Journal of Business Finance & Accounting, 33(1) & (2), 203–219, January/March 2006, 0306-686X
doi: 10.1111/j.0306-686X.2005.00654.x
The Real Options Component of Firm
Market Value: The Case of the
Technological Corporation
PABLO
DE
ANDRÉS-ALONSO, VALENTÍN AZOFRA-PALENZUELA
AND GABRIEL DE LA FUENTE-HERRERO*
Abstract: This paper tests whether stock prices reflect investor’s expectations regarding the
value of real options. The analysis is implemented based on a sample of 391 high-tech
companies listed on main OECD stock markets during the period December 1994 through
December 2000. Results confirm the predicted relation between the fraction of a firm’s
market value not accounted for by its assets-in-place, and a series of variables that are
assumed to disclose its real options value, variables such as research and development activity,
risk and skewness of stock returns, and size. The results are robust even after controlling for
valuation date, sub-industry, country, and alternative measures of risk.
Keywords:
Real options, assets-in-place, growth opportunities, valuation, Tech Company
1. INTRODUCTION
The recent evolution of the ‘new economy’ in capital markets–especially that of the
former dot.com bubble and its later crash–has re-opened debate relative to the
reliability of financial valuation models. The confidence that nearly all corporate
finance textbooks place in discounted cash flow (DCF) techniques contrasts sharply
with its limited precision in the valuation of corporate investments and corporations.
Scepticism regarding the DCF method is nothing new. In the early eighties,
managers and academics accused these financial models of hampering the innovation, productivity and competitiveness of companies following their precepts. Such
approach was regarded as shortsighted for not permitting the recognition of
sources of value other than cash flow, thereby ignoring other strategic aspects of
prime importance related to the survival of the company.
* The authors are from the Department of Financial Economics and Accounting, University of
Valladolid. They benefited from the useful comments of Michel Dubois, John Beaven, and participants
at the SMS 21st Annual International Conference, and at the 5th Workshop in Finance. They especially
thank two anonymous referees for many suggestions. Financial support from AECA, and Junta de Castilla y
León (grant: VA05204) is also acknowledged. Any errors are the responsibility of the authors. (Paper
received July 2002, revised version accepted February 2005.)
Address for correspondence: Pablo de Andrés-Alonso, Department of Financial Economics and
Accounting, University of Valladolid, Avda. Valle Esgueva 6, 47011-Valladolid, Spain.
e-mail: [email protected]
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In addition to such criticism, there has been a continual and renewed accumulation of empirical evidence against CAPM, a fundamental tool for estimating the
appropriate discount rate and, as such, an essential element in the practical application of DCF valuation. Growing empirical evidence suggests that cross-sectional
variation in stock returns is best explained by multi-factor models. Possible reasons
for this empirical phenomenon have been attributed to risk premia for omitted
variables (Fama and French, 1992, 1993 and 1996), survivorship biases (Kothari,
Shanken and Sloan, 1995), or behavioural biases (Lakonishok, Shleifer and Vishny,
1994; La Porta, 1996; and La Porta et al., 1997), among others.
Recently, incipient and encouraging literature has begun to build a theoretical
explanation for risk-return dynamics, suggesting that both book-to-market and size
effects emerge as a consequence of their role in capturing unobservable changes
in a firm’s assets-in-place and growth options. Within a model that endogenizes
expected returns through firm investment choices, Berk, Green and Naik (1999)
explain the above-mentioned price anomalies as a consequence of predictable
changes in a firm’s systematic risk. Carlson, Fisher and Giammarino (2003)
contribute to this line of research by considering investment opportunities homogeneous in risk, arriving at a model where book-to-market relates to operating
leverage, and size captures the relative importance of growth options.
Underlying these models is the conviction that a significant part of the total
market value of a company is accounted for by its portfolio of real options, that is,
by decisions yet to be made, but for whose execution the company is particularly
well-resourced.1 However, few academic studies have attempted to offer empirical
evidence relative to the effective market valuation of a firm’s real options,2 save wellknown estimates in Kester (1984 and 1986) for a number of large stocks; in
Paddock, Siegel and Smith (1988) for petroleum leases; or in Quigg (1993) for
land transactions.
Most recently, Smit (2000) empirically evaluates the option characteristics of
growth stocks and provides inspiring evidence in favour of growth option influence
on prices of a sample of US companies during the period 1988–1998. Along similar
lines, Al-Horani, Pope and Stark (2003) find that the returns of a sample of UK
firms during the period 1990–1996 are associated with the ratios of research and
development expenditures to market value and book-to-market as predicted under
real options reasoning. Adam and Goyal (2002) estimate the value of growth options
of a sample of mining companies, and moreover observe that the market value of a
company’s investment opportunities is empirically related to the book-to-market
ratio of its assets.
The contribution of our paper is to extend current evidence on the market valuation of the real option portfolio through the empirical analysis of an international
1 A survey of real options valuation models can be found in Dixit and Pindyck (1994) and Trigeorgis
(1996). In addition, Amram and Kulatilaka (1999) and Copeland and Antikarov (2001) provide practical
guides to the implementation of real options.
2 Empirical evidence has basically focused on analysis of specific investment projects with the aim of
verifying the relevance of their embedded options and, thus, of demonstrating the suitability of the
options quantitative models for their valuation. For an interesting collection of similar case studies, see
Trigeorgis (1999).
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sample of technological companies.3 Selecting the technological industry responds to
a double motivation. First, it is to be expected that technological firms will exhibit a
large proportion of their market value derived from their real options, typically
greater than that observable in companies found in other industries. And second,
focusing the analysis on a specific industry permits us, moreover, to isolate the effect
of hypothetically related firm-specific factors on market value. For this purpose, we
analyse a sample of 391 technological companies listed on the main OECD stock markets
during the period December 1994 through December 2000.
Should the real option approach be correct, market efficiency theory predicts that
the total market value of a firm will reflect available information regarding its real
options portfolio. But real options are commonly unobservable to outsiders. Under
such circumstances, the principal proposition that firms’ market valuations reflect
the value of real options is not directly testable. Nonetheless, this proposition can be
tested indirectly, through evaluating the relation between that portion of the market
value unaccounted for by assets-in-place and such variables disclosing information
relative to the presence and characteristics of real options. These variables include
research and development activity, risk and skewness of returns, corporate leverage, and size.4
Research and development expenditures is a frequent proxy for growth options
held by a firm (see, for example, Adam and Goyal, 2002; Smit, 2000; and Bernardo
et al., 2000). As stated in Mitchell and Hamilton (1988) and Newton and Pearson
(1994), the primary result of research and development projects is not cash flow,
but that knowledge and learning necessary for investing in future expansion projects. Thus, such portion of a firm’s market value due to growth options will be,
ceteris paribus, increasing on current research and development activity.
Risk of returns also reflects the effective holding and exercise of real options. Since
an option’s risk is greater than its underlying asset risk, and as option value is increasing on its underlying asset risk, an increase in risk of stocks will be associated, ceteris
paribus, with an increase in the fraction of value accounted for by options to invest.5
However, higher volatility of returns is not the principal effect that real options have
on return distribution. As option-defined discretionary decisions allow managers to
increase profits while limiting losses, the relevance of the real options portfolio will shift
the probability distribution of stock returns to the right, and as a result, that proportion
of the market value of a firm due to real options will be, ceteris paribus, increasing on the
skewness of its returns (Smit, 2000).
Among the variables usually identified as being suitable proxies vis-à-vis the firm’s
ability to manage options in an efficient way are corporate leverage and size.
Corporate leverage increases the probability of the appearance of under-investment
problems both due to agency problems and financial restrictions (Myers, 1977;
McConell and Servaes, 1995; and Callen and Gelb, 1999), and hence, an increase
3 Interest in valuating technology firms from a real option perspective may be found from the growing
number of studies. Some recent examples are Ottoo (2000) and Damodaran (2001), among others.
4 Note that our objective is not to model the market valuation of real options. Instead, we try to test
whether, under observability restrictions, that portion of the market value not due to assets-in-place could
be attributable to investors’ expectations regarding real options.
5 See Chung and Charoenwong (1991) and Chung and Kim (1997) for a more detailed description of
the link between growth opportunities and stock beta. Berk, Green and Naik (1999) provide a dynamic
model that explains the relation between investment decisions and systematic risk.
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ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
in corporate leverage will be associated, ceteris paribus, with a decrease in the
proportion of total market value accounted for by options to invest.
Finally, size is a source of information regarding the company’s possibilities of
raising funds for the acquisition, maintenance and exercise of its real options, and
hence positively related to real options value. As stated in Adam and Goyal (2002),
larger firms are not only typically better prepared to obtain necessary funding to
acquire and exercise their options, but simultaneously committed as well in different markets and businesses activities, thus favouring the accumulation of knowledge
and expertise, two principal sources of growth options.6
In summary, we would expect the market value of real options to be positively
related to the variables of research and development, risk and skewness of stock
returns, and firm size, and negatively related to corporate leverage.7 Therefore, if
that portion of market value unaccounted for by assets-in-place corresponds to the
value assigned to real options by investors, said market value component should be
linked to the aforementioned variables in the direction as postulated.8
The remainder of the paper is organized in straightforward fashion. Section 2
describes the sample and explains the definition of the variables. Empirical findings
and robustness analysis are presented in Section 3. Finally, Section 4 offers our
conclusions.
2. DATA AND DEFINITIONS
Our empirical analysis focuses on an international sample of technological companies. Data has been obtained from COMPUSTAT (GLOBAL VANTAGE). Our
sample begins with a total of 1,040 companies belonging to the technological
industry. Activities included are Computer Equipment (SIC codes: 3570, 3571,
3572, 3576 and 3577), Communication Equipment, Semiconductor and Optical
Recording Media (3661, 3663, 3669, 3674 and 3695), Measurement Instruments,
Ophthalmic Goods and Watches (3821 to 3827, 3829 and 3861), Computers and
Software-Wholesale (5045), and Programming and Data Processing (7370, 7371,
7372 and 7374).9
We exclude from this universe such firms not satisfying one or more of the
following four criteria: (1) being listed on an OECD stock market, (2) showing
monthly stock return data during the period December 1994 through December
6 Note that if size were closely related to age, we could also predict a negative relation between the
relative importance of growth options and firm size, given that the latter could be considered a proxy for
the situation of a firm as it grows in the logical process of substituting its options to expand with assets-inplace. This relation between the relative importance of growth options and age is addressed, for example,
in Bernardo et al. (2000) and Bernardo and Chowdhry (2002).
7 As remarked by one of the anonymous referees, it is possible to explain the reverse relation between
real options value and some of the independent variables. However, the signs of our propositions are
those expected to prevail in a technological corporation with valuable growth options, following similar
arguments employed in financial models for call options.
8 Note that these variables affect investors’ expectations with regard to the value of a firm’s real options,
although for different reasons. Research and development expenditures indicate the acquisition or
expansion of a firm’s growth options; the variables risk and skewness of returns reveal the effective
holding and exercise of growth options; and corporate leverage and size provide information regarding a
firm’s ability to manage its options in an efficient way.
9 These 19 four-digit SIC code criteria correspond to Compustat’s definition of the technological
industry.
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1999, (3) providing the income statement and balance sheet items necessary to
compute our proxies for a given firm’s real options market value and independent
variables (including research and development expenditures), and (4) having positive cash flow to the firm, equity book value, and estimate of real options market
value.10
The final sample comprises 391 companies accounting for nearly 65% of total
sales. Geographically, the sample has the following distribution: 39.9% from the
USA, 16.8% from Continental Europe, 15.5% from Japan, 6.4% from the UK, 5.1%
from Canada, 3.4% from Taiwan, 2.1% from the European Nordic Countries, and
10.8% from the rest of the OECD.
Variables are defined as follows. The dependent variable [ROR(K)] is defined as
that proportion of a firm’s total market value not arising from its assets-in-place
(VAIP).11 The total market value of assets (MV) is calculated as the difference between
the market value of equity (MVE) and the book value of equity (BVE) added to the
book value of assets (BVA):
RORðKÞ ¼
MV VAIP ðMVE BVE þ BVAÞ VAIP
¼
:
MV
MV
The value of a firm’s assets-in-place (VAIP) is estimated by the present value of its
current free cash flow (FCFAIP) treated as perpetuity, and discounted at its cost of
capital (KAIP):
VAIP ¼
FCFAIP
:
KAIP
To approximate the free cash flow generated by assets-in-place (FCFAIP), we
assume that replacement investments in current assets are equivalent to accounting
depreciation. Thus, we estimate FCFAIP by subtracting adjusted tax payments from
current earnings before interest and tax (EBIT):
FCFAIP ¼ EBIT TAX payments:
The discount rate appropriated to capitalise cash flow generated by assets-inplace (KAIP) should summarise the average systematic risk of a firm’s existing assets
(individual projects). As demonstrated in Chung and Kim (1997), the observed
unlevered beta of a company is affected by the greater risk of its real options, and
hence, the corresponding capital cost could be too high for estimating its assets-inplace value. However, such betas are impossible to estimate and a proxy is required.
To approximate KAIP, we estimate the firm-specific capital cost using a global
version of the CAPM, with the world market portfolio (RM) approximated using the
10 Continuous returns from 1994 to 1999 are required to estimate stock betas and skewness. We exclude
firms that do not report research and development expenditures, but we do consider those firms
reporting zero values.
11 Kester (1984) was a pioneer in attributing the portion of a firm’s capitalisation not explained by assetsin-place to the present value of its growth options. See Danbolt, Hirst and Jones (2002) for a critical
analysis of the empirical validity of Kester’s model.
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ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
Morgan Stanley Corporate Index (MSCI-W), and the risk-free rate (RF) using
returns on long-term US Treasury bonds:
KAIP ¼ RF þ ðRM þ RF Þ U
where U is the firm-specific beta of assets.12
In approximating this beta, we use the previous five-year monthly stock returns
and returns on MSCI-W, taking into account the effect of financial leverage and
taxes, and:
U ¼
MVE
ð1 TÞ L
MV
where T is the effective tax rate applied to earnings, and (L) is the equity’s beta.
We measure research and development intensity (R&D) as the ratio of research
and development expenditures to sales. We estimate stock beta (BETA) and
skewness (SKEW) using the monthly stock returns of each company from
December 1994 through December 1999. Financial leverage (LEV) is calculated
by the ratio of debt-with-cost book value to total assets. Finally, we approximate
the dimension of the firm (ACT) on the basis of the natural logarithm of assets
book value.
To obtain robust empirical results, we explicitly control a number of specifications
possibly affecting the strength of our findings. First, our analysis includes the
variable of capital stock (CS) as control variable, frequently used as a proxy for
that proportion of a firm’s investment opportunities already realised. This variable
is defined as the ratio of the book value of property, plant, and equipment to total
assets. Second, we include industry and country dummies. We consider five subindustry classifications based on SIC codes: 35 (Computer and office equipment); 36
(Electrical equipment excluding computers); 38 (Measuring instruments); 73
(Computer programming, software and services); and the remainder of
Compustat technology segments. Country dummies classify our sample into six
groups: USA, UK, Canada, Japan, Europe, and the rest of the world.
Third, stock risk and skewness are jointly considered on the basis of Leland’s beta
(LBETA), which synthesizes the combined effect of beta and skewness in stock
returns, thus allowing for considering the effect of real options management on
stock returns probability distribution and investor preference for positively skewed
returns. Specifically, LBETA is defined as:
LBETA i ¼
cov½Ri ; ð1 þ RM Þb cov½RM ; ð1 þ RM Þb where Ri and RM are the returns on stock i and the market, and the coefficient b
represents the market’s instantaneous excess rate of return divided by the variance
12 Nevertheless, we have examined sensitivity to this proxy of our results. Analysis indicates that our
principal results prevail when KAIP is estimated using the arithmetic average of capital costs for sample
companies.
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THE REAL OPTIONS COMPONENT OF FIRM MARKET VALUE
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of the market’s instantaneous rate of return.13 We estimate LBETA using monthly
stock returns, Morgan Stanley Corporate Index (MSCI-W) returns, and returns on
US Treasury bonds from December 1994 through December 1999.
Fourth, we re-estimate the size variable using the logarithm of market capitalisation (CAP). Fifth, we analyse the sensitivity of the results to discount factor parameterisation. To test the effect of overstating the true discount rate on our valuation
results, we defined a new approximation of the proportion of a firm’s market value
not due to its assets-in-place ½RORðKÞ, which approximation is based on the
industry-average CAPM cost of capital ðKÞ. Thus, we estimate industry beta as the
arithmetic average of asset betas for the sample companies.
Finally, we check our results using accounting and market data as of the end of
Year 2000 (one year after our base date) to evaluate the effect of the dot.com crash.
3. EVIDENCE
(i) Main Regression Results
Table 1 shows descriptive statistics for key model variables. Generally, this data confirms the predictable relevance of that portion of market value not due to assets-inplace in the technological industry, but moreover shows large dispersion among
companies. We find the proportion of market value attributable to growth options
accounts, on average, for 75% of total market value. Individual values range from a low
of 1% to a peak of 356%, with a median near to 85% and a standard deviation of 47%.
To test the significance of the aforementioned variables in explaining the proportion of total market value not due to assets-in-place, we estimate the following crosssectional regression model:
RORðKÞi ¼ þ i R&Di þ 2 BETA i þ 3 SKEWi
þ 4 LEVi þ 5 ACTi þ 6 CSi þ "i
ð1Þ
where i represents each company (i ¼ 1, . . . , N), and j (j ¼ 1, . . . , 6) the
coefficients to be estimated, and "i the error term. In the Appendix, we report
cross-correlations among these variables.
Estimation results from OLS regression of the above model are presented in Table 2.
Column A refers to the principal model, whereas Column B extends it to incorporate
sub-industry and regional adscription. These results reveal that the market value unaccounted for by the value of assets-in-place [ROR(K)] is increasing in the variables research
and development (R&D), stock beta (BETA), skewness of stock returns (SKEW), size
(ACT) and capital stock (CS), and decreasing in financial leverage (LEV). Moreover, we
find that four of five key explanatory variables (R&D, BETA, LEV and ACT) are
statistically significant at the 10% level or lower for both regression specifications.
These findings indicate that the proportion of market value not due to assets-inplace responds to changes in the independent variables as predicted by the real
13 Leland (1999) proposes a simple modification of CAPM beta capturing all elements of risk, including
skewness and kurtosis. The resulting beta is a risk measure consistent with the equilibrium pricing
equation proposed by Rubinstein (1976), but requiring no additional information for implementation
than that required by the CAPM.
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ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
Table 1
Descriptive Statistics
N
Mean
Median
Std. Dev.
Min
Max
Percentile
25
50
75
ROR(K)
R&D
BETA
SKEW
LEV
ACT
CS
369
0.7522
0.8472
0.4700
0.0089
3.5604
391
0.0847
0.0743
0.0622
0.0000
0.3172
369
1.3197
1.2589
0.7325
0.7454
4.1214
369
0.6706
0.4723
0.9732
1.9445
6.9546
391
0.1440
0.0969
0.1492
0.0000
0.5771
391
6.1635
6.0067
1.7414
2.4249
11.3793
391
0.1849
0.1562
0.1288
0.0103
0.6876
0.7281
0.8472
0.9262
0.0353
0.0743
0.1261
0.8331
1.2589
1.7308
0.1415
0.4723
1.0462
0.0059
0.0969
0.2492
4.9772
6.0067
7.2374
0.0965
0.1562
0.2424
Notes:
1
ROR(K) measures the proportion of a firm’s market value not due to assets-in-place. It is defined as the
ratio of total market value minus value of assets-in-place to total market value. Total market value is
calculated as market value of equity minus book value of equity plus book value of assets. Value of assetsin-place is estimated as the present value of current free cash-flow to the firm treated as perpetuity. The
discount rate selected to capitalize current cash-flows is the CAPM cost of capital (K). Cost of capital is
estimated using a global version of the CAPM, where global market portfolio is approximated by the
Morgan Stanley Corporate Index, and the risk-free rate by returns on long term US Treasury bonds.
2
R&D is defined as the ratio of research and development expenses to sales.
3
BETA is the CAPM coefficient of systematic risk of stock.
4
SKEW measures the skewness of stock returns.
5
LEV is calculated as the ratio of book value of corporate debt with cost to total assets.
6
ACT is estimated on the basis of the log of the book value of assets.
7
CS is defined as the ratio of the book net value of property, plant, and equipment to total assets.
8
Data is obtained from Compustat (Global Vantage) database. BETA and SKEWNESS coefficients are
calculated using monthly returns from December 1994 through December 1999. The remaining variables are estimated using accounting and market data at the end of 1999. Sample is all firms included in
the Compustat technology sample, and listed on the main OECD stock markets. We exclude companies
for which data is not available, and those reporting negative free cash-flows, negative book value of equity,
or ROR(K) < 0.
options approach, suggesting that this portion of a firm’s market value is linked to
investors’ expectations regarding the real options value.
The positive and significant coefficient of R&D indicates that investors consider
the value of growth opportunities derived from investing in research and development activity when pricing firms. This same relation is found in Smit (2000) and
Adam and Goyal (2002), among others. The positive and significant coefficient of
size (ACT) suggests that investors understand the dimension of a company as a
source of value. This finding is also consistent with the real option valuation
hypothesis, since size can be understood as a sign of a firm’s capability to manage
efficiently its options (Adam and Goyal, 2002).
The positive and significant coefficients of beta (BETA) and skewness (SKEW)
again confirm the hypothesis that the proportion of a firm’s market value not due to
assets-in-place corresponds to its real options.14 As predicted by the real options
approach and observed in Smit (2000) and Chung and Charoenwong (1991), the
14 The coefficient of skewness is statistically significant in Column A, but not in Column B. We have studied
in depth the explanatory power of the variables of risk and skewness in the following robustness
analysis through the estimation of a combined measure.
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THE REAL OPTIONS COMPONENT OF FIRM MARKET VALUE
Table 2
OLS Regressions of ROR(K) on R&D, BETA, SKEW, LEV, ACT, CS
Constant
R&D
BETA
SKEW
LEV
ACT
CS
(A)
(B)
0.584
(10.042)***
0.373
(1.742)*
0.0595
(3.308)***
0.0245
(1.924)*
0.257
(3.600)***
0.0161
(2.200)**
0.160
(1.693)
0.6050
(5.455)***
0.6070
(2.613)***
0.0665
(3.557)***
0.0105
(0.808)
0.1940
(2.701)***
0.0136
(1.788)*
0.0492
(0.500)
0.0827
(1.329)
0.1590
(2.574)**
0.0433
(0.689)
0.0500
(0.639)
0.1450
(1.980)**
0.0376
(0.473)
0.0760
(0.971)
0.0281
(0.349)
0.0568
(0.729)
USA
UK
JAP
CAN
EUR
SIC38
SIC36
SIC35
SIC73
No. in sample
R squared
Adj-R squared
F statistic
358
0.126
0.111
8.457***
358
0.203
0.168
5.816***
Notes:
1
This table presents results from OLS regressions of the proportion of a firm’s market value not due to
assets-in-place [ROR(K)] on research and development activity (R&D), stock beta (BETA), skewness of
stock returns (SKEW), financial leverage (LEV), size (ACT) and capital stock (CS):
.
RORðKÞi ¼ þ 1 R& Di þ 2 BETA i þ 3 SKEWi þ 4 LEVi þ 5 ACTi þ 6 CSi þ "i
2
ROR(K), R&D, BETA, SKEW, CS, LEV and ACT are defined as in Table 1.
Column B includes sub-industry and regional adscription. We consider five sub-industry groups based
on SIC codes: 35 (Computer), 36 (Electrical equipment excluding computers), 38 (Measuring
instruments), 50 (Computer and software wholesale) and 73 (Computer programming, software and
services). Country dummies classify the sample in six groups: USA, UK, Canada, Japan, Europe, and the
rest of the countries.
4
t-statistics in parentheses; *** denotes significance at the 1% level; ** at the 5% level; and * at the 10%
level.
3
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ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
coefficients of stock return skewness and beta15 reflect the impact of growth options on
shifting their distribution to the right and increasing their systematic risk.
The negative and significant coefficient of leverage (LEV) follows evidence provided in previous literature relative to the negative relation between financial
leverage and growth opportunities due to the under-investment problem analysed
by Myers. Finally, the coefficient of the control variable representing capital stock
(CS) is negative but not significantly different from zero, strengthening the aforementioned relevant role of independent variables in explaining that portion of the
market value not due to assets-in-place.
Column B shows that the coefficients of industry dummies are not statistically
significant, suggesting that differences in the dependent variable are not due to
segment adscription. However, some such coefficients indicate that investors consider country provenance when valuing firms. In particular, we find that dummies
for Europe and UK present a significant coefficient, while the remaining dummies
do not exhibit additional explanatory power.
(ii) Robustness
To test the robustness of these results, the model is sequentially re-estimated by
including a combined measure of beta and skewness (LBETA), another typical
measure of size (CAP), the effect of the recent technological crash, and alternative
measures of the dependent variable.16
First, we analyse whether our results are sensitive to the estimation of the
unobservable cost of capital associated with assets-in-place. For this purpose, we
redefine the dependent variable ½RORðKÞ as the portion of market value not due to
assets-in-place when current free cash flow to the firm is discounted at the
industry-average cost of capital ½K. This average rate permits us to test whether
previous results depend on potential errors in estimating the relative importance
of real options.
Table 3 presents the estimation results of regression (1) when the fraction of
market value not due to assets-in-place is approximated on the basis of the industryaverage cost of capital. Again, Column A refers to the main model, whereas Column
B includes sub-industry and regional adscription. These estimates allow for corroborating the majority of previous findings relative to, first, the relevance of this
component of market value, and second, the sign and statistical significance of the
relation between this valuation ratio and the proposed set of independent variables.
When industry cost of capital is used, the valuation ratio ½RORðKÞ presents a
higher mean of 81% and a lower standard deviation of 16´ 3%, as one might expect.
More importantly, we find that OLS regression results do not materially depend on
whether we approximate the market value of assets-in-place on the basis of firmspecific or industry-average cost of capital. These results confirm the positive and
significant relation between that portion of market value not due to assets-in-place
15 The findings in Chung and Charoenwong (1991) refer only to stock beta.
16 In addition to these kinds of checks, we analyzed the possible presence of errors in variables resulting
from the use of Leland’s beta and CAPM beta to measure stock risk and skewness. For this purpose, twostage-least-squares (2SLS) estimation of equation (1) is conducted, using as instruments a number of
variables such as stock returns or lagged values of independent variables. However, we find no evidence
that error-in-variables affect our previous estimations.
# 2006 The Authors
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213
THE REAL OPTIONS COMPONENT OF FIRM MARKET VALUE
Table 3
Alternative Specifications: Definition of the Dependent Variable.
OLS Regressions of RORðKÞ on R&D, BETA, SKEW, LEV, ACT and CS
Constant
R&D
BETA
SKEW
LEV
ACT
CS
(A)
(B)
0.5964
(15.590)**
0.3266
(2.210)**
0.0281
(2.334)**
0.0153
(1.767)*
0.0475
(0.809)
0.022
(4.415)***
0.0366
(0.569)
0.631
(8.605)***
0.599
(3.907)***
0.0318
(2.605)**
0.0012
(0.146)
0.0215
(0.376)
0.0151
(3.005)***
0.0526
(0.806)
Included
Regional&Ind.
No. in sample
R squared
Adj-R squared
F statistic
369
0.105
0.090
7.097***
369
0.235
0.203
7.248***
Notes:
1
This table presents results from OLS regressions of the proportion of a firm’s market value not due to
assets-in-place ½RORðKÞ on research and development activity (R&D), stock beta (BETA), skewness of
stock returns (SKEW), financial leverage (LEV), size (ACT) and capital stock (CS):
.
RORðKÞi ¼ þ 1 R&Di þ 2 BETA i þ 3 SKEWi þ 4 LEVi þ 5 ACTi þ 6 CSi þ "i :
2
We approximate RORðKÞ based on the industry-average cost of capital. Value of assets-in-place is
estimated as the present value of current free cash-flow to the firm, discounted at the industry-average
CAPM cost of capital ðKÞ. We estimate this industry cost of capital as the arithmetic average of asset betas
for the sample companies.
3
R&D, BETA, SKEW, CS, LEV and ACT are defined as in Table 1.
4
Column B includes sub-industry and regional adscription, which are defined as in Table 2.
5
t-statistics in parentheses; *** denotes significance at the 1% level; ** at the 5% level; and * at the 10%
level.
and variables R&D, BETA and ACT. The coefficients of these variables are statistically significant at the 5% or lower level in both regressions.
In addition, we find that skewness of stock returns is positive and significant at
the 10% level in Column A, but not statistically different from zero when considering regional and industry characteristics. Table 3 also indicates that financial
leverage is not related to this specification of the dependent variable.17
17 Furthermore, we have also repeated our analysis on the basis of the risk-free rate. Discounting the
free cash flow to the firm at this unlikely low discount factor provides an upper boundary for the value of
assets-in-place (and a lower boundary for the market value attributable to real options). Not surprisingly,
these new estimates of the portion of market value attributable to real options decline appreciably: the
mean ratio falls to 43% and its median drops to 55%. However, regression results are qualitatively the
same and are, thus, not reported here. These estimations are available to interested readers and may be
obtained on request from the authors.
# 2006 The Authors
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214
ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
As a second check of robustness, we re-define our model to consider the combined effect of stock beta and skewness on dependent variables, considering as well
an alternative measure for size. Table 4 shows the results of estimating the OLS
regression of these alternative specifications. In Columns A and C, we substitute the
variables of beta and skewness with Leland’s beta. Specification in Columns B and C
employs market capitalisation instead of book value of assets.
Notwithstanding the model specification, results in Table 4 provide insights
consistent with previous conclusions for the base regression. First, results
Table 4
Alternative Specifications: Definition of the Independent Variables. OLS
Regressions of ROR(K) on Three Alternative Sets of Variables
(A)
Constant
R&D
0.6161
(5.556)***
0.6180
(2.667)***
BETA
SKEW
LBETA
LEV
ACT
0.0683
(3.511)***
0.2023
(2.810)***
0.0121
(1.639)*
CAP
CS
Regional & Ind.
No. in sample
R squared
Adj-R squared
F statistic
0.0491
(0.496)
Included
358
0.196
0.193
5.971***
(B)
0.5447
(5.107)***
0.5168
(2.237)**
0.0578
(3.083)***
0.0191
(1.476)
0.1833
(2.164)**
(C)
0.5597
(5.226)***
0.5226
(2.260)**
0.0623
(3.200)***
0.1929
(2.270)**
0.0224
(3.775)***
0.0709
(0.717)
Included
0.0206
(3.567)***
0.0693
(0.697)
Included
356
0.218
0.164
6.332***
356
0.208
0.176
6.406***
Notes:
1
This table presents results from OLS regressions of the proportion of a firm’s market value not due to assetsin-place [ROR(K)] on research and development activity (R&D), stock beta (BETA) and skewness (SKEW) or a
joint measure of beta and skewness (LBETA), financial leverage (LEV), two alternative proxies for size (ACT or
CAP), and capital stock (CS).
2
ROR(K), R&D, BETA, SKEW, CS, LEV and ACT are defined as in Table 1.
3
CAP is the natural logarithm of market capitalisation.
4
LBETA is defined as:
cov½Ri ; ð1 þ RM Þb =cov½RM ; ð1 þ RM Þb where Ri and RM are, respectively, the returns on stock i and the market, and coefficient b is the market’s
instantaneous excess rate of return divided by the variance of the market’s instantaneous rate of return.
5
Sub-industry and regional dummies are defined as in Table 2.
6
t-statistics in parentheses; *** denotes significance at the 1% level; ** at the 5% level; and * at the 10%
level.
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THE REAL OPTIONS COMPONENT OF FIRM MARKET VALUE
215
corroborate that that proportion of market value not due to assets-in-place is positively
related to R&D and negatively related to LEV. Moreover, this relation is statistically
significant at the 5% or lower level in all columns. Second, results confirm the expected
positive and statistically significant coefficient of Leland’s beta. This effect of LBETA on
the dependent variable is consistent with the fact that investors judge the shape of a
firm’s return distribution as a sign of the relevance of real options within total assets.
And third, we find that the coefficient of size remains positive and statistically
significant in all regressions, independent of the size proxy.
Finally, we re-estimate the alternative specifications of the set of independent
variables so as to test the robustness of our results for a different valuation date.
Table 5 shows the results of previous regressions with accounting and market
observations at the end of Year 2000. Specification in Columns A and B begins
with the base regression. Regressions in Columns C and D employ Leland’s beta
rather than the individual variables of beta and skewness, while Columns E and F
replace book value of assets with market capitalisation for approximating size.
Specification in Columns G and H use both Leland’s beta and market capitalisation.
Lastly, regressions in Columns B, D, F and H include regional dummies.
Our analysis reveals that the valuation ratios at the end of year 2000 generally fall
with respect to those registered at the end of 1999: the average ratio declines from
75% to 66%. However, our regression results continue to hold after controlling for
the valuation date, thereby indicating that they were not induced by a highly
optimistic valuation of the technological companies. Again, coefficients of R&D
effort and financial leverage yield the expected sign, and are statistically significant
at the 5% level or better. Results also reveal that both CAPM beta and Leland’s beta
are positive and significantly related to the valuation ratio. Individually considered,
the coefficient of skewness is statistically significant when size is measured by market
capitalization. Simultaneously, results in all columns indicate that the valuation ratio
is positive and significantly related to size, irrespective of the proxy used and the
specification of remaining independent variables.
The only difference with previous results is the statistical significance of the control
variable capital stock. These findings reflect some changes in the primary sources of
information for investors in valuing technology firms, but are again consistent with the
real option hypothesis: its coefficient remains negative in all regressions.
By way of summary, our analysis has provided new evidence in favour of the
relevance of that fraction of a technological firm’s market value not due to assets-inplace. Our results reveal as well a sound relation between this fraction of market
value and the variables research and development, beta of stock returns, financial
leverage, and size. We have found that, on average, neither statistical significance of
explanatory variables, nor the sign of their relation with the dependent variable,
depends on the valuation date, sub-industry adscription, country provenance, or
alternative measurements of risk and skewness. These findings support the hypothesis that this fraction of a firm’s market value is linked to investors’ expectations
regarding its real option value.18
18 The unique exception is the significance of the size coefficient for data at the end of Year 2000.
However, this may be due to the competing role of the control variable of capital stock in disclosing the
value of a firm’s real options as the negative and statistically significant coefficient of capital stocks seems
to suggest.
# 2006 The Authors
Journal compilation # Blackwell Publishing Ltd. 2006
382
0.267
0.255
22.87***
0.4099
(4.57)***
0.1600
(2.08)**
0.0082
(1.09)***
0.4812
(8.10)***
0.4915
(2.93)**
0.1076
(6.72)***
0.0063
(0.41)
382
0.306
0.285
14.84***
0.334
(3.66)***
Included
0.160
(2.12)**
0.014
(1.78)*
0.325
(4.31)***
0.342
(1.92)**
0.111
(6.68)***
0.010
(0.62)
(B)
343
0.264
0.253
24.19***
0.4325
(4.58)***
0.1128
(6.32)***
0.1902
(2.38)***
0.0132
(1.77)*
0.4542
(7.92)***
0.4192
(2.38)**
(C)
382
0.313
0.295
16.92***
0.325
(3.6)***
Included
0.116
(7.3)***
0.151
(2.01)**
0.012
(1.70)*
0.326
(4.62)***
0.365
(2.08)**
(D)
381
0.329
0.318
30.54***
0.0367
(5.97)***
0.4116
(4.79)***
0.1530
(2.11)**
0.2756
(5.06)***
0.4505
(2.80)***
0.0965
(6.29)***
0.0293
(2.00)**
(E)
381
0.357
0.34
20.58***
0.038
(6.28)***
0.389
(4.54)***
Included
0.154
(2.16)**
0.255
(4.66)***
0.373
(2.24)**
0.101
(6.32)***
0.029
(1.93)*
(F)
342
0.325
0.315
32.32***
0.035
(5.81)***
0.424
(4.66)***
0.105
(6.16)***
0.187
(2.48)**
0.299
(5.65)***
0.383
(2.26)**
(G)
342
0.3510
0.333
19.96***
0.0368
(6.11)***
0.4099
(4.48)***
Included
0.1097
(6.23)***
0.1854
(2.49)**
0.2737
(4.97)***
0.3614
(2.05)**
(H)
Notes:
1
This table presents results from OLS regressions of the proportion of a firm’s market value not due to assets-in-place [ROR(K)] on research and development
activity (R&D), stock beta (BETA) and skewness of stock returns (SKEW) or a joint measure of beta and skewness (LBETA), financial leverage (LEV), two
alternative proxies for size (ACT or CAP), and capital stock (CS).
2
ROR(K), R&D, BETA, SKEW, CS, LEV and ACT are defined as in Table 1; and CAP and LBETA as in Table 4.
3
Regional dummies classify our sample in five groups: USA, UK, Canada, Japan, Europe, and the rest of the world. When size is approximated by the natural
logarithm of market capitalisation, the USA dummy is dropped. This is to resolve the multicollinearity problem due to high intercorrelation among market
capitalisation and this dummy.
4
t-statistics in parentheses; *** denotes significance at the 1% level; ** at the 5% level; and * at the 10% level.
5
Data is obtained from the Compustat (Global Vantage) database. Observations are as of the end of Year 2000. Beta and skewness coefficients are calculated
using total monthly returns from December 1995 through December 2000.
No. in sample
R squared
Adj.-R sq.
F statistic
Regional
CS
CAP
ACT
LEV
LBETA
SKEW
BETA
R&D
Constant
(A)
Alternative Valuation Date: Observations at 31 December, 2000; OLS regressions
of ROR(K) on Eight Alternative Sets of Variables
Table 5
216
ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
# 2006 The Authors
Journal compilation # Blackwell Publishing Ltd. 2006
THE REAL OPTIONS COMPONENT OF FIRM MARKET VALUE
217
4. CONCLUSIONS
The real option approach establishes that the total market value of a firm is the
sum of the value of its assets-in-place and the value of its real options. If the real
option approach is correct, the efficient-market hypothesis predicts that stock
prices will reflect the available information regarding a firm’s real option portfolio. This information is contained in variables such as research and development, the risk and skewness of stock returns, size, and financial leverage, among
others.
We have used real option reasoning to predict the relation between the component
of a firm’s market value not explained by its assets-in-place and the aforementioned
variables. That is, if this portion of a firm’s market value corresponds to the value
assigned by investors to its real options, it should be positively related to the variables
of research and development, risk, skewness, and size, and negatively correlated to
financial leverage.
This hypothesis was tested using a sample of technology companies listed on the
main OECD stock markets. Our results are generally consistent with predictions.
First, we find that a large portion of the market value of technological firms cannot
be explained by the value of its assets-in-place. At the end of 1999, the estimate of a
company’s market value not explained by its assets-in-place presented a mean of
75%. We have also found that these results are not induced by an over-optimistic
valuation of such companies in 1999 as several analysts have suggested. The estimate
of the aforementioned portion of value, calculated after the decline of stock prices in
2000, averaged approximately 66%.
Secondly, our results also confirm the relation between the proportion of the
total market value of a firm not due to assets-in-place and some of the variables
affecting investors expectations regarding its real options value, as predicted by
the real option approach. We have analysed the effect of research and development, size, beta and skewness of stock returns, and financial leverage on estimates of the valuation ratio. Our evidence confirms a positive and statistically
significant effect of the first three variables, and the negative and statistically
significant effect of financial leverage. In addition, we have explored the robustness of our results after controlling for the valuation date, sub-industry and
country adscription, the measure of the dependent variable, size, and beta and
skewness. On average, our findings appear not to be sensitive to crossdifferences.
While we have obtained a certain quantity of evidence regarding the market
valuation of real options and some of its explanatory variables, future research
may prosper by extending the model to include a more accurate estimation of
the dependent variable and some of the independent variables. These results
also highlight the necessity of obtaining a suitable model for quantifying the
value assigned by investors to real options embedded in resource allocations and
strategies. However, as real options are generally unobservable to external
investors, this model should include those variables used by investors to
approximate the market value of real options held by a company. We have
found that research and development, stock beta (or a combined measure of
beta and return skewness), leverage, and size could be four of them. Future
research could help complete this list.
# 2006 The Authors
Journal compilation # Blackwell Publishing Ltd. 2006
218
ANDRÉS-ALONSO, AZOFRA-PALENZUELA AND FUENTE-HERRERO
APPENDIX
Correlation between ROR(K) and Dependent Variables
R&D
BETA
SKEW
ACT
LEV
CS
ROR(K)
R&D
BETA
SKEW
ACT
LEV
0.169
0.258
0.100
0.079
0.225
0.008
0.300
0.126
0.027
0.272
0.202
0.098
0.090
0.203
0.108
0.222
0.082
0.038
0.160
0.045
0.258
Notes:
1
This table presents the Pearson correlations between the proportion of a firm’s market value not due to
assets-in-place (ROR(K)), research and development expenses (R&D), stock beta (BETA), skewness of
stock returns (SKEW), financial leverage (LEV), size (ACT), and capital stock (CS).
2
ROR(K) measures the proportion of a firm’s market value not due to assets-in-place. It is defined as the
ratio of the difference of total market value and the value of assets-in-place to total market value. Total
market value is calculated as the market value of equity minus the book value of equity plus the book
value of assets. The value of assets-in-place is estimated as the present value of current free cash-flow to
the firm treated as perpetuity. The discount rate selected to capitalize current cash flow is the CAPM cost
of capital (K). Cost of capital is estimated using a global version of the CAPM, where world market portfolio
is approximated by the Morgan Stanley Corporate Index, and the risk-free rate by returns on long term US
Treasury bonds.
3
R&D is defined as the ratio of research and development expenses to sales.
4
BETA is the CAPM coefficient of the systematic risk of stock.
5
SKEW measures the skewness of stock returns.
6
LEV is calculated as the ratio of book value of corporate debt-with-cost to total assets.
7
ACT is estimated on the basis of the log of the book value of assets.
8
CS is defined as the ratio of the book net value of property, plant, and equipment to total assets.
9
Data is obtained from Compustat (Global Vantage) database. BETA and SKEWNESS coefficients are
calculated using monthly returns from December 1994 through December 1999. The remaining variables
are estimated using accounting and market data at the end of 1999. The sample includes technological
firms in the Compustat database and listed on the main OECD stock markets. We exclude companies for
which data is not available, or those reporting negative free cash-flows, negative book value of equity, or
ROR(K) < 0.
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Journal compilation # Blackwell Publishing Ltd. 2006