Topic 7: Alternative investment appraisal rules, identifying
relevant cash flows and WACC
Activity 8: Net Present Value’s competitors
Alternative investment appraisal rules
We have already explained that the NPV rule is the rule that companies should
use in capital budgeting. However, we need to recognize that in practice firms do use
other criteria. We will shortly look at two in particular (the IRR and the payback rule).
The reasons for doing this are: (i) because firms use them in practice so it’s important
to understand them; and (ii) to point out their deficiencies compared with NPV and, in
the case of the IRR, to show how it might nevertheless result in the same decision as
the NPV rule. This doesn’t really provide a theoretical rationale for the IRR; the NPV
rule is the only rule that we provide a fundamental rationale for, but sometimes a
decision based on the IRR may coincide with a decision based on NPV.
Do companies always and exclusively use the NPV rule?
Despite the theoretical pedigree of the NPV rule and its implementation via
DCF, in practice companies use several alternative investment appraisal rules.
Research by Graham and Harvey (2001)1 shows that firms use IRR as frequently as
NPV and that other techniques such as hurdle rates and payback are also popular.
1
Graham, J.R., Harvey, C.R., 2001. The theory and practice of corporate finance: evidence from the
field, Journal of Financial Economics 60, 187–243.
We focus on two of these alternative investment appraisal rules, i.e. the payback
period rule and the IRR.
The payback period rule
Section 5.2 of chapter 5 of BAF-CF discusses the payback period rule. The
payback period is the number of years needed to recover the initial investment outlay
through accumulated future cash flows. A five year payback rule, for example, means
the firm accepts all projects that recover their initial outlay within 5 years. Let’s take
an example to understand how the payback period rule works.
Example
A new investment project costing £10,000 promises cash flows of £3,000 in
each of the first three years, £4,000 in each of the next two years and £6,000 in
the final year. Investors require a 14% return from this type of project. The
firm operates a three-year payback period rule.
Answer
The payback period is 3¼ years.2 Therefore the firm rejects the project.
Comment
If the firm uses a strict policy on payback periods then it rejects the project.
This is the wrong decision. Look at the large cash flows from the project in
years 4 to 6. Indeed, you should check that the NPV of the project using a
discount rate of 14% is £4,144. This is a simple example that illustrates how
investment decisions using a payback period rule can be in conflict with the
NPV rule.3
One reason why the payback period rule is popular among financial managers
is because it’s easy to compute and understand. It’s possible to argue that it has other
advantages: it encourages cash generation and values early cash flows over later cash
flows. However, it suffers from many disadvantages. One disadvantage of using the
2
When calculating the payback period, the normal convention is to assume that cash flows occur
evenly over the year. Note that this contrasts with NPV calculations where the normal convention is to
assume that cash flows occur at the end of the year.
3
The example illustrates a case where using the payback period rule, the firm rejects a positive NPV
project. The payback period rule can also result in cases where the firm accepts negative NPV projects.
2
payback period rule is that it adds cash flows ignoring the time value of money.
Another disadvantage is that the choice of the cut-off period is arbitrary. If in the
above example the firm uses a payback period of 3½ years instead of 3 years, it
accepts the project. The payback period rule also ignores cash flows after the cut-off
period and is biased towards rejecting long-lived projects that may increase
shareholder wealth. A variant of payback is the discounted payback period rule. The
difference here is that a project’s discounted payback is the number of years until the
firm recovers the initial outlay through discounted cash flows. This criterion takes the
time value of money into account but still ignores cash flows occurring after the
payback cut-off.
So why do so many managers use the payback period rule? BAF-CF guesses
that this could be because managers don’t believe more distant cash-flow forecasts
and therefore disregard them entirely beyond the payback period. Other reasons could
be that a payback period rule may be more persuasive in the capital budgeting
negotiating process. Further, divisions of some firms may use payback because they
perceive a constraint on the size of their capital budget.
The internal rate of return (IRR)
Section 5.3 of BAF-CF introduces the concept of the IRR. The IRR is the rate
that discounts project cash flows to zero.
C0 
C1
C2
CT

 .... 
 0.
2
1  IRR (1  IRR)
(1  IRR)T
Many authorities, including BAF-CF, define the IRR as the discount rate that gives a
zero NPV. We prefer to avoid this terminology because the NPV of a project is the
value of the cash flows discounted at the required capital market rate of return. It’s
better to say that the IRR is the discount rate that gives a zero discounted cash flow
(DCF) value.
Solving for the IRR does not present a challenge if the project has a life of one
or two years. For projects with a life of more than two years, we can use trial and
error (as shown in BAF-CF), Excel [=IRR(values,guess)], or more sophisticated
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iterative procedures. Usually financial managers use scientific calculators to find the
IRR of their projects.
Example
Consider a project that produces the following cash flows:
t0
t1
t2
10,000
8,000
5,625
What is the project’s IRR?
Answer
Solving for the IRR
10000 

8000
5625

0
1  IRR (1  IRR)2
IRR = 25%.
The IRR decision rule is to accept a project if it’s IRR is greater than the cost
of capital. If in the above example the cost of capital is 14% (or, in fact,
anything less than 25%) then the firm should accept this project.
The IRR is “a measure” of the profitability of a project but it is not a true
measure of the return of a T-period project because the company does not re-invest
cash flows in periods 1, …, T1 back into the project. Because the IRR is not a true
return, despite its name, an IRR of 25% does not mean that a firm generates an annual
return of 25% from investing in the project. This is one reason why using the IRR as
a decision rule can result in problems (e.g. a higher IRR is not necessarily better as
this depends on the pattern of cash flows).
As is the case with other capital budgeting tools, IRR is also not without its
problems. BAF-CF shows that solving the IRR equation has a number of pitfalls. Two
of these that merit particular attention are multiple rates of return and ranking
mutually exclusive projects.
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The first, multiple rates of return, is well illustrated in the textbook. If a project
has non-conventional cash flows then the project has multiple IRRs.4
Example
Consider a project that produces the following cash flows.
t0
t1
t2
400
960
572
At what discount rate(s) is the DCF of this project equal to zero?
Answer
You can check that the discounted cash flows of this project are zero at both
10% and 30%, giving two IRRs.
The following diagram illustrates the
solution.
DCF profile
4.00
2.00
0.00
DCF
-2.00
0%
5%
10%
15%
20%
25%
30%
35%
-4.00
-6.00
-8.00
-10.00
-12.00
-14.00
Comment
The example considered here is slightly contrived, but any project that
involves substantial decommissioning costs (e.g. a nuclear power plant) results
in a non-conventional cash flow pattern. In this case, if the opportunity cost of
capital (the market interest rate) is, say, 8%, we could use either IRR of 10%
or 30% and mistakenly infer that because the IRR exceeds the cost of capital,
4
A conventional investment project has an initial negative cash outflow followed by a series of positive
cash inflows.
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the firm should accept the project. In fact, we can see from the diagram that at
a cost of capital of 8%, the project has a negative NPV (of 1.51).
BAF-CF cite Descartes’ ‘rule of signs’ to state that a project can have as many
IRRs as there are changes in the sign of its cash flows. They also show an example
where no (real) IRR exists.
BAF-CF provide a clear discussion of the second problem. This second
problem with IRR arises when the firm has to choose between investment projects.
Selecting the project with the higher IRR does not always result in the highest NPV.
Example
Consider two mutually exclusive projects that produce the following cash
flows.
A
100
80
60
B
60
40
50
Which of these projects should the firm accept?
Answer
The following slide depicts the DCF profiles for these two projects.
40.00
30.00
A
B
20.00
27.18%
10.00
30.52%
21.71%
0.00
0%
10%
20%
-10.00
-20.00
Norman Strong © 2006
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30%
40%
50%
Ranking on the basis of IRR, B has the higher IRR (30.52% v. 27.18%).
However, A has the higher NPV at any cost of capital less than 21.71%.
Comment
As these projects are mutually exclusive, the company must choose one and
reject the other. Project B has the higher IRR, but this is misleading as a
measure of the project’s return as the intermediate cash flow of 40 is not reinvested back in the project. If we instead compare DCFs, we have the
problem that A’s discounted cash flows exceed B’s at any required return less
than 21.71%, while the reverse holds for required returns greater than 21.71%,
where 21.71% is the so-called cross-over rate, which is the discount rate that
equates the DCFs of the two projects. As always, NPV is the proper criterion
so that if the required rate of return is less than 21.71% the company should
accept A, if it is greater than 21.71% but less than 30.52%, the company
should accept B, while the company should reject both projects otherwise. In
relation to this, BAF-CF also discusses the introduction of capital constraints,
which it discusses in detail in Section 5.4.
Section 5.4 of BAF-CF introduces you to the issue of capital rationing, which
we can classify as either soft or hard rationing. Soft rationing is self-imposed whereas
hard rationing results from market imperfections. In an ideal world of perfect capital
markets, firms have access to unlimited capital and therefore should accept every
project with a positive NPV. However, some firms may find themselves facing a
capital constraint in certain situations5 (mostly their own doing) and therefore they
need a method of selecting projects that are (i) within their financing capability and
(ii) provide the highest NPV to the firm. To address this problem, BAF-CF introduces
the profitability index (PI), defining it as the ratio of NPV to initial investment.
However, the PI only works if capital is rationed in only one period and fails when the
rationing exists for more than one period or if there are other constraints on project
choice. In such cases, a firm can employ linear programming to work out the
combination of projects it can finance within the available budget and constraints and
which gives the highest NPV to the firm.
5
As BAF-CF points out, hard rationing will only take place if the markets are imperfect.
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You should now read Sections 5.2 to 5.4 of chapter 5 of BAF-CF and attempt the end
of chapter ‘Basic’ problem sets.
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