Optimal Timing to Invest
in E-commerce
Jow-Ran Chang
National Tsing Hua University Mao-Wei Hung
National Taiwan University
ABSTRACT
The timing of investment in e-commerce remains hotly debated in both the academic and investment communities. This study develops a framework for analyzing the optimal timing for a company to invest in e-commerce for conducting its business-to-business (B2B) or business-to-consumer (B2C) transactions. This study applies a real option theory to assess a new risk–reward dynamic for investing in e-commerce. The numerical results demonstrate that the optimal timing of investment in e-commerce depends on uncertainties regarding future cash flows and the opportunity costs associated with e-commerce. Implications with regard to the behavior of Inter-net companies from a financial perspective are discussed. © 2006 Wiley Periodicals, Inc.
E-commerce business has been growing rapidly during recent years. The Census Bureau of the Department of Commerce reported that total e-com-merce sales for 2004 were estimated at $69.2 billion, an increase of 23.5% from 2003 in the United States. In comparison, total retail sales for 2004 increased just 7.8% from 2003. E-commerce sales in 2004 accounted for 1.9% of total sales, up from 1.6% in 2003. Regarding global e-commerce figures, at the end of 2004, the United States had nearly 186 million internet users and worldwide the number of users exceeded 945 million (ETForecasts, 2005).
Psychology & Marketing, Vol. 23(4): 335–348 (April 2006)
Published online in Wiley InterScience (www.interscience.wiley.com) © 2006 Wiley Periodicals, Inc. DOI: 10.1002/mar.20114
The success of e-commerce business is a key question. Lubbe and Pather (2002) denoted that adding business value through e-commerce investment is probably a key organizational concern of CEOs. The role of information technology (IT) has also been redefined by some organ-izations to include attempts to engage in e-commerce operations. Quayle (2003) observed that no relationship exists between organiza-tional performance and the proportion of resources allocated to IT. Moreover, Kearns (2004) stated that although IT investment potentially can provide competitive advantage, actual returns on such investment vary significantly and most CEOs rate past IT investment as being disappointing. Lubbe (2004) studies the existence of a link between organizational performance and information technology investment intensity in SME organizations using e-commerce for the period 2001/2002.
A growing body of research exists on e-commerce investment, but a comprehensive understanding of the optimal timing for a company to invest in e-commerce remains elusive. Raghunathan and Madey (1999) designed a firm-level framework for electronic commerce infor-mation systems (ECIS) infrastructure planning. Moreover, McDon-ald and Siegel (1986) proposed that the option to defer uncertain investment is very valuable and should be considered by companies making investment decisions. Kulatilaka and Perotti (1998) noted that the benefits of early preemptive investment may exceed the ben-efits of waiting given intense competition.
E-commerce investment has two main characteristics. First, expen-ditures are partly irreversible. Restated, sunk costs cannot be recov-ered. Second, the optimal timing for investment in e-commerce can be delayed. That is, the company can wait for new information regarding prices, costs, and other market conditions before investing in e-com-merce. In most books, the income approach, cost approach, market approach, discount cash flow, and real option method, all of which may be combined with game models, are mentioned, as, for example, in Amram, Kulatilaka, and Henderson (1999). All of these approaches are adopted in reality, but none of them are satisfactory. However, the real option method is superior to the others when uncertain future situations involving well-defined models are considered. Unlike stan-dard corporate resource allocation approaches, the real options approach recognizes the importance of managerial flexibility and strategic adaptability. Recently, Benaroth and Kauffman (2000) and Taudes, Feurstein, and Mild (2000) applied the real options theory to real-world examples.
Real options are derived from financial options, and are used to price investment projects. Several studies have examined real options. Tourinho (1979) demonstrated that natural resource reserves can be viewed as options that produce a resource and are valued accordingly. Moreover, Cukierman (1980) and Bernanke (1983) designed models
in which firms have an incentive to postpone irreversible investment decisions until the arrival of new information. The survey articles by Dixit (1992) and Pindyck (1991) mention other studies. Cortazar and Schwartz (1998) applied the flexible Monte Carlo simulation to assess the real option in relation to an oil field. Additionally, Pindyck (1999) analyzed the long-term behavior of oil prices and their effect on real options. Finally, Dias (2002) provided an overview of the exploration and production of real options models.
The real option valuation method has been applied in e-commerce business for several years. However, few works have considered invest-ment time horizon. Bicher and Ahnefeld (2002) applied and tested a variation of the real option method designed for private equity invest-ments. The case-study approach is applied to discuss the case of a fic-titious company involved in B2B during the year 2000. Li and John-stone (2002) considered the real options theory in relation to strategic IT investment. They divided IT investment opportunities into four categories according to two criteria: technology switching costs and nature of competition. This study applies a real option approach to describe the timing of firm investment in e-commerce. This investi-gation presents a jump diffusion process for describing the new dynamic of investing in e-commerce. Unlike traditional diffusion processes, jump diffusion can determine the influence of catastrophic economic shocks or jump events on project value. The numerical results presented in this work demonstrate that three distinct components help to determine the optimal time for launching e-commerce. The first component is the project value volatility. The critical value of the project increases with volatility, thus reducing the actual investment required of the company. The second component is the size of the jump in the project value. The investment opportunity value decreases with increasing jump size. This smaller investment opportunity value leads to smaller opportunity cost for investing now rather than waiting. Finally, the third component is the jump probability of the project. The critical value of the project increases with increasing jump prob-ability, which thus increases the investment amount.
METHODOLOGY
Before designing the proposed methodology, this study presents an example to illustrate to readers the investment timing problem. A company faces an e-commerce investment. The company plans to spend $100 to construct an e-commerce information system. However, because e-commerce remains immature, the company is unsure about the acceptance of e-commerce by its customers. Assuming that the uncertainty regarding e-commerce information systems can be resolved during the next year, the company is trying to maximize the
expected return from its $100 investment. According to the firm esti-mates, the e-commerce information system has a 50% chance of being widely accepted during the next year. If the e-commerce information system becomes popular during the next year, the expected increase in cash inflow from this investment is estimated to reach $16 a year. If the e-commerce information system does not become popular dur-ing the next year, the expected annual net cash inflow from this invest-ment will be $6. Assuming that the discount rate for this investinvest-ment is 10%, the net present value (NPV) of this investment can be calcu-lated as:
Suppose that the company waits 1 year to monitor market acceptance of the new e-commerce technology and then decides to proceed with the investment if the reaction is favorable or otherwise give up the invest-ment. The NPV of the investment then can be calculated as:
Basically, this example demonstrates that the value of option of defer-ring investment. However, in the event of industrywide uncertainty, wait-ing has no value, owwait-ing to the asymmetric effects of uncertainty, such as the influence of random competitive arrivals. Intuitively, competitive pressure will reduce the value of the option of deferring an e-commerce investment.
Recognizing the potential of real options in capital budgeting, the the-oretical model presented here can be used to optimize the timing of a firm investing in e-commerce investment decisions made by a manager. This study considers the problem of determining the point at which it is optimal to pay a sunk cost I in return for a project whose value is P, given that P evolves according to the following mixed Brownian motion and jump process:
(1) where dB denotes the increment of a Wiener process and dJ represents the increment of a Poisson process with mean arrival rate , and dB and
dJ are independent. This work assumes that if an event occurs J reduces
by some fixed percentage u with probability 1. That is
(2) Equation (1) implies that the current value of the project is known, but
P fluctuates like a geometric Brownian motion, and over each time
inter-val dt there is a small probability that dt will drop to (1 – u) times its
− = . y probabilit with , 1 y probabilit with 0 dt u dt dJ λ λ PdJ PdB gPdt dP = +σ + 27 . 27 ] %) 10 1 ( 16 100 [ %) 10 1 ( 5 . 0 1 1 = + + − + =
∑
i∞= i NPV∑
∞ = + = + + − = 1 *0.5 10 %) 10 1 ( 6 16 100 i t NPVoriginal value. Therefore, the future value of the project remains uncer-tain despite the continuous arrival of new information. Equation (1) is an abstraction from the e-commerce investment. Uncertainty is some-times discrete, resembling a jump in the P process. Competitors enter the industry with better e-commerce technology or stricter new regulations, thus destroying the value of existing business.
A company’s investment opportunity is equivalent to a perpetual call option. Moreover, manager investment decisions involve deciding when to exercise such an option. Consequently, investment decisions can be considered valuation problems.
The following section denotes the value of the investment option by
V(P). This study attempts to maximize expected present value of the
payoff from investing at time T:
(3) where E denotes the expectation, r represents the discount rate, and the maximization of the expected present value is subject to Eq. (1) for P. If
g⬎ r, waiting longer is a better policy and the optimum would exist. To
understand this problem, this study assumes that g⬍ r.␦ is defined as the difference of r – g and ␦ ⬎ 0.
The only return from the holding project, V(P), is its capital appreci-ation. The project yields no cash flows up to time T. The optimal invest-ment rule can be derived with the use of a dynamic program. Conse-quently, the Bellman equation can be presented as
(4) Equation (4) implies that over time interval dt, the total expected return from the project, rVdt, equals its expected rate of capital appre-ciation. This study expands dV with the use of Ito’s lemma for the com-bined Brownian and Poisson processes. Then
(5) Given g⫽ r –␦, the Bellman equation becomes the following differential equation, which must be satisfied by V(P):
(6) Next, the boundary is considered. First, the limiting behavior of V(P) near zero yields the first condition:
(7) Equation (7) means that the option to invest has no value when P⫽ 0. The investment rule presented here has the form of the critical value P* such that the optimal timing for investing is when P⬎ ⫽ P*. The other
0 ) 0 ( = V 0 ] ) 1 [( ) ( ) ( ) ( ) ( ) ( 2 1σ2P2V′′ P + r−δ PV′ P − r+λ V P +λV −u P = dt P u V P V dt P V P dt P V gP rVdt ( ) { ( ) [(1 ) ]} 2 1 ) ( + 2 2 ′′ − − − ′ = σ λ ) (dV E rVdt = ] ) [( max ) ( rT T I e P E P V = − −
two conditions stem from the concern of this study with optimal invest-ment. The behavior of V(P) at P* is considered. At this threshold, it becomes optimal to exercise the option, and therefore acquire the project with value
P* by incurring the exercise price of investment I. However, two conditions
must be fulfilled. The first condition is that the value of the option must equal the net value obtained by exercising it; this is the value-matching condition: (8) Equation (8) has another interpretation. We could write the equation as P* – V(P*) ⫽ I. The project is valued P, but involves giving up the opportunity or option to invest, which is valued at V(P) when the com-pany invests in the e-commerce project. Hence, the gain associated with the project is P – V(P) and the critical value V* indicates where this net gain equals the direct cost of investment I.
The second condition is that the graphs of V(P) and P – I should meet tangentially at P*; this is the smooth-pasting condition:
(9) Equation (9) indicates that if V(P) was not continuous and smooth at the critical exercise point V*, better results could be achieved by exercising this option at a different point.
To identify V(P), Eq. (6) must be solved subject to the boundary con-ditions (7)–(9). Functional forms can be guessed, and substitution used to determine whether they work. Equation (6) is simply a second order homogeneous linear equation. To satisfy boundary condition (7), the solu-tion of Eq. (6) must be denoted as
(10) where constant A remains to be determined, and 1⬎ 1 is a known con-stant with a value that depends on parameters , r, and ␦ of the differ-ential equation.
The remaining boundary conditions, as well as Eqs. (8) and (9), can be used to identify the two remaining unknowns, constant A and critical value P*, at which it is optimal to invest. Substituting (10) into Eqs. (8) and (9) and rearranging yields
(11) and
(12) Equations (10) and (12) provide the value of the investment opportu-nity; that is, the option value of the e-commerce project V(P). Meanwhile, Eq. (11) yields the optimal investment rule, namely, the critical value P* at which it is optimal to invest. When 1⬎ 1, then 1/(1– 1) ⬎ 1 and P*
1 1 1 1 * * 1 1 1 1 ( ) ) 1 ( ) ( − − − = − = β β ββ β β I P I P A I P 1 1 1 * − =ββ 1 ) ( β AP P V = 1 ) ( * = ′ P V I P P V( *)= *−
⬎ I. Therefore, the traditional net present value ( NPV) rule is incorrect. Uncertainty and irreversibility drive a wedge between the critical value
P* and I. Consequently, it is important to examine its magnitude for
realistic values of the underlying parameter 1and its response to changes in these parameters.
A key question is the value of P for which immediate investment is opti-mal. If P ⬎ P* then immediate investment in e-commerce projects is desirable. Therefore, investment timing or rules can be expressed in terms of V(P) as
(13) Substitute Eq. (10) into (6); then ‚ yields a positive solution to a non-linear equation:
(14) The value of ‚ that satisfies Eq. (14) can be found numerically. Then, given 1, P* and A can be derived from Eqs. (11) and (12). If u⫽ 1 (so that the event is P falling to zero), then Eq. (14) can be simplified to produce a quadratic equation:
(15) The two roots are
(16) and
(17) so the general solution to Eq. (6) can be represented as
(18) where A1and A2are constants requiring determination. In the present problem, the boundary condition (7) implies that A2⫽ 0.
2 1 2 1 ) (P APβ A Pβ V = + 0 ) ( 2 ) 2 1 ( 2 1 2 2 2 2 2 = − σ−δ − σ−δ − + σ+λ < β r r r 1 ) ( 2 ) 2 1 ( 2 1 2 2 2 2 1 = − σ−δ + σ−δ − + σ+λ > β r r r 0 ) ( ) ( ) 1 ( 2 1σ2β β − + r−δ β − r+λ = 0 ) 1 ( ) ( ) ( ) 1 ( 2 1σ2β β − + r−δ β − r+λ +λ −u β = > − ≤ = . , ) ( * * 1 P P for I V P P for AP P V β
NUMERICAL ANALYSIS
The characteristics of the optimal investment timing and the value of the e-commerce project can now be examined, as indicated by Eqs. (10)–(13). Numerical results help to illustrate how they depend on the values of the various parameters.
In each case, unless otherwise noted, the cost of investment is set as follows: I⫽ 1, r ⫽ 0.04,␦ ⫽ 0.04, ⫽ 0.2, u ⫽ 0.4, and ⫽ 0.1. Figure 1 illustrates a function of V for these parameter values, as well as for ⫽ 0, ⫽ 0. 3. The tangency point of V(P) with the line P – I gives the crit-ical value P*. Moreover, the opportunity cost is V(P). When P⬍ P*, then
V(P)⬎ P – I and P ⬍ I ⫹ V(P), the value of the project is below its full
cost, and the direct cost I is added to the opportunity cost V(P).
Figure 2 shows the dependence of P* on . Notably, P* increases markedly with . P* increases with increasing , which tends to depress investments. This phenomenon occurs because investments are highly sensitive to volatility in project values, regardless of investor risk preferences.
Figures 3 and 4 show the dependence of V(P) and P* on u. Notably, an increase in u from 0 to 1 causes a decrease in V(P), and consequently a decrease in critical value P*. This decrease occurs because a larger u value implies a smaller investment opportunity value, leading to a smaller opportunity cost for investing now rather than later. Firms engaged in e-commerce business face competitors, each trying to develop their own e-commerce businesses, and eventually additional competitors may enter the market, causing P to continue to fall.
A positive can affect the value of V(P), the opportunity cost of the proj-ect, in two ways. First, a positive value of increases the variance of per-centage change in P, which tends to increase V(P). Second, a positive value of reduces the expected rate of capital gain on P, thus decreas-ing V(P). As shown in Figures 5 and 6, the net effect is the reduction of
V(P), therefore reducing critical value P*.
DISCUSSION
The precipitous decline in the valuations of e-commerce companies since March 2000 is an interesting phenomenon. Ofek and Richardson (2001) contended that part of the reason for these declines has been an increase in the number of shareholder selling driven by the expiration of lock-up agreements. Garicano and Kaplan (2002) found that after the bursting of the tech bubble in 2000, in valuing B2B and B2C e-commerce busi-nesses, the market reduced its expectations regarding future growth, the extent of transaction cost reductions, the speed of the adoption net-work effect, and the level of competition. Quayle (2003) pointed out that no relationship exists between organizational performance and the pro-portion of resources allocated to IT investment. Thus whether a positive
or negative correlation between IT investment and profitability exists in firms with heavy investment in e-commerce remains uncertain.
This study explains that uncertainties facing e-commerce business increase when the market reduces its expectations regarding future Figure 1. Value of investment V(P) for ⫽ 0, 0.2, and 0.3.
growth. The critical value P* increases with increasing , which tends to depress investment. Thus the optimum strategy to adopt is to wait for the arrival of new information. Investing now will result in large losses for Figure 3. Value of investment V(P) for u⫽ 0, 0.4, and 1.0.
Internet companies. Therefore, the option to defer uncertain investment is very valuable and should be considered by companies making e-com-merce investment decisions. Li and Johnson (2002) presented a wireless Internet trading infrastructure example. Li and Johnson observed that Figure 5. Value of investment V(P) for ⫽ 0, 0.2, and 0.6.
technology that enables high-speed wireless data access has been avail-able for over a decade. However, no electronic brokerage companies offered wireless trading services before late 1998.
Garicano and Kaplan (2002) proposed an exception for cases like eBay, which provides a service that is not available off-line. It benefits from net-work effects because it connects large numbers of buyers and sellers. The market share of eBay increases with the number of buyers and sell-ers using its services. Unlike many other firms involved in e-commerce, the market value of eBay has only declined by a little over 50% from its tech-bubble peak. In addition, research groups maintain that e-pro-curement can turn 10% to 20% of proe-pro-curement expenses directly into pretax profit. Moreover, PC Week asserts that more companies are enter-ing an e-procurement market that users now see as providenter-ing the fastest return on an e-commerce investment. Ford provides another example, indicating that competition is a more important factor than deferring an e-commerce investment. Ford uses an e-procurement system to estab-lish connection with between 3000 and 5000 suppliers globally.
The framework developed in this study is now applied to explain these cases. Competition reduces profit in the Internet auction market. A jump in e-commerce value can explain the eBay case. An increase in jump size
u from 0 to 1 or jump probability decreases the opportunity cost V(P),
and hence the critical value P*. The best way for a company to apply e-commerce transaction is to act in a timely fashion. eBay has been extremely efficient and effective in launching and expanding its busi-ness and thus has continued to outperform its competitors since 2001.
In conclusion, uncertainty and jump behavior depend on the industry sector in which a firm is completing. Some industry sectors have low uncertainty and high jump behavior. Firms should launch e-commerce transaction systems early, achieving large reduction in transaction costs and boosting further growth by establishing a strong foundation for com-petitiveness. Other industry sectors are characterized by high uncer-tainty and low jump behavior, and firms in these sectors should wait for the arrival of further information before deciding the timing of the launch of their e-commerce transaction system.
CONCLUSION
This article employed a financial framework to analyze the optimal tim-ing for firm introduction of e-commerce to B2B or B2C transactions. This study applies a jump diffusion process to describe the new dynamics involved in investing in e-commerce. The numerical results demonstrate that the timing for firm introduction of e-commerce to its transactions depends on uncertainties regarding future cash flows and the opportu-nity costs associated with using e-commerce. Discussing the behavior of Internet companies from a financial perspective helps to determine which
companies should apply e-commerce business early and which companies should wait to obtain new information before investing in e-commerce.
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Correspondence regarding this article should be sent to: Mao-Wei Hung, National Taiwan University, 50, Lane 144, Keelung Road, Section 4, Taipei 106, Taiwan ([email protected]).
