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 6, Problem 22P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution
Check Mark

Explanation of Solution

Table -1 shows the cash flow of different models.

Table -1

ModelsLAINCO
First cost (C)-150,000-900,000 
AOC (MO) per year-95,000-60,000-140,000
Salvage value (SV)25,000300,000 
Time period (n)462
Interest  (i)10%10%10%

The equivalent annual worth of project LA (AWL) can be calculated as follows:

AWL=C(i(1+i)n(1+i)n1)+MO+SV(i(1+i)n1)=150,000(0.1(1+0.1)4(1+0.1)41)95,000+25,000(0.1(1+0.1)41)=150,000(0.1(1.4641)1.46411)95,000+25,000(0.11.46411)=150,000(0.146410.4641)95,000+25,000(0.10.4641)=150,000(0.315471)95,000+25,000(0.215471)=47,320.6595,000+5,386.775=136,933.88

The annual worth of the project LA is -$136,933.88.

The equivalent annual worth of model IN (AWI) can be calculated as follows:

AWI=C(i(1+i)n(1+i)n1)+MO+SV(i(1+i)n1)=900,000(0.1(1+0.1)6(1+0.1)61)60,000+300,000(0.1(1+0.1)61)=900,000(0.1(1.771561)1.7715611)60,000+300,000(0.11.7715611)=900,000(0.17715610.771561)60,000+300,000(0.10.771561)=900,000(0.229607)60,000+300,000(0.129607)=206,646.360,000+38,882.1=227,764.2

The annual worth of the model IN is -$227,764.2.

Since the annual worth of the project LA is greater than the other two project, select the project LA.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution
Check Mark

Explanation of Solution

The time period for project LA should be equated with the time period of project IN and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWL=AWL((1+i)n1i(1+i)n)=136,933.88((1+0.1)1210.1(1+0.1)12)=136,933.88(3.13842810.1(3.138428))=136,933.88(2.1384280.313843)=136,933.88(6.813687)=933,024.6

The present worth of the project LA is -$933,024.6.

The time period for project IN should be equated with time period of project LA and CO to compare the present worth. The common time period for all the projects is 12 years. The present worth of project LA (PWL) can be calculated as follows:

PWI=AWI((1+i)n1i(1+i)n)=227,764.2((1+0.1)1210.1(1+0.1)12)=227,764.2(3.13842810.1(3.138428))=227,764.2(2.1384280.313843)=227,764.2(6.813687)=1,551,913.97

The present worth of the project IN is -$1,551,913.97.

The time period for project CO should be equated with time period of project LA and IN to compare the present worth. The common time period for all the projects is 12 years. The present worth of project CO (PWC) can be calculated as follows:

PWC=AWC((1+i)n1i(1+i)n)=140,000((1+0.1)1210.1(1+0.1)12)=140,000(3.13842810.1(3.138428))=140,000(2.1384280.313843)=140,000(6.813687)=953,916.18

The present worth of the project CO is -$953,916.18.

Since the present worth of the project LA is greater than the other two project, select the project LA.

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