Project management chapter 6

Project Management for Construction
Fundamental Concepts for Owners, Engineers, Architects and Builders

Chapter 6
Economic Evaluation of Facility Investments

Economic Evaluation of
Facility Investments
6.1 Project Life Cycle and Economic Feasibility

6.1 Project Life Cycle and
Economic Feasibility
Facility investment decisions represent major commitments of
corporate resources and have serious consequences on the
profitability and financial stability of a corporation. In the public
sector, such decisions also affect the viability of facility
investment programs and the credibility of the agency in charge
of the programs. It is important to evaluate facilities rationally
with regard to both the economic feasibility of individual projects
and the relative net benefits of alternative and mutually
exclusive projects.

This chapter will present an overview of the decision process for
economic evaluation of facilities with regard to the project life
cycle. The cycle begins with the initial conception of the project
and continues though planning, design, procurement,
construction, start-up, operation and maintenance. It ends with
the disposal of a facility when it is no longer productive or
useful. Four major aspects of economic evaluation will be
examined:

1. The basic concepts of facility investment evaluation,
including time preference for consumption, opportunity cost,
minimum attractive rate of return, cash flows over the
planning horizon and profit measures.
2. Methods of economic evaluation, including the net present
value method, the equivalent uniform annual value method,
the benefit-cost ratio method, and the internal rate of return
method.

3. Factors affecting cash flows, including depreciation and tax
effects, price level changes, and treatment of risk and
uncertainty.
4. Effects of different methods of financing on the selection of
projects, including types of financing and risk, public policies
on regulation and subsidies, the effects of project financial
planning, and the interaction between operational and
financial planning.

In setting out the engineering economic analysis methods for
facility investments, it is important to emphasize that not all
facility impacts can be easily estimated in dollar amounts. For
example, firms may choose to minimize environmental impacts
of construction or facilities in pursuit of a "triple bottom line:"
economic, environmental and social. By reducing environmental
impacts, the firm may reap benefits from an improved reputation
and a more satisfied workforce. Nevertheless, a rigorous
economic evaluation can aid in making decisions for both
quantifiable and qualitative facility impacts.

It is important to distinguish between the economic evaluation of
alternative physical facilities and the evaluation of alternative
financing plans for a project. The former refers to the evaluation
of the cash flow representing the benefits and costs associated
with the acquisition and operation of the facility, and this cash
flow over the planning horizon is referred to as the economic
cash flow or the operating cash flow. The latter refers to the
evaluation of the cash flow representing the incomes and
expenditures as a result of adopting a specific financing plan for
funding the project, and this cash flow over the planning horizon
is referred to as the financial cash flow.

In general, economic evaluation and financial evaluation are
carried out by different groups in an organization since
economic evaluation is related to design, construction,
operations and maintenance of the facility while financial
evaluations require knowledge of financial assets such as
equities, bonds, notes and mortgages. The separation of
economic evaluation and financial evaluation does not
necessarily mean one should ignore the interaction of different
designs and financing requirements over time
which may influence the relative desirability of specific
design/financing combinations.

All such combinations can be duly considered. In practice,
however, the division of labor among two groups of specialists
generally leads to sequential decisions without adequate
communication for analyzing the interaction of various
design/financing combinations because of the timing of
separate analyses.

As long as the significance of the interaction of design/financing
combinations is understood, it is convenient first to consider the
economic evaluation and financial evaluation separately, and
then combine the results of both evaluations to reach a final
conclusion. Consequently, this chapter is devoted primarily to
the economic evaluation of alternative physical facilities while
the effects of a variety of financing mechanisms will be treated
in the next chapter. Since the methods of analyzing economic
cash flows are equally applicable to the analysis of financial
cash flows, the techniques for evaluating financing plans and
the combined effects of economic and financial cash flows for
project selection are also included in this chapter.

6.2 Basic Concepts of Economic Evaluation

6.2 Basic Concepts of
Economic Evaluation
A systematic approach for economic evaluation of facilities
consists of the following major steps:
1. Generate a set of projects or purchases for investment
consideration.
2. Establish the planning horizon for economic analysis.
3. Estimate the cash flow profile for each project.

Economic Evaluation
4. Specify the minimum attractive rate of return (MARR).
5. Establish the criterion for accepting or rejecting a proposal,
or for selecting the best among a group of mutually exclusive
proposals, on the basis of the objective of the investment.
6. Perform sensitivity or uncertainty analysis.
7. Accept or reject a proposal on the basis of the established
criterion.

Economic Evaluation
It is important to emphasize that many assumptions and
policies, some implicit and some explicit, are introduced in
economic evaluation by the decision maker. The decision
making process will be influenced by the subjective judgment of
the management as much as by the result of systematic
analysis.

Economic Evaluation
The period of time to which the management of a firm or agency
wishes to look ahead is referred to as the planning horizon.
Since the future is uncertain, the period of time selected is
limited by the ability to forecast with some degree of accuracy.
For capital investment, the selection of the planning horizon is
often influenced by the useful life of facilities, since the disposal
of usable assets, once acquired, generally involves suffering
financial losses.

Economic Evaluation
In economic evaluations, project alternatives are represented by
their cash flow profiles over the n years or periods in the
planning horizon. Thus, the interest periods are normally
assumed to be in years t = 0,1,2, ...,n with t = 0 representing
the present time. Let Bt,x be the annual benefit at the end of
year t for a investment project x where x = 1, 2, ... refer to
projects No. 1, No. 2, etc., respectively. Let Ct,x be the annual
cost at the end of year t for the same investment project x. The
net annual cash flow is defined as the annual benefit in excess
of the annual cost, and is denoted by At,x at the end of year t for
an investment project x. Then, for t = 0,1, . . . ,n:

Economic Evaluation
where At,x is positive, negative or zero depends on the values of Bt,x and
Ct,x, both of which are defined as positive quantities.

Economic Evaluation
Once the management has committed funds to a specific
project, it must forego other investment opportunities which
might have been undertaken by using the same funds.
The opportunity cost reflects the return that can be earned from
the best alternative investment opportunity foregone. The
foregone opportunities may include not only capital projects but
also financial investments or other socially desirable programs.
Management should invest in a proposed project only if it will
yield a return at least equal to the minimum attractive rate of
return (MARR) from foregone opportunities as envisioned by
the organization.

Economic Evaluation
In general, the MARR specified by the top management in a
private firm reflects the opportunity cost of capital of the firm,
the market interest rates for lending and borrowing, and the
risks associated with investment opportunities. For public
projects, the MARR is specified by a government agency, such
as the Office of Management and Budget or the Congress of
the United States. The public MARR thus specified reflects
social and economic welfare considerations, and is referred to
as the social rate of discount.

Economic Evaluation
Regardless of how the MARR is determined by an organization,
the MARR specified for the economic evaluation of investment
proposals is critically important in determining whether any
investment proposal is worthwhile from the standpoint of the
organization. Since the MARR of an organization often cannot
be determined accurately, it is advisable to use several values
of the MARR to assess the sensitivity of the potential of the
project to variations of the MARR value.

6.3 Costs and Benefits of a Constructed Facility

6.3 Costs and Benefits of a
Constructed Facility
The basic principle in assessing the economic costs and
benefits of new facility investments is to find the aggregate of
individual changes in the welfare of all parties affected by the
proposed projects. The changes in welfare are generally
measured in monetary terms, but there are exceptions, since
some effects cannot be measured directly by cash receipts and
disbursements. Examples include the value of human lives
saved through safety improvements or the cost of
environmental degradation.

The difficulties in estimating future costs and benefits lie not
only in uncertainties and reliability of measurement, but also on
the social costs and benefits generated as side effects.
Furthermore, proceeds and expenditures related to financial
transactions, such as interest and subsidies, must also be
considered by private firms and by public agencies.

To obtain an accurate estimate of costs in the cash flow profile
for the acquisition and operation of a project, it is necessary to
specify the resources required to construct and operate the
proposed physical facility, given the available technology and
operating policy. Typically, each of the labor and material
resources required by the facility is multiplied by its price, and
the products are then summed to obtain the total costs. Private
corporations generally ignore external social costs unless
required by law to do so. In the public sector, externalities often
must be properly accounted for.

An example is the cost of property damage caused by air
pollution from a new plant. In any case, the measurement of
external costs is extremely difficult and somewhat subjective for
lack of a market mechanism to provide even approximate
answers to the appropriate value.

In the private sector, the benefits derived from a facility
investment are often measured by the revenues generated from
the operation of the facility. Revenues are estimated by the total
of price times quantity purchased. The depreciation allowances
and taxes on revenues must be deducted according to the
prevailing tax laws. In the public sector, income may also be
accrued to a public agency from the operation of the facility.
However, several other categories of benefits may also be
included in the evaluation of public projects. First, private
benefits can be received by users of a facility or service in
excess of costs such as user charges or price charged.

After all, individuals only use a service or facility if their private
benefit exceeds their cost. These private benefits or consumer
surplus represent a direct benefit to members of the public. In
many public projects, it is difficult, impossible or impractical to
charge for services received, so direct revenues equal zero and
all user benefits appear as consumers surplus. Examples are a
park or roadways for which entrance is free. As a second
special category of public benefit, there may be external or
secondary beneficiaries of public projects, such as new jobs
created and profits to private suppliers. Estimating these
secondary benefits is extremely difficult since resources
devoted to public projects might simply be displaced from
private employment and thus represent no net benefit.

6.4 Interest Rates and the Costs of Capital

6.4 Interest Rates and the
Costs of Capital
Constructed facilities are inherently long-term investments with
a deferred pay-off. The cost of capital or MARR depends on the
real interest rate (i.e., market interest rate less the inflation rate)
over the period of investment. As the cost of capital rises, it
becomes less and less attractive to invest in a large facility
because of the opportunities foregone over a long period of
time.

Costs of Capital
In Figure 6-1, the changes in the cost of capital from 1974 to
2002 are illustrated. This figure presents the market interest
rate on short and long term US treasury borrowing, and the
corresponding real interest rate over this period. The real
interest rate is calculated as the market interest rate less the
general rate of inflation. The real interest rates has varied
substantially, ranging from 9% to -7%. The exceptional nature
of the 1980 to 1985 years is dramatically evident: the real rate
of interest reached remarkably high historic levels.

Costs of Capital
Figure 6-1 Nominal and Real Interest Rates on U.S. Bonds,

Costs of Capital
With these volatile interest rates, interest charges and the
ultimate cost of projects are uncertain. Organizations and
institutional arrangements capable of dealing with this
uncertainty and able to respond to interest rate changes
effectively would be quite valuable. For example, banks offer
both fixed rate and variable rate mortgages. An owner who
wants to limit its own risk may choose to take a fixed rate
mortgage even though the ultimate interest charges may be
higher. On the other hand, an owner who chooses a variable
rate mortgage will have to adjust its annual interest charges
according to the market interest rates.

Costs of Capital
In economic evaluation, a constant value of MARR over the
planning horizon is often used to simplify the calculations. The
use of a constant value for MARR is justified on the ground of
long-term average of the cost of capital over the period of
investment. If the benefits and costs over time are expressed in
constant dollars, the constant value for MARR represents the
average real interest rate anticipated over the planning horizon;
if the benefits and costs over time are expressed in then-current
dollars, the constant value for MARR reflects the average
market interest rate anticipated over the planning horizon.

6.5 Investment Profit Measures

6.5 Investment Profit
Measures
A profit measure is defined as an indicator of the desirability of
a project from the standpoint of a decision maker. A profit
measure may or may not be used as the basis for project
selection. Since various profit measures are used by decision
makers for different purposes, the advantages and restrictions
for using these profit measures should be fully understood.

Measures
There are several profit measures that are commonly used by
decision makers in both private corporations and public
agencies. Each of these measures is intended to be an
indicator of profit or net benefit for a project under
consideration. Some of these measures indicate the size of the
profit at a specific point in time; others give the rate of return per
period when the capital is in use or when reinvestments of the
early profits are also included.

Measures
If a decision maker understands clearly the meaning of the
various profit measures for a given project, there is no reason
why one cannot use all of them for the restrictive purposes for
which they are appropriate. With the availability of computer
based analysis and commercial software, it takes only a few
seconds to compute these profit measures. However, it is
important to define these measures precisely:

Measures
1. Net Future Value and Net Present Value. When an
organization makes an investment, the decision maker looks
forward to the gain over a planning horizon, against what might
be gained if the money were invested elsewhere. A minimum
attractive rate of return (MARR) is adopted to reflect this
opportunity cost of capital. The MARR is used for compounding
the estimated cash flows to the end of the planning horizon, or
for discounting the cash flow to the present.

Measures
The profitability is measured by the net future value (NFV)
which is the net return at the end of the planning horizon above
what might have been gained by investing elsewhere at the
MARR. The net present value (NPV) of the estimated cash
flows over the planning horizon is the discounted value of the
NFV to the present. A positive NPV for a project indicates the
present value of the net gain corresponding to the project cash
flows.

Measures
2. Equivalent Uniform Annual Net Value. The equivalent
uniform annual net value (NUV) is a constant stream of benefits
less costs at equally spaced time periods over the intended
planning horizon of a project. This value can be calculated as
the net present value multiplied by an appropriate "capital
recovery factor." It is a measure of the net return of a project on
an annualized or amortized basis. The equivalent uniform
annual cost (EUAC) can be obtained by multiplying the present
value of costs by an appropriate capital recovery factor.

Measures
The use of EUAC alone presupposes that the discounted
benefits of all potential projects over the planning horizon are
identical and therefore only the discounted costs of various
projects need be considered. Therefore, the EUAC is an
indicator of the negative attribute of a project which should be
minimized.

Measures
3. Benefit Cost Ratio. The benefit-cost ratio (BCR), defined as
the ratio of discounted benefits to the discounted costs at the
same point in time, is a profitability index based on discounted
benefits per unit of discounted costs of a project. It is
sometimes referred to as the savings-to-investment ratio (SIR)
when the benefits are derived from the reduction of undesirable
effects. Its use also requires the choice of a planning horizon
and a MARR. Since some savings may be interpreted as a
negative cost to be deducted from the denominator or as a
positive benefit to be added to the numerator of the ratio, the
BCR or SIR is not an absolute numerical measure.

Measures
However, if the ratio of the present value of benefit to the
present value of cost exceeds one, the project is profitable
irrespective of different interpretations of such benefits or costs.

Measures
4. Internal Rate of Return. The internal rate of return (IRR) is
defined as the discount rate which sets the net present value of
a series of cash flows over the planning horizon equal to zero. It
is used as a profit measure since it has been identified as the
"marginal efficiency of capital" or the "rate of return over cost".
The IRR gives the return of an investment when the capital is in
use as if the investment consists of a single outlay at the
beginning and generates a stream of net benefits afterwards.

Measures
However, the IRR does not take into consideration the
reinvestment opportunities related to the timing and intensity of
the outlays and returns at the intermediate points over the
planning horizon. For cash flows with two or more sign
reversals of the cash flows in any period, there may exist
multiple values of IRR; in such cases, the multiple values are
subject to various interpretations.

Measures
5. Adjusted Internal Rate of Return. If the financing and
reinvestment policies are incorporated into the evaluation of a
project, an adjusted internal rate of return (AIRR) which reflects
such policies may be a useful indicator of profitability under
restricted circumstances. Because of the complexity of
financing and reinvestment policies used by an organization
over the life of a project, the AIRR seldom can reflect the reality
of actual cash flows.

Measures
However, it offers an approximate value of the yield on an
investment for which two or more sign reversals in the cash
flows would result in multiple values of IRR. The adjusted
internal rate of return is usually calculated as the internal rate of
return on the project cash flow modified so that all costs are
discounted to the present and all benefits are compounded to
the end of the planning horizon.

Measures
6. Return on Investment. When an accountant reports income
in each year of a multi-year project, the stream of cash flows
must be broken up into annual rates of return for those years.
The return on investment (ROI) as used by accountants usually
means the accountant's rate of return for each year of the
project duration based on the ratio of the income (revenue less
depreciation) for each year and the undepreciated asset value
(investment) for that same year. Hence, the ROI is different
from year to year, with a very low value at the early years and a
high value in the later years of the project.

Measures
7. Payback Period. The payback period (PBP) refers to the
length of time within which the benefits received from an
investment can repay the costs incurred during the time in
question while ignoring the remaining time periods in the
planning horizon. Even the discounted payback period
indicating the "capital recovery period" does not reflect the
magnitude or direction of the cash flows in the remaining
periods. However, if a project is found to be profitable by other
measures, the payback period can be used as a secondary
measure of the financing requirements for a project.

6.6 Methods of Economic Evaluation

6.6 Methods of Economic
Evaluation
The objective of facility investment in the private sector is
generally understood to be profit maximization within a specific
time frame. Similarly, the objective in the public sector is the
maximization of net social benefit which is analogous to profit
maximization in private organizations. Given this objective, a
method of economic analysis will be judged by the reliability and
ease with which a correct conclusion may be reached in project
selection.

Evaluation
The basic principle underlying the decision for accepting and
selecting investment projects is that if an organization can lend
or borrow as much money as it wishes at the MARR, the goal of
profit maximization is best served by accepting all independent
projects whose net present values based on the specified
MARR are nonnegative, or by selecting the project with the
maximum nonnegative net present value among a set of
mutually exclusive proposals.

Evaluation
The net present value criterion reflects this principle and is most
straightforward and unambiguous when there is no budget
constraint. Various methods of economic evaluation, when
properly applied, will produce the same result if the net present
value criterion is used as the basis for decision. For
convenience of computation, a set of tables for the various
compound interest factors is given in Appendix A

Evaluation
Net Present Value Method

Let BPVx be the present value of benefits of a project x and
CPVx be the present value of costs of the project x. Then, for
MARR = i over a planning horizon of n years,

where the symbol (P|F,i,t) is a discount factor equal to (1+i)-
t and reads as follows: "To find the present value P, given the
future value F=1, discounted at an annual discount rate i over a
period of t years." When the benefit or cost in year t is multiplied
by this factor, the present value is obtained. Then, the net
present value of the project x is calculated as:

If there is no budget constraint, then all independent projects
having net present values greater than or equal to zero are
acceptable. That is, project x is acceptable as long as

For mutually exclusive proposals (x = 1,2,...,m), a proposal j
should be selected if it has the maximum nonnegative net
present value among all m proposals, i.e.
provided that NPVj 0.

Evaluation
Net Future Value Method

Since the cash flow profile of an investment can be represented
by its equivalent value at any specified reference point in time,
the net future value (NFVx) of a series of cash flows At,x (for
t=0,1,2,...,n) for project x is as good a measure of economic
potential as the net present value. Equivalent future values are
obtained by multiplying a present value by the compound
interest factor (F|P,i,n) which is (1+i)n. Specifically,

Consequently, if NPVx 0, it follows that NFVx 0, and vice versa.

Evaluation
Net Equivalent Uniform Annual Value Method

Net Equivalent Uniform
Annual Value Method
The net equivalent uniform annual value (NUVx) refers to a
uniform series over a planning horizon of n years whose net
present value is that of a series of cash flow At,x (for t= 1,2,...,n)
representing project x. That is,

Net Equivalent Uniform
Annual Value Method
where the symbol (U|P,i,n) is referred to as the capital recovery
factor and reads as follows: "To find the equivalent annual
uniform amount U, given the present value P=1, discounted at
an annual discount rate i over a period of t years." Hence, if
NPVx 0, it follows that NUVx 0, and vice versa.

Evaluation
Benefit-Cost Ratio Method

The benefit-cost ratio method is not as straightforward and
unambiguous as the net present value method but, if applied
correctly, will produce the same results as the net present value
method. While this method is often used in the evaluation of
public projects, the results may be misleading if proper care is
not exercised in its application to mutually exclusive proposals.

The benefit-cost ratio is defined as the ratio of the discounted
benefits to the discounted cost at the same point in time. In view
of Eqs. (6.4) and (6.6), it follows that the criterion for accepting
an independent project on the basis of the benefit-cost ratio is
whether or not the benefit-cost ratio is greater than or equal to
one:

However, a project with the maximum benefit-cost ratio among
a group of mutually exclusive proposals generally does not
necessarily lead to the maximum net benefit. Consequently, it is
necessary to perform incremental analysis through pairwise
comparisons of such proposals in selecting the best in the
group. In effect, pairwise comparisons are used to determine if
incremental increases in costs between projects yields larger
incremental increases in benefits. This approach is not
recommended for use in selecting the best among mutually
exclusive proposals.

Evaluation
Internal Rate of Return Method

Internal Rate of Return
Method
The term internal rate of return method has been used by
different analysts to mean somewhat different procedures for
economic evaluation. The method is often misunderstood and
misused, and its popularity among analysts in the private sector
is undeserved even when the method is defined and interpreted
in the most favorable light. The method is usually applied by
comparing the MARR to the internal rate of return value(s) for a
project or a set of projects.

Internal Rate of Return
Method
A major difficulty in applying the internal rate of return method to
economic evaluation is the possible existence of multiple values
of IRR when there are two or more changes of sign in the cash
flow profile At,x (for t=0,1,2,...,n). When that happens, the
method is generally not applicable either in determining the
acceptance of independent projects or for selection of the best
among a group of mutually exclusive proposals unless a set of
well defined decision rules are introduced for incremental
analysis. In any case, no advantage is gained by using this
method since the procedure is cumbersome even if the method
is correctly applied. This method is not recommended for use
either in accepting independent projects or in selecting the best
among mutually exclusive proposals.

Evaluation
Example 6-1: Evaluation of Four Independent Projects

Example 6-1: Evaluation of
Four Independent Projects
The cash flow profiles of four independent projects are shown in
Table 6-1. Using a MARR of 20%, determine the acceptability of
each of the projects on the basis of the net present value
criterion for accepting independent projects.

t At,1 At,2 At,3 At,4
0
1
2
3
4
5
-77.0
0
0
0
0
235.0
-75.3
28.0
28.0
28.0
28.0
28.0
-39.9
28.0
28.0
28.0
28.0
-80.0
18.0
10.0
-40.0
-60.0
30.0
50.0
TABLE 6-1 Cash Flow Profiles of Four
Independent Projects (in $ million)

Using i = 20%, we can compute NPV for x = 1, 2, 3, and 4 from
Eq. (6.5). Then, the acceptability of each project can be
determined from Eq. (6.6). Thus,
[NPV1]20% = -77 + (235)(P|F, 20%, 5) = -77 + 94.4 = 17.4
[NPV2]20% = -75.3 + (28)(P|U, 20%, 5) = -75.3 + 83.7 = 8.4
[NPV3]20% = -39.9 + (28)(P|U, 20%, 4) - (80)(P|F, 20%, 5)
= -39.9 + 72.5 - 32.2 = 0.4
[NPV4]20% = 18 + (10)(P|F, 20%, 1) - (40)(P|F, 20%, 2)
- (60)(P|F, 20%, 3) + (30)(P|F, 20%, 4) +
(50)(P|F, 20%, 5)
= 18 + 8.3 - 27.8 - 34.7 + 14.5 + 20.1 = -1.6
Hence, the first three independent projects are acceptable,
but the last project should be rejected.

It is interesting to note that if the four projects are mutually
exclusive, the net present value method can still be used to
evaluate the projects and, according to Eq. (6.7), the project (x
= 1) which has the highest positive NPV should be selected.
The use of the net equivalent uniform annual value or the net
future value method will lead to the same conclusion. However,
the project with the highest benefit-cost ratio is not necessarily
the best choice among a group of mutually exclusive
alternatives. Furthermore, the conventional internal rate of
return method cannot be used to make a meaningful evaluation
of these projects as the IRR for both x=1 and x=2 are found to
be 25% while multiple values of IRR exist for both the x=3 and
x=4 alternatives.

6.7 Depreciation and Tax Effects

6.7 Depreciation and Tax
Effects
For private corporations, the cash flow profile of a project is
affected by the amount of taxation. In the context of tax
liability, depreciation is the amount allowed as a deduction due
to capital expenses in computing taxable income and, hence,
income tax in any year. Thus, depreciation results in a reduction
in tax liabilities.

Effects
It is important to differentiate between the estimated useful life
used in depreciation computations and the actual useful life of a
facility. The former is often an arbitrary length of time, specified
in the regulations of the U.S. Internal Revenue Service or a
comparable organization. The depreciation allowance is a
bookkeeping entry that does not involve an outlay of cash, but
represents a systematic allocation of the cost of a physical
facility over time.

Effects
There are various methods of computing depreciation which are
acceptable to the U.S. Internal Revenue Service. The different
methods of computing depreciation have different effects on the
streams of annual depreciation charges, and hence on the
stream of taxable income and taxes paid. Let P be the cost of
an asset, S its estimated salvage value, and N the estimated
useful life (depreciable life) in years. Furthermore, let Dt denote
the depreciation amount in year t, Tt denote the accumulated
depreciation up to year t, and Bt denote the book value of the
asset at the end of year t, where t=1,2,..., or n refers to the
particular year under consideration. Then,

Effects
and

Effects
The depreciation methods most commonly used to compute
Dt and Bt are the straight line method, sum-of-the-years'-digits
methods, and the double declining balanced method. The U.S.
Internal Revenue Service provides tables of acceptable
depreciable schedules using these methods. Under straight line
depreciation, the net depreciable value resulting from the cost
of the facility less salvage value is allocated uniformly to each
year of the estimated useful life.

Effects
Under the sum-of-the-year's-digits (SOYD) method, the annual
depreciation allowance is obtained by multiplying the net
depreciable value multiplied by a fraction, which has as its
numerator the number of years of remaining useful life and its
denominator the sum of all the digits from 1 to n. The annual
depreciation allowance under the double declining balance
method is obtained by multiplying the book value of the
previous year by a constant depreciation rate 2/n.

Effects
To consider tax effects in project evaluation, the most direct
approach is to estimate the after-tax cash flow and then apply
an evaluation method such as the net present value method.
Since projects are often financed by internal funds representing
the overall equity-debt mix of the entire corporation, the
deductibility of interest on debt may be considered on a
corporate-wide basis. For specific project financing from internal
funds, let after-tax cash flow in year t be Yt. Then, for
t=0,1,2,...,n,

Effects
where At is the net revenue before tax in year t, Dt is the
depreciation allowable for year t and Xt is the marginal
corporate income tax rate in year t.
Besides corporate income taxes, there are other provisions in
the federal income tax laws that affect facility investments, such
as tax credits for low-income housing. Since the tax laws are
revised periodically, the estimation of tax liability in the future
can only be approximate.

Effects
Example 6-2: Effects of Taxes on Investment

Example 6-2: Effects of
Taxes on Investment
A company plans to invest $55,000 in a piece of equipment
which is expected to produce a uniform annual net revenue
before tax of $15,000 over the next five years. The equipment
has a salvage value of $5,000 at the end of 5 years and the
depreciation allowance is computed on the basis of the straight
line depreciation method. The marginal income tax rate for this
company is 34%, and there is no expectation of inflation. If the
after-tax MARR specified by the company is 8%, determine
whether the proposed investment is worthwhile, assuming that
the investment will be financed by internal funds.

Using Equations (6.11) and (6.13), the after-tax cash flow can
be computed as shown in Table 6-2. Then, the net present
value discounted at 8% is obtained from Equation (6.5) as
follows:

The positive result indicates that the project is worthwhile.
Year
t
Before-
tax Cash
Flow
At
Straight-
line
Depreciati
on
Dt
Taxable
Income
At-Dt
Income
Tax
Xt(At-Dt)
After-Tax
Cash-
Flow
Yt
0
1-5 each
5 only
- $55,000
+ $15,000
+ $5,000
$10,000 $5,000 $1,700
- $55,000
+ $13,300
+ $5,000
TABLE 6-2 After-Tax Cash Flow Computation

6.8 Price Level Changes: Inflation and Deflation

6.8 Price Level Changes:
Inflation and Deflation
In the economic evaluation of investment proposals, two
approaches may be used to reflect the effects of future price
level changes due to inflation or deflation. The differences
between the two approaches are primarily philosophical and
can be succinctly stated as follows:

1. The constant dollar approach. The investor wants a
specified MARR excluding inflation. Consequently, the cash
flows should be expressed in terms of base-year or constant
dollars, and a discount rate excluding inflation should be
used in computing the net present value.
2. The inflated dollar approach. The investor includes an
inflation component in the specified MARR. Hence, the cash
flows should be expressed in terms of then-current or
inflated dollars, and a discount rate including inflation should
be used in computing the net present value.

If these approaches are applied correctly, they will lead to
identical results.
Let i be the discount rate excluding inflation, i' be the discount
rate including inflation, and j be the annual inflation rate. Then,
and

When the inflation rate j is small, these relations can be
approximated by

Note that inflation over time has a compounding effect on the
price levels in various periods, as discussed in connection with
the cost indices in Chapter 5.

If At denotes the cash flow in year t expressed in terms of
constant (base year) dollars, and A't denotes the cash flow in
year t expressed in terms of inflated (then-current) dollars, then
or

It can be shown that the results from these two equations are
identical. Furthermore, the relationship applies to after-tax cash
flow as well as to before-tax cash flow by replacing At and
A't with Yt and Y't respectively in Equations (6.17) and (6.18).

Example 6-3: Effects of Inflation

Inflation
Suppose that, in the previous example, the inflation expectation
is 5% per year, and the after-tax MARR specified by the
company is 8% excluding inflation. Determine whether the
investment is worthwhile.

Inflation
In this case, the before-tax cash flow At in terms of constant
dollars at base year 0 is inflated at j = 5% to then-current dollars
A't for the computation of the taxable income (A't - Dt) and
income taxes. The resulting after-tax flow Y't in terms of then-
current dollars is converted back to constant dollars. That is, for
Xt = 34% and Dt = $10,000. The annual depreciation charges
Dt are not inflated to current dollars in conformity with the
practice recommended by the U.S. Internal Revenue Service.
Thus:

Inflation
A't = At(1 + j)t = At(1 + 0.05)t
Y't = A't - Xt(A't - Dt) = A't - (34%)(A't - $10,000)
Yt = Y't(1 + j)t = Y't(1 + 0.05)t
The detailed computation of the after-tax cash flow is recorded
in Table 6-3. The net present value discounted at 8% excluding
inflation is obtained by substituting Yt for At in Eq. (6.17). Hence,
[NPV]8%) = -55,000 + (13,138)(P|F, 8%, 1) + (12,985)(P|F,
8%, 2) + (12,837)(P|F, 8%, 3)
+ (12,697)(P|F, 8%, 4) + (12,564 + 5,000)(P|F, 8%, 5) = -
$227

Inflation
With 5% inflation, the investment is no longer worthwhile
because the value of the depreciation tax deduction is not
increased to match the inflation rate.

Inflation
Time
t
Consta
nt $ B-
Tax CF
At
Current
$ B-Tax
CF
A't
Current
$
deprecia
tion
Dt
Current
$ after
deprecia
tion
A't-Dt
Current
$
income
tax
Xt(A't-Dt)
Current
$ A-Tax
CF
Y't
Consta
nt $ A-
Tax CF
Yt
0
1
2
3
4
5
5
-$55,000
+15,000
+15,000
+15,000
+15,000
+15,000
+5,000
+$55,00
0
+15,750
16,540
17,365
18,233
19,145
$10,000
10,000
10,000
10,000
10,000
$5,750
6,540
7,365
8,233
9,145
$1,955
2,224
2,504
2,799
3,109
-$55,000
+13,795
+14,316
+14,861
+15,434
+16,036
-$55,000
+13,138
+12,985
+12,837
+12,697
+12,564
+5,000
TABLE 6-3 After-Tax Cash Flow Including Inflation
Note: B-Tax CF refers to Before-Tax Cash Flow;
A-Tax CF refers to After-Tax Cash Flow

Example 6-4: Inflation and the Boston Central Artery
Project

Example 6-4: Inflation and the
Boston Central Artery Project
The cost of major construction projects are often reported as
simply the sum of all expenses, no matter what year the cost
was incurred. For projects extending over a lengthy period of
time, this practice can combine amounts of considerably
different inherent values. A good example is the Boston Central
Artery/Tunnel Project, a very large project to construct or re-
locate two Interstate highways within the city of Boston.

In Table 6-4, we show one estimate of the annual expenditures
for the Central Artery/Tunnel from 1986 to 2006 in millions of
dollars, appearing in the column labelled "Expenses ($ M)." We
also show estimates of construction price inflation in the Boston
area for the same period, one based on 1982 dollars (so the
price index equals 100 in 1982) and one on 2002 dollars. If the
dollar expenditures are added up, the total project cost is $ 14.6
Billion dollars, which is how the project cost is often reported in
summary documents.

However, if the cost is calculated in constant 1982 dollars
(when the original project cost estimate was developed for
planning purposes), the project cost would be only $ 8.4 Billion,
with price inflation increasing expenses by $ 6.3 Billion. As with
cost indices discussed in Chapter 5, the conversion to 1982 $ is
accomplished by dividing by the 1982 price index for that year
and then multiplying by 100 (the 1982 price index value). If the
cost is calculated in constant 2002 dollars, the project cost
increases to $ 15.8 Billion. When costs are incurred can
significantly affect project expenses!

Year
t
Price Index
1982 $
Price Index
2002 $
Project Expenses
($ M)
Project Expenses
(1982 $ M)
Project Expenses
(2002 $ M)
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Sum
100
104
111
118
122
123
130
134
140
144
146
154
165
165
165
175
172
176
181
183
189
195
202
208
215
53
55
59
62
65
65
69
71
74
76
77
82
88
88
87
93
91
94
96
97
100
103
107
110
114
33,000
82,000
131,000
164,000
214,000
197,000
246,000
574,000
854,000
852,000
764,000
1,206,000
1,470,000
1,523,000
1,329,000
1,246,000
1,272,000
1,115,000
779,000
441,000
133,000
14,625,000
27,000
67,000
101,000
122,000
153,000
137,000
169,000
372,000
517,000
515,000
464,000
687,000
853,000
863,000
735,000
682,000
674,000
572,000
386,000
212,000
62,000
8,370,000
51,000
126,000
190,000
230,000
289,000
258,000
318,000
703,000
975,000
973,000
877,000
1,297,000
1,609,000
1,629,000
1,387,000
1,288,000
1,272,000
1,079,000
729,000
399,000
117,000
15,797,000

6.9 Uncertainty and Risk

Since future events are always uncertain, all estimates of costs
and benefits used in economic evaluation involve a degree of
uncertainty. Probabilistic methods are often used in decision
analysis to determine expected costs and benefits as well as to
assess the degree of risk in particular projects.

In estimating benefits and costs, it is common to attempt to
obtain the expected or average values of these quantities
depending upon the different events which might occur.
Statistical techniques such as regression models can be used
directly in this regard to provide forecasts of average values.
Alternatively, the benefits and costs associated with different
events can be estimated and the expected benefits and costs
calculated as the sum over all possible events of the resulting
benefits and costs multiplied by the probability of occurrence of
a particular event:

where q = 1,....,m represents possible events, (Bt|q) and (Ct|q)
are benefits and costs respectively in period t due to the
occurrence of q, Pr{q} is the probability that q occurs, and E[Bt]
and E[Ct] are respectively expected benefit and cost in period t.
Hence, the expected net benefit in period t is given by:

For example, the average cost of a facility in an earthquake
prone site might be calculated as the sum of the cost of
operation under normal conditions (multiplied by the probability
of no earthquake) plus the cost of operation after an earthquake
(multiplied by the probability of an earthquake). Expected
benefits and costs can be used directly in the cash flow
calculations described earlier.

In formulating objectives, some organizations wish to avoid risk
so as to avoid the possibility of losses. In effect, a risk
avoiding organization might select a project with lower expected
profit or net social benefit as long as it had a lower risk of
losses. This preference results in a risk premium or higher
desired profit for risky projects. A rough method of representing
a risk premium is to make the desired MARR higher for risky
projects. Let rf be the risk free market rate of interest as
represented by the average rate of return of a safe investment
such as U.S. government bonds.

However, U.S. government bonds do not protect from
inflationary changes or exchange rate fluctuations, but only
insure that the principal and interest will be repaid. Let rp be the
risk premium reflecting an adjustment of the rate of return for
the perceived risk. Then, the risk-adjusted rate of return r is
given by:

In using the risk-adjusted rate of return r to compute the net
present value of an estimated net cash flow At (t = 0, 1, 2, ..., n)
over n years, it is tacitly assumed that the values of At become
more uncertain as time goes on. That is:
(6.23)

More directly, a decision maker may be confronted with the
subject choice among alternatives with different expected
benefits of levels of risk such that at a given period t, the
decision maker is willing to exchange an uncertain At with a
smaller but certain return atAt where at is less than one.
Consider the decision tree in Figure 6-2 in which the decision
maker is confronted with a choice between the certain return of
atAt and a gamble with possible outcomes (At;)q and respective
probabilities Pr{q} for q = 1,2,...,m. Then, the net present value
for the series of "certainty equivalents" over n years may be
computed on the basis of the risk free rate. Hence:

Note that if rfrp is negligible in comparison with r, then
(1 + rf)(1 + rp) = 1 +rf + rp + rfrp = 1 + r
Hence, for Eq. (6.23)
At(1 + r)-t = (atAt/at)(1 + rf)-t(1 + rp)-t =[(atAt)(1 + rf)-t][(1 + rp)-
t/at]
If at = (1 + rp)-t for t = 1,2,...,n, then Eqs. (6.23) and (6.24) will be
identical. Hence, the use of the risk-adjusted rate r for
computing NPV has the same effect as accepting at = (1 + rp)-
t as a "certainty equivalent" factor in adjusting the estimated
cash flow over time.

Figure 6-2 Determination of a Certainty
Equivalent Value

6.10 Effects of Financing on Project Selection

6.10 Effects of Financing on
Project Selection
Selection of the best design and financing plans for capital
projects is typically done separately and sequentially. Three
approaches to facility investment planning most often adopted
by an organization are:

Project Selection
1. Need or demand driven: Public capital investments are
defined and debated in terms of an absolute "need" for
particular facilities or services. With a pre-defined "need,"
design and financing analysis then proceed separately. Even
when investments are made on the basis of a demand or
revenue analysis of the market, the separation of design and
financing analysis is still prevalent.

Project Selection
2. Design driven: Designs are generated, analyzed and
approved prior to the investigation of financing alternatives,
because projects are approved first and only then
programmed for eventual funding.
3. Finance driven: The process of developing a facility within a
particular budget target is finance-driven since the budget is
formulated prior to the final design. It is a common
procedure in private developments and increasingly used for
public projects.

Project Selection
Typically, different individuals or divisions of an organization
conduct the analysis for the operating and financing processes.
Financing alternatives are sometimes not examined at all since
a single mechanism is universally adopted. An example of a
single financing plan in the public sector is the use of pay-as-
you-go highway trust funds. However, the importance of
financial analysis is increasing with the increase of private
ownership and private participation in the financing of public
projects.

Project Selection
The availability of a broad spectrum of new financing
instruments has accentuated the needs for better financial
analysis in connection with capital investments in both the
public and private sectors. While simultaneous assessment of
all design and financing alternatives is not always essential,
more communication of information between the two evaluation
processes would be advantageous in order to avoid the
selection of inferior alternatives.

Project Selection
There is an ever increasing variety of borrowing mechanisms
available. First, the extent to which borrowing is tied to a
particular project or asset may be varied. Loans backed by
specific, tangible and fungible assets and with restrictions on
that asset's use are regarded as less risky. In contrast, specific
project finance may be more costly to arrange due to
transactions costs than is general corporate or government
borrowing.

Project Selection
Also, backing by the full good faith and credit of an organization
is considered less risky than investments backed by generally
immovable assets. Second, the options of fixed versus variable
rate borrowing are available. Third, the repayment schedule and
time horizon of borrowing may be varied. A detailed discussion
of financing of constructed facilities will be deferred until the
next chapter.

Project Selection
As a general rule, it is advisable to borrow as little as possible
when borrowing rates exceed the minimum attractive rate of
return. Equity or pay-as-you-go financing may be desirable in
this case. It is generally preferable to obtain lower borrowing
rates, unless borrowing associated with lower rates requires
substantial transaction costs or reduces the flexibility for
repayment and refinancing. In the public sector, it may be that
increasing taxes or user charges to reduce borrowing involves
economic costs in excess of the benefits of reduced borrowing
costs of borrowed funds.

Project Selection
Furthermore, since cash flow analysis is typically conducted on
the basis of constant dollars and loan agreements are made
with respect to current dollars, removing the effects of inflation
will reduce the cost of borrowing. Finally, deferring investments
until pay-as-you-go or equity financing are available may unduly
defer the benefits of new investments.

Project Selection
It is difficult to conclude unambiguously that one financing
mechanism is always superior to others. Consequently,
evaluating alternative financing mechanisms is an important
component of the investment analysis procedure. One possible
approach to simultaneously considering design and financing
alternatives is to consider each combination of design and
financing options as a specific, mutually exclusive alternative.
The cash flow of this combined alternative would be the sum of
the economic or operating cash flow (assuming equity
financing) and the financial cash flow over the planning horizon.

6.11 Combined Effects of Operating and Financing Cash
Flows

6.11 Combined Effects of Operating
and Financing Cash Flows
A general approach for obtaining the combined effects of
operating and financing cash flows of a project is to make use
of the additive property of net present values by calculating an
adjusted net present value. The adjusted net present value
(APV) is the sum of the net present value (NPV) of the
operating cash flow plus the net present value of the financial
cash flow due to borrowing or raising capital (FPV). Thus,

where each function is evaluated at i=MARR if both the
operating and the financing cash flows have the same degree of
risk or if the risks are taken care of in other ways such as by the
use of certainty equivalents. Then, project selection involving
both design and financing alternatives is accomplished by
selecting the combination which has the highest positive
adjusted present value. The use of this adjusted net present
value method will result in the same selection as an evaluation
based on the net present value obtained from the combined
cash flow of each alternative combination directly.

To be specific, let At be the net operating cash flow, be the net
financial cash flow resulting from debt financing, and AAt be the
combined net cash flow, all for year t before tax. Then:

Similarly, let and YYt be the corresponding cash flows after tax
such that:
The tax shields for interest on borrowing (for t = 1, 2, ..., n) are
usually given by

where It is the interest paid in year t and Xt is the marginal
corporate income tax rate in year t. In view of Eqs. (6.13), (6.27)
and (6.28), we obtain

When MARR = i is applied to both the operating and the
financial cash flows in Eqs. (6.13) and (6.28), respectively, in
computing the net present values, the combined effect will be
the same as the net present value obtained by applying MARR
= i to the combined cash flow in Eq.

In many instances, a risk premium related to the specified type
of operation is added to the MARR for discounting the operating
cash flow. On the other hand, the MARR for discounting the
financial cash flow for borrowing is often regarded as relatively
risk-free because debtors or holders of corporate bonds must
be paid first before stockholders in case financial difficulties are
encountered by a corporation. Then, the adjusted net present
value is given by

where NPV is discounted at r and FPV is obtained from the
rf rate. Note that the net present value of the financial cash flow
includes not only tax shields for interest on loans and other
forms of government subsidy, but also on transactions costs
such as those for legal and financial services associated with
issuing new bonds or stocks.

The evaluation of combined alternatives based on the adjusted
net present value method should also be performed in dollar
amounts which either consistently include or remove the effects
of inflation. The MARR value used would reflect the inclusion or
exclusion of inflation accordingly. Furthermore, it is preferable to
use after-tax cash flows in the evaluation of projects for private
firms since different designs and financing alternatives are likely
to have quite different implications for tax liabilities and tax
shields.

In theory, the corporate finance process does not necessarily
require a different approach than that of the APV method
discussed above. Rather than considering single projects in
isolation, groups or sets of projects along with financing
alternatives can be evaluated. The evaluation process would be
to select that group of operating and financing plans which has
the highest total APV.

Unfortunately, the number of possible combinations to evaluate
can become very large even though many combinations can be
rapidly eliminated in practice because they are clearly inferior.
More commonly, heuristic approaches are developed such as
choosing projects with the highest benefit/cost ratio within a
particular budget or financial constraint. These heuristic
schemes will often involve the separation of the financing and
design alternative evaluation. The typical result is design-driven
or finance-driven planning in which one or the other process is
conducted first.

Example 6-5: Combined Effects of Operating and Financing
Plans

Example 6-5: Combined Effects of
Operating and Financing Plans
A public agency plans to construct a facility and is considering
two design alternatives with different capacities. The operating
net cash flows for both alternatives over a planning horizon of 5
years are shown in Table 6-4. For each design alternative, the
project can be financed either through overdraft on bank credit
or by issuing bonds spanning over the 5-year period, and the
cash flow for each financing alternative is also shown in Table
6-4. The public agency has specified a MARR of 10% for
discounting the operating and financing cash flows for this
project. Determine the best combination of design and financing
plan if:

a) a design is selected before financing plans are considered,
or
b) the decision is made simultaneously rather than
sequentially.

The net present values (NPV) of all cash flows can be
computed by Eq.(6.5), and the results are given at the bottom of
Table 6-4. The adjusted net present value (APV) combining the
operating cash flow of each design and an appropriate financing
is obtained according to Eq. (6.25), and the results are also
tabulated at the bottom of Table 6-4.

Under condition (a), design alternative 2 will be selected since
NPV = $767,000 is the higher value when only operating cash
flows are considered. Subsequently, bonds financing will be
chosen because APV = $466,000 indicates that it is the best
financing plan for design alternative 2

Under condition (b), however, the choice will be based on the
highest value of APV, i.e., APV = $484,000 for design
alternative one in combination will overdraft financing. Thus, the
simultaneous decision approach will yield the best results.

Year
Design Alternative One Design Alternative Two
Operating
Cash
Flow
Overdraft
Financing
Bond
Financing
Operating
Cash
Flow
Overdraft
Financing
Bond
Financing
0
1
2
3
4
5
-$1,000
-2,500
1,000
1,500
1,500
1,700
$1,000
2,500
-1,000
-1,500
-1,500
-921
$3,653
-418
-418
-418
-418
-4,217
$-2,500
-1,000
1,000
1,500
1,500
1,930
$2,500
1,000
-1,000
-1,500
-1,500
-1,254
$3,805
-435
-435
-435
-435
-4,392
NPV or
FPV at
10%
761 -277 -290 767 -347 -301
APV =
NPV +
FPV
484 471 420 466

6.12 Public versus Private Ownership of Facilities

6.12 Public versus Private
Ownership of Facilities
In recent years, various organizational ownership schemes
have been proposed to raise the level of investment in
constructed facilities. For example, independent authorities are
assuming responsibility for some water and sewer systems,
while private entrepreneurs are taking over the ownership of
public buildings such as stadiums and convention centers in
joint ventures with local governments. Such ownership
arrangements not only can generate the capital for new
facilities, but also will influence the management of the
construction and operation of these facilities. In this section, we
shall review some of these implications

A particular organizational arrangement or financial scheme is
not necessarily superior to all others in each case. Even for
similar facilities, these arrangements and schemes may differ
from place to place or over time. For example, U.S. water
supply systems are owned and operated both by relatively large
and small organizations in either the private or public sector.
Modern portfolio theory suggest that there may be advantages
in using a variety of financial schemes to spread risks. Similarly,
small or large organizations may have different relative
advantages with respect to personnel training, innovation or
other activities.

Differences in Required Rates of Return

Differences in Required
Rates of Return
A basic difference between public and private ownership of
facilities is that private organizations are motivated by the
expectation of profits in making capital investments.
Consequently, private firms have a higher minimum attractive
rate of return (MARR) on investments than do public agencies.
The MARR represents the desired return or profit for making
capital investments..

Rates of Return
Furthermore, private firms often must pay a higher interest rate
for borrowing than public agencies because of the tax exempt
or otherwise subsidized bonds available to public agencies.
International loans also offer subsidized interest rates to
qualified agencies or projects in many cases. With higher
required rates of return, we expect that private firms will require
greater receipts than would a public agency to make a particular
investment desirable

Rates of Return
In addition to different minimum attractive rates of return, there
is also an important distinction between public and private
organizations with respect to their evaluation of investment
benefits. For private firms, the returns and benefits to cover
costs and provide profit are monetary revenues. In contrast,
public agencies often consider total social benefits in evaluating
projects. Total social benefits include monetary user payments
plus users' surplus (e.g., the value received less costs incurred
by users), external benefits (e.g., benefits to local businesses or
property owners) and nonquantifiable factors (e.g.,
psychological support, unemployment relief, etc.). Generally,
total social benefits will exceed monetary revenues.

Rates of Return
While these different valuations of benefits may lead to radically
different results with respect to the extent of benefits associated
with an investment, they do not necessarily require public
agencies to undertake such investments directly. First, many
public enterprises must fund their investments and operating
expenses from user fees. Most public utilities fall into this
category, and the importance of user fee financing is increasing
for many civil works such as waterways. With user fee
financing, the required returns for the public and private firms to
undertake the aforementioned investment are, in fact, limited to
monetary revenues. As a second point, it is always possible for
a public agency to contract with a private firm to undertake a
particular project.

Rates of Return
All other things being equal, we expect that private firms will
require larger returns from a particular investment than would a
public agency. From the users or taxpayers point of view, this
implies that total payments would be higher to private firms for
identical services. However, there are a number of mitigating
factors to counterbalance this disadvantage for private firms.

Tax Implications of Public Versus Private Organizations

Tax Implications of Public
Versus Private Organizations
Another difference between public and private facility owners is
in their relative liability for taxes. Public entities are often
exempt from taxes of various kinds, whereas private facility
owners incur a variety of income, property and excise taxes.
However, these private tax liabilities can be offset, at least in
part, by tax deductions of various kinds.

For private firms, income taxes represent a significant cost of
operation. However, taxable income is based on the gross
revenues less all expenses and allowable deductions as
permitted by the prevalent tax laws and regulations. The most
significant allowable deductions are depreciation and interest.
By selecting the method of depreciation and the financing plan
which are most favorable, a firm can exert a certain degree of
control on its taxable income and, thus, its income tax.

Another form of relief in tax liability is the tax credit which allows
a direct deduction for income tax purposes of a small
percentage of the value of certain newly acquired assets.
Although the provisions for investment tax credit for physical
facilities and equipment had been introduced at different times
in the US federal tax code, they were eliminated in the 1986
Tax Reformation Act except a tax credit for low-income housing.

Of course, a firm must have profits to take direct advantage of
such tax shields, i.e., tax deductions only reduce tax liabilities if
before-tax profits exist. In many cases, investments in
constructed facilities have net outlays or losses in the early
years of construction. Generally, these losses in early years can
be offset against profits occurred elsewhere or later in time.
Without such offsetting profits, losses can be carried forward by
the firm or merged with other firms' profits, but these
mechanisms will not be reviewed here.

Effects of Financing Plans

Major investments in constructed facilities typically rely upon
borrowed funds for a large portion of the required capital
investments. For private organizations, these borrowed funds
can be useful for leverage to achieve a higher return on the
organizations' own capital investment.

For public organizations, borrowing costs which are larger than
the MARR results in increased "cost" and higher required
receipts. Incurring these costs may be essential if the
investment funds are not otherwise available: capital funds must
come from somewhere. But it is not unusual for the borrowing
rate to exceed the MARR for public organizations. In this case,
reducing the amount of borrowing lowers costs, whereas
increasing borrowing lowers costs whenever the MARR is
greater than the borrowing rate.

Although private organizations generally require a higher rate of
return than do public bodies (so that the required receipts to
make the investment desirable are higher for the private
organization than for the public body), consideration of tax
shields and introduction of a suitable financing plan may reduce
this difference. The relative levels of the MARR for each group
and their borrowing rates are critical in this calculation.

Effects of Capital Grant Subsidies

Effects of Capital Grant
Subsidies
An important element in public investments is the availability of
capital grant subsidies from higher levels of government. For
example, interstate highway construction is eligible for federal
capital grants for up to 90% of the cost. Other programs have
different matching amounts, with 50/50 matching grants
currently available for wastewater treatment plants and various
categories of traffic systems improvement in the U.S. These
capital grants are usually made available solely for public
bodies and for designated purposes.

Effects of Capital Grant
Subsidies
While the availability of capital grant subsidies reduces the local
cost of projects, the timing of investment can also be affected.
In particular, public subsidies may be delayed or spread over a
longer time period because of limited funds. To the extent that
(discounted) benefits exceed costs for particular benefits, these
funding delays can be costly. Consequently, private financing
and investment may be a desirable alternative, even if some
subsidy funds are available.

Implications for Design and Construction

Implications for Design and
Construction
Different perspectives and financial considerations also may
have implications for design and construction choices. For
example, an important class of design decisions arises relative
to the trade-off between capital and operating costs. It is often
the case that initial investment or construction costs can be
reduced, but at the expense of a higher operating costs or more
frequent and extensive rehabilitation or repair expenditures. It is
this trade-off which has led to the consideration of "life cycle
costs" of alternative designs. The financial schemes reviewed
earlier can profoundly effect such evaluations.

Construction
For financial reasons, it would often be advantageous for a
public body to select a more capital intensive alternative which
would receive a larger capital subsidy and, thereby, reduce the
project's local costs. In effect, the capital grant subsidy would
distort the trade-off between capital and operating costs in favor
of more capital intensive projects.

Construction
The various tax and financing considerations will also affect the
relative merits of relatively capital intensive projects. For
example, as the borrowing rate increases, more capital
intensive alternatives become less attractive. Tax provisions
such as the investment tax credit or accelerated depreciation
are intended to stimulate investment and thereby make more
capital intensive projects relatively more desirable. In contrast, a
higher minimum attractive rate of return tends to make more
capital intensive projects less attractive.

6.13 Economic Evaluation of Different Forms of Ownership

6.13 Economic Evaluation of
Different Forms of Ownership
While it is difficult to conclude definitely that one or another
organizational or financial arrangement is always superior,
different organizations have systematic implications for the
ways in which constructed facilities are financed, designed and
constructed. Moreover, the selection of alternative investments
for constructed facilities is likely to be affected by the type and
scope of the decision-making organization.

As an example of the perspectives of public and private
organizations, consider the potential investment on a
constructed facility with a projected useful life of n years. Let t =
0 be the beginning of the planning horizon and t = 1, 2, ... n
denote the end of each of the subsequent years. Furthermore,
let Co be the cost of acquiring the facility at t = 0, and Ct be the
cost of operation in year t. Then, the net receipts At in year t is
given by At = Bt - Ct in which Bt is the benefit in year t and
At may be positive or negative for t = 0, 1, 2, ..., n.

Let the minimum attractive rate of return (MARR) for the owner
of the facility be denoted by i. Then, the net present value
(NPV) of a project as represented by the net cash flow
discounted to the present time is given by

Then, a project is acceptable if NPV0. When the annual gross
receipt is uniform, i.e., Bt = B for t = 1, 2, ..., n and B0 = 0, then,
for NPV = 0:
Thus, the minimum uniform annual gross receipt B which
makes the project economically acceptable can be determined
from Equation (6.32), once the acquisition and operation costs
Ct of the facility are known and the MARR is specified

Example 6-6: Different MARRs for Public and Private
Organizations

Example 6-6: Different MARRs for
Public and Private Organizations
For the facility cost stream of a potential investment with n = 7
in Table 6-5, the required uniform annual gross receipts B are
different for public and private ownerships since these two types
of organizations usually choose different values of MARR. With
a given value of MARR = i in each case, the value of B can be
obtained from Eq. (6.32). With a MARR of 10%, a public agency
requires at least B = $184,000.

By contrast, a private firm using a 20% MARR before tax while
neglecting other effects such as depreciation and tax deduction
would require at least B = $219,000. Then, according to Eq.
(6.31), the gross receipt streams for both public and private
ownerships in Table 6-5 will satisfy the condition NPV = 0 when
each of them is netted from the cost stream and discounted at
the appropriate value of MARR, i.e., 10% for a public agency
and 20% (before tax) for a private firm. Thus, this case
suggests that public provision of the facility has lower user
costs.

ar t
Facility
cost, Ct
Public Ownership Private Ownership
Gross
Receipt,
Bt
Net
Receipt
At=Bt - Ct
Gross
Receipt,
Bt
Net
Receipt
At=Bt - Ct
0
1
2
3
4
5
6
7
$500
76
78
80
82
84
86
88
$0
184
184
184
184
184
184
184
-$500
108
106
104
102
100
98
96
$0
219
219
219
219
219
219
219
-$500
143
141
139
137
135
133
131
TABLE 6-6 Required Uniform Annual Gross Receipts for Public and Private
Ownership of a Facility (in $ thousands)

Example 6-7: Effects of Depreciation and Tax Shields for
Private Firms

Example 6-7: Effects of Depreciation
and Tax Shields for Private Firms
Using the same data as in Example 6-6, we now consider the
effects of depreciation and tax deduction for private firms.
Suppose that the marginal tax rate of the firm is 34% in each
year of operation, and losses can always be offset by company-
wide profits. Suppose further that the salvage value of the
facility is zero at the end of seven years so that the entire
amount of cost can be depreciated by means of the sum-of-the-
years'-digits (SOYD) method. Thus, for the sum of digits 1
through 7 equal to 28, the depreciation allowances for years 1
to 7 are respectively 7/28, 6/28, ..., 1/28 of the total depreciable
value of $ 500,000, and the results are recorded in column 3 of
Table 6-6.

For a uniform annual gross receipt B = $219,000, the net
receipt before tax in Column 6 of Table 6-5 in Example 6-5 can
be used as the starting point for computing the after-tax cash
flow according to Equation (6.13) which is carried out step-by-
step in Table 6-6. (Dollar amounts are given to the nearest
$1,000). By trial and error, it is found that an after-tax MARR =
14.5% will produce a zero value for the net present value of the
discounted after-tax flow at t = 0. In other words, the required
uniform annual gross receipt for this project at 14.5% MARR
after tax is also B = $219,000. It means that the MARR of this
private firm must specify a 20% MARR before tax in order to
receive the equivalent of 14.5% MARR after tax.

Year t
Net
Receipt
Before-tax
At
Depreciati
on
(SOYD)
Dt
Taxable
Income
(At - Dt)
Income
Tax
Xt(At - Dt)
After-tax
Cash Flow
0
1
2
3
4
5
6
7
-$500
143
141
139
137
135
133
131
$0
125
107
89
71
54
36
18
$0
18
34
50
66
81
97
113
$0
6
12
17
22
28
33
38
-$500
137
129
122
115
107
100
93
TABLE6-7 Effects of Depreciation and Tax Deductions for Private Ownership
in a Facility (in $ thousands)

Example 6-8: Effects of Borrowing on Public Agencies

Borrowing on Public Agencies
Suppose that the gross uniform annual receipt for public
ownership is B = $190,000 instead of $184,000 for the facility
with cost stream given in Column 2 of Table 6-5. Suppose
further that the public agency must borrow $400,000 (80% of
the facility cost) at 12% annual interest, resulting in an annual
uniform payment of $88,000 for the subsequent seven years.
This information has been summarized in Table 6-7. The use of
borrowed funds to finance a facility is referred to as debt
financing or leveraged financing, and the combined cash flow
resulting from operating and financial cash flows is referred to
as the levered cash flow.

To the net receipt At in Column 4 of Table 6-7, which has been
obtained from a uniform annual gross receipt of $190,000, we
add the financial cash flow , which included a loan of $400,000
with an annual repayment of $88,000 corresponding to an
interest rate of 12%. Then the resulting combined cash flow
AAt as computed according to Equation (6.26) is shown in
column 6 of Table 6-7. Note that for a loan at 12% interest, the
net present value of the combined cash flow AAt is zero when
discounted at a 10% MARR for the public agency. This is not a
coincidence, but several values of B have been tried until B =
$190,000 is found to satisfy NPV = 0 at 10% MARR. Hence, the
minimum required uniform annual gross receipt is B =
$190,000.

Year
t
Gross
receipt
Bt
Facility
cost
Ct
Net
receipt
(no loan)
At
Loan and
payment
(12%
interest)
Combined
cash flow
(12%
interest)
AAt
0
1
2
3
4
5
6
7
$0
190
190
190
190
190
190
190
$500
76
78
80
82
84
86
88
-$500
114
112
110
108
106
104
102
+$400
-88
-88
-88
-88
-88
-88
-88
-$100
26
24
22
20
18
16
14
TABLE 6-8 Effects of Borrowing on a Publicly Owned Facility (in $ thousands)

Example 6-10: Comparison of Public and Private
Ownership

Example 6-9: Comparison of
Public and Private Ownership
In each of the analyses in Examples 6-5 through 6-8, a
minimum required uniform annual gross receipt B is computed
for each given condition whether the owner is a public agency
or a private firm. By finding the value of B which will lead to
NPV = 0 for the specified MARR for the organization in each
case, various organizational effects with or without borrowing
can be analyzed. The results are summarized in Table 6-9 for
comparison. In this example, public ownership with a 80% loan
and a 10% MARR has the same required benefit as private
ownership with an identical 80% loan and a 14.5% after-tax
MARR.

Organizational
condition
Financial
arrangement
Minimum benefit
required
Public, no tax
(MARR = 10%)
No loan
80% loan at 12%
interest
$184,000
190,000
Private, before tax
(MARR = 20%)
No loan 219,000
219,000
Private, after tax
(MARR = 14.5%)
No loan
80% loan at 12%
interest
219,000
190,000
TABLE 6-19 Summary effects of Financial Leverage and Tax Shields on Private
Ownership

6.14 References

6.14 References
1. Au, T., "Profit Measures and Methods of Economic Analysis
for Capital Project Selection," ASCE Journal of Management
in Engineering, Vol. 4, No. 3, 1988.
2. Au, T. and T. P. Au, Engineering Economics for Capital
Investment Analysis, Allyn and Bacon, Newton, MA, 1983.
3. Bierman, H., Jr., and S. Smidt, The Capital Budgeting
Decision, 5th Ed., Macmillan, New York, 1984.
4. Brealey, R. and S. Myers, Principles of Corporate
Finance, Second Edition, McGraw-Hill, New York, 1984.

6.14 References
5. Edwards, W.C. and J.F. Wong, "A Computer Model to
Estimate Capital and Operating Costs," Cost
Engineering, Vol. 29, No. 10, 1987, pp. 15-21.
6. Hendrickson, C. and T. Au, "Private versus Public
Ownership of Constructed Facilities," ASCE Journal of
Management in Engineering,Vol. 1, No. 3, 1985, pp. 119-
131.
7. Wohl, M. and C. Hendrickson, Transportation Investment
and Pricing Principles, John Wiley, New York, 1984.

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