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

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

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

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:

= [(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

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:

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

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

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

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:

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.

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

(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

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

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.

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

<

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

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

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.

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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