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 17P

(a)

To determine

Calculate the equivalent annual worth.

(a)

Expert Solution
Check Mark

Explanation of Solution

Model G: First cost (C) is $36,000. Operating cost (A) is $4,000. Salvage value (SV) is $15,000. Time period (n) is 3 years. Interest rate (i) is 15%.

Model F: First cost (C) is $32,000. Operating cost (A) is $3,100. Salvage value (SV) is $15,000. Time period (n) is 4 years. Interest rate (i) is 15%.

The equivalent annual worth of Model G (AWG) can be calculated as follows:

AWG=C(i(1+i)n(1+i)n1)A+SV(i(1+i)n1)=36,000(0.15(1+0.15)3(1+0.15)31)4,000+15,000(0.15(1+0.15)31)=36,000(0.15(1.520875)1.5208751)4,000+15,000(0.151.5208751)=36,000(0.2281310.520875)4,000+15,000(0.150.520875)=36,000(0.437976)4,000+15,000(0.287977)=15,767.1364,000+4,319.655=15,447.48

The annual worth of Model G is -$15,447.48.

The equivalent annual worth of Model F (AWF) can be calculated as follows:

AWF=C(i(1+i)n(1+i)n1)A+SV(i(1+i)n1)=32,000(0.15(1+0.15)4(1+0.15)41)3,100+15,000(0.15(1+0.15)41)=32,000(0.15(1.749006)1.7490061)3,100+15,000(0.151.7490061)=32,000(0.2623510.749006)3,100+15,000(0.150.749006)=32,000(0.350266)3,100+15,000(0.200265)=11,208.5123,100+3,003.975=11,304.54

The annual worth of  Model F is -$11,304.54. Since the annual worth of Model F is greater than Model G, select Model F.

(b)

To determine

Calculate the present worth.

(b)

Expert Solution
Check Mark

Explanation of Solution

The time period to calculate the present worth is 12 years (4×3). The present worth of Model G (PG) can be calculated as follows:

PG=AWG((1+i)n1i(1+i)n)=15,447.48((1+0.15)1210.15(1+0.15)12)=15,447.48(5.3502510.15(5.35025))=15,447.48(4.350250.80254)=15,447.48(5.420602)=83,734.64

The present worth of Model G is -$83,734.64.

The present worth of Model F (PF) can be calculated as follows:

PF=AWF((1+i)n1i(1+i)n)=11,304.54((1+0.15)1210.15(1+0.15)12)=11,304.54(5.3502510.15(5.35025))=11,304.54(4.350250.80254)=11,304.54(5.420602)=61,277.41

The annual worth of Model F is -$61,277.41.

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