(a):
Calculate the economic service life.
(a):

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
Year | AC | SV |
1 | 84,000 | 45,000 |
2 | 84,000 | 45,000 |
3 | 89,000 | 45,000 |
4 | 94,000 | 45,000 |
5 | 99,000 | 45,000 |
Total annual value (TA) of the cost can be calculated using the formula as follows:
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.
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
Year | Total 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):
Calculate the economic service life using spreadsheet.
(b):

Explanation of Solution
Total annual value (TA) of the cost can be calculated using the spreadsheet as follows:
Thus, the lower value of the total annual value is -$135,934 and the economic service life is 5.
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Chapter 11 Solutions
ENGINEERING ECONOMY DIGITAL ACCESS
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