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Many happy returns.

NPV and IRR discounted cash flow methods are widely used, but they can create conflicting signals. Stephen Keef and Melvin Roush return to the original theorists for a solution

Irving Fisher and John Keynes were, without doubt, giants among economists. Fisher, in his book The Theory of Interest, introduced the concept of "the rate of return over cost". This is the market-determined rate of interest where the net present value (NPV) of two projects are identical (figure 1). In Keynes' book, The General Theory of Employment Interest and Money, he advanced the concept of the "marginal efficiency of capital". This is the interest rate that sets the NPV of a project to zero. Today, it is known as the internal rate of return (IRR).


There is a strong link between these two concepts. Fisher's rate of return over cost is the internal rate of return of the marginal cash flows of the two projects. In essence, Fisher compared a new project with an existing project, using the example of a farmer contemplating forestry as an optional use of the land.

Keynes' IRR is the rate of return over cost where the project is compared with its opportunity cost derived from the market.

Put this way, the two theories are almost identical. In both cases, the objective yardstick used to gauge the relative merits of the two projects -- the discount rate -- is exogenously derived from the market. The methods differ only in the definition of the status quo. Fisher compared a new project with an existing project, Keynes a new project with the market (which is easy to conceive as an existing project).

These original and insightful thoughts live on today in most management accounting texts. They are manifest in the competing merits of the NPV and IRR methods. These techniques are discussed, to varying degrees, in all management accounting texts when addressing capital budgeting.

They are often known as the discounted cash flow methods since they rely on the concept of discounting. Discounting acknowledges the time preference rate of money; that is to say, a dollar today is worth more than a dollar tomorrow.

It is generally well recognised that the two methods can create conflicting signals in the ranking of two independent projects. Figure 1 shows the conflict that can arise. For a market-derived discount rate greater than the rate of return over cost -- the Fisher rate -- the two methods generate consistent results. Project B is preferable to Project A in terms of both net present value and internal rate of return.

However, a conflict arises for discount rates below the Fisher rate. The internal rates of return remain unchanged, but there is a reversal in the net present values of the two projects. This conflict is a continual headache for supporters of the IRR method. Textbooks are full of adjustments designed to overcome the defects of the IRR method.

One possible solution to the NPV versus IRR conflict focuses on the internal rate of return on the marginal, or incremental, cash flows of the two projects. The marginal internal rate of return, the Fisher rate, can be used to determine whether it is advantageous to invest in the project with the greater original cost. The argument is compelling.

In essence, the cash flows from the smaller project, in terms of initial outlay, are subtracted from the cash flows of the larger project. Careful attention is paid to the matching of their time and size. The marginal IRR seeks to determine whether the increased initial cost is more than adequately compensated by the increased cash flows in the future -- ie, is the net present value positive when the increased initial cost is compared with the increased cash inflows in the future?

The conflict has been translated into the accept/reject decision of an independent project -- the Keynes IRR (figure 2). Some people believe this method can generate the correct signal in this environment.


However, this is not always the case. The potential problems encountered with the Keynes IRR method are generally well known. They are:

* the conflict with the NPV method;

* the size or scale effect;

* that internal rates of return are not additive;

* the case of borrowing v investing (lending);

* the possibility of multiple returns;

* the possibility that a return does not exist;

* the complications arising with a non-flat-term structure of interest rates;

* the difficulty in accommodating differences in systematic risk.

There is no doubt that the marginal IRR can suffer from some of the same problems as the Keynesian IRR. But the marginal project would seem to have eliminated the conflict with the NPV method. We can ignore the scale effect and the non-additive effect -- irrelevant in a Keynesian IRR context. We can also ignore the borrowing versus lending problem, since it can be assumed that the cash flows of the smaller project, in terms of initial cost, are subtracted from the cash flows of the larger project.

But what about the other problems? Can we brush these aside once we have discovered the blinding insight of using marginal cash flows? The answer, we believe, is no.

First, there is the possibility that the IRR on the marginal project may have more, or less, than one internal rate of return. The absence of a solution shows that the marginal IRR method "falls over" since it just cannot arrive at a ranking conclusion for those situations. Some may raise the weak counter argument that this is not a serious problem since the conflict is probably also absent. A prudent manager, however, would not want to rely on this doubtful defence of the marginal IRR.

A standard protection for multiple internal rates of return is to use a modified IRR (MIRR) method. The MIRR method should address the multiple return problem in the context of Keynes' IRR. But we believe it is a pity to go only this far when a better tool is available much closer to home. MIRR is just one small step away from the NPV method.

Second, the presence of a team structure in the market-determined discount rate is a, problem that is not adequately addressed by the IRR method. Fisher and Keynes were instrumental in the development of term structure theories. The suggestion that the term structure is invariably ignored in a practical capital budgeting setting is seductive.

We need to be aware of the potential differences in the systematic riskiness of the two projects. The marginal IRR method just cannot cope with this problem. The application of the NPV method to the marginal cash flows is also flawed in this respect. The problem -- an intractable one -- is in the determination of the risk-adjusted discount rate for the marginal cash flows.

We are left with the conclusion that the marginal IRR will not always produce the same signal as the NPV method -- something made clear with the Keynes IRR, but not always with the marginal IRR method.

The practical economic importance of the defects of the marginal IRR method is debatable -- different people will naturally have different views. There is always the chance that the defects may be relatively uncommon and their economic significance small.

That aside, the insidious problem is that it is not immediately obvious from the calculated internal rate of return when these problems are present. One answer, for those addicted to the IRR method, is to use the NPV method to confirm the validity of the IRR decision. It is widely recognised that this method always provides the correct economic signal concerning the different wealth effects of two projects.


I Fisher, The Theory of Interest, Macmillan, New York, 1930 (reprinted 1986)

J M Keynes, The General Theory of Employment Interest and Money, Macmillan, 1936

Stephen Keef and Melvin Roush are senior lecturers at the faculty of commerce and administration at Victoria University of Wellington, New Zealand
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Author:Keef, Stephen; Roush, Melvin
Publication:Financial Management (UK)
Geographic Code:4EUUK
Date:Jun 1, 2001
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