REVERSION, TIMING OPTIONS, AND LONG-TERM DECISION-MAKING

Many observers of managerial processes have come to the conclusion tha t discounted cash flow methods lead to a damaging neglect of long-term and strategic investments (e.g., Hayes and Garvin [5], MacCallum [9], and Dertouzos et al [4]). Some critics have argued for putting less w eight on financial analysis and more on managerial intuition. Myers [1 0] has countered that the problem is the inappropriate application of financial analysis rather than the use of financial analysis in genera l. He suggests that improper accounting for risk in future cash flows frequently leads to the use of discount rates that are too high. This results in relative undervaluation of typical long-term decision alter natives. He also suggests that organizations may underestimate, or neg lect altogether, the value of options stemming from managerial decisio ns. Because the creation and exercise of future options-is of the esse nce of strategic decision-making, and since there tend to be more opti ons imbedded in longer-term investments, the undervaluation of future options would induce a bias against strategic or long-term decision al ternatives. In this paper, we use modem asset pricing methods to exami ne one possible reason for excessive risk discounting. If the cash flo ws being discounted have an increasing dependence on an uncertain vari able that tends to revert to a long-term equilibrium path in the face of short-term shocks and this reversion is ignored, then the uncertain ty in the cash flows will be overestimated. If this uncertainty leads to excessive, systematic risk discounting, then the project will be un dervalued. We show how to classify the effects of such reversion on as set value, as well as the implications of ignoring it. Our examples in clude both ''now-or-never'' decisions about a production project and c hoices that involve a project timing option. The reverting variable in these examples is the project output price. For some examples, the me asure of ''long-term versus short-term'' is the operating duration of the project; for others, it is the length of the timing option. Throug hout, we use a set of valuation models designed for relative case of c alculation and usefulness for managers. 1 All of the situations that w e examine satisfy three conditions. First, the investing organization is a price-taker in the output market, so that the price is an underly ing exogenous variable. Second, uncertainty in future output prices is the only uncertainty underlying the decisions to be made, and this un certainty results in positive risk discounting in the valuation of cla ims to any fixed future output. Third, the structure of the potential production opportunity (i.e., the profiles of production and sales, an d project costs) is independent of when the project is undertaken. The first two conditions allow us to focus on a simple specific model. Th e third condition is imposed so that the effects of reversion can be i solated from those due to any direct dependence of the project cash fl ows on time. Output price reversion has a straightforward effect on '' now-or-never'' decisions about project alternatives, provided there ar e no operating options to be considered. The stronger the reversion, t he lower the uncertainty in long-term revenues, which, in turn, may re quire less risk discounting. Thus, any neglect or underestimation of r eversion may bias against project alternatives with more long-term rev enues, other things being constant. Moreover, the use of a single disc ount rate to value (on a now-or-never basis) project alternatives with different operating lives may introduce a bias against long-term inve stments when there is reversion in the project output price. If option s are imbedded in the project alternatives being considered, the effec ts of output price reversion are more complex. As noted, because rever sion tends to decrease long-term price uncertainty, it may reduce the risk premium or discount factor and raise the value of the underlying asset claim (here, a claim to a cash flow proportional to the long-ter m output price). This may increase the value of claims to cash flows t hat increase with long-term prices, such as call options, and decrease the value of claims to cash flows that decrease with price, such as p ut options. This phenomenon may be referred to as the ''risk-discounti ng'' effect. Less uncertainty also tends to reduce directly the value of long-term options of any type. This may be called the option ''vari ance'' effect, which reinforces the risk-discounting effect for put op tions and mitigates, if not overwhelms, it for call options. Finally, the reversion of future term structures for central tendencies of the price can have direct effects on asset values. These may be called ''f uture-reversion'' effects. They exist for American options, for which the timing of the option exercise is discretionary, and may exist for options whose payoffs occur over a period of time. The details of thes e effects on an option can depend on whether or not the option is in-t he-money now, and whether the reversion is to prices where the option would be in- or out-of-the-money in the future.In Section I, we introd uce the class of price models to be examined. We restrict the analysis to price processes that have a lognormal structure. This condition al lows us to present an easily integrated form of the conditional distri bution (in any future state) of the term structure of prices, and perm its us to apply a nonstochastic discounting framework to the valuation of related price claims. We also wish to facilitate the valuation of project options, such as the initial timing option considered below. T herefore, we examine price models that result in a simple state space (i.e., a one-dimensional state space indexed by the contemporaneous ou tput price). The output price models we use are each specified using a process for the expectation of prices where the key feature is an exp onentially decaying term structure of expectation volatilities. New in formation has a greater impact on expectations for the prices that wil l occur a year or two in the future than on expectations for prices th at will occur in ten or 20 years. Moreover, the-proportional drift in the resulting process for the price itself has a term that is logarith mic in the price, illustrating the reversion forces at work in the pri ce itself. Finally, the pattern of future conditional term structures of price medians shows the reversion directly. 2 In Section