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 15P

(a):

To determine

Calculate the economic service life.

(a):

Expert Solution
Check Mark

Explanation of Solution

First cost (FC) is $180,000. Annual cost (AC) in year 1 and 2 is $84,000 after it increases by $5,000 per year. Salvage value (SV) is 25% to the first cost. MARR (i) is 15%. Time period (n) is 5 years.

Table -1 shows the total annual salvage value for different years as follows:

Table -1

YearACSV
184,00045,000
284,00045,000
389,00045,000
494,00045,000
599,00045,000

Total annual value (TA) of the cost can be calculated using the formula as follows:

TAYear n=(FC(i(1+i)n(1+i)n1)(AC1(1+i)1+AC2(1+i)2+AC3(1+i)3+AC4(1+i)4+AC5(1+i)5)(i(1+i)n(1+i)n1)+SV(i(1+i)n1))        (1)

The value of n1 in the first year is 1. Substitute the respective values in Equation (1) to calculate the total annual value in the year 1.

TA1=(180,000(0.15(1+0.15)1(1+0.15)11)(84,000(1+0.15)1+0(1+0.15)2+0(1+0.15)3+0(1+0.15)4+0(1+0.15)5)(0.15(1+0.15)1(1+0.15)11)+45,000(0.15(1+0.15)11))=(180,000(0.15(1.15)(1.15)1)(84,0001.15)(0.15(1.15)(1.15)1)+45,000(0.151.151))=(180,000(0.17250.15)(84,0001.15)(0.17250.15)+45,000(0.150.15))=(180,000(1.15)(84,0001.15)(1.15)+45,000(1))=(207,00084,000+45,000)=246,000

The total annual value in the year 1 is -$246,000.

Table -2 shows the total annual value for the different years that are obtained using Equation (1) as follows:

Table -2

YearTotal annual value
1-246,000
2-173,791
3-1581,317
4-141,190
5-135,934

Economic service life occurs at the time period where the annual value of the cost is lower. The lower total annual value -$135,934 occurs at the year 5. Thus, economic service life is 5.

(b):

To determine

Calculate the economic service life using spreadsheet.

(b):

Expert Solution
Check Mark

Explanation of Solution

Total annual value (TA) of the cost can be calculated using the spreadsheet as follows:

Engineering Economy, Chapter 11, Problem 15P

Thus, the lower value of the total annual value is -$135,934 and the economic service life is 5.

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