Engineering Economy
Engineering Economy
8th Edition
ISBN: 9781259683312
Author: Blank
Publisher: MCG
Question
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Chapter 11, Problem 33P
To determine

Calculate the annual worth.

Expert Solution & Answer
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Explanation of Solution

Defender: At the beginning of each year, payment (BP) is $180,000. Time period (n) is 5. Interest (i) is 15%.

Challenger: Initial cost is $1,600,000. Annual operating cost (AC) is $58,000. Annual saving (AS) is $220,000. Salvage value (SV) is 30% to the initial cost. Thus, it is 480,000(1,600,000×0.3)  Time period (n) is 5. Interest (i) is 15%.

Annual worth (AV) of the defender can be calculated as follows:

AV=(BPBP((1+n)n11i(1+n)n1))(i(1+i)n(1+i)n1)=(180,000180,000((1+0.15)5110.15(1+0.15)51))(0.15(1+0.15)5(1+0.15)51)=(180,000180,000(1.7490110.15(1.74901)))(0.15(2.01136)(2.01136)1)=(180,000180,000(0.749010.26235))(0.30171.01136)=(180,000513,900)(0.29831)=206,997.31

The annual worth of the defender is -$206,997.31.

Annual worth (AV) of the challenger can be calculated as follows:

AV=FC((1+n)n1i(1+n)n)AC+AS+SV(i(1+i)n1)=1,600,000(0.15(1+0.15)5(1+0.15)51)58,000+220,000+480,000(0.15(1+0.15)51)=1,600,000(0.15(2.01136)(2.01136)1)58,000+220,000+480,000(0.152.011361)=1,600,000(0.30171.01136)58,000+220,000+480,000(0.151.01136)=1,600,000(0.29831)58,000+220,000+480,000(0.14831)=477,29658,000+220,000+71,188.8=244,107.2

The annual worth of the defender is -$244,107.2.

Since the annual cost of the defender is lower than challenger, retain the defender.

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