The American University in Cairo
Mohamed Ibrahim Badawi
ENGR 345-01
Summer 2003
Lecture on Monday July 14th 2003
ESL is “the Economic Service Life”. Is the number of years n at which the equivalent
uniform annual worth of costs is the minimum.
Example 11.2 page 377
Given: Year
1
2
3
4
5
MV
$9000
$8000
$6000
$2000
$0
AOC
-$2500
-$2700
-$3000
-$3500
-$4500
For n = 1
Capital Return “CR” = -$13,000*(1.1) + $9,000
= -$5,300
Total AW= CR + AOC
= -$5,300 + -$2,500
= -$7,800
For n = 2
Capital Return “CR” = (-$13,000*(1.1)^2 + $8,000) (A/F, 10%, 2)
= -$3,681
Total AW= CR + AOC
= -$3,681 + (-$2,700 + $2,500 (1.1)) (A/F, 10%, 2)
= -$6,276
For n = 3
CR = (-$13,000 + $6,000 (1.1)^-3)(A/P, 10%, 3)
= -$3,414.8
Total AW= CR + AOC
= -$3,414.8 + (-$3,000 - $2,700(1.1) - $2,500(1.1)^2) (A/F, 10%, 3)
= -$3,414.8 + (-$2,77.52)
= -$6,132
N.B There are several ways of solving such problem, such as bringing everything to the
present or the future and then get the Annuity.