Chapter 2 - Cost Estimation: Concepts and Methodology, Lecture notes of Accounting

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Section 1

Introduction

Chapter 2

Cost Estimation: Concepts and Methodology

John L. Sorrels

Thomas G. Walton

Air Economics Group

Health and Environmental Impacts Division

Office of Air Quality Planning and Standards

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

November 2017

2.1 Introduction

This chapter presents a methodology that will enable the user, having knowledge of the

source being controlled, to produce study-level estimates of the costs incurred by regulated entities

for a control system applied to that source. The methodology, which applies to each of the control

systems included in this Manual, is general enough to be used with other “add-on” systems as well.

Further, the methodology can apply to estimating the costs of fugitive emission controls and other

non-stack abatement methods.

There are several types of users for this Manual. Industrial users are the most common,

but State, local, other officials, and other environmental stakeholders (e.g., environmental groups)

are other users of the Manual. EPA strongly recommends that the methodology in this Manual be

followed as part of compliance with various Clean Air Act programs.

The cost estimation methodology can be used in the development of assessing private

compliance decisions/strategies or effects of permits as various alternatives are considered. If the

regulation or permit prescribes a particular control technology (e.g., installation of a scrubber),

then the costs of individual controls can be estimated for affected entities. If the regulation or

permit establishes performance standards, with flexibility as to how the standards can be achieved,

then the cost estimation methods can be used to estimate the costs of various options for achieving

the standards.

We note that these cost estimation procedures are meant to support the calculation of the

costs of purchasing and installing pollution control equipment, and then operating and maintaining

this equipment, at a facility. Such costs are private costs because they reflect the private choices

and decisions of the owners and operators of the facilities. Broader costs associated with the

installation and operation of pollution control equipment, such as impacts on society (e.g., changes

in prices to consumers due to the impact on a producer from additional pollution control) are

analyzed using methods that assess the social costs of regulatory intervention.

Again, the methods provided in this Manual is to aid in assessing private choices that

regulated entities may undertake in complying with regulation. Analyzing private decisions and

the associated costs are important in and of itself and can be used as inputs to assessing the likely

effects of regulations. In other words, the cost estimation methodology in this Manual is meant

for private cost estimation, not social cost estimation. Information on social cost estimation can

be found in the EPA Economic Guidelines and the U.S. Office of Management and Budget’s

Circular A-4. This Manual is not intended to assess the likely effects of federal regulations to

society, but is intended to provide assessment of private actions which can be inputs to social

impacts analysis.

Users with the role of developing or reviewing compliance plans can use this Manual to

estimate private costs of installing and operating control equipment. Regulated entities facing

regulation can use this Manual to help decide how to comply with the requirements they are facing.

2. 2 Private Versus Social Costs

Before delving deeper into a discussion on estimating private costs, identifying the

differences between private and social costs is important. The Manual focuses on private cost,

which refers to the costs borne by a private entity for an action the private entity decides. For

example, if the private entity pays for the cost of installing and operating pollution control

equipment, among many options available to the entity, the entirety of these costs would be

considered private costs.

The EPA’s Guidelines for Preparing Economic Analysis define social cost as follows:

“Social cost represents the total burden a regulation will impose on the economy; it can be defined

as the sum of all opportunity costs incurred as a result of a regulation. These opportunity costs

consist of the value lost to society of all the goods and services that will not be produced and

consumed if firms comply with the regulation and reallocate resources away from production

activities and towards pollution abatement. To be complete, an estimate of social cost should

include both the opportunity costs of current consumption that will be forgone as a result of the

regulation, and the losses that may result if the regulation reduces capital investment and thus

future consumption.”

1

The term social cost refers to the overall cost of an action to society, not just to the private

entity that incurs the expense to control pollution. Social cost is based on the concept of

opportunity cost, the value associated with production and consumption that are reduced or

changed as a result of reallocating resources to reduce pollution.

Assessing private cost is more straightforward because it attempts to tally up expenses that

individual entities or facilities incur to purchase, finance, and operate pollution abatement

equipment or strategies. Suppose a state government wanted to encourage pollution control for a

certain industry and provided grants to pay half of the costs of a scrubber. The private cost for the

industry would be 50% of the cost of a scrubber. Using another example, suppose a firm purchases

equipment, pays sales tax on the item, and receives an immediate tax rebate. The private cost to

the firm is the sum of the equipment price plus the sales tax amount minus the excise tax amount.

The estimation of private costs is the focus of the cost estimation procedures and data in

this Manual. Both EPA and OMB have developed guidance on methods appropriate for use in

estimating social costs for regulatory impact analysis or economic impact analysis where the social

costs of government interventions are assessed. The guidelines presented in this Manual are not

suitable in conducting regulatory impact analysis or economic impact analysis where the social

costs of government interventions are assessed. Because this Manual focuses on private costs to

facilities of installing and operating pollution control equipment, we will not present the

1

U.S. Environmental Protection Agency, Office of Policy, National Center for Environmental Economics.

Guidelines for Preparing Analysis. May 2014. Pp. 8- 1 – 8 - 2.

probable error bounds are greater than 30%. (However, according to Perry’s, “… no

limits of accuracy can safely be applied to it.”) The sole input required for making this

level of estimate is the control system’s capacity (often measured by the maximum

volumetric flow rate of the gas passing through the system).

 Scope, Budget Authorization, or Preliminary. This estimate, with probable error of

20%, requires more detailed knowledge than the study estimate regarding the site,

flow sheet, equipment, buildings, etc. In addition, rough specifications for the

insulation and instrumentation are also needed.

 Project Control or Definitive. This estimate, with a probable error of 10%, requires yet

more information than the scope estimates, especially concerning the site, equipment,

and electrical requirements.

 Firm, Contractor’s, or Detailed. This is the most accurate (probable error of 5%) of the

estimate types, requiring complete drawings, specifications, and site surveys.

Consequently, detailed cost estimates are typically not available until right before

construction, since “time seldom permits the preparation of such estimates prior to an

approval to proceed with the project.”[1]

ACCURACY

± 0 % ± 5 % ± 10 % ± 20 % ± 30 %

Post- Detailed Project Scoping Study Order of Magnitude

Construction Control

Reports

Figure 2.1: The Continuum of Accuracy for Cost Analyses

These error bands are attempts at assessing the probable errors associated with each

estimation method based on past practices of the engineering cost-estimation discipline. However,

the error bands do not shed any light on the distribution of the likely errors. The users of this

Manual should not draw conclusions about probable errors that this Manual does not intend.

Study-level estimates represent a compromise between the less accurate order-of-

magnitude estimates and the more accurate estimate types. The former is too imprecise to be of

much value in the context of pollution control installation and operation, while the latter are very

expensive for an entity to prepare, and require detailed site- and process-specific knowledge that

some Manual users are unlikely to have. Over time, this Manual has become the standard for air

pollution control costing methodologies for many State regulatory agencies. For example, Virginia

requires that the Manual be used in making cost estimates for BACT and other permit applications,

unless the permit applicant can provide convincing proof that another cost reference should be

used.

2

Texas accepts the Manual methodology “as a sound source for the quantitative cost

analysis” for BACT analyses it reviews.

3

The industrial user is more likely to have site-specific and detailed information than the

average cost and sizing information used in a study estimate. The methodology laid out in this

Manual can provide cost estimates that are more accurate when using detailed site-specific

information. The anecdotal evidence from most testimonials volunteered by industrial users

indicates that much greater accuracy than 30 percent probable error can be attained. However,

this Manual does not assume that detailed site-specific information will always be available to

estimate costs associated with installing and operating pollution abatement equipment at a much

higher accuracy level. This Manual retains the conclusion that the cost methodology laid out in

this chapter and information in each control measure chapter with 30% probable error is relevant

to be used in air pollution control cost estimation for permitting actions. It is the affected industry

source that bears the burden of providing information of sufficient quality that will yield cost

estimates of at least a study-level estimate for permitting decisions pertaining to their facilities.

2. 4 Cost Categories Defined

The terminology addressing cost categories used in the earlier editions of this Manual was

adapted from the AACEI. [2]. However, different disciplines give different names to the same cost

components, and the objective of this edition is to reach out to a broader scientific audience. For

example, engineers determine a series of equal payments over a long period of time that fully funds

a capital project (and its operations and maintenance) by multiplying the present value of those

costs by a capital recovery factor, which produces an Equivalent Uniform Annual Cost (EUAC)

value. This is identical to the process used by accountants and financial analysts, who adjust the

present value of the project’s cash flows to derive an annualized cost number.

2. 4 .1 Elements of Total Capital Investment

In assessing the total capital investment, this Manual takes the viewpoint of an owner, the

firms making the investment, or those who have material interest in the project. Total capital

investment (TCI) includes all costs required to purchase equipment needed for the control system

(purchased equipment costs), the costs of labor and materials for installing that equipment (direct

installation costs), costs for site preparation and buildings, and certain other costs (indirect

installation costs). TCI also includes costs for land, working capital, and off-site facilities.

4

Taxes,

permitting costs, and other administrative costs are covered in Section 2. 6 .5.8. Financing costs

2

State of Virginia, Department of Environmental Quality. Draft PSD Guidelines, August 4, 2011. Pp. 4-4 to 4-5.

3

Texas Commission on Environmental Quality. Air Permits Division. Air Permit Reviewer Reference Guide,

APDG 6110. Appendix G. p. 45. January 2011.

4

Estimates of TCI for some control measures may not necessarily be calculated in this way due to availability

of public information on capital investment costs and equations for those measures, such as the SNCR and SCR

chapters in this Manual.

a

Typically factored from the sum of the primary control device and auxiliary equipment costs.

b

Typically factored from the purchases equipment cost.

c

Usually required only at “grass roots” installations.

d

Unlike the other direct and indirect costs, costs for these items usually are not factored from the purchased equipment

cost. Rather, they are sized and costed separately.

e

Normally not required with add-on control systems.

Figure 2.2: Elements of Total Capital Investment

As Figure 2.2 shows, the installation of pollution control equipment may also require land,

but since some add-on control systems take up very little space (often a quarter-acre or less), this

cost may be relatively small. Certain control systems, such as those used for flue gas

desulfurization (FGD) or selective catalytic reduction (SCR), require larger quantities of land for

the equipment, chemicals storage, and waste disposal. In these cases, especially when performing

a retrofit installation, space constraints can significantly influence the cost of installation, and the

purchase of additional land and remediation of existing land and property may be a significant

factor in the development of the project’s capital costs.

e

However, land is not treated the same as other capital investments, since it is not

depreciated for accounting purposes. The value of the land may fluctuate depending on the market

conditions, but for accounting purposes and assessing private costs, land is not depreciated. The

purchase price of new land needed for siting a pollution control device can be added to the TCI,

but it must not be depreciated. If the firm plans on dismantling the device at some future time, the

value of the land should be included at the disposal point as an “income” to the project to net it

out of the cash flow analysis (more on cash flow analysis later, in section 2. 5 .4).

One might expect initial operational costs (the initial costs of fuel, chemicals, and other

materials, as well as labor and maintenance related to start-up) to be included in the operating

cost section of the cost analysis instead of in the capital component, but such an allocation would

be inappropriate. Routine operation of the control does not begin until the system has been

tested, balanced, and adjusted to work within its design parameters. Until then, all utilities

consumed, all labor expended, and all maintenance and repairs performed are a part of the

construction phase of the project and are included in the TCI in the “Start-Up” component of the

indirect installation costs.

In addition, the TCI of controls for sources that affect fan capacity (e.g., FGD scrubbers,

SCRs) may be impacted by the unit’s elevation with respect to sea level. Cost calculations for the

control measures within the Manual have typically been developed for systems located at sea level.

For systems located at higher elevations (generally over 500 feet above sea level), the purchased

equipment cost and balance of plant cost should be increased based on the ratio of the atmospheric

pressure between sea level and the location of the system, i.e., atmospheric pressure at sea level

divided by atmospheric pressure at the elevation of the unit.

5

The method for estimating TCI in this Manual is an “overnight” estimation method. This

method estimates capital cost as if no interest was incurred during construction and therefore

estimates capital cost as if the project is completed “overnight.” An alternate way of describing

this method is the present value cost that would have to be paid as a lump sum up front to

completely pay for a construction project. Cost items such as Allowance for Funds Used During

Construction (AFUDC), which is defined as the costs of debt and equity funds used to finance

plant construction, and is an amount credited on the firm’s statement of income and charged to

construction in progress on the firm’s balance sheet, is treated separately in Section 2. 5 .3 in this

Manual. This item is an estimate that is incurred over the timespan of construction. For

example, this is considered as a cost item within the electric power industry.

6

[15] Other cost

items similarly treated separately include escalation of costs to a future year due to inflation in

Section 2. 5 .4. We provide more discussion later in this chapter on these cost items that are not

included in this section.

5

One instance of this is the estimates of costs for the recently revised SNCR and SCR Control Cost Manual

chapters, which are available at http://www.epa.gov/ttn/ecas/costmodels.html.

6

See the National Energy Technology Laboratory’s “Quality Guidelines for Energy System Studies: Cost

Estimation Methodology for NETL Assessments of Power Plant Performance.”

Figure 2.3: Elements of Total Annual Cost

Indirect, or “fixed” annual costs are independent of the level of production (or whatever

unit of measure serves as the analytical metric) and, in fact, would be incurred even if the control

system were shut down. Indirect costs include such categories as administrative charges, property

taxes, insurance, administrative charges including permitting costs and capital cost amortized into

capital recovery.

Capital is depreciable, indicating that, as the capital is used, it wears out and that lost value

cannot be recovered. Economic depreciation, which is the lost value due to wear and tear, is

different than accounting depreciation, the declared lost value, that is usually used in a cost

analysis. Depreciation costs are a variable or semi-variable cost that is also included in the

calculation of tax credits (if any) and depreciation allowances whenever taxes are considered in a

cost analysis. However, taxes are not uniformly applied, and subsidies, tax moratoriums, and

deferred tax opportunities distort how the direct application of a tax works.

Finally, direct and indirect annual costs can be offset by recovery credits, taken for

materials or energy recovered by the control system, which may be sold, recycled to the process,

or reused elsewhere at the site. An example of such credits is the by-product of controlling sulfur

with a FGD scrubber. As the lime or limestone reagent reacts with the sulfur in the exhaust gas

stream, it becomes transformed into CaSO 4 - gypsum - which can be landfilled inexpensively (a

direct cost) or collected and sold to wallboard manufacturers (a recovery credit). These credits,

must be calculated as net of any associated processing, storage, transportation, and any other costs

required to make the recovered materials or energy reusable or resalable. Great care and judgment

must be exercised in assigning values to recovery credits, since materials recovered may be of

small quantity or of doubtful purity, resulting in their having less value than virgin material. Like

direct annual costs, recovery credits are variable, in that their magnitude is directly proportional

to level of production.

A more thorough description of these costs and how they may be estimated is provided in

Section 2. 6

2. 5 Financial Concepts

Firms have latitude in developing compliance strategies. For standards that are

performance oriented, firms have great latitude. Even for standards that are fairly prescriptive and

technical in nature, firms still have to make some choices on how to comply. How do they compare

these choices or alternatives?

Alternatives will usually have expenditures at multiple times. Not only may the

expenditures be different but the timing of expenditures may also be different. When comparing

two different investment opportunities, how do you distill all of these data into one comprehensive

and coherent form so that an informed decision can be made? This section deals with a number of

the concepts and operations that are needed to make a meaningful comparison. They include:

selection of an appropriate timeframe, addressing the time value of money, adjusting for prices

over time, and selection of the appropriate measure of cost.

2. 5 .1 Time Frame

To compare two alternatives in a meaningful way, the comparison is more meaningful

when the alternatives are examined over the same time frame or calculate the net present value of

the alternatives. For example, if one alternative uses a control device that lasts two years and

another alternative uses a device that lasts three years, the alternatives may be difficult to compare

directly because of the inconsistent lifetimes of the devices. One approach to developing a more

meaningful comparison would be to assume a common time frame by using each type of device

for six years, with the two-year alternative being replaced two times and the three-year alternative

being replaced once. Another approach is to calculate the net present value of the two alternatives.

Amortization or the EUAC method also can be helpful in comparing alternatives with different

lifetimes.

2.5.2 Interest Rates

Firms may borrow to finance the expenses associated with their compliance strategies. The

interest rate at which a firm borrows is a key component in estimating the total costs of compliance.

Financial markets set different interest rates for different activities depending on many factors.

System.

7

The bank prime rate is the “rate posted by a majority of the top 25 (by assets in

domestic offices) insured U.S. chartered commercial banks. The bank prime rate is one of

several base rates used by banks to price short-term business loans.”

8

Analysts should use the

bank prime rate with caution as these base rates used by banks do not reflect entity and project

specific characteristics and risks including the length of the project, and credit risks of the

borrowers.

For input to analysis of rulemakings, assessments of private cost should be prepared

using firm-specific nominal interest rates if possible, or the bank prime rate if firm-specific

interest rates cannot be estimated or verified. If neither of these types of private nominal rates are

available, then the cost analysis should use 3% or 7%, rates that are used for social cost

estimation as discussed later in this section, as a default. Analysts should be especially cautious

using 3% and 7% rates in assessing cost of short term assets or projects. These rates represent

long-run, real interest rates as described later in this section. Conflating real and nominal interest

rates may lead to different conclusions than using consistent interest rates throughout the

analysis. Private interest rates are but one component of the overall cost analysis, which will

include social cost estimation to reflect relevant guidance from OMB.

To clarify potential confusion that might arise, this Manual discusses the difference

between private interest rate and social discount rate. If capital markets are perfect with no

distortions (e.g., no taxes, no risk), then the return to savings (the consumption rate of interest)

equals the return on private sector investments. Therefore, when the government needs to convert

future costs and benefits into present value terms in the same way as the affected individuals would

do so, it should also discount using this single market rate of interest. In other words, in this “first

best” world, the private market interest rate would be an unambiguous choice for the social

discount rate. However, ‘real-world’ issues make the issue much more complicated. For example,

private sector investment returns are taxed (often at multiple levels), capital markets are not

perfect, and capital investments often involve risks reflected in market interest rates (i.e., lenders

charge riskier projects higher rates of interest to compensate for lenders’ risk). All of these factors

drive a wedge between the social rate at which consumption can be traded through time (the pre-

tax rate of return to private investments) and the rate at which individuals can trade consumption

over time (the post-tax consumption rate of interest).

As stated earlier, interest rate accounts for the time value of money, inflation, and other

premiums, including risks, faced by lenders. The social discount rate is the rate at which society

can trade consumption through time (i.e., the time value of money). When assessing the societal

effect of regulations, such as for EPA rulemakings that are economically significant according to

Executive Order 12866, analysts should use the 3% and 7% real discount rates as specified in the

U.S. Office of Management and Budget (OMB)’s Circular A-4 [6]. The 3% discount rate

represents the social discount rate when consumption is displaced by regulation and the 7% rate

7

Board of Governors of the Federal Reserve System. “Selected Interest Rate (Daily) – H.15.” Available at:

https://www.federalreserve.gov/releases/h15/ (Accessed August 4, 2017).

8

Board of Governors of the Federal Reserve System. “Selected Interest Rate (Daily) – H.15.” Available at:

https://www.federalreserve.gov/releases/h15/ (Accessed August 4, 2017).

represents the social discount rate when capital investment is displaced. Regardless, these are real

social discount rates that are riskless. Therefore, they are not appropriate to use to assess private

costs that will be incurred by firms in making their investment decisions. In assessing these private

decisions, interest rates that face firms must be used, not social rates.

2. 5 .3 Prices and Inflation

With changes in prices over time for all relevant goods and services such as capital

equipment, engineering services, other materials and reagents used in the construction and

operation of control equipment, inflation’s impacts on prices and their effect on cost estimates is

of concern to Manual users. The prices in the Manual were not standardized. Some chapters had

prices for materials and reagents developed in the late 1990s, and other chapters had prices

developed from as far back as 1985. Because these differences were not explicitly discussed in

these earlier additions, the Agency attempted to standardize all prices into a particular base year’s

dollar in subsequent editions of the Manual to reduce the chance for analytical error. In the sixth

edition of the Manual, EPA updated all the costs to at least 1990. For the seventh edition of the

Manual, EPA will update the costs to at least 2012.

Updating costs for this Manual is an effort with a goal of standardizing all costs to one base

year for a particular analysis. Each chapter of the Manual fully discloses the limitations of the

costing information found in that chapter. This allows the analyst to make any adjustment they

deem necessary, provided sufficient basis exists, and assuming the approval of the appropriate

regulatory agency.

To develop the costs used in each of the chapters of this Manual, we attempted to survey

the largest possible group of vendors and collected information from industry literature and other

technical reports to determine an industry average price for each cost component. In many cases,

this involved contact with a number of vendors, including trade associations, and the assimilation

of large amounts of data. In other cases, the pollution control equipment was supplied by only a

few vendors, which limited the robustness of our models. And, in still other cases, the number of

existing manufacturers or the highly site-specific nature of their installation made it difficult for

us to develop robust prices for some components. While recognizing the difficulties in providing

manufacturer-specific or site-specific information, this Manual also knowledges that timeliness of

such information is important. If the survey information is not timely, errors to the cost estimation

would be introduced in unknown ways. Thus, every effort is made to update the information in as

timely a manner as possible.

In collecting and using prices in estimating pollution control costs, one should be cognizant

of the effect of inflation. We can define prices in “real” and “nominal” terms. Real and nominal

prices act in the same way as real and nominal interest rates. Nominal prices are actual prices (i.e.,

the sticker or spot price) and represent the value of a particular good at a particular point in time.

Real prices remove the effect of inflation. The reason for using real price is that purchases may

happen over several years especially for projects that invest heavily in capital. Because purchasing

industries.

9

Other indexes are also available from industry and academic sources through the

Internet, industry publications, trade journals, and financial institutions. One index that has been

used extensively by EPA for escalation purposes is the Chemical Engineering Plant Cost Index

(CEPCI), an index that tracks costs of equipment, construction labor, buildings, and supervision

in chemical process industries.

10

Other cost indexes exist, such as Marshall & Swift (M&S),

another equipment cost index that is widely used.

11

It should be noted that the accuracy associated with escalation (and its reverse, de-

escalation) declines the longer the time period over which this is done. Escalation with a time

horizon of more than five years is typically not considered appropriate as such escalation does not

yield a reasonably accurate estimate. [ 9 ] Thus, obtaining new price quotes for cost items is

advisable beyond five years. If longer escalation periods are unavoidable due to limited recent

cost data that is reasonably available, then the analysis should use the principles in this Manual

chapter to provide as accurate an escalation as possible consistent with the Manual given the

limitations of the cost analysis. The appropriate length of time for escalation can vary as a result

of significant changes in the cost of major production inputs (e.g., energy, steel, chemical reagents,

etc.) and technological changes in control measures, particularly if these changes occur in an

unusually short period of time. Hence, shorter time periods for escalation and de-escalation are

clearly preferred over longer ones.

2. 5 .4 Financial Analysis

Firms make purchase decisions that occur at different times for different durations and

schedule paybacks which also occur at different times as well. Because of these reasons, the

following financial analysis tools are necessary because they allow firms, state regulators, and

other users of the Manual to be able to compare the costs of different compliance strategies.

2. 5. 4. 1 Net Present Value

The process through which future cash flows are translated into current dollars is called

present value analysis. When the cash flows involve income and expenses, it is also commonly

referred to as net present value (NPV) analysis. In either case, the calculation is the same: adjust

the value of future money to values based on the same year (generally year zero of the project),

employing an appropriate interest (discount) rate and then add them together, after all income and

expenses have been converted into the same year dollar using appropriate price indices.

Derivation of a cash flow’s net present value involves the following steps:

9

U.S. Bureau of Labor Statistics. “Comparing the Consumer Price Index with the gross domestic product price

index and gross domestic product implicit price deflator.” Monthly Labor Review. March 2016.

10

This index is available at http://www.chemengonline.com/pci. It is also available in Chemical Engineering

magazine. Mention of this index is not meant to offer commercial endorsement by EPA.

11

More information on this cost index can be found at http://www.corelogic.com/products/marshall-swift-

valuation-service.aspx.

• Identification of alternatives. For example, the choice between a fabric

filter/baghouse and an electrostatic precipitator (ESP) for removing particulate

matter (PM) from a flue gas stream.

• Determination of costs and cash flows over the life of each alternative. Each of the

subsequent chapters of this Manual offers detailed costing information on specific

air pollution control devices and equipment.

• Determination of an appropriate real interest or discount rate(s). The appropriate

interest rate in private cost assessment is the private interest rate for each firm

affected. Determining private interest rates may be difficult due to the firm-specific

nature of the private nominal interest rates faced by firms. If firm-specific private

nominal interest rates are available, then the appropriate rates are simply the

difference between the nominal interest rate minus the prevailing inflation in the

industry. Industrial and other users of this Manual should consult with their

financial officers and/or trade associations for input regarding such rates. More

extensive discussion of interest rates can be found earlier in this Manual in Section

2.5.2. If discounting is performed using the same rate across all alternatives,

ranking of alternatives by cost will always yield the same order, no matter which

rate is used.

• For each alternative: Calculate a discounting factor for each year over the life of

the equipment. The discount factor formula is: DF t

={1/(1+i)

t

} where i is the

discount rate and t is the number of years. For example, using a seven percent

discount rate produces discount factors of: 0.9346, 0.8734, 0.8163, 0.7629, and

0.7130 for the 1

st

nd

rd

th

, and 5

th

years of a piece of equipment’s life,

respectively. Table A.1 in Appendix A displays discount factors for interest rates

from 5.5 to 15 percent, in half-percent increments for 25 years.

• For each year’s cash flows, sum all incomes and expenses to determine the net cash

flow for that year in nominal terms.

• Multiply each years’ net cash flow by the appropriate discount factor.
• Sum the discounted net cash flows to derive the net present value.
• Compare the net present values from each alternative. The net present value of a stream of cash

flows over the life of an investment can be calculated using equation 2.6:

NPV =∑ NCF

t

*[i/(1-(1+i)

- t

)] (2.6)

where NCF t

represents the net cash flow for year t, and i is the interest rate.