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Chapter Four
Discounting and Alternative
Investment Criteria
4.1 Introduction This chapter discusses the alternative investment criteria commonly used
in the appraisal of investment projects. The net present value (NPV) of a
project criterion is widely accepted by accountants, financial analysts,
and economists as the one that yields the correct project choices in all
circumstances. However, some decision-makers have frequently relied
upon other criteria, such as the internal rate of return (IRR), the
benefit–cost ratio (BCR), the pay-back period, and the debt service
coverage ratio. The strengths and weaknesses of these criteria are
examined in this chapter in order to demonstrate why the NPV criterion
is the most reliable.
Section 4.2 explains the concept of discounting and discusses the
choice of discount rate. Section 4.3 elaborates on and compares
alternative investment criteria for the appraisal investment projects.
Conclusions are made in the final section.
4.2 Time Dimension of a Project
Investment decisions are fundamentally different from consumption
decisions. For example, fixed assets such as land and capital equipment
are purchased at one point in time, and are expected to generate net cash
flows, or net economic benefits, over a number of subsequent years. To
determine whether the investment is worthwhile, it is necessary to
compare its benefits and costs with those of alternative projects, which
may occur at different time periods. A dollar spent or received today is
worth more than a dollar spent or received in a later time period. It is not
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possible simply to add up the benefits and the costs of a project to see
which are greater without taking account of the fact that amounts spent
on investment today are worth more today than the same amount
received as a benefit in the future.
The time dimension of a project’s net cash flows and net economic
benefits can be captured by expressing the values in terms of either
future or present values. When moving forward in time to compute future
values, analysts must allow for the compounding of interest rates. In
contrast, when bringing future values back to the present for comparison
purposes, it is necessary to discount them. Discounting is simply the
inverse of compounding.
4.2.1 Time Value of Money
Time enhances the value of a dollar today and erodes the value of a
dollar spent or received in the future. It is necessary to compensate
individuals for forgoing their consumption today or lending their funds to
a bank. In turn, banks and other financial institutions have to offer
lenders interest in order to induce them to part temporarily with their
funds. If the annual market interest rate is 5 percent, then 1 dollar today
would be worth 1.05 dollars one year in the future. This means that in
equilibrium, lenders value 1.05 dollars in one year’s time the same as 1
dollar today.
4.2.2 Compounding
There are two main ways in which interest can be included in future
values, namely simple interest and compound interest. Simple interest is
paid only on the principal amount that is invested, while compound
interest is paid on both the principal and the interest as it accumulates.
Compound interest, which is the most commonly used way of charging
interest, can cause the future value of 1 dollar invested today to increase
by substantially more than simple interest over time. The difference is
caused by the interest on the cumulative interest. The formula for
compound interest payment is Vt = (1+r)t, where Vt stands for the value
in Year t of 1 dollar received in Year 0, and r denotes the rate of interest.
Interest may be compounded annually. However, it is common for
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interest to be compounded more frequently, for example, semi-annually,
quarterly, monthly, or even daily. The number of compounding intervals
will also affect the future value of an amount of cash invested today.
Thus, the two factors affecting the future value of a dollar invested today
are the time period of the investment and the interest rate.
Furthermore, when comparing two debt contracts, it is essential that
they be judged on the basis of equivalent rates, for example, annual rates
in the case of loan agreements, and semi-annual rates in the case of
bonds. The magnitude of the interest rate is certainly a major determinant
of the future value of a series of cash flow items.
4.2.3 Discounting
The discount factor allows the present value of a dollar received or paid
in the future to be calculated. Since this involves moving backward
rather than forward in time, the discount factor is the inverse of the
compound interest factor. For example, an amount of 1 dollar now will,
if invested, grow to (1+r) a year later. It follows that an amount B to be
received in n years in the future will have a present value of B / (1+r)n.
The greater the rate of discount used, the smaller its present value.
The nature of investment projects is such that their benefits and costs
usually occur in different periods over time. The NPV of a future stream
of net benefits, (B0 − C0), (B1 − C1), (B2 − C2), …., (Bn − Cn), can be
expressed algebraically as follows:
= (4.1)
where n denotes the length of life of the project. The expression 1 / (1+r)t
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is commonly referred to as the discount factor for Year t.
For the purposes of illustration, the present value of the stream of net
benefits over the life of an investment is calculated in Table 4.1 by
multiplying the discount factors, which are given in line 4, by the values
of the net benefits for the corresponding periods, shown in line 3. The
NPV of $1,000 is the simple sum of the present values of net benefits
arising each period throughout the life of the project.
Table 4.1: Calculating the Present Value of Net Benefits from an
Investment Project (dollars)
Items 0 1 2 3 4 5
1. Benefits 3,247 4,571 3,525 2,339
2. Costs 5,000 2,121 1,000 1,000 1,000 1,000
3. Net benefits (= 1−2) −5,000
−2,12
1 +2,24
7 +3,5
71 +2,52
5 +1,33
9
4. Discount factor at 6%
(= 1 / (1+r)t) 1.000 0.943 0.890 0.840 0.792 0.747
5. Present values (= 43) −5,000
−2,00
0 +2,00
0 +3,0
00 +2,00
0 +1,00
0
6. NPV 1,000
Equation (4.1) shows that the net benefits arising during the project’s
life are discounted to Year 0. Instead of discounting all the net benefit
flows to the initial year of a project, we could evaluate the project’s
stream of net benefits as of a year k, which does not even need to fall
within the project’s expected life. In this case, all the net benefits arising
from Year 0 to Year k must be cumulated forward at a rate of r to Year k.
Likewise, all net benefits associated with years k+1 to n are discounted
back to Year k at the same rate r. The expression for the NPV as of Year
k becomes:
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= [(Bt − Ct) (1+r)k-t
]
= [(Bt − Ct) / (1+r)t] (1+r)
k
(4.2)
The term (1+r)k is a constant value as it is a function of the discount
rate and the date to which the present values are calculated. The rankings
of alternative projects will not be altered if the project’s net benefits are
discounted to Year k instead of Year 0. The present values of their
respective net benefits discounted at Year 0 are all multiplied by the
same constant term. Hence, the ranking of the NPVs of the net benefits
of the alternative projects will not be affected.
4.2.4 Variable Discount Rates
Up to this point it has been assumed that the discount rate remains
constant throughout the life of a project. This need not be the case.
Suppose that funds are presently very scarce relative to the historical
experience of the country. In such circumstances, the cost of funds would
be expected to be currently abnormally high, and the discount rate is
likely fall over time as the supply and demand for funds return to normal.
On the other hand, if funds are abundant at present, the cost of funds and
the discount rate would be expected to be below their long-term average.
In this case, the discount rate would be expected to rise as the demand
and supply of funds return to their long-term trend over time. This
process is illustrated in Figure 4.1.
Figure 4.1: Adjustment of Cost of Funds through Time
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Suppose that the discount rates will vary from year to year over the
life of a four-year project. The discount rate r1 is the cost of capital, or
the rate of discount extending from Year 0 to Year 1. The NPV of the
project should be calculated as:
where r1, r2, and r3 are the discount rates for Year 1, Year 2, and Year 3,
respectively. Each discount factor after Year 2 will be made up of more
than one discount rate. For example, the discount factor for Year 3’s net
benefits is 1/[(1+r1)(1+r2)(1+r3)]. The general expression for the NPV of
the project with a life of n years, evaluated as of Year 0, becomes:
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NPV0 = (B0 − C0) +
(4.3)
As in the case of the constant rate of discount, when comparing two
or more projects, the period to which the net benefits of the projects are
discounted does not matter, provided that the present values of the net
benefits of each of the projects being compared are discounted to the
same date.
4.2.5 Choice of Discount Rate
The discount rate is a key variable in the application of investment
criteria for project selection. Choosing the discount rate correctly is
critical given the fact that a small variation in its value may significantly
alter the results of the analysis and affect the final choice of a project.
The discount rate, stated in simple terms, is the opportunity cost of
funds that are invested in the project. In financial analysis, the discount
rate depends upon the viewpoints of analysis. For instance, when a
project is being appraised from the point of view of the equity holders,
the relevant cost of funds is the return to equity that is being earned in its
alternative use. Thus, if the equity holders are earning a return of
15percent on their current investments and decide to invest in a new
project, the cost of funds, or the discount rate, from their perspective for
the new project is 15 percent.
When an economic analysis of a project is being conducted, the
relevant discount rate is the economic opportunity cost of capital for the
country. Estimating this cost starts with the capital market as the
marginal source of funds, and involves determining the ultimate sources
of funds obtained via the capital market and estimating the respective
cost of each source. The funds are generally drawn from three sources.
First, funds that would have been invested in other investment activities
have now been displaced by the project. The cost of these funds is the
gross-of-tax return that would have been earned by the alternative
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investments, which have now been forgone. Second, funds come from
different categories of savers in the economy, who postpone some of
their consumption in the expectation of obtaining a return on their
savings. The cost of this part of the funds is the cost of postponing this
consumption. Third, some funds may be coming from abroad, that is,
from foreign savers. The cost of these funds is the marginal cost of
foreign borrowing. Thus, the economic opportunity cost of capital will
simply be a weighted average of the costs of funds from three alternative
sources. The detailed methodology for measuring the economic
opportunity cost of capital will be discussed later.
4.3 Alternative Investment Criteria
Various criteria have been used in the past to evaluate whether an
investment project is financially and economically viable. In this section,
six of these criteria will be reviewed, namely the NPV, the IRR, the BCR,
the pay-out or pay-back period, the debt service coverage ratio, and
cost-effectiveness.
4.3.1 Net Present Value Criterion
The NPV is the algebraic sum of the present values of the expected
incremental net cash flows for a project over the project’s anticipated
lifetime. It measures the change in wealth created by the project.
a) When to Accept and Reject Projects
If the NPV of the project is 0, investors can expect to recover their
incremental investment and also earn a rate of return on their capital that
would have been earned elsewhere and is equal to the private discount
rate used to compute the present values. This implies that investors
would be neither worse nor better off than they would have been if they
had left the funds in the capital market. A positive NPV for a project
means that investors can expect not only to recover their capital
investment but also to receive a rate of return on capital higher than the
discount rate. However, if the NPV is less than 0, investors cannot expect
to earn a rate of return equal to the discount rate, nor can they expect to
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recover their invested capital, and, hence, their real net worth is expected
to decrease. Only projects with a positive NPV are attractive to private
investors. Such investors are unlikely to pursue a project with a negative
NPV unless there are strategic reasons for doing so. Many of these
strategic reasons can also be evaluated in terms of their NPVs through
the valuation of the real options made possible by the strategic project.
This leads to Decision Rule 1 of the NPV criterion, which holds under all
circumstances.
Rule 1: Do not accept any project unless it generates a positive NPV
when discounted by the opportunity cost of funds.
b) Budget Constraints
Often, investors cannot obtain sufficient funds to undertake all the
available projects that have a positive NPV. This is also the case for
governments. When such a situation arises, a choice must be made
between the projects to determine the subset that will maximize the NPV
produced by the investment package while fitting within the budget
constraint. Thus, Decision Rule 2 is:
Rule 2: Within the limit of a fixed budget, choose the subset of the
available projects that maximizes the NPV.
Since a budget constraint does not require that all the money be spent,
the rule will prevent any project that has a negative NPV from being
undertaken. Even if not all the funds in the budget are spent, the NPV
generated by the funds in the budget will be increased if a project with a
negative NPV is dropped from consideration. It should be kept in mind
that the funds assigned by the budget allocation but not spent will simply
remain in the capital market and continue to generate a rate of return
equal to the economic opportunity cost of capital.
Suppose the following set of projects describes the investment
opportunities faced by an investor with a fixed budget for capital
expenditures of $4.0 million:
Project A Project B Project C Project D
PV investment
costs $1.0 milli
on $3.0 milli
on $2.0 milli
on $2.0 milli
on
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NPV of net
benefits +$60,000 +$400,00
0 +$150,00
0 +$225,00
0
Given a budget constraint of $4 million, all possible combinations
that fit within this constraint would be explored. Combinations BC and
BD are not feasible as they cost too much. AC and AD are within the
budget, but are overshadowed by the combination AB, which has a total
NPV of $460,000. The only other feasible combination is CD, but its
NPV of $375,000 is not as high as that of AB. If the budget constraint
was expanded to $5 million, Project A should be dropped and Project D
undertaken in conjunction with Project B. In this case, the NPV from this
package of projects (BD) is expected to be $625,000, which is greater
than the NPV of the next best alternative (BC), $550,000.
Suppose that Project A, instead of having an NPV of +$60,000, has
an NPV of −$60,000. If the budget constraint was still $4.0 million, the
best strategy would be to undertake only Project B, which would yield an
NPV of $400,000. In this case, $1 million of the budget would remain in
the capital market, even though it is the budget constraint that is
preventing the undertaking of potentially favourable Projects C and D.
c) No Budget Constraints
In evaluating investment projects, situations are often encountered in
which there is a choice between mutually exclusive projects. It may not
be possible for all projects to be undertaken, for technical reasons. For
example, in building a road between two towns, there are several
different qualities of road that can be built, given that only one road will
be built. The problem facing the investment analyst is to choose from
among the mutually exclusive alternatives such that the project will yield
the maximum NPV. This can be expressed as Decision Rule 3:
Rule 3: When there is no budget constraint but a project must be
chosen from mutually exclusive alternatives, investors should always
choose the alternative that generates the largest NPV.
Consider three projects — E, F, and G — that are mutually exclusive for technical reasons and have the following characteristics:
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Project E Project F Project G
PV investment
costs $1.0 million $4.0 million $1.5 million
NPV of net
benefits +$300,000 +$700,000 +$600,000
In this situation, all three are good potential projects that would yield a
positive NPV. However, only one can be undertaken.
Project F involves the highest expenditure; it also has the largest
NPV, $700,000. Thus, Project F should be chosen. Although Project G
has the highest NPV per dollar of investment, this is not relevant if the
discount rate reflects the economic opportunity cost of the funds. If
Project F is undertaken rather than Project G, there is an incremental gain
in NPV of $100,000 over and above the opportunity cost of the
additional investment of $2.5 million. Therefore, Project F is preferred. It
is worth pointing out that the NPV of a project measures the value or
surplus generated by a project over and above what would be gained or
generated by these funds if they were not used in the project in question.
d) Projects with Different Lifetimes
In some situations, an investment in a facility such as a road can be
carried out in a number of mutually exclusive ways. For example, the
road services could be provided by a series of projects with short lives,
such as installing a gravel surface, or by ones with longer lives, such as
installing a paved surface. If the return on the expansion of the facility
over its lifetime is such as to be an investment opportunity that would
yield a significantly positive NPV, it would not be meaningful to
compare the NPV of a project that produced road services for the full
duration with the NPV of a project that produced road services for only
part of the period. The same issue arises when alternative investment
strategies are evaluated for power generation. It is not correct to compare
the NPV of a gas turbine plant with a life of ten years to a
coal-generation station having a life of 30 years. In such a case, the
comparison must be between investment strategies that have
approximately the same length of life. This may involve comparing a
series of gas turbine projects followed by other types of generation that
in total have the same length of life as the coal plant.
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When projects of short duration lead to further projects that yield
supra-marginal returns, the comparison of alternative projects of
different lengths that will provide the same services at a point in time
will require adjustments to be made to investment strategies so that they
span approximately the same period of time. One such form of
adjustment is to consider the same project being repeated through time
until the alternative investment strategies have the same duration.
Consider the following three types of road surface.
Alternative Investment Projects Duration of Road
A: Gravel surfaced road 3 years
B: Gravel-tar surfaced road 5 years
C: Asphalt surface road 15 years
Comparing the NPVs of these three alternatives lasting three, five,
and fifteen years could produce misleading results. However, it is
possible to make a correct comparison of these projects by constructing
an investment strategy consisting of five gravel road projects, each
undertaken at a date in the future when the previous one is worn out. A
comparison could then be made of five gravel road projects, extending
15 years into the future, with three tar surface roads and one asphalt road
of 15-year duration. This comparison can be written as follows:
Alternative Strategies Duration of Road
(i) (A + A + A + A +
A) 15 years (i.e., 1–3, 4–6, 7–9, 10–12, 13–15)
(ii) (B + B + B) 15 years (i.e., 1–5, 6–10, 11–15)
(iii) (C) 15 years (i.e., 1–15)
Alternatively, it might be preferable to consider investment strategies
made up of a mix of different types of road surfaces through time, such
as:
Alternative Strategies Duration of Road
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(iv) (A + A + A + B +
C) 29 years (i.e., 1–3, 4–6, 7–9, 10–14, 15–29)
(v) (A + B + B + C) 28 years (i.e., 1–3, 4–8, 9–13, 14–28)
In this situation, a further adjustment should be made to the 29-year
strategy (iv) to make it comparable to strategy (v), which is expected to
last for only 28 years. This can be done by calculating the NPV of the
project after dropping the benefits accruing in Year 29 from the NPV
calculation, while at the same time multiplying the present value of its
costs by the fraction (PVB1–28)/PVB, where PVB denotes the present
value of the benefits of the entire strategy, including year 29, and
PVB1–28 is the present value of the benefits that arise in the first 28 years
of the project’s life. In this way, the present value of the costs of the
project are reduced by the same fraction as the present value of its
benefits so that it will be comparable in terms of both costs and benefits
to the strategy with the shorter life.
Although the NPV criterion is widely used in making investment
decisions, alternative criteria are also frequently employed. Some of
these alternatives have serious drawbacks compared with the NPV
criterion and are therefore judged to be not only less reliable but also
potentially misleading. When two or more criteria are used to appraise a
project, there is a chance that they will point to different conclusions, and
a wrong decision could be made (see, e.g., Ley, 2007). This creates
unnecessary confusion and, potentially, mistakes.
4.3.2 Internal Rate of Return Criterion
The IRR for a project is the discount rate () that is obtained by the solution of the following equation:
[(Bj − Cj) / (1+)j] = 0
(4.4)
where Bj and Cj are the respective cash inflow and outflow in Year j to
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capital. This definition is consistent with the meaning of an NPV of 0:
that investors recover their invested capital and earn a rate of return equal
to the IRR. Thus, the IRR and the NPV criteria are related in terms of the
way they are derived. To calculate the NPV, the discount rate is given
and used to find the present value of benefits and costs. In contrast, when
finding the IRR of a project, the procedure is reversed by setting the
NPV of the net benefit stream to 0.
The IRR criterion has seen considerable use by both private and
public sector investors as a way of describing the attractiveness of a
particular project. However, it is not a reliable investment criterion, as
there are several problems associated with it.
Problem 1: The IRR may not be unique
The IRR is, strictly speaking, the root of a mathematical equation. The
equation is based on the time profile of the incremental net cash flows,
like those in Figure 4.2. If the time profile crosses the horizontal axis
from negative to positive only once, as in Figure 4.2 a), the root, or IRR,
will exist. However, if the time profile crosses the axis more than once,
as in Figure 4.2 b) and Figure 4.2 c), it may not be possible to determine
a unique IRR. Projects whose major items of equipment must be replaced
from time to time will give rise to periodic negative net cash flows in the
years of reinvestment. Road projects have this characteristic, as major
expenditures on resurfacing must be undertaken periodically for them to
remain serviceable.
Figure 4.2: Time Profiles of the Incremental Net Cash Flows for
Various Types of Projects
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There are also cases in which the termination of a project entails
substantial costs. Examples of such situations are the land reclamation
costs required to meet environmental standards at the closing down of a
mine, or the agreement to restore rented facilities to their former state.
These cases are illustrated by Figure 4.2 c). These project files may yield
multiple solutions for the IRR; these multiple solutions, when present,
represent a problem of proper choice of the rate of return.
Consider the simple case of an investment of $100 in Year 0, a net
benefit of $300 in Year 1, and a net cost of $200 in Year 2. The solutions
for the IRR are 0 and 100 percent.
Even when the IRR can be unambiguously calculated for each
project under consideration, its use as an investment criterion poses
difficulties when some of the projects in question are strict alternatives.
This can arise in three ways: projects require different sizes of
investment, projects are of different durations, and projects represent
different timings for a project. In each of these three cases, the IRR can
lead to the incorrect choice of project.
Problem 2: Projects of different scale
The problem of having to choose between two or more mutually
exclusive projects arises quite frequently. Examples include two
alternative buildings being considered for the same site and a new
highway that could run down two alternative rights of way. Whereas the
NPV takes explicit account of the scale of the project by means of the
investment that is required, the IRR ignores the differences in scale.
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Consider a case in which Project A has an investment cost of $1,000
and is expected to generate net cash flows of $300 each year in
perpetuity. Project B is a strict alternative and has an investment cost of
$5,000. It is expected to generate net cash flows of $1,000 each year in
perpetuity. The IRR for Project A is 30 percent (ρA = 300/1,000), while
the IRR for Project B is 20 percent (ρB = 1,000/5,000). However, the
NPV of Project A using a 10 percent discount rate is $2,000, while the
NPV of Project B is $5,000.
In this example, if a choice is made between Projects A and B, the
IRR criterion would lead to Project A being chosen because it has an
IRR of 30 percent, which is higher than the 20 percent for Project B.
However, the fact that Project B is larger enables it to produce a greater
NPV even if its IRR is smaller. Thus, the NPV criterion indicates that
Project B should be chosen. This illustration demonstrates that when a
choice has to be made among mutually exclusive projects with different
sizes of investment, the use of the IRR criterion can lead to the incorrect
choice of projects.
Problem 3: Projects with different lengths of life
In this case there are two projects, C and D. Project C calls for the
planting of a species of tree that can be harvested in five years, while
Project D calls for the planting of a type of tree that can be harvested in
ten years. The investment costs are the same for both projects at $1,000.
It is also assumed that neither of the projects can be repeated. The two
projects can be analyzed as follows:
Project C Project D
Investment costs: $1,000 in Year 0 $1,000 in Year 0
Net benefits: $3,200 in Year 5 $5,200 in Year 10
NPV criterion @ 8%:
= $1,178 =
$1,409
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<
IRR criterion: C
= 26.2% D
= 17.9%
C>
D
According to the NPV criterion, Project D is preferred. However, the
IRR of Project D is smaller than that of Project C. Thus, the IRR
criterion is unreliable for project selection when alternative projects have
different lengths of life.
Problem 4: Projects with different timing
Suppose two projects, E and F, are started at different times and both last
for one year. Project F is started five years after Project E. Both projects
have investment costs of $1,000. They are summarized as follows:
Project E Project F
Investment costs: $1,000 in Year 0 $1,000 in Year 5
Net benefits: $1,500 in Year 1 $1,600 in Year 6
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NPV criterion @ 8%:
= $389 =
$328
>
IRR criterion: E
= 50% F
= 60%
E<
F
Evaluating these two projects according to the NPV criterion would
indicate that Project E should be chosen over Project F because
> . However, the fact that E<
F
suggests that Project F should be chosen if the IRR criterion is used.
Again, because Projects E and F are strict alternatives, use of the IRR
criterion can result in the incorrect choice of project being made.
Problem 5: Irregularity of cash flows
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In many situations the cash flows of a project may be negative in a single
(investment) period, though this does not occur at the beginning of the
project. An example of such a situation would be a
build–operate–transfer (BOT) arrangement from the point of view of the
government. During the operating stage of this project, the government is
likely to receive tax benefits from the private operator. At the point when
the project is turned over to the public sector, the government has agreed
to pay a transfer price. Such a cash flow from the government’s point of
view can be illustrated as Project A in Table 4.2, where the transfer price
at the end of the contract is $8,000.
Table 4.2: IRR for Irregular Cash Flows
Year 0 1 2 3 4 IRR
Project A 1,000 1,200 800 3,600 −8,000
10%
Project B 1,000 1,200 800 3,600 −6,400
−2%
Project C 1,000 1,200 800 3,600 −4,800
−16
%
Project D −1,000
1,200 800 3,600 −4,800
4%
Project E −1,325
1,200 800 3,600 −4,800
20%
Results:
Project B is obviously better than Project A, yet
IRRA > IRRB.
Project C is obviously
better than Project B, yet IRRB > IRRC.
Project D is worse than Project C, yet IRRD >
IRRC.
Project E is worse than
Project D, yet IRRE >
IRRD.
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This four-year project has an IRR of 10 percent. However, suppose
the negotiators for the government were successful in obtaining a lower
transfer price at the end of the private sector’s contract period. The
situation where the contract price is reduced to $6,400 is shown as
Project B. Everything else is the same as Project A except for the lower
transfer payment at the end of that period. In this case, the IRR falls from
10 to −2 percent. It is obvious that the arrangement under Project B is
better for the government than Project A, yet it has a lower IRR. If the
transfer price were reduced further to $4,800, the IRR falls to −16
percent, yet it is obvious that it is a better project than either Project A or
Project B.
Now consider the situation if the government were required to pay an
amount of $1,000 at the start of the project in addition to a final transfer
price of $4,800 at the end. It is obvious that this is an inferior
arrangement (Project D) for the government over the previous one
(Project C), in which no upfront payment is required. However,
according to the IRR criterion, it is a much improved project, with an
IRR of 4percent.
In the final case, Project E, the situation for the government is made
worse by requiring an upfront fee of $1,325 in Year 0, in addition to the
transfer price of $4,800 in Year 4. Yet according to the IRR criterion, the
arrangement is more attractive with an IRR of 20 percent.
None of these situations are unusual. Such patterns in the case flow
are common in project finance arrangements. However, the IRR is found
to be a highly unreliable measure of the financial attractiveness of such
arrangements when irregular cash flows are likely to exist.
4.3.3 Benefit–Cost Ratio Criterion
The BCR, sometimes referred to as the profitability index, is the ratio of
the present value of the cash inflows (or benefits) to the present value of
the cash outflows (or costs) using the opportunity cost of funds as the
discount rate:
-
Using this criterion, in order for a project to be acceptable, the BCR
must have a value greater than 1. Moreover, for choices between
mutually exclusive projects, the rule would be to choose the alternative
with the highest BCR.
However, this criterion may produce an incorrect ranking of projects
if the projects differ in size. Consider the following cases of mutually
exclusive projects A, B, and C:
Project A Project B Project C
PV investment costs $1.0 million $8.0 million $1.5 million
PV benefits $1.3 million $9.4 million $2.1 million
NPV of net benefits $0.3 million $1.4 million $0.6 million
BCR 1.3 1.175 1.4
In this example, if the projects were ranked according to their BCRs,
Project C would be chosen. However, since the NPV of Project C is less
than the NPV of Project B, the ranking of the projects should result in
Project B being selected; thus, the BCR criterion would lead to an
incorrect investment decision.
The second problem associated with the use of the BCR, and perhaps
its most serious drawback, is that the BCR of a project is sensitive to the
way in which costs are defined in setting out the cash flows. For example,
if a good being sold is taxed at the manufacturer’s level, the cash flow
item for receipts could be recorded either net or gross of sales taxes.
In addition, costs can also be recorded in more than one way.
Suppose that a project has the recurrent costs. In this case, the BCR will
be altered by the way these costs are accounted for. All the costs and
benefits are discounted by the cost of capital at 10 percent and expressed
in dollars.
Project D Project E
PV investment costs $1,200 $100
PV gross benefits $2,000 $2,000
PV recurrent costs $500 $1,800
-
If the recurrent costs are netted out from cash inflows, Project E
would be preferred to Project D according to the BCR because:
BCRD = (2,000 − 500)/1,200 = 1.25 BCRE
= (2,000 − 1,800)/100 = 2.00
However, if the recurrent costs are instead added to the present value of
cash outflows, Project D appears to be more attractive than Project E:
BCRD = 2,000/(500 + 1,200) = 1.18
BCRE = 2,000/(1,800 + 100) = 1.05
Hence, the ranking of the two projects can be reversed depending on the
treatment of recurrent costs in the calculation of the BCR. On the other
hand, the NPV of a project is not sensitive to the way the costs are
treated, and therefore, it is far more reliable than the BCR as a criterion
for project selection.
4.3.4 Pay-Out or Pay-Back Period
The pay-out or pay-back period measures the number of years it will take
for the net cash flows to repay the capital investment. Projects with the
shortest pay-back period are preferred. This method is easy to use when
making investment decisions. The criterion puts a large premium on
projects that have a quick pay-back, and thus, it has been a popular
criterion in making business investment choices.1 Unfortunately, it may
provide the wrong results, especially in the case of investments with a
long life, where future net benefits are known with a considerable degree
of certainty.
In its simplest form, the pay-out period measures the number of
years it will take for the undiscounted net cash flows to repay the
investment. A more sophisticated version of this rule compares the
discounted benefits over a number of years from the beginning of the
project with the discounted investment costs. An arbitrary limit may be
set on the maximum number of years allowed, and only those
investments that have enough benefits to offset all investment costs
within this period will be acceptable.
1 This criterion has similar characteristics to the loan life cover ratio (LLCR)
used by bankers. This might explain its continued use in business
decision-making.
-
The use of the pay-back period as an investment criterion by the
private sector is often a reflection of a high level of risk, especially
political risk. Suppose a private venture is expected to receive a subsidy
or be allowed to operate only as long as the current government is in
power. In such circumstances, in order for a private investor to go ahead
with this project, it is critical that the pay-back period of the project is
shorter than the expected tenure of the government.
The implicit assumption of the pay-out period criterion is that
benefits accruing beyond the time set as the pay-out period are so
uncertain that they should be disregarded. It also ignores any investment
costs that might occur beyond that date, such as the landscaping and
replanting costs arising from the closure of a strip mine. While the future
is undoubtedly more uncertain than the present, it is unrealistic to assume
that beyond a certain date, the net benefits are 0. This is particularly true
for long-term investments such as bridges, roads, and dams. There is no
reason to expect that all quick-yielding projects are superior to long-term
investments.
As an example, two projects are illustrated in Figure 4.3. Both are
assumed to have identical capital costs (i.e., Ca = C
b). However, the
benefit profiles of the two projects are such that Project A has greater
benefits than Project B in each period until Period t*. From Period t
* to tb,
Project A yields 0 net benefits, but Project B yields positive benefits, as
shown in the shaded area.
With a pay-out period of t* years, Project A will be preferred to
Project B because for the same costs, it yields greater benefits earlier.
However, in terms of the NPV of the overall project, it is very likely that
Project B, with its greater benefits in later years, will be significantly
superior. In such a situation, the pay-back period criterion would give the
wrong recommendation for the choice between investments.
Figure 4.3: Comparison of Two Projects with Differing Lives using
Pay-out Period
-
4.3.5 Debt Service Coverage Ratios
The debt service coverage ratio is a key factor in determining the ability
of a project to pay its operating expenses and to meet its debt servicing
obligations. It is used by bankers who want to know the annual debt
service capacity ratio (ADSCR) of a project on a year-to-year basis, and
to obtain a summary ratio of the loan life cover ratio (LLCR) (Yescombe,
2002).
The ADSCR is the ratio of the annual net cash flow of the project
over the amount of debt repayment due. It is calculated on a year-to-year
basis as follows:
ADSCRt = [ANCFt / (Annual Debt Repaymentt)]
where ANCFt is annual net cash flow of the project before financing for
Period t and Annual Debt Repaymentt is annual interest expenses and
principal repayment due in the specific period t of the loan repayment
period.
The overall project’s LLCR is calculated as the present value of net
cash flows divided by the present value of loan repayments from the
current period t to the end period of loan repayment:
LLCRt = PV(ANCFt to end year of debt) /
PV(Annual Debt Repaymentt to end year of debt)
where PV(ANCFt to end year of debt) and PV(Annual Debt Repaymentt to end year of
-
debt) are the sum of the present values of annual net cash flows and annual
debt repayments, respectively, over the current period t to the end of loan
repayment. The discount rates used are the same as the interest rate being
paid on the loan financing. The LLCR tells the banker whether there is
enough cash from the project to make bridge financing in one or more
specific periods when there is inadequate cash flow to service the debt.
Table 4.3 illustrates the example of an investment of $2 million
being undertaken with a proposal for financing that includes a loan of
$1 million bearing a nominal interest rate of 15percent, with a
repayment period of five years (with an equal repayment) beginning one
year after the loan is given. The required rate of return on equity is
assumed at 20 percent.
Table 4.3 shows the annual cash flows net of operating expenses,
along with the annual debt service obligations. The project is not
attractive to the banker since the ADSCRs are low, at only 1.07 in Years
1 and 2, with no single years giving a debt service ratio of more than
1.47. This means that there could be a cash shortfall and an inability to
pay the lenders the principal repayment and interest that is due.
Table 4.3: Calculation of Annual Debt Service Capacity Ratio
(dollars)
Year 0 1 2 3 4 5
Net cash flow −2,000,000
320,00
0 320,0
00 360,0
00 440,0
00 380,0
00
Debt
repayment 0 298,31
6 298,3
16 298,3
16 298,3
16 298,3
16
ADSCR 1.07 1.07 1.21 1.47 1.27
Year 6 7 8 9 10
Net cash flow 100,000 200,000
480,0
00 540,0
00 640,0
00
Debt
repayment
ADSCR
-
The question now is how the ADSCRs can be improved. There are
fundamentally only three alternatives:
decrease the interest rate on the loan;
decrease the amount of debt financing; or
increase the duration of the loan repayment.
a) Decrease the Interest Rate on the Loan
If the terms of the loan can be restructured so that the ADSCRs look
better, it may be attractive to the banker to provide financing. Table 4.4
shows the effect of obtaining a concessional interest rate or interest rate
subsidy for the loan. In this case it is assumed that a 1 percent interest
rate can be obtained for the full five-year period that the loan is
outstanding. The ADSCRs are much larger now, never becoming less
than 1.55; however, such a financing subsidy might be very difficult to
obtain.
Table 4.4: Decrease the Interest Rate on the Loan (dollars)
Year 0 1 2 3 4 5
Net cash flow −2,000,000
320,00
0 320,0
00 360,0
00 440,0
00 380,0
00
Debt
repayment 0 206,04
0 206,0
40 206,0
40 206,0
40 206,0
40
ADSCR 1.55 1.55 1.75 2.14 1.84
Year 6 7 8 9 10
Net cash flow 100,000 200,000
480,0
00 540,0
00 640,0
00
Debt
repayment
ADSCR
b) Decrease the Amount of Debt Financing
-
Table 4.5 shows a case in which the amount of the loan is reduced from
$1 million to $600,000. Here, the ADSCRs are found to increase greatly,
so that they now never fall below a value of 1.79. Since the amount of
the annual repayment of that loan becomes smaller (equity financing is
increased), the ability of the project to service the debt becomes much
more certain.
Table 4.5: Decrease the Amount of Borrowing by Increasing
Equity to $1.4 Million (dollars)
Year 0 1 2 3 4 5
Net cash flow −2,000,000
320,00
0 320,0
00 360,0
00 440,0
00 380,0
00
Debt
repayment 0 178,98
9 178,9
89 178,9
89 178,9
89 178,9
89
ADSCR 1.79 1.79 2.01 2.46 2.12
Year 6 7 8 9 10
Net cash flow 100,000 200,000
480,0
00 540,0
00 640,0
00
Debt
repayment
ADSCR
c) Increase the Duration of the Loan Repayment
Table 4.6 shows the case in which the duration of the loan is increased
from five to ten years. If a financial institution is able to extend a loan for
such a long period, the annual debt service obligations will fall greatly.
The result is that except for Years 6 and 7, the annual debt service
obligation never falls below 1.61. In Years 6 and 7, the ADSCRs are
projected to be only 0.50 and 1.00, respectively. This is due to a
projected fall in the net cash flows that might arise because of the need to
make reinvestments or heavy maintenance expenditures in those years.
-
Table 4.6: Increase the Duration of Loan Repayment (dollars)
Year 0 1 2 3 4 5
Net cash flow −2,000,000
320,00
0 320,0
00 360,0
00 440,0
00 380,0
00
Debt
repayment 0 199,25
2 199,2
52 199,2
52 199,2
52 199,2
52
ADSCR 1.61 1.61 1.81 2.21 1.91
Year 6 7 8 9 10
Net cash flow 100,000 200,000
480,0
00 540,0
00 640,0
00
Debt
repayment 199,252 199,25
2 199,2
52 199,2
52 199,2
52
ADSCR 0.50 1.00 2.41 2.71 3.21
The question now is whether the project has sufficiently strong net
cash flows in the years following Years 6 and 7 to warrant the financial
institution providing the project bridge financing for these two years.
This additional new loan would be repaid from the surplus net cash flows
in later years. In addressing this question, the LLCR is the appropriate
criterion to determine whether the project should qualify for bridge
financing. The present value of the net cash flows remaining until the
end of the debt repayment period, discounted at the loan interest rate, is
divided by the present value of the debt repayments for the remaining
duration of the loan. It is also discounted at the loan interest rate. These
estimations are presented in Table 4.7.
The LLCRs for Years 6 and 7 are 1.77 and 2.21, respectively. This
indicates that there are likely to be more than adequate net cash flows
from the project to safely repay the bridge financing that is needed to
cover the likely shortfalls in cash during Years 6 and 7.
If for some reason the banks were not comfortable providing the
bridge financing needed to cover the cash flow shortfalls during Years 6
and 7, they might instead require the firm to build up a debt service
-
reserve account during the first five years of the loan’s life from the cash
that is over and above the requirements for servicing the debt.
Alternatively, the banker may require the debt service reserve account to
be immediately financed out of the proceeds of the loan and equity
financing. This debt service reserve account would be invested in
short-term liquid assets that could be drawn down to meet the financing
requirements during Years 6 and 7.
Table 4.7: Is Bridge Financing an Option? (dollars)
Year 0 1 2 3 4 5
Net cash
flow −2,000,0
00 320,00
0 320,0
00 360,0
00 440,0
00 380,0
00
Debt
repayment 0 199,25
2 199,2
52 199,2
52 199,2
52 199,2
52
ADSCR 1.61 1.61 1.81 2.21 1.91
NPV of NCF 2,052,134
1,991,
954 1,922,
747 1,797,
159 1,560,
733
PV of debt
repayments 1,150,
000 1,093,
360 1,028,
224 953,3
18 867,1
76
LLCR
1.78 1.82 1.87 1.89 1.80
Year 6 7 8 9 10
Net cash
flow 100,000 200,00
0 480,0
00 540,0
00 640,0
00
Debt
repayment 199,252 199,25
2 199,2
52 199,2
52 199,2
52
ADSCR 0.50 1.00 2.41 2.71 3.21
NPV of NCF 1,357,843
1,446,
519 1,433,
497 1,096,
522 640,0
00
PV of debt
repayments 768,112 654,18
9 523,1
78 372,5
15 199,2
52
LLCR 1.77 2.21 2.74 2.94 3.21
It is sometimes the case that the financial institutions servicing the
-
loan will stipulate that if the ADSCR ever falls below a certain
benchmark, say 1.8, it must stop paying dividends to the owners of the
equity until a sinking fund of a specified size is created or a certain
amount of the loan is repaid. In this way, the lenders are protected from
what might become an even more precarious situation in the future.
The actual benchmark requirements for the ADSCRs and the overall
project’s LLCRs will depend on the business and financial risk
associated with a particular sector and the specific enterprise. The
sensitivity of the net cash flows from the project to movements in the
economy’s business cycle will be an important determinant of what the
adequate ratios for any specific project are. The existence of creditable
government guarantees for the repayment of interest and principal will
also serve to lower the benchmark values of the debt service coverage
ratios for a project.
4.3.6 Cost–Effectiveness Analysis2
This is an appraisal technique primarily used in social projects and
programs, and sometimes in infrastructure projects, where it is difficult
to quantify benefits in monetary terms. For instance, when there are two
or more alternative approaches to improving the nutrition levels among
children in a community, the selection criterion could simply be to select
the alternative that has the least cost. A similar case occurs when there
are two alternatives for providing irrigation facilities to farmers in a
certain region, for example, a canal system and a tube well network, and
they cover the same area and provide the same volume of water in a year.
The benefits in such cases are treated as identical, and, therefore, it is not
necessary to quantify them or to place a monetary value on them if the
problem is to select the project that will produce these benefits at the
lowest possible cost.
This approach is also useful for choosing between different
technologies for providing the same services, for example, when there
are two alternative technologies related to the supply of drinking water or
the generation of electricity. When the same quantity and quality of
water per annum can be delivered using pipes of different diameters, and
2 See Curry and Weiss (1993) and Gittinger (1994) for discussion
of cost–effectiveness analysis.
-
the smaller pipe involves greater pumping costs but has lower capital
costs, a cost–effectiveness analysis may be used for making a choice. A
similar situation occurs when there are two alternative ways of
generating electricity, one with a lower investment cost but higher
operating expenses (single-cycle versus combined-cycle technologies).
Again, if the decision has been made to provide this service, there is no
need to calculate the benefit in monetary terms. The cost–effectiveness
analysis may be used in all such cases for selecting the best project or the
best technology.
If the amount of benefits of the alternative projects differ, and if the
benefits cannot be measured in monetary terms but can be physically
quantified, the pure cost–effectiveness of a project can be calculated by
dividing the present value of total costs of the project by the present
value of a non-monetary quantitative measure of the benefits it generates.
The ratio is an estimate of the amount of costs incurred to achieve a unit
of the benefit from a program. For example, in a health project, what are
the costs, expressed in dollars, incurred in saving a person’s life?
Presumably, there are alternative ways to save a life; what are their costs?
The analysis does not evaluate benefits in monetized terms, but is an
attempt to find the least-cost option to achieve a desired quantitative
outcome.
In applying the cost–effectiveness approach, the present values of
costs need to be computed. While using the cost–effectiveness analysis,
it is important to include all external costs – such as waiting time, coping
costs, enforcement costs, regulatory costs, and compliance costs in the
case of health care, offset by the salvage values at the end of the projects
– and to choose the discount rate carefully. The preferred outcome will
often change with a change in the discount rate.
Pure cost–effectiveness analysis can be extended to more
sophisticated and meaningful ways of measuring benefits. A quantitative
measure can be made by constructing a composite index of two or more
benefit categories, including quantity and quality. For example, the cost
utility analysis in health care uses quality-adjusted life-years (QALYs) as
a measure of benefits. The QALY measure integrates two dimensions of
health improvement, namely the additional years of life (reduction in
mortality) and the quality of life (morbidity) during these years. On the
basis of the costs incurred, expressed in dollars, the decision-maker
would still choose the option with the least cost per QALY achieved by
the project or the program (see, e.g., Garber and Phelps, 1997).
-
Cost–utility analysis attempts to include some of the benefits excluded
from a pure cost–effective analysis, hence moving it a step closer to a
full cost–benefit analysis.
One should be aware of some of the shortcomings inherent in the
cost–effectiveness approach. It is a poor measure of consumers’
willingness to pay in principle because there is no monetary value placed
on the benefits. Furthermore, in the calculation of the cost–effectiveness
ratio, the numerator does not take into account the scale of alternative
options. Nevertheless, this ratio is still a very useful criterion for
selection of alternative options when the benefits cannot be monetized.
4.4 Conclusion
This chapter first described the concept of time value of money and the
proper use of the discount rate in project appraisal. It reviewed six
important criteria used by various analysts for judging the expected
performance of investment projects. While each one may have its own
merit in specific circumstances, the NPV criterion is the most reliable
and satisfactory one for both the financial and the economic evaluation.
For bankers and other financial lending institutions, measurements of
the ADSCR and LLCR are the key factors that enable them to determine
whether a project can generate enough cash to meet the debt service
obligations before financing of the project should be approved.
The chapter has also discussed the situation in which the benefits of
a project or a program cannot be expressed in monetary values in a
meaningful way; in such a case, a cost–effectiveness analysis should be
carried out to assist in making welfare-improving investment decisions.
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Cost-Benefit Analysis: Concepts and Practice, 2nd
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NJ: Prentice Hall.
Curry, S. and J. Weiss. 1993. Project Analysis in Developing Countries. New
York: St. Martin’s Press.
Garber, A.M. and C.E. Phelps. 1997. “Economic Foundations of
Cost-Effectiveness Analysis”, Journal of Health Economics 16(1), 1–31.
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Gitman, L.J. 2009. Principles of Managerial Finance, 12th
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Pearson Prentice Hall.
Gittinger J.P. 1994. Economic Analysis of Agricultural Projects. Baltimore, MD:
Johns Hopkins University Press.
Gramlich, E.M. 1997. A Guide to Cost-Benefit Analysis. Englewood Cliffs, NJ:
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Ley, E. 2007. “Cost-Benefit Analysis: Evaluation Criteria (Or: ‘Stay away from
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