ESL is “the Economic Service Life”

```The American University in Cairo
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.
```