Engineering Economic Analysis

Graphical Solutions 251

At 6%, (PW of benefits) = (Uniform annual benefit) x (Series present worth factor).

PW of benefits=(Uniform annual benefit)(P/A,6%, 20)

PW of benefits for Alt.A=$410(11.470) =$4703

Alt.B=$639(11.470)=$7329

Alt. C=$700(11.470)-$8029

Figure 8-6 is a plot of the situation; we see that the slope of the line from the origin toAis greater

than the 6% line (NPW=0). Thus therate ofretumfor Ais greater than 6%. For the increment of

additional cost ofBoverA,the slope of lineB-A is greater than the 6% line. This indicates that

the rate of return on theincrement of investmentalso exceeds 6%. But J:4eslope of incrementC-B

indicates its rate of return is less than 6%, b,ence,undesirable. We conclude that the Ainvestment

is satisfactory as well as theB-,-Aincrement; therefore,Bis satisfactory.TheC-B increment is

unsatisfactory; so C is undesirable ip comparison toB. Our decision is to select AlternativeB,

E'IGURE 8-6 Benefit--cost graph for

Example 8-3.

$9000

$8000

$3000 $5000 $7000

PresentWorthof Cost

Further study of the three alternativesof Ex:ample8-3 reveals that Alt.A'suniform annual benefit
was overstated.It is now projected to be $122 rather than $410. Replotthebep.efit-cost graph for
~ this cbanged,situ,<i.tiop. '"~ '= ~ ; em' III~= ~ IB ~,; '" ~ i:i: ""'.>"iI
L -, ,____

I

1

I

'"

ilii1'

1'Ii

.

.1

1'I'

,I

,ql'

I

I

;

\

1

I

.'I!:11

If'

-- -