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 71APQ
To determine

Benefit–cost ratio.

Expert Solution & Answer
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Explanation of Solution

The first cost (C) is $700,000 and the maintenance cost (M) is $25,000 per year. The initial property value (P) is $400,000 and increased property value (IP) is $600,000. The interest rate is 6% and time period (n) is 10 years.

Option (b):

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

BC=IPP(C(i(1+i)n(1+i)n1)+M)1.7=600,000400,000(700,000(0.06(1+0.06)10(1+0.06)101)+25,000)1.7=200,000(700,000(0.06(1.790848)1.7908481)+25,000)1.7=200,000(700,000(0.1074510.790848)+25,000)1.7=200,000(700,000(0.1074510.790848)+25,000)1.7=200,000(700,000(0.135868)+25,000)1.7=200,000(95,107.6+25,000)1.7=1.7

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

Option (a):

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

BC=IPP(C(i(1+i)n(1+i)n1)+M)1.3=600,000400,000(700,000(0.06(1+0.06)10(1+0.06)101)+25,000)1.3=200,000(700,000(0.06(1.790848)1.7908481)+25,000)1.3=200,000(700,000(0.1074510.790848)+25,000)1.3=200,000(700,000(0.1074510.790848)+25,000)1.3=200,000(700,000(0.135868)+25,000)1.3=200,000(95,107.6+25,000)1.3<1.7

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

Option (c):

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

BC=IPP(C(i(1+i)n(1+i)n1)+M)2.1=600,000400,000(700,000(0.06(1+0.06)10(1+0.06)101)+25,000)2.1=200,000(700,000(0.06(1.790848)1.7908481)+25,000)2.1=200,000(700,000(0.1074510.790848)+25,000)2.1=200,000(700,000(0.1074510.790848)+25,000)2.1=200,000(700,000(0.135868)+25,000)2.1=200,000(95,107.6+25,000)2.1>1.7

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

Option (d):

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

BC=IPP(C(i(1+i)n(1+i)n1)+M)2.8=600,000400,000(700,000(0.06(1+0.06)10(1+0.06)101)+25,000)2.8=200,000(700,000(0.06(1.790848)1.7908481)+25,000)2.8=200,000(700,000(0.1074510.790848)+25,000)2.8=200,000(700,000(0.1074510.790848)+25,000)2.8=200,000(700,000(0.135868)+25,000)2.8=200,000(95,107.6+25,000)2.8>1.7

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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