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 18, Problem 11P
To determine

Calculate the annual worth.

Expert Solution & Answer
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Explanation of Solution

Time period is indicated by (n). Interest rate is indicated by ‘i’.

The annual worth (AW) of interest rate 7% can be calculated as follows:

AW=Borrowing(i(1+i)n(1+i)n1)MO+Selling price(i(1+i)n1)=12,000,000(0.07(1+0.07)5(1+0.07)51)3,100,000+2,000,000(0.07(1+0.07)51)=12,000,000(0.24389)3,100,000+2,000,000(0.17389)=5,678,907

Therefore, the annual worth is -$5,678,907, which is less than the -$6,100,000. Thus, it is acceptable.

The annual worth (AW) of interest rate 10% can be calculated as follows:

AW=Borrowing(i(1+i)n(1+i)n1)MO+Selling price(i(1+i)n1)=12,000,000(0.1(1+0.1)5(1+0.1)51)3,100,000+2,300,000(0.1(1+0.1)51)=12,000,000(0.2638)3,100,000+2,300,000(0.1638)=5,888,836

Therefore, the annual worth is -$5,888,836, which is less than the -$6,100,000. Thus, it is acceptable.

The annual worth (AW) of interest rate 15% can be calculated as follows:

AW=Borrowing(i(1+i)n(1+i)n1)MO+Selling price(i(1+i)n1)=12,000,000(0.15(1+0.15)5(1+0.15)51)3,100,000+2,500,000(0.15(1+0.15)51)=12,000,000(0.29832)3,100,000+2,500,000(0.14832)=6,309,040

Therefore, the annual worth is -$6,309,040, which is greater than the -$6,100,000. Thus, it is not acceptable. Since the annual worth exceeds $6,100,000 at interest rate 15%, the decision is sensitive.

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