Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
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Chapter 9, Problem 33P
To determine

Calculate the incremental benefit–cost ratio.

Expert Solution & Answer
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Explanation of Solution

Table-1 shows the cash flow of two different projects.

Table-1

Item12
Initial cost (C)1,200,0002,000,000
Annual maintenance cost (AM)80,00075,000
Annual benefit (B)520,000580,000
Annual disbenefit (DB)90,000140,000
Time period (n)1020

The interest rate (i) is 8%.

The alternatives are ranked based on the initial cost of the alternate. The first is do nothing, the second is alternate 1, and the third is alternate 2.

The incremental benefit–cost ratio (BC) between the initial alternate, do nothing, and the new alternate 1 can be calculated as follows.

BC=B1DB1C1(i(1+i)n1(1+i)n11)+AM1=520,00090,0001,200,000(0.08(1+0.08)10(1+0.08)101)+80,000=430,0001,200,000(0.08(2.158925)2.1589251)+80,000=430,0001,200,000(0.1727141.158925)+80,000=430,0001,200,000(0.149029)+80,000=430,000178,834.8+80,000=430,000258,834.8=1.66

The incremental benefit–cost ratio is 1.66. Since the incremental benefit–cost ratio is greater than 1, select the new alternate 1 and eliminate the initial alternate do nothing.

The incremental benefit–cost ratio (BC) between the initial alternate 1 and new alternate 2 can be calculated as follows:

BC=(B2B1)(DB2DB1)(C2(i(1+i)n2(1+i)n21)+AM2)C1(i(1+i)n1(1+i)n11)+AM1=(580,000520,000)(140,00090,000)(2,000,000(0.08(1+0.08)20(1+0.08)201)+75,000)(1,200,000(0.08(1+0.08)10(1+0.08)101)+80,000)=60,00050,000(2,000,000(0.08(4.660957)4.6609571)+75,000)(1,200,000(0.08(2.158925)2.1589251)+80,000)=10,000(2,000,000(0.3728773.660957)+75,000)(1,200,000(0.1727141.158925)+80,000)=10,000(2,000,000(0.101852)+75,000)(1,200,000(0.149029)+80,000)=10,000(203,704+75,000)(178,834.8+80,000)=10,0002798,704258,834.8=10,0002798,704258,834.8=10,00019,869.2=0.503

The incremental benefit–cost ratio is 0.503. Since the incremental benefit–cost ratio is less than 1, select the initial alternate 1 and eliminate the new alternate 2.

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Chapter 9 Solutions

Engineering Economy

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