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 36P

(a):

To determine

Calculate the incremental benefit–cost ratio of the mutual alternative.

(a):

Expert Solution
Check Mark

Explanation of Solution

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

Table-1

Item12
Initial cost (C)60500
Benefit (B) per month1.258
Time period (n)6060

The discount rate (i) is 0.5%.

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

BC=B1C1(i(1+i)n(1+i)n1)=1.2560(0.005(1+0.005)60(1+0.005)601)=1.2560(0.005(1.34885)(1.34885)1)=1.2560(0.00674(0.34885))=1.2560(0.01932)=1.251.1592=1.08

The incremental benefit–cost ratio is 1.08. 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(C2C1)(i(1+i)n(1+i)n1)=81.25(50060)(0.005(1+0.005)60(1+0.005)601)=6.75440(0.005(1.34885)(1.34885)1)=6.75440(0.00674(0.34885))=6.75440(0.01932)=6.758.5008=0.79

The incremental benefit cost ratio is 0.79. Since the incremental benefit cost ratio is less than 1, select the initial alternate 1 and eliminate the new alternate 2.

(b):

To determine

Calculate the incremental benefit–cost ratio of the independent alternative.

(b):

Expert Solution
Check Mark

Explanation of Solution

The benefit–cost ratio (BC) of alternate 1 can be calculated as follows:

BC=B1C1(i(1+i)n(1+i)n1)=1.2560(0.005(1+0.005)60(1+0.005)601)=1.2560(0.005(1.34885)(1.34885)1)=1.2560(0.00674(0.34885))=1.2560(0.01932)=1.251.1592=1.08

The benefit–cost ratio is 1.08. Since the benefit–cost ratio is greater than 1, select the alternate 1.

The benefit–cost ratio (BC) of alternate 2 can be calculated as follows:

BC=B2C2(i(1+i)n(1+i)n1)=8500(0.005(1+0.005)60(1+0.005)601)=8500(0.005(1.34885)(1.34885)1)=8500(0.00674(0.34885))=8500(0.01932)=89.66=0.83

The incremental benefit–cost ratio is 0.83. Since the benefit–cost ratio is less than 1, eliminate the new alternate 2.

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Chapter 9 Solutions

Engineering Economy

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