It is now widely understood that conventional economic analysis based on discounted cash flow (DCF) methods fails to capture the strategic impact of projects. In particular, DCF methods ignore the ''operating flexibilities'' that give project managers options to revise decisions in response to changing exogenous economic conditions. The importance of such operating options becomes critical when the environment is highly volatile and the technology is flexible, thus permitting managerial intervention at little cost. For example, when facing exogenous stochastic prices a project with operating options can protect -itself against some of the adverse price movements by switching into an alternative ''mode of operation'' that is less affected by the adverse price realizations. In effect, the irreversibility assumption of conventional investment analysis is violated. Real options techniques, by endogenizing the optimal operating rules and explicitly capturing the flexibility and its effects on uncertainty, provide for a consistent treatment of risk in the valuation of flexible projects. The growing literature on real options has revealed several important lessons: 1 (i) the volatility of prices becomes an important determinant of investment, both in terms of the type of investment (e.g., rigid versus flexible technologies) and in terms of the quantity of investment (in that high volatility increases the value and Tobin's q of flexible systems); (ii) the value of flexibility per se may be determined explicitly, given the dynamics for relative input prices; (iii) input price elasticities have less meaning at the microlevel than critical input price boundaries (i.e., the price levels at which decisions must be revised); (iv) switching costs may be treated realistically rather than with ad hoc costs of adjustment models; (v) it may be optimal for a firm to utilize a short-run inefficient technology, creating a hysteresis (i.e., a bias towards maintaining the status quo); and (vi) investment decisions take on a long-run strategic view. While the theoretical literature on real options has provided many useful insights, specific applications have been limited and heavily stylized for mathematical tractability. In this paper, we present a general model of flexibility that is computationally simple and is more amenable to empirical implementation than those that rely on analytical solutions.2 We then apply the model to the case of an industrial steam boiler that can switch between using residual fuel oil and natural gas. This technology is ideally suited for such an analysis because (i) both flexible and rigid systems are being produced, suggesting that, at the margin, price differences between the installed cost of the two types of technologies should be roughly equal to the incremental value of flexibility, and (ii) the technology is extremely simple in that it uses a single variable input (fuel) to produce a single output (steam). The rest of the paper is organized as follows. In Section I, we compare investment in fixed-fuel boilers and a dual-fuel boiler to motivate the need for the special tools of option valuation. The example makes two important points: first, projects with embedded options typically call for discount rates that change endogenously as the value of some underlying state variable evolves (where NPV analysis takes the discount rate as fixed, or at most exogenously determined), and second, the decisions to exercise real options must be determined jointly with the valuation analysis, meaning that even expected cash flows (which are taken as exogenous in NPV analysis) can not be determined without a proper valuation framework. Hence, neither discount rates nor expected cash flows can be taken as strictly exogenous. In Section II, we introduce a dynamic programming procedure that would be appropriate to project valuation in an economy with risk-neutral agents. This section shows how project valuation and option exercise interact and must be jointly determined. We then extend the analysis to show how the basic methodology can be modified to accommodate the considerations of risk-aversion. Section III presents an application of the model to the case of dual-fuel boilers. Finally, Section IV concludes.
