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 9, Problem 72APQ
To determine

Benefit–cost ratio.

Expert Solution & Answer
Check Mark

Explanation of Solution

Initial cost (C) is $2,800,000. Additional cost (AC) for every 5 years is $200,000. Maintenance cost (M) is $20,000 per year. Decreased damage amount (B) is $310,000 per year. Interest rate is 6%. Time period (n) is 5.

Option (c):

The benefit–cost ratio (BC) can be calculated as follows:

BC=B(C×i)+M+AC(i(1+i)n1)1.4=310,000(2,800,000×0.06)+20,0000+200,000(0.06(1+0.06)51)1.4=310,000168,000+20,0000+200,000(0.061.3382261)1.4=310,000188,000+200,000(0.060.338226)1.4=310,000188,000+35,479.21.4=310,000188,000+35,479.21.4=1.4

The calculated BC value is nearly equal to the given value. Thus, option ‘c’ is correct.

Option (a):

The benefit–cost ratio (BC) can be calculated as follows:

BC=B(C×i)+M+AC(i(1+i)n1)0.46=310,000(2,800,000×0.06)+20,0000+200,000(0.06(1+0.06)51)0.46=310,000168,000+20,0000+200,000(0.061.3382261)0.46=310,000188,000+200,000(0.060.338226)0.46=310,000188,000+35,479.20.46=310,000188,000+35,479.20.46<1.4

The calculated BC value is greater than the given value. Thus, option ‘a’ is incorrect.

Option (b):

The benefit–cost ratio (BC) can be calculated as follows:

BC=B(C×i)+M+AC(i(1+i)n1)1.02=310,000(2,800,000×0.06)+20,0000+200,000(0.06(1+0.06)51)1.02=310,000168,000+20,0000+200,000(0.061.3382261)1.02=310,000188,000+200,000(0.060.338226)1.02=310,000188,000+35,479.21.02=310,000188,000+35,479.21.02<1.4

The calculated BC value is greater than the given value. Thus, option ‘b’ is incorrect.

Option (d):

The benefit–cost ratio (BC) can be calculated as follows:

BC=B(C×i)+M+AC(i(1+i)n1)1.96=310,000(2,800,000×0.06)+20,0000+200,000(0.06(1+0.06)51)1.96=310,000168,000+20,0000+200,000(0.061.3382261)1.96=310,000188,000+200,000(0.060.338226)1.96=310,000188,000+35,479.21.96=310,000188,000+35,479.21.96>1.4

The calculated BC value is less than the given value. Thus, option ‘d’ is incorrect.

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Chapter 9 Solutions

Engineering Economy

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