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 19P

(a):

To determine

Calculate the benefit–cost ratio.

(a):

Expert Solution
Check Mark

Explanation of Solution

Table-1 shows the cash flow.

Table -1

ItemCash flow
First cost (F)13,000,000
Benefit (B) per year3,800,000
Future value of disbenefit (DB)6,750,000
Maintenance cost (MC) per year400,000
Time period (n)20
Discount rate (i)10%

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

BC=BDB(i(1+i)n1)F(i(1+i)n(1+i)n1)+MC=3,800,0006,750,000(0.1(1+0.1)201)13,000,000(0.1(1+0.1)20(1+0.1)201)+400,000=3,800,0006,750,000(0.16.72749991)13,000,000(0.1(6.7274999)6.72749991)+400,000=3,800,0006,750,000(0.15.7274999)13,000,000(0.67274995.7274999)+400,000=3,800,0006,750,000(0.0174596)13,000,000(0.1174596)+400,000=3,800,000117,852.31,526,974.8+400,000=3,682,147.71,926,974.8=1.91

Benefit–cost ratio is 1.91. Since the benefit–cost ratio is greater than 1, the project is economically justified.

(b):

To determine

Minimum value of the first cost.

(b):

Expert Solution
Check Mark

Explanation of Solution

The project is acceptable when at least the benefit–cost ration (BC) is equal to 1. If it is less than 1, then the project would not be accepted. The minimum value of the first cost (F) can be calculated as follows:

BC=BDB(i(1+i)n1)F(i(1+i)n(1+i)n1)+MC1=3,800,0006,750,000(0.1(1+0.1)201)F(0.1(1+0.1)20(1+0.1)201)+400,0001=3,800,0006,750,000(0.16.72749991)F(0.1(6.7274999)6.72749991)+400,0001=3,800,0006,750,000(0.15.7274999)F(0.67274995.7274999)+400,0001=3,800,0006,750,000(0.0174596)F(0.1174596)+400,0001=3,800,000117,852.3F(0.1174596)+400,0001(F(0.1174596)+400,000)=3,682,147.7F(0.1174596)=3,682,147.7400,000F=3,282,147.7(0.1174596)=27,942,779.47

To accept this project, the first cost must be greater than $27,942,779.47. If the first cost is less than $27,942,779.47, then the project would not be accepted.

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Chapter 9 Solutions

Engineering Economy

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