L17: Annual Equivalent
Worth Criterion
ECON 320 Engineering Economics
Mahmut Ali GOKCE
Industrial Systems Engineering
Computer Sciences
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Which Brand Would you Pick?
Brand A
Brand B
$799
$55/Year
$699
$85/Year
How Would you calculate the hourly
operating cost?
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Chapter 6
Annual Equivalence Analysis
Annual equivalent criterion
Applying annual worth analysis
Mutually exclusive projects
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Chapter Opening Story
 Capstone Turbine
Corporation
 Manufacturer of microturbine (mini-Power
Plant)
 At Issue: Economics of
MicroCHP
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Annual Worth Analysis
 Principle: Measure an investment worth on
annual basis
 Benefit: By knowing the annual equivalent
worth, we can:
• Seek consistency of report format
• Determine the unit cost (or unit profit)
• Facilitate the unequal project life
comparison
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Example 6.1 Computing Equivalent Annual Worth
$9.0
$12
$10
$5
PW(15%) = $6.946
0
$8
1
2
3
4
5
6
$3.5
$6.946
$15
A = $1.835
0
1
2
3
4
5
6
0
AE(12%) = $6.946(A/P, 15%, 6)
= $1.835
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Annual Equivalent Worth - Repeating
Cash Flow Cycles
$700
$500
$1,000
$800
$800
$700
$400 $400 $500
$400 $400
$1,000
Repeating cycle
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• First Cycle:
PW(10%) = -$1,000 + $500 (P/F, 10%, 1)
+ . . . + $400 (P/F, 10%, 5)
= $1,155.68
AE(10%) = $1,155.68 (A/P, 10%, 5) = $304.87
• Both Cycles:
PW(10%) = $1,155.68 + $1,155.68 (P/F, 10%, 5)
+ . . . + $400 (P/F, 10%, 5)
= $1,873.27
AE(10%) = $1,873.27 (A/P, 10%,10) = $304.87
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 When only costs are
involved, the AE
method is called the
annual equivalent cost.
 Revenues must cover
two kinds of costs:
Operating costs and
capital costs.
Annual Equivalent Costs
Annual Equivalent Cost
Capital
costs
+
Operating
costs
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Capital (Ownership) Costs
 Def: Owning an equipment
is associated with two
transactions—(1) its initial
cost (I) and (2) its salvage
value (S).
 Capital costs: Taking these
items into consideration, we
calculate the capital costs
as:
CR(i)  I ( A / P, i, N )  S( A / F, i, N )
 ( I  S)( A / P, i, N )  iS
S
0
N
I
0 1
2
3
N
CR(i)
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Vehicle
Value after three
years
Monthly lease
Acura MDX 4WD
$21,400
588
Toyota 4Runner 4WD 4-door
Limited (with moonroof)
$18,750
646
Lexus RX300 2 WD
$18,750
651
GMC Envoy 4WD 4door SLT (with
Bose audio, CD changer and
moonroof)
$15,050
733
Mitsubishi Montero 4WD 4 door
Limited
$15,225
743
Ford Explorer 4WD 4-door Eddie
Bauer edition (with moonroof, rear
air and third seat)
$14,425
754
Isuzu Trooper 4WD 4-door
Limited
$11,675
823
Source: Automotive Lease Guide
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SEGMENT
BEST MODELS
ASKING
PRICE
PRICE AFTER 3
YEARS
Compact car
Mini Cooper
$19,800
$12,078
Midsize car
Volkswagen
Passat
$28,872
$15,013
Sports car
Porsche 911
$87,500
$48,125
Near luxury car
BMW 3 Series
$39,257
$20,806
Luxury car
Mercedes CLK
$51,275
$30,765
Minivan
Honda
Odyssey
$26,876
$15,051
Subcompact SUV
Honda CR-V
$20,540
$10,681
Compact SUV
Acura MDX
$37,500
$21,375
Full size SUV
Toyota Sequoia
$37,842
$18,921
Compact truck
Toyota Tacoma
$21,200
$10,812
Full size truck
Toyota Tundra
$25,653
$13,083
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Example - Capital Cost Calculation
for Mini Cooper
 Given:
I = $19,800
N = 3 years
S = $12,078
i = 6%
 Find: CR(6%)
$12,078
0
3
$19,800
CR (i ) = (I -S ) (A/P, i , N ) + iS
CR (6%) = ($19,800 - $12,078) (A/P, 6%, 3)
+ (0.06)$12,078
= $3,613.55
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Example 6.2
Justifying an investment based on AE Method
• Given: I = $20,000, S =
$4,000, N = 5 years, i =
10%
• Find: see if an annual
revenue of $4,400 is large
enough to cover the
capital costs.
• Solution:
CR(10%) = $4,620.76
• Conclusion: Need an
additional annual revenue
in the amount of $220.76.
$4,000
$4,400
0
1
2
3
4
5
$20,000
$4,000
0
1
2
3
4
5
+
$20,000
$4,400
0
1
2
3
4
5
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