Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
Question
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Chapter 11, Problem 36P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution
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Explanation of Solution

Defender: Upgrade cost (UC) is $79,000. Market value (MV) is $40,000. Annual operating cost (AC) is $85,000. Salvage value (SV) is $30,000. Interest rate (i) is 15%. Time period (n) is 3.

Challenger: First cost (FC) is $220,000. Annual operating cost (AC) is $45,000. Salvage value (SV) is $50,000. . Interest rate (i) is 15%. Time period (n) is 3.

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

AV=(MV+UC)(i(1+i)n(1+i)n1)AC+SV(i(1+i)n1)=(40,000+79,000)(0.15(1+0.15)3(1+0.15)31)85,000+30,000(0.15(1+0.15)31)=(119,000)(0.15(1.52088)1.520881)85,000+30,000(0.151.520881)=(119,000)(0.228130.52088)85,000+30,000(0.150.52088)=(119,000)(0.43797)85,000+30,000(0.28797)=52,118.4385,000+8,639.1=128,479.33

The annual worth of the defender is -$128,479.33.

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

AV=FC(i(1+i)n(1+i)n1)AC+SV(i(1+i)n1)=220,000(0.15(1+0.15)3(1+0.15)31)45,000+50,000(0.15(1+0.15)31)=220,000(0.15(1.52088)1.520881)45,000+50,000(0.151.520881)=22,000(0.228130.52088)45,000+50,000(0.150.52088)=220,000(0.43797)45,000+50,000(0.28797)=96,353.445,000+14,398.5=126,954.9

The annual worth of the challenger is -$126,954.9.

The challenger can be replaced, if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender for the challenger.

(b):

To determine

Calculate the annual worth for the next three years.

(b):

Expert Solution
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Explanation of Solution

The annual worth for the next three years is -$126,954.9, which is calculated in the subpart ‘a’.

(c):

To determine

Calculate the annual worth through spreadsheet.

(c):

Expert Solution
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Explanation of Solution

The spreadsheet function to calculate the annual worth of defender through the spreadsheet is given below:

= -PMT(15%,3,-119000,30000)-85000

The above function gives the value of -$128,479.95.

The spreadsheet function to calculate the annual worth of challenger through the spreadsheet is given below:

= -PMT(15%,3,-220000,50000)-45000

The above function gives the value of -$126,956.08.

(d):

To determine

Calculate the annual worth through spreadsheet for 8 years.

(d):

Expert Solution
Check Mark

Explanation of Solution

The spreadsheet function to calculate the annual worth of challenger for 8 years through the spreadsheet is given below:

= -PMT(15%,8,-220000,10000)-45000

The above function gives the value of -$93,298.52. This reveals that there is a reduction of $33,657.56 per year recovery from the annual worth of the challenger with the 3 year time period.

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