Capital Budgeting : Some Exceptions to the Net Present Value Rule

Textbooks tend to emphasize the net present value (NPV) rule, often arguing that it is theoretically superior to other methods. Yet other methods, many of which do not involve discounting, are also used in practice. Hence, one of two conclusions can be drawn: (1) firms are making suboptimal decisions or (2) the assumptions underlying the NPV rule are not always met in practice. The purpose of this paper is to present simple numerical examples wherein applying the NPV rule leads to erroneous decisions. The examples highlight the assumptions underlying the NPV rule. INTRODUCTION Capital budgeting is a vital activity. It is the process by which organizations make long-term investment decisions. Textbooks in accounting and finance discuss numerous evaluation criteria, including payback period, accounting rate of return, internal rate of return, and Net Present Value (NPV).i These criteria can lead to differing conclusions. The NPV rule of "accepting a project if and only if its NPV is positive" is based on the intuitive premise that money today is worth more than the same amount of money in the future. Textbooks tend to emphasize the NPV rule, often arguing that it is theoretically superior to other methods (see, for example, Kaplan and Atkinson 1989, 474-475; Zimmerman 1995,119). Yet other methods, many of which do not involve discounting, are also used in practice. For example, in a survey referred to in Horngren et al. (1997, 794), more firms reported using the payback method either as a primary or secondary criterion to evaluate projects than any other method.^ Since companies use these other methods, one of two conclusions can be drawn: (1) firms are maMng suboptimal decisions or (2) the assumptions underlying the NPV rule are not ' See, for example, Horngren et al. (1997), Kaplan and Atkinson (1989), Ross et al. (1995) and Zimmerman (1995). 2 Another survey reported that the payback method is commonly used as a secondary criterion, but not as a primary criterion (see Ross etal. 1995,219). Anil Arya is an Associate Professor and John C. Fellingham is a Professor at Ohio State University and Jonathan C. Glover is an Associate Professor at Carnegie Mellon University. We thank Doug Schroeder, Li Zhang, students at Carnegie Mellon University and Ohio State University, Wanda Wallace (the editor), and two anonymous referees for helpful comments. Anil Arya acknowledges support from Ernst & Young. John Fellingham acknowledges support from theH. P. Wolfe Foundation. 500 Issues in Accounting Education always met in practice. The purpose of this paper is to present numerical examples wherein applying the NPV nale leads to erroneous decisions. The examples highlight the assumptions underlying the NPV rule. Although the simplest version of the NPV rule deals with the case in which cash flows are known with certainty, uncertainty in cash flows can be incorporated by taking expectations over cash flows and discounting using a risk-adjusted interest rate. However, uncertainty is related to two assumptions underlying the NPV rule that are not so easily dealt with. The NPV rule assumes that (1) the project approval decision is a "now-or-never" decision (if a project is turned down now it cannot be undertaken in the future) and (2) decisions are made either in a single-person firm or in a multi-person firm in which there are no information asymmetries among individuals.^ Our examples deal with cases in which these assumptions do not hold. The examples are intentionally simple. They are intended to provide the reader with an appreciation for management's use of a variety of criteria and an understanding of some of the underlying considerations. In practice, uncertainty, information asymmetry problems, and multiperiod, multi-project considerations greatly complicate capital budgeting, beyond the focus of this paper. When the NPV rule's assumptions are violated, the use of multiple criteria is a way of evaluating the project from different perspectives. If many of the criteria suggest the project should be taken, the chance is greater that the project is desirable. As Demski (1994, 385) writes, there is "ambiguity in the present value frame itself... .In this case, we then acknowledge an ambiguous framing exercise coupled with a portfolio of approaches to the framing task." Ross et al. (1995, 218-219) present a similar view: "[b]ecause the true NPV is unknown, the astute financial manager seeks clues to assess whether the estimated NPV is reliable. For this reason, firms would typically use multiple criteria for evaluating a project... [if] different indicators seem to agree [then] it's 'all systems go.'" The remainder of the paper is organized into three sections. The second section relaxes the now-or-never assumption in order to study the option value of waiting. The third section relaxes the "no information asymmetries" assumption and, in particular, studies decentralized information. The fourth section studies the effect of reducing information asymmetries. OPTION VALUE OF WAITING Textbooks suggest an exception to the NPV rule: If two mutually exclusive projects are being considered, then only the project with the higher NPV is to be accepted, even if both projects have positive NPVs (see, for example, Brealey and Myers 1996, 97100). Two projects are mutually exclusive if undertaking one precludes undertaking the other. For example, if a firm owns a tract of land and has a choice of building either a warehouse or a plant on the land, then these two projects are mutually exclusive. The issue of mutually exclusive projects is traditionally discussed in the context of multiple projects. More For analyses in which the first assumption is relaxed, see, for example, Balakrishnan and Bhattacharya (1997), Dixit and Pindyck (1994),Ross (1995) andTrigeorgis (1996). For analyses in which the second assumption is relaxed, see, for example, Antle and Eppen (1985) and Harris et al. (1982). Arya, Fellingham and Glover 501 recently, the evaluation of mutually exclusive projects has been extended to the case of one project—a project may be in competition with itself taken at a later date. Often, by turning a project down today, the firm preserves the option to invest in the project at a later date. By investing today, this option is lost. When is keeping the investment option alive better than investing in the project today?^ The Resolution of Uncertainty One advantage of waiting to invest in a project is that the firm may receive better information about the project's cash fiows, i.e., uncertainty may be reduced over time. Consider the following example. If a project is undertaken, the required cash outflow (investment/cost) today is 100. The project generates a cash inflow of 120 or 90, each equally likely, in one year from now. For simplicity, assume the discount rate is 0 throughout the paper. Alternatively, one can view the cash flow numbers as being in today's dollars (they are already discounted). The project's expected NPV is .5(120 100) + .5(90 100) = 5, and the NPV rule would lead the firm to accept the project. Suppose that by rejecting the project this year and waiting until next year to make a final Investment decision, the firm leams exactly what the project's cash inflow will be. If the firm waits, it will invest in the project if and only if it leams the cash infiow is going to be 120. The project's expected NPV is .5(120 100) + .5(0) = 10. Because of the reduction in uncertainty, it is better to wait to make the investment decision. The Luck of the Draw Even if uncertainty is not reduced, it may be worthwhile to wait to accept a project. By waiting, it is possible the project will be undertaken under more favorable circumstances (e.g., interest rates may decline). Consider the following example. If a project is undertaken, it generates a cash inflow of 100. The cost is 60 or 90, each equally likely. When the project is undertaken, the project's exact cost is known. Whether the cost is 60 or 90, the NPV rule dictates the project be accepted, since its NPV is either 40 or 10. If the project approval decision is delayed, the cost depends on the prevailing economic conditions. Suppose the cost in the second period is again equally likely to be 60 or 90, and costs are uncorrelated across periods. Returning to the initial project approval decision, it is optimal to reject the project if the cost is 90; by waiting, the environment either stays the same or improves. If the cost is 90, the expected NPV of accepting the project today is 100 90 = 10 but by waiting is .5(100 60) + .5(100 90) = 25. Waiting enables the firm to obtain a new, potentially more favorable environment in which to undertake the project. Why does the NPV rule not yield the correct answer in the above examples? The NPV rule implicitly assumes the project choice is a now-ornever decision. In both examples, we assumed the firm's opportunity to invest in a project is not lost if the investment decision is delayed, i.e., the project choice is a "now-orlater" decision. Our discussion of the option value perspective to capital budgeting is based on Dixit and Pindyck (1994) and Ross (1995). 502 Issues in Accounting Education