Discounted Cash Flow (DCF) Analysis: The Need For A New Conceptual Framework Arturo Cifuentes Departamento de Ingenieria Industrial Universidad de Chile August 2011

Table of Contents Introduction The Problem The Standard DCF Approach Issues with the Standard DCF Approach A Better Approach Conclusions

INTRODUCTION

What’s the Ultimate (the Most Fundamental) Financial Question? Answer: How Much Should I Pay for This? OR What’s the Value of This?

THE PROBLEM

More Formally… Time …. N X 1 X 2 X 3 X 4 X N A Financial Asset Generates Future Cash Flows (X 1, X 2, …, X N ) What’s the Value of this Asset? Answer: The Present Value (PV) of These Cash Flows But How Do We Calculate the PV of These Cash Flows?

THE STANDARD DCF APPROACH

Time …. N X 1 X 2 X 3 X 4 X N The Main Issue Is That the Future Cash Flows (X 1, X 2, …, X N ) Are “Uncertain” (Strictly Speaking, They Are Stochastic, NOT Deterministic) The Standard Approach Is To Calculate The Present Value (PV) Using An “Appropriate” Discount Rate In Short…

Time …. N X 1 X 2 X 3 X 4 X N Risk Free Rate R represents the “appropriate” discount rate: (i) WACC (weighted average cost of capital) or (ii) opportunity cost of capital

Time …. N X 1 X 2 X 3 X 4 X N can be rewritten as… Let us disassemble the DCF expression…

Step 1: Bring cash flow X i to time = 0 (time value of money). We discount with the risk free rate Step 2: Reduce the value of the discounted cash flow (due to its uncertain nature) In summary, the standard DCF method consists of two steps…

Alternatively, the standard DCF approach can be interpreted as a special case of the Certainty Equivalent (CE) approach…

NOTE: Implicit behind the certainty equivalent (CE) idea is the Utility Function concept. In fact, invoking the definition of CE, we can write that must satisfy the following relationship

ISSUES WITH THE STANDARD DCF APPROACH

Time …. N X 1 X 2 X 3 X 4 X N PROBLEM # 1. Let Us Assume That All Cash Flows Are Positive. The First, of Course (t=0; Initial Investment) Is Assumed To Be Negative. Implicit in this formula there are two very significant assumptions: (i) The uncertainty associated with the cash flows increases as we move forward in time; and (ii) Furthermore, the uncertainty increases according to a very precise (restrictive) pattern

Time …. N X 1 X 2 X 3 X 4 X N For Example, Take … Time (Years ) λ 3 λ 4 λ 5

Unfortunately, there is no reason to believe that in a general case the cash flows will fit such characterization (uncertainty will grow according to ). In fact, it could well happen that the uncertainty associated with the cash flows could: increase according to a different pattern decrease (following many different decay patterns) exhibit a more complex combination of increase/decrease pattern remain stable over time In all these cases the standard DCF method will give a wrong estimate of the PV of the cash flows

Time …. N X 1 X 2 X 3 X 4 X N PROBLEM #2. Suppose Now That One of the Cash Flows is Negative (an Expenditure); say X 3 = -$ 145 Since x (-145) = the net result is that the standard DCF method underestimates all cash outflows (optimistic with expenditures) In short, in this case the conventional DCF method introduces a systematic error in the valuation process

Time …. N X 1 X 2 X 3 X 4 X N PROBLEM # 3. Suppose Now That All Cash Flows Are Identical (Characterized By the Same Mean and the Same Standard Deviation) It follows then that the CE of all cash flows should be identical; in short CE(X 1 )= …. = CE(X N ). But this is incompatible with the decay function implicitly assumed by the standard DCF approach… Unless we are willing to assume that the Utility Function of the decision maker is a function not only of the Mean and St. Dev. but also is a function of time t. VERY WEIRD!!!!!!

PROBLEM # 4. Assume We Have to Choose Between Two Projects: (A) and (B). Moreover, Assume That the “Level of Uncertainty” in the Cash Flows of (A) [X 1, X 2, …] and (B) [Y 1, Y 2, …] Is Different. (For Example, In Case (A) We Might Have Better Estimates of the Cash Flows). The Standard DCF Method Cannot Deal With This Situation: It Treats The Cash Flows From (A) and (B) As If They Were Subject To the Same “Uncertainty” Same Level of Uncertainty Will Lead to the Wrong Decision

In Summary… Several Problems with the Standard DCF Method – If the cash flows are positive it assumes that (as we move forward in time) the cash flows are subject to an increasing level of uncertainty dictated by a very specific (and peculiar) decay function – Any negative cash flow is treated in a very “forgiving” (overly-optimistic) fashion – Particularly bad when the uncertainty of the cash flows is more or less constant over time (or worse, it goes down) – Particularly bad for situations in which one has to decide between two projects with different levels of uncertainty

A More Philosophical (However Practical) Consideration… [1] The problem in question is interesting because the cash flows (numerator) are uncertain (stochastic). However, the standard DCF approach has chosen to deal with this uncertainty by INCREASING THE VALUE OF THE DENOMINATOR (that is, manipulating the wrong target) [2] As a result, all the efforts have been placed on trying to determine the “correct WACC” (denominator) instead of paying attention to the numerator (Utility Function implicit in the computation) WACC

Other Issues… [3] The conventional DFC method was probably born out of a faulty analogy with the credit (fixed income) market [4] What’s wrong with assuming ?

A BETTER APPROACH

A New Approach Should… Be more intellectually honest (accept the fact that the cash flows are uncertain and treat them accordingly using conventional statistical tools, for example, the way things are handled in the context of portfolio theory) Bring into the picture the risk preferences of the decision-maker (natural person or company)

For example (one possibility, a bit naïve perhaps but… ): Start with the basic relationship… [1] Try to characterize the cash flows in a more “precise” fashion, say, using their means and standard deviations… [2] Incorporate the risk aversion profile of the decision maker openly (via a reasonable utility function) and then calculate the CE of each cash flow: CE(X 1 ), CE(X 2 ), … For instance Risk Aversion Parameter

A second possibility, less naïve… Time value of money Uncertainty of Cash Flows (Correlation Matrix)

Having characterized the cash flows statistically, we can now –using a Utility Function that captures the risk preferences of the decision-maker-- estimate the present value of such cash flows (PV)

This New Approach Is Much Cleaner (And Honest) Conceptually… It Deals Openly and Explicitly (and Separately) With the Three Elements of Any Valuation… [1] Time Value of Money (Discount with the Risk Free Rate) [2] Uncertainty in the Cash Flows (Describes them Using their Means and Standard Deviations) [3] Risk Profile of the Decision Maker (Used in the Calculation of the CE of the Cash Flows via a suitable Utility Function)

CONCLUSIONS

This New Approach Is Very General and Can Accommodate Any Valuation (PV) Computation. However, It Is … Much More Suitable Than The Standard DCF Method for Projects Such As Utilities, Hotels, Regulated Entities, Matured Business and in General any Project in Which the Uncertainty Associated with the Cash Flows Remains Stable or Decrease with Time Much More Useful for Projects in Which There Could be Periods with Negative Cash Flows Better Suited for Situations in Which One Must Select One Project Out of Many Better Suited for Situations in Which the Risk Profile of the Decision Maker Plays a Role

Two Suggestions for the Future… [1] Abandon all research on “What’s the right WACC?” OR “What’s the correct discount rate?” [2] Instead shift the attention to: Different ways to characterize the cash flows using conventional statistical tools Different ways to incorporate into the decision process the risk aversion profile of the decision maker. That is, investigate the structure of different utility functions (different ways to estimate CE(X i ))