**Many happy returns **

NPV and IRR are widely used discounted cash-flow methods. But they
can create conflicting signals, say

Stephen Keef and Melvin Roush

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 (Chart
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.

Chart 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
IR seeks to determine whether the increased initial cost is more than
adequately compensated by the increased cash flows in the future -- that is, is
the net present value positive when increased initial cost is compared with
increased cash inflows in the future?

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

However, this is not always the case. Potential problems
encountered with Keynes IRR method are generally known. They are: i) the
conflict with the NPV method; ii) the size or scale effect; iii) that internal
rates of return are not additive; iv) the case of borrowing versus investing
(lending); v) the possibility of multiple returns; vi) the possibility that a
return does not exist; vii) the complications arising with a non-flat-term
structure of interest rates; and viii) 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.

(Edited extracts from Financial Management, a journal of CIMA,
London. www.cimaglobal.com)

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