(a):
Calculate the present worth without considering the inflation.
(a):
![Check Mark](/static/check-mark.png)
Explanation of Solution
Table-1 shows the cash flow of different alternatives.
Table-1
Alternative | A | B |
First cost (C) | -31,000 | -48,000 |
Annual cost (AM) per year | -28,000 | -19,000 |
Salvage value (SV) | 5,000 | 7,000 |
Time period (n) | 5 | 5 |
The interest rate (i) is 10%, and the inflation rate (f) is 3%.
The present worth (PW) for Alternative A can be calculated as follows:
The present worth is -$134,038.9. The present worth for Alternate A can be calculated using a spreadsheet as follows:
= - PV(10%,5,-28000,5000) – 31000
The above spreadsheet function gives the value of -$134,37.42.
The present worth (PW) for Alternative B can be calculated as follows:
The present worth is -$115,678.9. Since the present worth of the cost is lower for Alternate B, select Alternate B. The present worth for alternate B can be calculated using a spreadsheet as follows:
= - PV(10%,5,-19000,7000) - 48000
The above spreadsheet function gives the value of -$115,678.5.
(b):
Calculate the present worth with considering the inflation.
(b):
![Check Mark](/static/check-mark.png)
Explanation of Solution
The real interest rate (if) can be calculated as follows:
The real interest rate is 13.3%.
The present worth (PW) for Alternative A can be calculated as follows:
The present worth is -$126,086.8. The present worth for Alternate A can be calculated using a spreadsheet as follows:
= - PV(13.3%,5,-28000,5000) - 31000
The above spreadsheet function gives the value of -$126,87.79.
The present worth (PW) for Alternative B can be calculated as follows:
The present worth is -$115,678.9. Since the present worth of the cost is lower for Alternate B, select Alternate B. The present worth for Alternate B can be calculated using a spreadsheet as follows:
= - PV(13.3%,5,-19000,7000) - 48000
The above spreadsheet function gives the value of -$110,591.83.
(c):
Calculate the interest rate that makes both the alternates equal.
(c):
![Check Mark](/static/check-mark.png)
Explanation of Solution
The interest rate that makes both alternates’ present worth equal can be calculated using the spreadsheet as follows:
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Chapter 14 Solutions
ENGR.ECONOMY CUSTOM FOR TAMU ISEN 667
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