Option value theory has led to a rich literature pertaining to empirical applications that analyze investment opportunities. The method has been utilized in a number of studies of the environment and in agriculture. Purvis et al (1995) examined the adoption of free-stall dairy housing for Texas producers, using stochastic milk production and feed costs. Khanna et al (2000) studied the adoption of site-specific crop management under
Isik (2004) analyzed the impact of the uncertainty in cost-share subsidy policies on the adoption of site-specific technologies. With respect to energy policy, Hasset and Metcalf (1995) analyzed residential energy investments considering that the energy prices follow a Brownian motion, while Millock and Nauges (2004) estimate an option value model on a firms’ actual abatement choice, with the major uncertainty facing the firm being the future energy price.
The investment problem studied here can be included in a category of real options referred to by Trigeorgis (2001) as a time to build option (staged investment). This is important for R&D intensive industries and long-development capital-intensive projects. The development of a new market (e.g. biofuel market) has the following three
characteristics: 1) decisions and cash outlays take place sequentially over time; 2) there is a maximum rate of investment; and 3) there are no returns until the project is completed (Majd and Pindyck, 1987).
This work builds on several related studies in the real options literature. Roberts and Weitzman (1981) constructed a model of a “sequential development project” (SDP) which has the same features outlined above. By their definition, the project can be stopped in any stage and as the investment takes place, the cost of completing the project and its uncertainty (variance) are reduced. These authors derive an optimal sequential decision rule for R&D or exploration projects and they show that even if NPV is negative, the investor should go ahead with the first stages of the project. Weitzman, Newey and Rabin (1981) apply the sequential methodology to examine whether the
development of liquid synthetic fuels from the coal market should be subsidized by the US government. McDonald and Siegel (1986) considered a basic model of irreversible investment with two stochastic variables, each of which evolves in geometric Brownian motion - the sunk cost and the value of the project. Their results show that the optimal investment in this case is reached by waiting until the benefits are twice the investment cost.
Grossman and Shapiro (1986) studied optimal dynamic R&D investments considering that the total effort to reach a payoff is unknown. Their work concentrates more on the rate of investment rather than the decision to invest or not, considering that the rate of progress is a concave function of effort. They model the uncertainty in returns as a Poisson process with the arrival rate as a function of the cumulative effort expended. They find that when uncertainty is introduced in the model, firms prefer risky projects rather than the safe ones when both have the same level of expected cost of effort.
Majd and Pindyck (1987) determine an optimal investment rule for a sequential investment, when a firm can invest at a maximum rate, and the value of the project follows geometric Brownian motion. An important characteristic of their model is that expenditure flow can be adjusted as new information arrives. They show that the largest effects of time to build appear when uncertainty is very high, the opportunity cost of delay is high and when the maximum rate of investment is low.
Emery and McKenzie (1996) evaluated the subsidy granted to the Canadian Pacific Railway (CPR) from an “ex ante” perspective. They considered that the “ex post” studies which concluded that the subsidy was too large are limited by ignoring the uncertainty that existed at that time. They employed a real option approach to see the importance of timing in “once-and-for-all” investment decisions in an uncertain environment. They concluded that the “ex-ante” value of the subsidy is lower than the required level that it is necessary to compensate the company for forgoing its investment options and, also, the value of the subsidy is lower as the income stream becomes riskier.
Finally, Schwartz and Moon (2000) analyzed investment in R&D (the development of a new drug) considering three sources of uncertainty - uncertainty about investment cost, future payoffs and the possibility that a catastrophic event can stop the project. Their findings describe not only the value of the project, but also the optimal values for the state variables at which the investment should proceed.
The study that has inspired this research is “Investments of uncertain cost” by Robert S. Pindick in 1993. Pindyck (1993) exploited the same idea as in Majd and Pindyck (1987) with the exception that the cost of completing the project is uncertain as opposed to the value of the project. An extension of the paper considers the situation where both, the value of the project and the cost of investment, are characterized by uncertainty. Except for the uncertain cost, the investment is also considered irreversible, meaning that the investment cost is sunk. Thus, in his study, Pindyck (1993) determines a decision rule for irreversible investments given the cost uncertainty and allowing for the possibility of
abandoning the project midstream. He considered that the cost of completing the project includes two different kinds of uncertainty - technical uncertainty, which is related to the physical difficulty of completing the project, and this type of uncertainty can be solved only by undertaking the project; and input cost uncertainty, which is external to what the firm does and it is highly nondiversifiable as it might be related to the general economic activity. He makes clear that even both types of uncertainties increase the investment opportunity value, technical uncertainty makes investing more attractive10, while input uncertainty has the opposite effect11. The optimal investment rule is found using contingent claim analysis as the cost’s risk can be spanned by the existing assets. The optimal investment rule is that the investment should be undertaken as long as the cost of investment is below a critical number. The critical cost level and the investment value opportunity are found as solutions of the sequential real option problem. By numerically solving the real options model, Pindyck (1993) has concluded that for large industrial projects, input cost uncertainty is important, while technical uncertainty does not play a major role. For these types of projects, increasing input cost uncertainty will lead to investment reductions. On the other hand, for R&D projects, the opposite is true, meaning that technical uncertainty plays an important role. Pindyck (1993) applies the model for a specific example: the decision to build a nuclear power plant in the context of very uncertain market conditions (late 1982, 1983). In order to estimate the expectation, variance and variance decomposition of cost, Pindyck (1993) used the Tennessee Valley
10 Even a project with a negative NPV value can still be economically viable as only by investing, the
information about costs will be revealed and, thus, there is a shadow value that reduces the expected cost of investment (the same idea with a shadow value of production from a learning curve). There is no value of waiting.
11 Even a project with a positive NPV value can still be uneconomically viable as the input costs might
Authority (TVA) survey data on individual nuclear plant costs and a cross-section regression published by Perl (Pindyck, 1993). His results show that both types of uncertainty should be taken into account, but the input cost uncertainty has greater effect on the investment decision.