1. The document discusses various methods for analyzing engineering project alternatives using present worth analysis, including analyzing alternatives with equal lives, different lives, and infinite lives. 2. Key methods include using the least common multiple of lives or a specified study period to convert alternatives to equal service for comparison, and calculating the capitalized cost for alternatives with infinite lives. 3. The examples demonstrate how to use these present worth analysis methods to evaluate alternatives, convert cash flows to present worth, and select the alternative with the highest present worth value or lowest capitalized cost.

1. Present Worth AnalysisPresent Worth Analysis
EGN 3203 Engineering Economics
LO3 – a

2. 5-2
LEARNINGLEARNING OUTCOMESOUTCOMES
1. Formulate Alternatives
2. PW of equal-life alternatives
3. PW of different-life alternatives
4. Future Worth analysis
5. Capitalized Cost analysis
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3. Introduction Present WorthIntroduction Present Worth
• A future amount of money converted to its equivalent value now has a
present worth (PW) value
• This present value is always less than that of the actual future cash
flow,
• for any interest rate greater than zero, all P/F factors have a value less
than 1.0. For this reason, present worth values are often referred to
as discounted cash flows (DCF).
• Similarly, the interest rate may be referred to as the discount rate.
Besides PW, equivalent terms frequently used are present value (PV)
and net present value (NPV).
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4. • Alternatives are developed from project proposals to
accomplish a stated purpose.
• Some projects are economically and technologically
viable, and others are not. Once the viable projects are
defined, it is possible to formulate the alternatives.
• Alternatives are one of two types:
• mutually exclusive or independent.
• Each type is evaluated differently
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Formulating AlternativesFormulating Alternatives

5. 5-5
Formulating AlternativesFormulating Alternatives
Two types of economic proposals
Mutually Exclusive (ME) Alternatives: Only one can be selected;
Compete against each other
Independent Projects: More than one can be selected;
Compete only against DN
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Do Nothing (DN) – An ME alternative or independent project to
maintain the current approach; no new costs, revenues or savings

6. 5-6
Revenue: Alternatives include estimates of costs
(cash outflows) and revenues (cash inflows)
Two types of cash flow estimates
Cost: Alternatives include only costs; revenues and savings
assumed equal for all alternatives;
also called service alternatives
Formulating AlternativesFormulating Alternatives
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8. 5-8
Convert all cash flows to PW using MARR
Precede costs by minus sign; receipts by
plus sign
For mutually exclusive alternatives, select
one with numerically largest PW
For independent projects, select all with PW > 0
PW Analysis of AlternativesPW Analysis of Alternatives
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For one project, if PW > 0, it is justified
EVALUATION

9. 5-9
Project ID Present Worth
A $30,000
B $12,500
C $-4,000
D $ 2,000
Solution: (a) Select numerically largest PW; alternative A
(b) Select all with PW > 0; projects A, B & D
Selection of Alternatives by PWSelection of Alternatives by PW
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10. 5-10
Example: PW Evaluation of Equal-Life ME Alts.Example: PW Evaluation of Equal-Life ME Alts.
Alternative X has a first cost of $20,000, an operating cost of $9,000 per year,
and a $5,000 salvage value after 5 years. Alternative Y will cost $35,000
with an operating cost of $4,000 per year and a salvage value of $7,000
after 5 years. At an MARR of 12% per year, which should be selected?
Solution: Find PW at MARR and select numerically larger PW value
PWX = -20,000 - 9000(P/A,12%,5) + 5000(P/F,12%,5)
= -$49,606
PWY = -35,000 - 4000(P/A,12%,5) + 7000(P/F,12%,5)
= -$45,447
Select alternative Y
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11. Example: PW Evaluation of Equal-LifeExample: PW Evaluation of Equal-Life
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Example: PW Evaluation of Equal-LifeExample: PW Evaluation of Equal-Life

13. • Present worth analysis requires an equal service comparison of alternatives,
that is, the number of years considered must be the same for all alternatives.
• If equal service is not present, shorter-lived alternatives will be favored
based on lower PW of total costs, even though they may not be economically
favorable.
• Fundamentally, there are two ways to use PW analysis to compare
alternatives with unequal life estimates;
• use the least common multiple of lives for each pair of alternatives
• or evaluate over a specific study period (planning horizon),
• In both cases, the PW is calculated at the MARR, and the selection guidelines
of the previous section are applied
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PW of Different-Life AlternativesPW of Different-Life Alternatives

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PW of Different-Life AlternativesPW of Different-Life Alternatives
Must compare alternatives for equal service
(i.e., alternatives must end at the same time)
Two ways to compare equal service:
(The LCM procedure is used unless otherwise specified)
Least common multiple (LCM) of lives
Specified study period
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15. Assumptions of LCM approachAssumptions of LCM approach
 Service provided is needed over the LCM or
more years
 Selected alternative can be repeated over
each life cycle of LCM in exactly the same
manner
 Cash flow estimates are the same for each life
cycle (i.e., change in exact accord with the
inflation or deflation rate)
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16. 5-16
Example: Different-Life AlternativesExample: Different-Life Alternatives
Compare the machines below using present worth analysis at i = 10% per year
Machine A Machine B
First cost, $
Annual cost, $/year
Salvage value, $
Life, years
20,000 30,000
9000 7000
4000 6000
3 6
Solution:
PWA = -20,000 – 9000(P/A,10%,6) – 16,000(P/F,10%,3) + 4000(P/F,10%,6)
= $-68,961
PWB = -30,000 – 7000(P/A,10%,6) + 6000(P/F,10%,6)
= $-57,100
LCM = 6 years; repurchase A after 3 years
Select alternative B
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20,000 – 4,000 in
year 3

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21. PW Evaluation Using a Study PeriodPW Evaluation Using a Study Period
Once a study period is specified, all cash flows after
this time are ignored
Salvage value is the estimated market value at the end
of study period
Short study periods are often defined by management
when business goals are short-term
Study periods are commonly used in equipment
replacement analysis
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22. 5-22
Example: Study Period PW EvaluationExample: Study Period PW Evaluation
Compare the alternatives below using present worth analysis at i = 10% per year
and a 3-year study period
Machine A Machine B
First cost, $
Annual cost, $/year
Salvage/market value, $
Life, years
-20,000 -30,000
-9,000 -7,000
4,000 6,000 (after 6 years)
10,000 (after 3 years)
3 6
Solution:
PWA = -20,000 – 9000(P/A,10%,3) + 4000(P/F,10%,3) = $-39,376
PWB = -30,000 – 7000(P/A,10%,3) + 10,000(P/F,10%,3)= $-39,895
Study period = 3 years; disregard all estimates after 3 years
Marginally, select A; different selection than for LCM = 6 years
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23. 5-23
Future Worth AnalysisFuture Worth Analysis
Must compare alternatives for equal service
(i.e. alternatives must end at the same time)
Two ways to compare equal service:
(The LCM procedure is used unless otherwise specified)
Least common multiple (LCM) of lives
Specified study period
FW exactly like PW analysis, except calculate FW
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24. 5-24
FW of Different-Life AlternativesFW of Different-Life Alternatives
Compare the machines below using future worth analysis at i = 10% per year
Machine A Machine B
First cost, $
Annual cost, $/year
Salvage value, $
Life, years
-20,000 -30,000
-9000 -7000
4000 6000
3 6
Solution:
FWA = -20,000(F/P,10%,6) – 9000(F/A,10%,6) – 16,000(F/P,10%,3) + 4000
= $-122,168
FWB = -30,000(F/P,10%.6) – 7000(F/A,10%,6) + 6000
= $-101,157
LCM = 6 years; repurchase A after 3 years
Select B (Note: PW and FW methods will always result in same selection)
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25. • Capitalized cost (CC) is the present worth of an alternative that will
last “forever.”
• Public sector projects such as bridges, dams, irrigation systems, and
railroads fall into this category, since they have useful lives of 30, 40,
and more years.
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Capitalized Cost (CC) AnalysisCapitalized Cost (CC) Analysis

26. Capitalized Cost (CC) AnalysisCapitalized Cost (CC) Analysis
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CC refers to the present worth of a project with a very
long life, that is, PW as n becomes infinite
Basic equation is: CC = P = A
i
“A” essentially represents the interest on a perpetual investment
For example, in order to be able to withdraw $50,000 per year forever
at i = 10% per year, the amount of capital required is 50,000/0.10 = $500,000
For finite life alternatives, convert all cash flows into
an A value over one life cycle and then divide by i
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27. 5-27
Example: Capitalized CostExample: Capitalized Cost
Solution:
Compare the machines shown below on the basis of their
capitalized cost. Use i = 10% per year
Machine 1 Machine 2
First cost,$
Annual cost,$/year
Salvage value, $
Life, years
-20,000 -100,000
-9000 -7000
4000 -----
3 ∞
Convert machine 1 cash flows into A and then divide by i
A1 = -20,000(A/P,10%,3) – 9000 + 4000(A/F,10%,3) = $-15,834
CC1 = -15,834 / 0.10 = $-158,340
CC2 = -100,000 – 7000/ 0.10 = $-170,000
Select machine 1
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Summary of Important PointsSummary of Important Points
PW method converts all cash flows to present value at MARR
PW comparison must always be made for equal service
Alternatives can be mutually exclusive or independent
Cash flow estimates can be for revenue or cost alternatives
Equal service is achieved by using LCM or study period
Capitalized cost is PW of project with infinite life; CC = P = A/i
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