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Real Options Valuation

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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 Rf

[ 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

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

Uncertain variables
(expected variables)
Number of internet users
Company´s market penetration rate
Transactions per user
Average ticket per transaction

115

Doubtful accounts

90

80

80

80

80

80

80

80

1.50%

Commission charged

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

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

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

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

Revenues
E-commerce revenues
Advertising revenues
Other revenues
Total revenues

Operating costs

Doubtful accounts

3,541,032

4,349,319

5,479,757

1,930,752

10,869,615

-1,307,067

-864,933

-319,575

762,999

2,427,726

4,463,539

6,874,320

9,985,248

Depreciation and amortization

-1,418,211

-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

2,587,334

3,240,000

-15,000,000

-3,103,639

-17,023,720

-17,220,236

-16,917,334

-16,003,688

-14,366,807

-684,896

-521,288

-196,516

302,902

913,646

1,636,880

2,570,159

-

Actual tax

-15,817,536

-817,536

Theoretical tax

-

-

-

-

-

-

-

16,502,432

-1,685,428

Journal of Applied Corporate Finance



-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

CApEX

Cash-flow

1,386,302

9,965,931

-1,685,427

-

985,320

8,380,304

EBITDA

Post-tax EBIT

686,622

7,090,335

325,298

Tax-loss-carry-forward

419,098

6,272,945

270,303

-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

m

=
=
=

Var (R m )

21%

=
=

k

8.21
0.01

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 )

cov (CFt , Rm ),

where λ is the market price of risk defined as:
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:
PV

T

∑ t1 T



E P (CFt )
(1 k ) t
E P (CFt )

t1

T

E Q (CFt )

∑ (1 t1 Rf )

cov( CFt , Rm )
(1 R f ) t

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:
PV

E P (CF0 )

T

E (CF ) E P (TV ) =12.1 million USD
T
(1 k )T

P
∑ (1 k )tt t1 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

K1

EP (CFt)

EQ CFt)

0
-137,621
-215,858
-222,340
-51,689
245,603
760,240
1,530,313
2,908,944
24,148,500

-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

14%

=

)

Exhibit 6 Traditional PV

Journal of Applied Corporate Finance



Volume 20 Number 2

2002
2003
2004
2005
2006
2007
2008
2009
2010
Terminal Value
Discount rate
Present Value

PV E Q (CF0 )

T

E Q (CFt ) E Q ( TVT)

∑ (1 t1 Rf )

t

(1

Rf)

T

= 12.1 million USD

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

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

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

(Y1) Number of Internet users

(Y2) Company´s market penetration rate

(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

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

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%

(Y4) Average ticket per transaction

(Y5) Commission charged

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 f uture 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: t E P CFt

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

134

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): cov CFop t , Rm op t

Step Three: Risk Adjustment

E P CFt

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
E Q FCop t op Journal of Applied Corporate Finance



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 * opi*, s TVi *T opi*,T i ,s
,
CFi ,t ∑
(1 R f ) s t
(1 R f ) T t st1 This results in the following decision rule: max 0;10 CFi ,t ; CFi ,t

T



CFop i*, s

st1

TVi *T
,

(1

(1

Rf )

opi*, s st op i*,T
Rf )

Tt

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
.
.
.

.
.
.
CF h
.
.

CF200.000

.
.
.

.
.
.
TVh
.
.

CF i
.
.
CF k
.
.
.

CF2
200 closest values .
.
.

Value of the
Going-on Alternative in the Event i

CFi Nearest Neighbors

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

.

.

CF i

TVopi

.

.

" = Max (0 ; 10 CFi ; CFi + TVi *) =

.

= TVi if going-on

The optimum alternative in event i of the period t is chosen

CFop

TVop

200.000

200.000

Exhibit 10 post-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

TV i* −

.
.
.
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 − 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

COV*(TVi ;Rm i,T )

Post-Option Cash-Flows
CFop1 ,t

opi* T
,

0

CFop i,s = 0

TVop i = 0

if abandon

CFop 1 ,s

...

TVop 1

CFop2 ,t

CFop 2 ,s



TVop 2

.
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

if sell

.

.

.

.

.

.

(1 + R f ) T−t

.

.

= CFop TVop i = TVop i if going-on i,s 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

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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 16 Traditional pV with no Real Options
Traditional pV

Traditional pV with
Simulated Cash Flows

2002

-1,685,428
-2,307,068

-2,301,584

2004

-1,864,933

-1,850,097

2005

-1,319,575
-237,001
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

Value Due to Traditional Cash-flow Discounting

-163,821

2007

Value Due to the Investment´s Optionality
Value Due to Jensen´s Inequality

-1,283,163

2006

USD
25,000,000

-1,685,428

2003

Exhibit 17 Sources of Value in the Expanded PV

12,844,648

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
)
CF expectations: E( (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

7000000

5000000

4000000

4000000

Cash-flows

Cash-flows

6000000

5000000

3000000
2000000
1000000
0
-1000000

35

40

45

50

55

60

65

3000000
2000000
1000000

-1000000

-2000000

Internet Users (mn)

2004

3.50%

7000000

4.00%

4.50%

5.00%

5.50%

6.00%

5000000

100

120

140

250000

270000

290000

2004

5000000

4000000

Penetration Rate (%)

6000000

4000000

Cash-flows

6000000

Cash-flows

3.00%

-3000000

7000000

3000000
2000000
1000000

-1000000

0
0

3000000
2000000
1000000
0

0.5

1

1.5

2

2.5

-1000000

0

20

40

60

80

-2000000

-2000000

2004

7000000

Average Ticket (USD)

-3000000

Transactions Per User

-3000000

2004

7000000
6000000

5000000

5000000

4000000

4000000

Cash-flows

6000000

Cash-flows

0
2.50%

-2000000

-3000000

3000000
2000000
1000000
0

12.00%
-1000000

14.00%

16.00%

18.00%

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)

2004

Sales and Marketing Fixed Costs (USD)

-3000000

7000000

7000000

5000000

5000000

4000000

2004

6000000

4000000

Cash-flows

6000000

Cash-flows

2004

7000000

6000000

3000000
2000000
1000000
0
390000
-1000000

410000

430000

450000

470000

490000

2000000
1000000
0
-1000000

0.2

0.25

0.3

0.35

0.4

0.45

-2000000

-2000000
-3000000

510000

3000000

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

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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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Real Options: Meeting the Georgetown Challenge. Journal of
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Journal of Applied Corporate Finance



Volume 20 Number 2

Moel, Albert and Tufano, Peter (2000a): Bidding for the
Antamina Mine: Valuation and Incentives in a Real Options
Context. In Brennan, Michael J. and Trigeorgis, Lenos (Ed.)
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Oxford University Press, New York.
Schwartz, Eduardo S. (2004): Patents and R&D as Real
Options. Economic Notes, vol. 33, no. 1, pp. 23-54.
Schwartz, Eduardo S. and Moon, Mark (2000): Rational
Pricing of Internet Companies. Financial Analysts Journal, vol.
56, no. 3, pp. 62-75.
Schwartz, Eduardo S. and Moon, Mark (2001): Rational
Pricing of Internet Companies Revisited. Financial Review, vol. 36, no. 4, pp. 7-26.
Triantis, Alexander J. (2000): Real Options and Corporate
Risk Management. Journal of Applied Corporate Finance, vol.
13, no. 2, pp. 64-73.
Triantis, Alexander J. and Borison, Adam (2001): Real
Options: State of the Practice. Journal of Applied Corporate
Finance, vol. 14, no. 2, pp. 8-23.
Trigeorgis, Lenos (1988): A Conceptual Options Framework for Capital Budgeting. Advances in Futures and Options
Research, vol. 3, pp. 145-167.
Trigeorgis, Lenos (1993): The Nature of Option Interactions and the Valuation of Investments with Multiple Real
Options. Journal of Financial and Quantitative Analysis, vol.
28, no. 1, pp.1-20.

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