ASTM E1057-99
(Practice)Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
SCOPE
1.1 This practice establishes a procedure for calculating and interpreting the IRR and AIRR measures in the evaluation of building designs, systems, and equipment.
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An American National Standard
Designation: E 1057 – 99
Standard Practice for
Measuring Internal Rate of Return and Adjusted Internal
Rate of Return for Investments in Buildings and Building
Systems
This standard is issued under the fixed designation E 1057; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The internal rate-of-return (IRR) and adjusted internal rate-of-return (AIRR) methods are members
of a family of economic evaluation methods that provide measures of economic performance of an
investment over time. Other methods in this family of evaluation methods are life-cycle cost analysis,
net benefits analysis, benefit-to-cost and savings-to-investment ratio analysis, and payback analysis.
The IRR and AIRR methods are the topic of a single standard practice because they both measure
economic performance as a compound yield on investment. The IRR is the compound rate of interest
that, when applied as a discount rate to a project’s stream of dollar benefits and costs, will equate them.
The AIRR is the overall yield taking into account earnings on receipts reinvested to the end of the
study period. The IRR or AIRR is compared against the investor’s minimum acceptable rate of return
(MARR), and the investment is considered economically attractive if the calculated yield exceeds the
MARR. If an investment entails an initial outlay and a single receipt at the end of the study period,
there is no difference between the IRR and the AIRR. But if cash flows occur over multiple time
periods, the two will normally be different. This arises because the AIRR includes in its measure the
return on reinvestment of receipts, whereas the IRR does not.
The AIRR is recommended for most applications in which a measure of yield is desired. Caution
is recommended in applying either measure, however, because problems arise under certain
conditions.
1. Scope Buildings and Building Systems
E 1185 Guide for Selecting Economic Methods for Evalu-
1.1 This practice establishes a procedure for calculating and
ating Investments in Buildings and Building Systems
interpreting the IRR and AIRR measures in the evaluation of
2.2 ASTM Adjuncts:
building designs, systems, and equipment.
Discount Factor Tables, Adjunct to Practices E 917, E 964,
2. Referenced Documents E 1057, and E 1074
Computer Program and User’s Guide to Building Mainte-
2.1 ASTM Standards:
nance, Repair, and Replacement Database for Life-Cycle
E 833 Terminology of Building Economics
Cost Analysis, Adjunct to Practices E 917, E 964, E 1057,
E 917 Practice for Measuring Life-Cycle Costs of Buildings
E 1074, and E 1121
and Building Systems
E 964 Practice for Measuring Benefit-to-Cost and Savings-
3. Terminology
to-Investment Ratios for Buildings and Building Systems
3.1 Definitions—For definitions of terms used in this prac-
E 1074 Practice for Measuring Net Benefits for Investments
2 tice, refer to Terminology E 833.
in Buildings and Building Systems
E 1121 Practice for Measuring Payback for Investments in
4. Summary of Practice
4.1 This practice is organized as follows:
4.1.1 Section 1, Scope—Identifies coverage.
This test method is under the jurisdiction of ASTM Committee E-6 on
Performance of Buildings and is the direct responsibility of Subcommittee E06.81
on Building Economics.
Current edition approved April 10, 1999. Published June 1999. Originally Available from ASTM Headquarters. Order PCN 12-509170-10.
published as E 1057 – 85. Last previous edition E 1057 – 93. Available from ASTM Headquarters. Order PCN 12-509171-10 for the 3.5 in.
Annual Book of ASTM Standards, Vol 04.11. disk. Order PCN 12-509172-10 for the 5.25 in. disk.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E1057–99
4.1.2 Section 2, Applicable Documents—Lists ASTM stan- 6.1.1 Identify objectives, constraints, and alternatives.
dards that are referenced. 6.1.2 Compile data.
4.1.3 Section 3, Terminology—Addresses definitions of 6.1.3 Compute IRR or AIRR based on a comparison of two
terms. alternatives (one of which may be to do nothing).
4.1.4 Section 4, Summary of Practice—Outlines the con-
6.1.4 Compare the computed IRR or AIRR against the
tents. MARR to determine the acceptability of the alternative with
4.1.5 Section 5, Significance and Use—Explains the rel- the higher investment cost.
evance of the IRR and AIRR and indicates their appropriate 6.1.5 If a limited budget is to be allocated among competing
uses.
alternatives, select alternatives in descending order of their
4.1.6 Section 6, Procedures—Summarizes the steps in IRR IRR or AIRR measures until the budget is exhausted.
and AIRR analysis.
6.1.6 Report the results.
4.1.7 Section 7, Objectives, Constraints, and Alternatives—
Discusses the first step in an analysis, that is, the identification
7. Objectives, Constraints, and Alternatives
of the objectives of the analysis, any constraints that must be
7.1 Specify clearly the objective of the economic analysis.
taken into account in finding a solution, and technically
7.1.1 Suppose, for example, an individual or organization
feasible project alternatives.
has funds on hand to invest in real estate projects. The problem
4.1.8 Section 8, Data and Assumptions—Discusses the sec-
is which projects to choose from potential candidates. The
ond step in an analysis; that is the data and assumptions that are
objective of the economic analysis in this case is to identify the
typically required for calculating the IRR and AIRR, and, in
project or set of projects within the budget that is expected to
particular, the requirement of the AIRR for specification of a
maximize profits over the long run.
reinvestment rate.
7.2 Identify any constraints that narrow the field of candi-
4.1.9 Section 9, IRR Calculation—Describes the third step,
dates.
performing calculations, as it applies to the IRR.
7.2.1 Constraints, for example, might include a budget of
4.1.10 Section 10, AIRR Calculation—Describes the third
$1 000 000; a geographical limitation to buildings located
step, performing calculations, as it applies to the AIRR.
within 100 km from downtown; and a strong preference for
4.1.11 Section 11, Choosing Between the IRR and AIRR—
nonresidential property.
Discusses how to choose between the IRR and the AIRR.
7.3 Identify feasible alternatives.
4.1.12 Section 12, Limitations—Discusses limitations and
7.3.1 Feasible alternatives include an office building in the
shortcomings of the IRR and AIRR.
suburbs costing $1 000 000; convenience shopping strips in
4.1.13 Section 13, Applications—Describes the types of
nearby towns costing a total of $900 000; two medical/dental
decisions to which the IRR and AIRR are applicable.
offices costing $500 000 each; and a $1 000 000 investment
4.1.14 Section 14, Report—Identifies information that shall
share in a downtown shopping complex.
be included in a report of an IRR or AIRR application.
8. Data
5. Significance and Use
8.1 To calculate the IRR or AIRR, data are needed. The
5.1 The IRR method has been used traditionally in finance
microcomputer program database and adjunct user’s guide are
and economics to measure the percentage yield on investment.
helpful in estimating maintenance, repair, and replacement
5.1.1 The IRR method is appropriate in most cases for
costs.
evaluating whether a given building or building system will be
8.2 Benefit and cost data that are often relevant when
economically efficient, that is, whether its time-adjusted ben-
calculating the IRR or AIRR are revenues, resale or salvage
efits will exceed its time-adjusted costs over the period of
value, subsidies (for example, grants), and costs of planning,
concern to the decision maker. However, it has deficiencies that
design, engineering, construction, purchase, installation, opera-
limit its usefulness in choosing among projects competing for
tion and maintenance, utilities, and repairs and replacement.
a limited budget.
8.3 The time of occurrence of each benefit and cost is also
5.2 The AIRR method is a measure of the overall rate of
needed.
return that an investor can expect from an investment over a
8.4 Taxes such as tax credits, property taxes, and income
designated study period. It is appropriate both for evaluating
taxes are also often relevant because they affect benefits and
whether a given building or building system will be economi-
costs. If benefits and costs are adjusted for taxes, the IRR or
cally efficient and for choosing among alternatives competing
AIRR measure gives the after-tax rate of return.
for a limited budget.
8.5 If the terms of financing are unique to each alternative,
5.2.1 The AIRR method overcomes some, but not all, of the
financing costs (and associated tax effects) should also be taken
deficiencies of the IRR. The AIRR is particularly recom-
into account.
mended over the IRR for allocating limited funding among
8.6 Choose a minimum acceptable rate of return (MARR)
competing projects.
for comparison against the calculated IRR or AIRR.
6. Procedure
8.6.1 The appropriate MARR indicates the investor’s op-
6.1 The recommended steps for applying the IRR or the portunity cost of foregoing the return on the next best invest-
ment opportunity in order to invest in the project in question.
AIRR method to an investment decision are summarized as
follows: 8.7 If the AIRR is used, a reinvestment rate is needed.
E1057–99
TABLE 1 Trial-and-Error Solution for Internal Rate of Return
(1) (2) (3) (4) (5) (6) (7) (8)
Net
SPV PVNB SPV PVNB
Year Benefits Costs Cash Flow
Factor at 25 % Factor at 22 %
¯ ¯
(t) (B ) (C ) (B − C )
t t t t
for i =25% (6) = (4) 3 (5) for i =22% (8) = (4) 3 (7)
(4) = (2) − (3)
0 0 $10 000 $−10 000 1.000 $−10 000 1.000 $−10 000
1 $ 4 000 3 000 1 000 0.8000 800 0.8197 820
2 11 500 4 500 7 000 0.6400 4 480 0.6719 4 703
3 10 000 4 000 6 000 0.5126 3 076 0.5507 3 304
4 8 000 5 000 3 000 0.4096 1 229 0.4514 1 354
Total $7 000 $−415 $181
8.7.1 The reinvestment rate is usually set equal to the approximately to balance benefits and costs over the project
MARR; hence, it equals the discount rate. This is because the
study period. Then present value calculations are made for that
reinvestment rate is an indicator of future opportunity cost, and trial rate. (For an illustration of discounting calculations, see
that is also the purpose of the discount rate. Setting the
Practice E 917.) If the PVNB is zero, then the trial rate is the
reinvestment rate and the discount rate equal makes the solution value of the internal rate of return. If the PVNB is
reinvestment rate assumption in the AIRR method consistent
negative, the trial rate is too high, and a second, lower trial rate
with the reinvestment rate assumption that is implicit in the net is then used. If the PVNB is positive for the original trial rate,
benefits method (Practice E 1074).
then the IRR is higher than the trial rate, and a second, higher
trial rate is used. When two trial rates are found such that one
9. IRR Calculation
yields a PVNB greater than zero and the other a PVNB less
9.1 The IRR is the compound rate of interest that, when
than zero, the IRR lies between those rates and can be
used to discount a project’s cash flows, will reduce the present
approximated by interpolation, provided the investment has a
value of net benefits (PVNB) to zero. (See Practice E 1074 for
unique IRR. Considerable time is saved in the trial-and-error
a discussion of how to compute the PVNB.) The solution value
approach if the first trial rate is close to the true rate. One
of i* in Eq 1 is the IRR. It is computed as a decimal, then
approach is to start with the MARR as the trial rate. If the
expressed as a percent.
PVNB is negative with the MARR, then the project is not
9.1.1 Find the value of i* for which:
economically feasible, and no further calculations are neces-
N
sary. If the PVNB is positive, then select higher trial rates in an
t
¯
PVNB 5 ~B 2 C !/~1 1 i*! 5 0 (1)
( t t
attempt to bound the true rate.
t 5 0
9.2.1.2 The UPV factor tables are useful in finding a trial
where:
rate. The first step is to sum the undiscounted cash flows (not
PVNB = present value of net benefits (or, if applied to a
including the initial cost) and divide the sum by the number of
cost-reducing investment, present value of net
years in the study period (excluding any planning/design/
savings),
construction period) to obtain an average annual cash flow.
N = number of discounting periods in the study period,
Then divide the initial project cost by the average to obtain a
B = dollar value of benefits in period t for the building
t
rough estimate of simple payback (SPB). The second step is to
or system evaluated less the counterpart benefits
search the UPV discount factor tables in the row that corre-
in period t for the mutually exclusive alternative
sponds to the study period for the UPV factor that is closest to
against which it is compared,
the estimated SPB. (Again exclude any years in the planning/
¯
C = dollar costs, including investment costs, in period
t
design/construction period.) The rate that appears at the top of
t for the building or system evaluated less the
the column in which the UPV factor is found is a promising
counterpart costs in period t for the mutually
trial rate. The more uniform the annual cash flow, the more
exclusive alternative against which it is compared,
likely that this trial rate will be close to the solution rate.
and
9.2.1.3 Table 1 illustrates the trial-and-error approach for
i* = interest rate for which PVNB = 0, that is, the IRR
calculating the IRR for an initial investment that yields an
measure expressed as a decimal.
uneven yearly cash flow over four years. Columns 2 and 3 list
9.2 An algebraic solution of i* is not possible with Eq 1 for
the dollar values of benefits and costs that accrue in each of the
all values of N. Use a computer program with built-in formulas
four years, and Column 4 shows the net cash flow for each of
to calculate IRR and AIRR. Or, use a manual approach to
those years, including the initial investment.
approximate the IRR such as the trial-and-error approach, the
graphical approach, and an approach that uses simple payback 9.2.1.4 From inspecting Column 4 in Table 1, one might
and uniform present value (UPV) factor tables. (See Practice expect a relatively high return over four years. Using the
E 1121 for a description of payback and the Adjunct on approach described in 9.2.1.2 to select a trial rate, the
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