Engineering Economic Analysis

Benefit-Cost Ratio Analysis 275

A finn is trying to decide which of two devices to install to reduce costs in a particular situation.

Both devices cost $1000 and have useful lives of 5 years and no salvage value. DeviceAcan

be expected to result in $300 savings annually. DeviceB will provide cost savings of $400

the first year, but savings will decline by $50 annually, making the second...yearsavings $350,

the third-year savings $300, and so forth. With interest at 7%, which device should the firm

purchase?

jSOtuTION

We have used three types of analysis thus far to solve this problem: present worthin Example 5-1,

annual cash flow in Example 6-5, and rate of return in Example 7-9.

DeviceA

PW of cost=$1000

PW of benefits=300(PjA, 7%,5)

• 300(4.100)=$J230

B PW of benefit 1230

• · --;---= 1.23
  C PW of costs 1000

DeviceB

r

I

PW of cost--$1000

PW of benefit =400(P j A,7%, 5)- 50(P fG-,7%, 5)

=400(4.100).--' 50(7.647)= 1640 --' 382= 1258

BPW of benefit 1258

---=.. .' ... ., = --- --1.26

CPWof costs 1000

To ma)!:imizethe benefit-cost ratio, select DeviceB,.

Two machines are being considered for purchase. Assuming 10% interest, which machine should

be bought?

r

1:

• --~
  , ---- -..

Initial cost

Unifonn, annual benefit

End-of-useful-lifesalvage value

.,,, UsefuUife,.in years

MachineX

$200

95

50

6

::I;;;: ~ 1

·-- .d

MachineY

$700

120

150

=~ :=.ef2'i1''I: ~=

..

-- - - -

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