Engineering Economic Analysis

Expected Value 315

With an expected PW of $10,209, this is an attractive project. While there is a 20% chance

of a negative PW, the possible positive outcomes are larger and more likely. Having analyzed

the project under uncertainty, we are much more knowledgeable about the potential result of the

decision to proceed.

The$~0,209 value is more aCClli"atethan the approximate value calculated in Example 10-7.

The values differ.because PW is a nonlinear function of the life. The more accurate value of

$~0,209 is lower because the annual benefit values for the longyrlife are discounted by 1/(1 +i)

formOry ye~.

In Examples 10-7 and 10-8, the question was whether the project had a positive

PW. With two or more alternatives, the criterion would have been to maximize the PW..

With equivalent uniform annualcosts(EUACs)the goal is to minimize the EUAC. Exam-

ple 10-9 uses the criterion of minimizing the EV of the EUAC to choose the best height for

a dam..

A dam is being considered to reduce river flooding. But if a dam is built, what height should it

be? Increasing the dam's height will (1) reduce a flood's probability, (2) reduce the damage when

floods OCClli",and (3) cost more. Which dam height minimizes the expected total annual cost?

The state uses an interest rate of 5% for flood protection projects, and all the dams should last

50 years.

Dam

Height (ft)

No dam

20

30

40

First Cost

$ 0

700,000

800,000

900,000

Annual

P(flood) > Height

0.25

0.05

0.01

0.002

Damages If

Flood Occurs

$800,000

500,000

300,000

200,000

The easiest way to solve this problem is to c400se the dam height with the lowest equivalent-
unifonn annual cost (EUAC). Calcu.lating the EUAC of the first cost requires multiplying the first
coSt by(4jP, 5%, 50). For example, for the da:m20ft high. this is700,000(Aj P,5%, 50).. ..
$38,344.
Calculating the annual expected.floodd.a:rp.ageco~tfo1"eachalternativeis simplifiedbecause
=-~! ~or~:."PJ~~ tt~tdr~! ~~t'?'2usethed.ama~eSi~no~ood,!!:~ ~~4Thus~e=ne~dto ~ ~~ J
GaJclllateonfy ffietermIorflo03111g.'I'lilSIS~~5YmartiPIymgIDeP(IIoOd)tU1lesthe damages 1
: if,a flood happens. For example, the expected annual flood da:mageco~twith no leveeis 0.25 x I
t\ ~ $80'p,000, ~i $2g0!OQQ~; f.I~: ~= =n ~ =- ~;::; ~;r,; ~ ; '" I
~ y- - - -_ """"'- J