CE 203
Present Worth Analysis
(EEA Chap 5)
ISU
CCEE
Three Techniques for Economic
Comparison of Alternatives
• Present Worth Analysis
(Chapter 5)
• Annual Cash Flow Analysis
(Chapter 6)
• Rate of Return Analysis
(Chapter 7)
ISU
CCEE
Present Worth and Economic Criteria
for Mutually Exclusive Alternatives
1: For Fixed Input : Maximize present
worth of benefits or other outputs
2: For Fixed Output : Minimize present
worth of costs or other inputs
3: For Variable Input and Output:
Maximize Net Present Worth (NPW) =
present worth of benefits minus
present worth of costs
ISU
CCEE
Net Present Worth (NPW)
NPW
= PW of Benefits – PW of Costs
= PWB – PWC
NPW
= P0 + n Fj (P/F, i, n)
where Fj = Bj – Cj
Fj is + for net benefits, Bj,
- for net costs, Cj
ISU
CCEE
Variations in Useful Lives of
Alternatives and Analysis Period
1: Useful life (and analysis period) are
equal among all alternatives
3: Analysis period is infinite, n =
ISU
CCEE
8
2: Useful lives of alternatives are not
equal
Case 1: If useful lives of alternatives
and analysis period are all equal…
… then choose the alternative with the
highest (or least negative) NPW
Example: Examine alternatives for railroad/
street intersections in downtown Ames.
Assume useful life for all alternatives is 25
years, i = 6%, yearly compounding.
1. Street overpasses at Duff, Kellogg, and Clark
2. Train tunnel through downtown Ames
3. Current (do nothing)
ISU
CCEE
Costs/benefits estimates for various RR/street
intersection alternatives for downtown Ames
(assume 25-year useful life/analysis period)
ISU
CCEE
Alternative
design
Initial
Costs1
Maintenance
Costs2
Annual
Benefits3
#1 (overpasses)
#2 (tunnel)
#3 (current)
$10M
$15M
$50k
$20k/y
$10k/y
$10k/y +
$50k @ 5y4
$0.75M
$1.0 M
$0
1.
2.
3.
4.
Design, construction, loss of business
Maintenance, major refurbishing as noted
Time savings, better safety, increased business
Every 5y
Present Worth evaluations for Costs/Benefits
of RR/street intersection alternatives
Alternative
Initial
design
Costs
#1 (overpasses) $10M
#2 (tunnel)
$15M
#3 (current)
$50k
Maintenance
Annual
Costs
Benefits
$20k*
$750k*
[P/A,6%,25]
[P/A,6%,25]
$10k*
$1M*
[P/A,6%,25]
[P/A,6%,25]
$10k*
[P/A,6%,25] +
$0
$50k [A/F,6%,5]*
[P/A,6%,20]
Note: for Alt. #3, $50k@5 y is evaluated as
[annualized value]*[series present worth]
ISU
CCEE
* means multiply
Net Present Worth of RR/street intersection
alternatives (in millions, benefits +, costs -)
Alternative
design
Initial Maintenance Annual
Costs
Costs
Benefits
#1 (overpasses) -$10.00
-$0.256
+$9.588
NPW
-$0.67
#2 (tunnel)
-$15.00
-$0.128
+$12.783
-$2.34
#3 (current)
-$0.05
-$0.230
$0
-$0.28
Note: though “problem” is real, estimates
for costs and benefits are largely fabricated!
ANALYSIS IS ONLY AS GOOD AS INPUT!!!
ISU
CCEE
Case 2: If useful lives of
alternatives are not equal…
… then choose an appropriate analysis
period:
1) the least common multiple
analysis period OR
2) a common analysis period with a
terminal (salvage) value
ISU
CCEE
Case 2: If useful lives of
alternatives are not equal…
Example: Alternatives for railroad/street
intersections in downtown Ames as for
Case 1, but assume useful life for
tunnel is 50 years and useful life for
overpasses is 25 years, i = 6%, yearly
compounding.
… choose (least common multiple)
50-year analysis period and assume
overpasses are replaced in 25 years
ISU
CCEE
Costs/benefits estimates for various RR/street
intersection alternatives for downtown Ames
(assuming 25-year useful life for overpasses, 50year useful life for tunnel, 50-year analysis)
ISU
CCEE
Alternative
design
#1 (overpasses)
Initial
Costs
$10M
#2 (tunnel)
$15M
#3 (current)
$50k
Maintenance
Costs
$20k/yr +
$10M @ 25 y
$10k/y
Annual
Benefits
$750k
$10k/y
$50k @ 5y
$0
$1M
Present Worth evaluations for Costs/Benefits of
RR/street intersection alternatives (Case 2)
Alternative
design
Initial
Costs
#1 (overpasses)
$10M
#2 (tunnel)
$15M
#3 (current)
$50k
ISU
CCEE
Maintenance
Costs
Annual
Benefits
$20k[P/A,6%,50]
$750k*
+
[P/A,6%,50]
$10M[P/F,6%,25]
$10k[P/A,6%,50]
$1M*
[P/A,6%,50]
$10k[P/A,6%,50]
+
$0
$50k[A/F,6%,5]*
[P/A,6%,45]
Net Present Worth* of RR/street intersection alternatives (in 106, benefits +, costs -)
Alternative
design
Initial
Costs
Maintenance Annual
Costs
Benefits
#1 (overpasses)
-$10
-$2.645
+$11.82
-$0.82
#2 (tunnel)
-$15
-$0.158
+$15.76
+$.60
#3 (current)
-$0.05
-$0.295
$0
-$0.35
NPW
*For Case 2 (50-year useful life for train tunnel,
25-year useful life for street overpasses)
ISU
CCEE
Variations in Useful Lives of
Alternatives and Analysis Period
1: Useful life (and analysis period) are
equal among all alternatives
2: Useful lives of alternatives are not
equal
3: Analysis period is infinite
- calculate an annualized cost
equivalent for each alternative
- then calculate the capitalized cost
ISU
CCEE
Capitalized Cost is money required
now to cover given cash flow forever
Capitalized Cost = A/i
where A is uniform amount required
each period to cover all future
cash flow amounts
ISU
CCEE
In-class Example (Capitalized Cost)
You have been very successful in
your career as a consulting civil
engineer and have decided to endow
a CE scholarship at ISU. How much
would you have to give ISU in order
to provide a $5000 dollar scholarship
each year indefinitely assuming you
were guaranteed 5% interest?
ISU
CCEE
Case 3: Capitalized Cost for infinite
analysis period (Present worth for
infinite analysis period)
Example: Alternatives for railroad/street
intersections in downtown Ames as for
Case 2 (useful life for tunnel is 50
years and useful life for overpasses is
25 years), i = 6%, yearly compounding,
infinite analysis period.
ISU
CCEE
Costs/benefits estimates for various RR/street
intersection alternatives for downtown Ames
(assuming 25-year useful life for overpasses, 50year useful life for tunnel)
Alternative
design
#1 (overpasses)
ISU
CCEE
Initial
Costs
$10M
#2 (tunnel)
$15M
#3 (current)
$50k
Maintenance
Costs
$20k/yr +
$10M @ 25
yrs
$10k/yr
Annual
Benefits
$10k/yr
$50k @ 5yrs
$0
$750k
$1M
Capitalized Cost for Alternative #1
Alternative
Initial
design
Costs
#1 (overpasses) $10M
Maintenance
Costs
$20k/y +
$10M @ 25 y
Annual
Benefits
$750k
CC of $20k/yr = $20k/0.06
= $333.33k = $0.333M (-)
CC of $10M @ 25 years
= $10M [A/F,0.06,25] / 0.06
= $3.038M (-)
PW of $750k/y = $750k/0.06 = $12.5M (+)
NPW = - 10 - 0.333 - 3.038 + 12.5
ISU
CCEE
= - $0.871M
Capitalized Cost evaluations for RR/street
intersection alternatives (Case 3)
Alternative
design
#1 (overpasses)
ISU
#2 (tunnel)
Maintenance
Costs
$20k/0.06 +
$10M[A/F,0.06,25]
0.06
$15M
$10k/0.06
#3 (current)
$50k
CCEE
Initial
Costs
$10M
$10k/0.06 +
$50k[A/F,0.06,5]
0.06
Annual
Benefits
$750k
0.06
$1M/0.06
$0
Capitalized Costs of RR/street intersection
alternatives (in millions; benefits +, costs -)
Alternative
design
#1 (overpasses)
CC of
Initial
Costs
-$10
CC of
PW of
Maintenance Annual
Costs
Benefits NPW
-$3.371*
+$12.500 -$0.87
#2 (tunnel)
-$15
-$1.028
#3 (current)
-$0.05
-$0.315
+$16.667 +$.64
$0
-$0.37
*As an example, the amount of $3.371M covers
the $20k/yr maintenance PLUS the capitalized
replacement cost at 25 years.
ISU
CCEE