Engineering Economic Analysis

324 UNCERTAINTY IN FUTURE EVENTS

Using the probability distribution for the PW from Example 10-6, calculate the PW's standard

deviation.

The following table adds a column for (PW) (probability) to calculate the EV(PW2).

Annual Life Joint PW x

Benefit Probability (years) Probability Probability PW Probability

$ 5,000 30% 6 66.7% 20.0% ~$ 3,224 -$ 645

8,000 60 666.7 40.0 9,842 3,937

10,000 10 6 66.7 6.7 18,553 1,237

5,000 30 9 33.3 10,0 3,795 380

8,000 60 9 33.3 20.0 21,072 4,2!4

10,000 10 9 33.3 3.3 32,590 1,086

EV $10,209

Standard deviation V{EV(X--:;;~ [EV(X)]2}

(J. '. J{l89,405,745~ [l0,209]2}'- y'85, 182,064=$9229

PW2x

Probability

$ 2,079,480

38,j47,9~4

22,950,061

1,442,100

88,797,408

35,392,740

$189,409,745

For those with stronger backgrounds in probability than this chapter assumes, let us

consider how the standard deviation in Example 10-13depends on the assumption of inde-

pendence between the variables. While exceptions exist, a positive statistical dependence

between variables often increases the PW's $tandarddeviation. Similarly,a negative statis-

tical dependence between variables often decreases the PW's standard deviation.

RISKVERSUS RETURN

A graph of risk versus return is one way to consider these items together. Figure 10-7 in

Example 10-14 illustrates the most common format. Risk measured by standard deviation

is placed on thexaxis, and return measured by expected value is placed on theyaxis. This

is usually done with the internal rates of return of the alternativesor projects.

A large firm is discontinuing an older product, so some facilities are becoming availablefor other
uses. The followingtable sunmiarizeseighfnew projects that would use the facilities.Coriside~ng
expected return and risk, wbjch projects are good candidates? The .firmbelieves it can earn 4%
on a risk-free investment in govel11p1entsecurities (labeled as PJ;Qject: =~ !!.~ ::: = == ::;=. == ~~, ~F).
t ~-- -- -- -