What is the value of an asset? That is the ultimate financial question, the equivalent of Hamlet’s “To be or not to be.” Of course, we all “know” the answer: the present value of its future cash flows. Push an expert for clarification, and the response is, “take the future cash flows and discount them with the appropriate rate.”
Unfortunately, those answers rely on two ill-defined concepts (“future cash flows” and “appropriate rate”), a faulty analogy, and a repudiation of statistics.
History of a Curious Analogy
Joel Dean, an American economist who died in 1979 and made important contributions to corporate finance, introduced the Discounted Cash Flow (DCF) approach as a valuation tool in 1951. The thought was that if the Net Present Value (NPV) of the cash flows of an asset or project, estimated with the DCF method, was positive, the investment was worth pursuing. The idea was motivated by an analogy with bond valuation. It had long been established that the price of a bond corresponds to its future cash flows, discounted with a rate determined by the market – a rate determined primarily by the credit risk associated with the issuer.
However, the analogy between bonds and project cash flows is not as clean as it seems. In the case of a bond, the future cash flows are well-defined. In essence –and this is critical – the uncertainty in the bond cash flows derives from the issuer’s potential inability to pay (credit risk). But there is no uncertainty as to the amount to be paid. To put it differently, the bond has no upside. Therefore, the probabilistic distribution of the cash flows is one-sided; it only includes downside scenarios.
In contrast, the uncertainty in a project comes from not knowing the cash flows rather than from the capacity of the project to pay them. Moreover, even if we make an optimistic estimate of the cash flows, there is always the possibility to exceed that estimate. That is, the cash flow distribution is two-sided: There is upside and downside potential.
These differences are further exacerbated because the life of a project is not as clearly defined as the time-to-maturity of a bond. Project cash flows have notoriously uncertain lifespans. Strangely, economics textbooks never address the shortcomings of the project-bond valuation analogy.
Having supposedly established a similarity between bonds and projects’ cash flows – despite the shortcomings discussed previously – corporate finance books indicate that the appropriate discount rate to use when evaluating a project is the opportunity cost of capital. That is, a number derived from a characteristic of the potential investor, not a number associated with any feature of the project cash flows.
Interestingly enough, in bond valuations the discount rate is derived from a characteristic of the issuer of the cash flows (credit risk). The opportunity cost of capital of the potential bond investor does not come into the picture.
From Uncertainty in the Numerator to Uncertainty in the Denominator
What do we mean by future cash flows? That is, the numerator in the DCF computation. Are we talking about expected cash flows (in the statistical sense of the term)? Or best-case scenario cash flows? Or baseline-scenario cash flows? Or typical-case cash flows? The vagueness of what to put in the numerator is astounding. Most textbooks circumvent the issue by simply referring to them as the “project cash flows” or sometimes the “risky cash flows” without much elaboration. In summary, the analyst is normally left in the dark as to what degree of precision or prudence to employ in estimating what is one of the most relevant inputs in the valuation analysis.
However, it is in the denominator of the DCF method where the most interesting anomaly takes place. Project valuation problems are challenging, because the cash flows are stochastic and difficult to estimate. Yet, in the DCF method, we have chosen not to deal with this issue. We have instead chosen to go directly to the denominator hoping that by performing a clever manipulation of it – adjusting the discount rate – can get the correct result.
Hence, we are attempting to transform a problem, which is probabilistic in nature, into a deterministic one, by means of a kind of safety factor that we hope will remove the uncertainty embedded in it.
A Few More Operational and Conceptual Difficulties
- Most financial textbooks present sanitized versions of real investment decisions: There is always only one negative cash flow (the amount invested, typically at time equals zero), followed by a sequence of positive cash inflows. In reality, most projects involve long periods with multiple outlays or negative cash flows. In such cases, the DCF approach is misleading, since by virtue of discounting both positive and negative cash flows with the same rate, it introduces a systematic error. More to the point, it treats the positive cash flows in a “pessimistic” fashion and the negative cash flows in a “forgiving” way.
- Estimating the correct discount rate is still a problematic issue. For example, the idea of using the weighted average cost of capital (WACC) of the firm is only feasible, at best, for firms that have publicly traded debt and equity. And for projects that have a time-varying capital structure (such as big civil engineering projects that combine various forms of financing, depending on the stage of completion) estimating the WACC is an operational nightmare. Additionally, when the investor is an actual person, the conventional recipe is to use the opportunity cost of a similar investment proposition as a proxy for the correct discount rate. This approach poses a sort of circular reasoning conundrum: how can we judge if two investments have the same risk profile if we don’t know the value of one of them?
- The DCF method assumes that the risk profile of the cash flows is fairly specific. In fact, it assumes that the uncertainty in the cash flows increases with time according to a rigid pattern, which depends on the ratio of the risk-free rate and the risk-adjusted discount rate. It is easy to think of many situations in which the uncertainty pattern of the cash flows might decrease with time, remain more or less the same, or simply vary according to a pattern different from the one imposed by the conventional DCF method. Again, this limitation of the DCF approach is never discussed in standard financial textbooks.
Much of the problems affecting the DCF method come from the fact that it tries to capture with one factor – the discount rate – two completely different effects: the time value of money and the stochastic nature of the cash flows. Not only that, it attempts to transform a problem which is probabilistic in nature (cash flows are uncertain) into a deterministic problem by appealing to the “right” discount rate.
Finance is undergoing a major review of its fundamentals as a result of the subprime mortgage crisis. Markets are more complex, more psychologically driven, more interconnected, and more unstable than previously recognized. The limitations of models based on questionable assumptions (normal distributions, stable volatilities, simplistic utility functions, efficiency of markets, rational decision makers, etc.) are being re-examined. There is no reason to exclude the DCF from this exercise.
In light of these arguments, there is a strong case for refocusing research on valuation techniques. We should abandon efforts aimed at determining the “correct” discount rates. An honest assessment of these efforts inevitably leads to one conclusion: After years of investigating this topic, basic guidelines are as elusive as they were 50 years ago. Instead, we should shift gears and focus on developing good tools aimed at characterizing cash flows probabilistically. That is, at developing tools to estimate their means, standard deviations, and correlations. Moreover, the merits of incorporating into the valuation calculation the benefits that a project could bring to the relevant stakeholders, as well as the risk tolerance of the potential investors, should be explored.
It is, in any event, unacceptable to argue that the complexity of cash flow valuation makes it an exception that can only be handled through amorphous concepts like discount factors and not with the normal rules of probability and statistics.
This post comes to us from Arturo Cifuentes, Ph.D., an adjunct professor of business in the Finance & Economics Division of Columbia University. It is based on his recent paper, “The Discounted Cash Flow (DCF) Method Applied to Valuation: Too Many Uncomfortable Truths” available here.