporate Finance
•
Volume 20 Number 2
factors (κop1 = λ ⋅ cov (CFopt, R m)) explained earlier (in the
third step). As shown in Exhibit 11, the resulting risk-neutral
expected cash flows EQ (CFopt) are discounted at R f to yield
the investment’s expanded present value with its embedded
real options—a value we estimate to be $20.7 million.
Such an expanded PV calculation does a better job than
DCF in reflecting the value of the company by capturing
A Morgan Stanley Publication • Spring 2008
137
Exhibit 13 Traditional PV vs. Expanded PV
USD
25,000,000
Value due to traditional cash-flow discounting
Value due to the investment´s real options
20.731.030
20,000,000
72 %
8,683,021
42%
15,000,000
12,048,009
10,000,000
5,000,000
0
Traditional PV
Expanded PV with both real options
Expanded Present Value
the flexibility of managerial decisions that can affect both the
cash flows and the risk of the investment. Exhibit 12 shows
the traditional PV in comparison with the expanded PV, with
both real options combined, and also with the expanded PV
with each real option analyzed on a stand-alone basis. It is clear
that the presence of real options adds value to the traditional
discounted cash flow methodology.
The expanded PV including both options is 72% higher
than traditional PV, (Exhibit 13). And 58% of the expanded
PV is due to traditional cash flow discounting, while 42% is
due to the embedded real options.
Looking at each real option on a stand-alone basis, we
find that the option to sell is much more valuable than the
abandonment option (see Exhibits 14 and 15). And it is also
exercised in a higher number of events. There is a certain
overlap between the two options when they are together, so
that their values interact and the combined value is lower than
the sum of their separate values.14
Finally, it is interesting to point out that the weight of
the terminal value in the expanded PV is irrelevant since the
14. This confirms previous works like Trigeorgis (1993) or Kulatilaka (1995).
138
Journal of Applied Corporate Finance
•
Volume 20 Number 2
number of events in which the company decides to continue
to operate (i.e., without exercising any options) is extremely
low (0.11% when both options are combined).15 We can
conclude that the possibility of reacting to the evolution of
future uncertain events brings part of the investment’s value
closer to the present moment.
Sources of Value in the Expanded Present
Value Approach
When we compare the traditional PV from the first step of
the model with the traditional PV obtained with the simulated cash flows from the second step (real options have not
been included yet), it is clear that the latter is slightly higher
(see exhibit 16), and that this increase in value cannot be
explained by the embedded options, but by differences in the
valuation methodology.
In the conventional way of calculating PV (first step), all
future cash flows are summarized in one single value—their
expected value—whereas option valuation models automatically take into account all possible outcomes in the future.
15. Of course when each option is analyzed on a stand alone basis, only part of the
outcomes would be covered (the negative ones by the option to abandon and the positive
ones by the option to sell the company). In these cases, the alternative of continuing to
operate is chosen more times (79% when only the abandonment option is considered,
and 12% when the selling option is analyzed on its own).
A Morgan Stanley Publication • Spring 2008
Exhibit 14 Traditional PV vs. Expanded PV with the Abandonment Option
USD
16,000,000
Value due to traditional cash-flow discounting
Value due to the abandonment real option
14,156,239
17%
14,000,000
2,108,229
15%
12,000,000
10,000,000
12,048,009
8,000,000
6,000,000
4,000,000
2,000,000
0
Traditional PV
Expanded PV with the abandonment option
Expanded PV with the abandonment option only
Exhibit 15 Traditional PV vs. Expanded PV with the Option to Sell the Company
USD
25,000,000
Value due to traditional cash-flow discounting
Value due to the opotion to sell the company
19,857,103
20,000,000
66%
7,809,094
39%
15,000,000
12,048,009
10,000,000
5,000,000
0
Traditional PV
Expanded PV with the selling option
Expanded PV with the Selling Option Only
Journal of Applied Corporate Finance
•
Volume 20 Number 2
A Morgan Stanley Publication • Spring 2008
139
Exhibit 16Traditional PV with No Real Options
Traditional PV
Traditional PV with
Simulated Cash Flows
2002
-1,685,428
-1,685,428
2003
-2,307,068
-2,301,584
2004
-1,864,933
-1,850,097
2005
-1,319,575
-1,283,163
2006
-237,001
-163,821
2007
927,726
1,071,467
2008
2,463,539
2,671,920
2009
4,374,320
4,657,320
2010
7,485,248
7,740,544
Terminal Value
62,138,547
64,257,875
Discount rate
0.21
0.21
Present Value
12,048,009
12,844,648
Exhibit 17Sources of Value in the Expanded PV
USD
25,000,000
Value Due to the Investment´s Optionality
Value Due to Jensen´s Inequality
Value Due to Traditional Cash-flow Discounting
20,731,030
20,000,000
7,886,383
38%
15,000,000
796,639
4%
10,000,000
12,048,009
58%
5,000,000
The traditional PV discounts an expected cash flow calculated
using the expected values of a number of uncertain variables.
In contrast, the traditional PV with option models (second
step) discounts the expectation of all possible cash flows using
the different values of the uncertain variables.
Thus, depending on the shape of the function relating
the cash flows and the uncertain variables, the traditional PV
obtained with option models could be different than the one
calculated with conventional discounting. If the function
is linear, both values would be equal, but if the function is
convex, then, due to Jensen’s inequality, the expectation of
future cash flows would be higher than the cash flow of the
expectations: E(CF (Yi ,t )) >CF (E (Y i ,t )).16 Our case study attributes 4% of the expanded PV to the presence of the Jensen´s
inequality, while the pure value of the real options would
represent 38% of this value (Exhibit 17).
When we checked the convexity of the cash flow function
with the 12 uncertain variables Y for all 9 periods, we found
convexity in all cases (Exhibit 18 presents some charts17 of the
cash flow function and the Y variables for the year 2004).
Finally, we checked the robustness of the model by
performing sensitivity analysis of the model’s deterministic parameters. The model is robust to most of them. Only
the multiple of the cash flow that determined the value of
the option to sell proved to be significant when explaining
the expanded PV. The chart in exhibit 19 shows how the
company’s expanded PV evolves as the multiple of cash flows
at which the company is sold increases. It is clear that the
value of the option to sell, and therefore of the expanded
0
Expanded PV with the Both Real Options
PV, depends on this multiple. (In fact, the option to sell has
no value for selling multiples below 6.2.) Market conditions,
trading comparables, and similar transactions should provide
a benchmark at any time for the correct multiple at which
these companies could be sold.
Conclusion
This work presents a five-step real option valuation model and
tests its validity with a real life application. The model expands
previous work—notably the approach of Copeland and Antikarov—that uses simulation in real option valuation.
In an effort to achieve a more realistic approach, our
method continues to use simulation results throughout the
whole valuation process. To make this possible, we present an
innovative risk-neutral adjustment that, instead of trying to
determine risk-neutral probabilities, looks for the certaintyequivalent correction factor that can transform expected cash
flows into risk-neutral expectations. We also had to look for
new ways to include real options into the analysis. We used
the “nearest neighbors” technique to find out the value of
going on without exercising any options so we can choose
the maximum value alternative in each event. The simulation
16. This insight has already been pointed out by Eduardo Schwartz. See Schwartz
(2004) or Schwartz and Moon (2000 and 2001).
17. The shape of these charts resembles a call option on the variables linked to revenues and a put option on the ones linked to costs.
140
Journal of Applied Corporate Finance
•
Volume 20 Number 2
A Morgan Stanley Publication • Spring 2008
Exhibit 18 The Cash-Flow Function Shows Convexity Regarding the Uncertainty
2004
6000000
5000000
5000000
4000000
4000000
3000000
2000000
1000000
0
-1000000
35
40
45
50
55
60
65
-3000000
7000000
2004
7000000
6000000
6000000
5000000
5000000
4000000
4000000
3000000
2000000
1000000
0
0
3.00%
3.50%
4.00%
4.50%
5.00%
5.50%
6.00%
1
1.5
2
2.5
100
120
140
250000
270000
290000
1000000
-1000000
20
40
60
80
2004
4000000
Cash-flows
5000000
3000000
2000000
1000000
16.00%
18.00%
2004
7000000
4000000
14.00%
Average Ticket (USD)
-3000000
Transactions Per User
5000000
20.00%
22.00%
24.00%
3000000
2000000
1000000
0
150000
-1000000
26.00%
170000
190000
210000
230000
-2000000
-2000000
-3000000
Doubtful Accounts (% E-commerce Revenues)
-3000000
7000000
2004
7000000
6000000
5000000
5000000
4000000
4000000
Cash-flows
6000000
3000000
2000000
1000000
0
390000
-1000000
0
-2000000
6000000
12.00%
-1000000
2004
2000000
6000000
0
Penetration Rate (%)
3000000
0
0.5
7000000
410000
430000
450000
470000
490000
510000
Sales and Marketing Fixed Costs (USD)
2004
3000000
2000000
1000000
0
-1000000
0.2
0.25
0.3
0.35
0.4
0.45
-2000000
-2000000
-3000000
0
2.50%
-2000000
Cash-flows
Cash-flows
1000000
Internet Users (mn)
-3000000
Cash-flows
2000000
-3000000
-2000000
Cash-flows
3000000
-1000000
-2000000
-1000000
2004
7000000
6000000
Cash-flows
Cash-flows
7000000
Product and Technology Fixed Costs (USD)
Journal of Applied Corporate Finance
•
Volume 20 Number 2
-3000000
Product and Technology Variable Costs (USD)
A Morgan Stanley Publication • Spring 2008
141
Exhibit 19 Sensitivity of the Company’s Present Value to the Multiple of CF for the Option to Sell
PV
140000000
120000000
100000000
Traditional PV
Expanded PV
80000000
60000000
40000000
20000000
0
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
40,00
45,00
50,00
Cash Flow Multiple for the Price of the Option to Sell
was done using the beta distribution, which provided a lot of
flexibility to adapt the information provided by the management of the company.
The e-commerce company identified 12 uncertain variables
during the nine-year time period 2002-2010. Each of these
variables was simulated 200,000 times per period using beta
distributions. Two real options were then included: the option
to abandon and the option to sell the company for a multiple
of the current year cash flow. Both options were quantified and
included in the valuation using the above mentioned nearest
neighbors technique, producing the new post-option cash
flows. These new cash flows were adjusted with the risk correction factors mentioned before and discounted at the risk-free
rate to yield the expanded present value of the company.
Our results show that the expanded present value is higher
than the traditional present value; that the real option to sell
the company is more valuable than the real option to abandon;
and that, although most of the time they are exercised in
142
Journal of Applied Corporate Finance
•
Volume 20 Number 2
different outcomes, both options interact, confirming previous works like Trigeorgis (1993) or Kulatilaka (1995). Also,
following Schwartz (2004) and Schwartz and Moon (2000
and 2001), we found that 4% of the expanded present value
is attributable to Jensen’s inequality, which led us to check and
confirm the presence of convexity between the value of each
year’s cash flow and each of the uncertain variables.
rocío sáenz-diez is a professor of Corporate Finance and Mergers
and Acquisitions at Universidad Pontificia Comillas.
ricardo gimeno is an economist at the Research Department of
Banco de España, (Spanish Central Bank).
carlos de abajo is a Managing Director of Morgan Stanley in the
firm’s investment bank, with considerable experience in both M&A and
capital markets transactions.
A Morgan Stanley Publication • Spring 2008
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Journal of Applied Corporate Finance
•
Volume 20 Number 2
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A Morgan Stanley Publication • Spring 2008
143
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