journal of applied corporate finance...pontificia comillas de madrid; pablo fernández of iese...

VOLUME 20 | NUMBER 2 | spRiNg 2008

APPLIED CORPORATE FINANCEJournal of

A M O R G A N S T A N L E Y P U B L I C A T I O N

In This Issue: Valuation and Corporate portfolio Management

Corporate portfolio Management RoundtablePresented 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 John Martin, Baylor University, and Sheridan Titman,

University of Texas at Austin

The Era of Cross-Border M&A: How Current Market Dynamics are Changing the M&A Landscape

84 Marc Zenner, Matt Matthews, Jeff Marks, and

Nishant Mago, J.P. Morgan Chase & Co.

Transfer pricing for Corporate Treasury in the Multinational Enterprise 97 Stephen L. Curtis, Ernst & Young

The Equity Market Risk premium and Valuation of Overseas investments 113 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

lthough both academics and practitioners have accepted the basic insight of the real options valuation method—that many corporate invest-ment opportunities contain valuable sources of

flexibility—progress in applying the method has been disap-pointing. 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 modi-fication of Copeland and Antikarov’s approach to an actual company in the e-commerce industry.

Internet companies suffered a dramatic reversal after reach-ing 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 valua-tion 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

by Rocío Sáenz-Diez, Universidad Pontificia Comillas de Madrid, Ricardo Gimeno, Banco de España, and Carlos de Abajo, Morgan Stanley*

Acontingent payoffs into their analysis and decision-making in a rigorous way.

The Valuation ModelIn 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 uncer-tain 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 probabili-ties 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

* 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 addi-tion, 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 Practitio-ner’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 mea-sure. 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 un-der 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 A Morgan Stanley Publication • Spring 2008 129

Real Options Valuation: A Case Study of an E-commerce Company

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.

Case Study: Valuing an E-commerce CompanyWe 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 (Y

1-Y

12) that are

expected to have material effects on cash flows. Five of the variables (shown as Y

1-Y

5 in Exhibit 2) are important funda-

mental drivers of revenue and seven of the variables (Y6-Y

12

shown in Exhibit 3) are drivers of expenses.

Step One: Traditional Present Value CalculationThe starting point for estimating the real options PV of this business is its traditional PV assuming no managerial flex-ibility or real option value. To calculate this PV we need an

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:

%21%)14%18(6.1%14])([ fmf RRERk

The data summarized in Exhibit 5 were provided by market practitioners. The market variance and returns corre-spond to the Morgan Stanley Capital International (MSCI) global index. The explanation for such a high risk-free rate (R

f =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

Exhibit 1 Summary of the Real Options Valuation Model

Traditional PV Monte Carlo simulation Risk adjustment Real options Expanded PV

* Expected cash-flows* Risk adjustment with CAPM discount rate/ certainty equivalent correction factor* Terminal value

* Identification of uncertain variables and how they behave * Simulation of variables to generate yearly cash-flows

* Certainty equivalent correction factor for the yearly post option cash-flows

* 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

* Adjustment of post option cash-flows (Step 4) with the certainty equivalent correction factor (Step 3)* Discounting with the risk-free rate

Step 1 Step 2 Step 3 Step 4 Step 5

(1) Number of Internet users (Y1)(2) Company´s market penetration rate (%) (Y2)(3) Transactions per user (Y3)(4) Average ticket per transaction (USD) (Y4)(5) Commission charged (%) (Y5)(6) Number of company´s users = (1) x (2) (7) Total transactions = (6) x (3) (8) Gross merchandise sales = (7) x (4) (9) E-commerce revenues = (8) x (5) (10) Advertising revenues (11) Other revenues (12) Total revenues = (9) + (10) + (11)

Exhibit 2 Uncertain Variables Related to Income

(13) Doubtful accounts (% over e-commerce revenues) (Y6)(14) Doubtful accounts = (9) x (13) (15) Sales and marketing fixed costs (USD) (Y7)(16) Product development and technology fixed costs (USD) (Y8)(17) General administration fixed costs (USD) (Y9)(18) Sales and marketing variable costs (USD / transaction) (Y10)(19) Product development and technology variable costs (%) (Y11)(20) General administration variable costs (%) (Y12)(21) Sales and marketing total costs = (15) + [(18) x (7)] (22) Product development and technology total costs = (16) + [(19) x (9)] (23) General administration total costs = (17) + [(20) x (12)] (24) Total operating costs = (21) + (22) + (23)

Exhibit 3 Uncertain Variables Related to Expenses

130 Journal of Applied Corporate Finance • Volume 20 Number 2 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

Company´s market penetration rate

6.50% 4.90% 4.28% 4.11% 3.91% 4.05% 4.19% 4.34% 4.5%

Transactions per user 0.32 0.50 0.80 1.10 1.40 1.70 2.00 2.30 2.50

Average ticket per transaction 115 90 80 80 80 80 80 80 80

Commission charged 1.50% 1.75% 2.00% 2.30% 2.50% 2.80% 3.20% 3.60% 4.00%

Doubtful accounts 24.5% 19.60% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00%

Sales and marketing fixed costs 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000

Product devel/technology fixed costs

420,000 420,000 420,000 420,000 420,000 420,000 420,000 420,000 420,000

General administration fixed costs

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

Sales and marketing variable costs

0.40 0.40 0.40 0.45 0.45 0.45 0.50 0.55 0.55

Product devel/technology variable costs

0.33 0.30 0.30 0.30 0.25 0.22 0.20 0.18 0.15

General administration variable costs

0.220 0.200 0.180 0.150 0.130 0.100 0.080 0.075 0.075

Number of company´s users 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

Total transactions 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

Gross merchandise sales 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 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

Advertising revenues 516,991 800,000 977,500 1,124,125 1,292,744 1,486,655 1,709,654 1,966,102 2,261,017

Other revenues 65,362 100,000 132,000 145,200 159,720 175,692 193,261 212,587 233,846

Total revenues 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 3,541,032 4,349,319 5,479,757 6,272,945 7,090,335 8,380,304 9,965,931 10,869,615

Doubtful accounts 270,303 325,298 419,098 686,622 985,320 1,386,302 1,930,752 2,587,334 3,240,000

EBITDA -1,685,427 -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

Tax-loss-carry-forward -15,000,000 -15,817,536 -

16,502,432 -17,023,720 -17,220,236 -16,917,334 -16,003,688 -14,366,807

Theoretical tax -817,536 -684,896 -521,288 -196,516 302,902 913,646 1,636,880 2,570,159

Actual tax - - - - - - - -

Post-tax 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

CApEX -1,000,000 -1,000,000 -1,000,000 -1,000,000 -1,500,000 -2,000,000 -2,500,000 -2,500,000

Cash-flow -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


using certainty-equivalent correction factors (κ1 = λ⋅cov (CF

t,

Rm) ). Using such factors together with the CAPM, one then

reduces the expected cash flows to yield the certainty-equiva-lent (or risk-neutral expectation) future cash flows E

Q (CF

1):

( ) ( ) ( )mttPtQ RCFCFECFE ,cov ,

where λ is the market price of risk defined as:

( )( )m

fm

RV

RRE

These certainly-equivalent cash flows can then be discounted at the risk-free rate to calculate the same PV as follows:

∑

∑∑T

tt

f

mttP

T

t f

tQT

tttP

R

RCFCFE

R

CFE

k

CFEPV

1

11

)1(

),cov()(

)1(

)(

)1(

)(

For the terminal value (TV) calculation, we used a growing perpetuity formula with two different growth rates: g

1=12% (between 2010 and 2015) and g

2= 4% (from 2010

onwards).Using all this information, we then proceeded to calculate

the company’s traditional PV as follows:

( ) ( )( )

( )( )T

TPT

tttP

Pk

TVE

k

CFECFEPV ∑

1110

=12.1 million USD

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:

( )( )

( )( )

( )Tf

TQT

tt

f

tQ

QR

TVE

R

CFECFEPV ∑

1110

= 12.1 million USD

Exhibit 6 shows, for each year from 2002-2010, the costs of capital (K

t), expected cash flows (E

P), and certainty equiva-

lents (EQ

) used for these calculations of traditional present values: either the expected cash flows (including the TV) or the certainty equivalent cash f lows (including TV). Certainty-equivalent correction factors for the expected cash flows according to CAPM (K

t) 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 tradi-tional 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 TechniquesWhile continuing to work with the traditional non-flexibility scenario, the second stage of the valuation process is to esti-mate the degree of uncertainty that surrounds the expected cash flows from the investment. After identifying the uncer-tain variables on which these cash flows depend, we use a Monte Carlo simulation software program to generate values

Exhibit 5 Risk-adjusted Discount Rate According to CAPM4

R f = 14%

E (R m ) = 18%

= 1.6

k = 21%

= 8.21Var (R m ) = 0.01

K1 EP (CFt) EQ CFt)

2002 0 -1,685,428 -1,685,4282003 -137,621 -2,307,068 -2,169,4462004 -215,858 -1,864,933 -1,649,0752005 -222,340 -1,319,575 -1,097,2362006 -51,689 -237,001 -185,3122007 245,603 927,726 682,1232008 760,240 2,463,539 1,703,2992009 1,530,313 4,374,320 2,844,0072010 2,908,944 7,485,248 4,576,305Terminal Value 24,148,500 62,138,547 37,990,046Discount rate 0.21 0.14Present Value 12,048,009 12,048,009

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.

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 certainty-equivalent of the cash flows are higher than the expected values when the amount is negative and lower when they are positive.

Exhibit 6 Traditional PV


Exhibit 7 Traditional PV

Traditional PV

1 2 3 4 5 6 7 8 9

Time Period

Cas

h-Fl

ows

Cert. Equiv.(TV) (LHS) E (TV) (LHS) Cert. Equiv.( CFt) (RHS) E(CFt) (RHS)

Exhibit 8 Forecast Evolution of Uncertain Variables Affecting Revenues

2002 2003 2004 2005 2006 2007 2008 2009 2010

(Y1) Number of Internet users

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%

(Y3) Transactions per user

Expected value 0.32 0.50 0.80 1.10 1.40 1.70 2.00 2.30 2.50

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%


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 Y

i 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

Step Three: Risk Adjustment Unlike the C&A approach, which reduces the simulation results to a recombining event tree that follows the bino-mial 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 certainty-equivalent provides us with the risk-neutral expectation of future cash flows, or EQ(CFt).

Expressed in equation form, EP (CF

t) – κ

t = E

Q (CF

t)

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:

tQmttPttP FCERCFCFECFE ,cov

Using the correction factors κt for the traditional (without

flexibility) cash flows shown in Exhibit 6, we can obtain cov (CF

t, R

m) 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 intro-

duce the real options and obtain the cash flows that reflect this optionality (CFop

t), we will need the risk-neutral expec-

tation EQ(CFop

t). But, again, we will not work with the

risk-neutral probabilities, but instead look for the new correc-tion factors:

tQoptP FCopECFopEt

The results of the Rm simulation will then be matched

with the new CFopt to get cov (CFop

t, R

m). 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):

mtop RCFopt

,cov

Step Four: Introducing Real OptionsAt 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 e-commerce 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 trans-action, 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 prospec-tive buyer will vary over time, but to illustrate the method

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 bino-mial 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 risk-neutral expected cash flows—that is, they concentrate on the right-hand side of the

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 forλ, 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.


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 choos-ing 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) Voa

t , Vos

t , and Vno

t,

respectively. The decision rule for a certain event i (i = 1,…, 200,000) can be formulated as follows:

maxi,t(Voa

i,t , Vos

i,t , Vno

i,t)

In every state, at any moment the value of abandoning (Voa

i) is assumed to be zero and the value of selling (Vos

i)

is estimated to be 10 times the cash flow in the state we are analyzing (10 ⋅ CF

i). 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 estab-lish 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 simplifica-tion 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 simplifi-cations, 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 neigh-bors) 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 CF

i,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 (TV

i*) is then used to determine

the value of continuing to operate, so that the decision rule

becomes:

( )*+ 2010,2010,2010, ;10;0max iii TVCFCF

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 ⋅ CF

i,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 CF

i,t and their corresponding

post-options cash flows and terminal values (CFopi,s; TVop

i,T

for s = t + 1, and T = 2010). We want to discount the averages of these 200 neighbors for the years after t (CFs, TVop

T); 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 R

f as the discount rate. For any state i at a

given moment t between 2002-2009, the value of the continu-ing-to-operate alternative is therefore estimated as follows: the value of the cash flow we are analyzing CF

i,t plus the value at

t of these discounted 200 elements averages:

( ) ( ) tTf

TiTiT

tsts

f

sisiti

R

opTV

R

opCFopCF

****

∑11

,,

1

,,,

This results in the following decision rule:

( )

( )

∑

tTf

TiTi

T

tsts

f

sisititi

R

opTV

R

opCFopCFCF

1

1;10;0max

*,

*,

1

*,

*,

,,

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 post-

option 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


Exhibit 9 post-option Cash Flows for Year 2010

CF1

TV1

. .CF

2TV

2. .

. . . .

. . CFh

TVh. . . .

CF2 . .

200 closest CFi

TVi averages = TV

i

*

values . .. .

CFk

TVk

. . . .

. . . .

. . . .CF200.000 TV200.000

CFop1 TVop1

0 TVopi = 0 if abandon CFop2 TVop2

Max (abandon, sell, going-on) = . .

CFop i = 10 CF i TVopi = 0 if sell . .

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

CFi TVopi = TVi if going-on

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

200.000TVop

200.000

Value of theGoing-on Alternative

in the Event i

CFi + TV i*

Post-option Cash-flows

Year 2010

Original Cash-flows CFi Nearest Neighbors

Decision Among the 3 Alternativesin Event i

Determination of the Post-option Cash-flow(CFop) in Event i of Year 2010

Exhibit 10 post-Option Cash Flows for Year 2010

CF1, t

CFop1, t+1 . . . CFop

1,TTVop

1. . . .

CF2, t

CFop2, t+1 . . . CFop

2,TTVop

2. . . .. . . .

. . . . CF h,t CFop h,t+1 . . . CFop h,T TVoph

CFop h,s ; Rmh,s TVop h Rmh,T. . . . . . . .

. . . . CFi,t . . . .200 closest CF i,t CFop i,t+1 . . . CFop i,T TVop

iCOV CFop

i,s Rm

i,s COV TVop

iRm

i,T

values . . . .. . . .

CF k,t CFop k,t+1 . . . CFop k,T TVopk

CFop k,s Rmk,s TVop k Rmk,T

. . . . . . . .

. . . . . . . .

. . . . . . . .CF

200.000, tCFop

200.000, t+1. . . CFop

200.000, TTVop

200.000COV*(CFop i,s ;Rmi,s )

Value of the going-on alternative = CFop1 ,tCFop 1 ,s ... TVop1

0 CFop i,s = 0 TVop i = 0 if abandon CFop2 ,tCFop 2 ,s … TVop2

. . .

CFop i,t 10 CFi,t CFop i,s = 0 TVop i = 0 if sell . . .

Value of the option to abandon = 0 . . .

Value of the option to sell = CFi,t 10 CF i,t CFop = CFopi,si,s TVop i = TVop i if going-on

The optimum alternative in event i of the period t is chosen CFop200.000, t

CFop200.000, s…

TVop200.000

Max (abandon, sell, going-on)

Original Cash-Flows in Year t

Determination of the Post-option Cash-FlowsPost-Option Cash-Flows(CFop) in the Eventi,t and Afterwards Decision Among the 3 Alternatives in Event i

Obtaining the Covariances for the Risk-Neutral AdjustmentCFi,t Nearest Neighbors

COV*(TVi ;Rm i,T)CFop *i,s & TV*

i

( ) ( ) tTf

TiiT

tsts

f

siti

R

opTV

R

opCFopCF

−

**

+=−

**

+

−+

+

−+= ∑

11

,

1

, si ,,

Years 2002 – 2009

average =

;

;

;

;

;


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 CalculationThe post-options cash flows (CFop

t) obtained in the fourth

step are adjusted using the certainty-equivalent correction

factors (κop1

= λ⋅cov(CFopt,Rm)) explained earlier (in the

third step). As shown in Exhibit 11, the resulting risk-neutral expected cash flows E

Q(CFop

t) 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

Exhibit 11 Computation of the Expanded Present Value

cov (CFt, Rm) E(CFopt) κopt = EQ(CFopt) = λ⋅cov(CFopt, Rm)

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

Real Options Contribution to the Expanded PV

8,683,021

2,108,229

7,809,094

12,048,009

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

Traditional PV Expanded PV with both real options Expanded PV with theabandonment option

Expanded PV with the selling option

Value due to traditional cash-flow discounting

Value due to the investment´s real options

20,731,030

14,156,239

19,857,103

USD


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

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 ApproachWhen we compare the traditional PV from the first step of the model with the traditional PV obtained with the simu-lated 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 automati-cally take into account all possible outcomes in the future.

Exhibit 13 Traditional PV vs. Expanded PV

Expanded Present Value

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000Value due to traditional cash-flow discounting

Value due to the investment´s real options

USD

8,683,021

12,048,009

Traditional PV Expanded PV with both real options

20.731.030

72 %

42%

14. This confirms previous works like Trigeorgis (1993) or Kulatilaka (1995). 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).


Exhibit 14 Traditional pV vs. Expanded pV with the Abandonment Option

Exhibit 15 Traditional pV vs. Expanded pV with the Option to Sell the Company


Value due to the opotion to sell the company

USD

Expanded PV with the Selling Option Only

Traditional PV Expanded PV with the selling option

7,809,094

12,048,009

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

19,857,103

39%

66%

Expanded PV with the abandonment option only


Value due to the abandonment real option

USD

12,048,009

2,108,229

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

16,000,000

Traditional PV Expanded PV with the abandonment option

14,156,239

15%

17%


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: ( )( )tiYCFE ,

> ( )( )tiYECF , .16 Our case study attri-butes 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 determinis-tic 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

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.

ConclusionThis 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 Anti-karov—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 certainty-equivalent 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

Exhibit 16 Traditional 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 17 Sources of Value in the Expanded PV

Value Due to the Investment´s Optionality

Value Due to Traditional Cash-flow Discounting

Value Due to Jensen´s Inequality

USD

Expanded PV with the Both Real Options

12,048,009

796,639

7,886,383

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

20,731,030

38%

4%

58%

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 rev-enues and a put option on the ones linked to costs.


Exhibit 18 The Cash-Flow Function Shows Convexity Regarding the Uncertainty

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

35 40 45 50 55 60 65

Internet Users (mn)

Cas

h-flo

ws

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% 6.00%

Penetration Rate (%)

Cas

h-flo

ws

Cas

h-flo

ws

Cas

h-flo

ws

Cas

h-flo

ws

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

0 0.5 1 1.5 2 2.5

Transactions Per User

Cas

h-flo

ws

Cas

h-flo

ws

Cas

h-flo

ws

2004 2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

0 20 40 60 80 100 120 140

Average Ticket (USD)

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

12.00% 14.00% 16.00% 18.00% 20.00% 22.00% 24.00% 26.00%

Doubtful Accounts (% E-commerce Revenues)

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

150000 170000 190000 210000 230000 250000 270000 290000

Sales and Marketing Fixed Costs (USD)

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

Product and Technology Variable Costs (USD)

2004

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

Product and Technology Fixed Costs (USD)

390000 410000 430000 450000 470000 490000 510000 0.2 0.25 0.3 0.35 0.4 0.45


was done using the beta distribution, which provided a lot of flexibility to adapt the information provided by the manage-ment 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 correc-tion 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

different outcomes, both options interact, confirming previ-ous 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.

Exhibit 19 Sensitivity of the Company’s Present Value to the Multiple of CF for the Option to Sell

Cash Flow Multiple for the Price of the Option to Sell

0

20000000

40000000

60000000

80000000

100000000

120000000

140000000

0,00 5,00 10,00 15,00 20,00 25,00 30,00 35,00 40,00 45,00 50,00

PV

Traditional PVExpanded PV


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of Options and Corporate Liabilities. Journal of Political Economy, vol. 81, no. 3, pp. 637-654.

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