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 18, Problem 1CS1
To determine

Calculate the present worth analysis.

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Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. Time period 1 (n) is 40. Time period 2 (n1) is 20.

The present worth (PW) of Plan A can be calculated using the following formula:

PW=First cost+AOC×((1+i)n1i(1+i)n)+Salvage value×(1(1+i)n)        (1)

Substitute the respective values in Equation (1) to calculate the present worth of Plan A with the actual time period.

PW=10,000500((1+0.1)4010.1(1+0.1)40)+1,000×(1(1+0.1)40)=10,000500(9.7791)+1,000×(0.0221)=14,867

Thus, the present worth is -$14,867.

Location is denoted by ‘L’. Present worth (PW) of Plan B can be calculated using the following formula:

PW=(First costL 1+AOCL 1×((1+i)n1i(1+i)n)+Salvage valueL 1×(1(1+i)n)+First costL 2+AOCL 2×(1(1+i)n1)+First costL 2(1(1+i)n1)+Salvage valueL 2×(1(1+i)n)+AOCL 2×((1+i)n1i(1+i)n))        (2)

Substitute the respective values in Equation (1) to calculate the present worth of Plan B with the actual time period.

PW=(30,000100×((1+0.1)4010.1(1+0.1)40)+5000(1(1+0.1)40)5,000200×(1(1+0.1)20)5,000(1(1+0.1)20)200×(1(1+0.1)40)200×((1+0.1)4010.1(1+0.1)40))=(30,000100×(9.7791)+5000(0.0221)5,000200×(0.1486)5,000(0.1486)200×(0.0221)200×(9.7791))=38,600

Thus, the present worth is -$38,600.

Table 1 shows the value of present worth by changing the time period to different percentages that is obtained using Equations (1) and (2):

Table 1

MARRPW APW B
0.1-14,867-38,600
0.07-16,599-40,023
0.04-19,688-42,311

Table 1 reveals that at different levels of MARR, the present worth of alternate A is greater than alternate B. Thus, there is no sensitivity. Plan A is selected for different levels of MARR.

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