Engineering Economy
Engineering Economy
8th Edition
ISBN: 9781259683312
Author: Blank
Publisher: MCG
Question
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Chapter 5, Problem 15P
To determine

Compare the projects based on the present worth.

Expert Solution & Answer
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Explanation of Solution

Project A:  Cost (C) is $80,000, salvage value (S) is $15,000, operating cost (OC) is $30,000 in year 1 and it increases (IO) by $4,000 each year, time period (n) is 3 years, and interest rate (i) is 12% per year.

Project A:  Cost (C) is $120,000, salvage value (S) is $40,000, operating cost (OC) is $8,000 in year 1 and it increases (IO) by $6,500 each year, time period (n) is 3 years, and interest rate (i) is 12% per year.

The present worth of project A (PW) can be calculated as follows:

PWA=C(OC((1+i)n1i(1+i)n)+IO×1i((1+i)n1i(1+i)nn(1+i)n))+SV(1+i)n=80,000(30,000((1+0.12)310.12(1+0.12)3)+4,000×10.12((1+0.12)310.12(1+0.12)33(1+0.12)3))+15,000(1+0.12)3=80,000(30,000(1.40492810.12(1.404928))+4,000×8.3333(1.40492810.12(1.404928)31.404928))+15,0001.404928=80,000(30,000(0.4049280.16859136)+4,000×8.3333(0.4049280.168591362.135341))+10,676.7037=80,000(30,000(2.401831)+4,000×8.3333(2.4018312.135341))+10,676.7037=80,000(30,000(2.401831)+4,000×8.3333(0.26649))+10,676.7037=80,000(72,054.93+8,882.96)+10,676.7037=150,258.19

The present worth of project A is -$142,444.19.

The present worth of project B (PW) can be calculated as follows:

PWA=C(OC((1+i)n1i(1+i)n)+IO×1i((1+i)n1i(1+i)nn(1+i)n))+SV(1+i)n=120,000(8,000((1+0.12)310.12(1+0.12)3)+6,500×10.12((1+0.12)310.12(1+0.12)33(1+0.12)3))+40,000(1+0.12)3=120,000(8,000(1.40492810.12(1.404928))+6,500×8.3333(1.40492810.12(1.404928)31.404928))+40,0001.404928=120,000(8,000(0.4049280.16859136)+6,500×8.3333(0.4049280.168591362.135341))+28,471.2099=120,000(8,000(2.401831)+6,500×8.3333(2.4018312.135341))+28,471.2099=120,000(8,000(2.401831)+6,500×8.3333(0.26649))+28,471.2099=120,000(19,214.648+14,434.82)+28,471.2099=112,475.62125,178.26

The present worth of project B is -$125,178.56. Since the present worth of project B is greater than project A, select project B.

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