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 11, Problem 37P

(a):

To determine

Calculate the annual worth.

(a):

Expert Solution
Check Mark

Explanation of Solution

Defender: The first cost (FC) is $160,000. The annual operating cost (AC) is $7,000. The salvage value for the first year (SV1) is $50,000 and for the second year (SV2) is $40,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212) .

Challenger: The first cost (FC) is $210,000. The annual operating cost (AC) is $5,000. The salvage values for first year (SV1) is $100,000, second year (SV2) is $7,000, and third year (SV3) is $45,000. The interest rate is 12% compounded monthly. Thus, the effective interest rate (i) is 1%(0.1212).

The annual worth (AV) is calculated using the following formula:

AV=FC(i(1+i)n(1+i)n1)AC+SVn(i(1+i)n1)        (1)

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of defender in 12-month period.

AV=160,000(0.01(1+0.01)12(1+0.01)121)7,000+50,000(0.01(1+0.01)121)=160,000(0.01(1.12683)1.126831)7,000+50,000(0.011.126831)=160,000(0.011270.12683)7,000+50,000(0.010.12683)=160,000(0.08885)7,000+50,000(0.07885)=14,2167,000+3,942.5=17,274

The annual worth of the defender for 12 months is -$17,2754.

Substitute the respective values in Equation (1) to calculate the annual worth (AV) of challenger in 12-month period.

AV=210,000(0.01(1+0.01)12(1+0.01)121)5,000+100,000(0.01(1+0.01)121)=210,000(0.01(1.12683)1.126831)5,000+100,000(0.011.126831)=210,000(0.011270.12683)5,000+100,000(0.010.12683)=210,000(0.08885)5,000+100,000(0.07885)=18,658.55,000+7,885=15,774

The annual worth of the challenger for 12 months is -$15,774.

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(b):

To determine

Calculate the annual worth for 2 years.

(b):

Expert Solution
Check Mark

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 2 years (24 months), which were obtained using Equation (1).

Table 1

ProjectAV
Defender-13,048
Challenger-12,290

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

(c):

To determine

Calculate the annual worth for 3 years.

(c):

Expert Solution
Check Mark

Explanation of Solution

Table 1 shows the annual worth of the defender and challenger for 3 years (36 months), which were obtained using Equation (1).

Table 1

ProjectAV
Defender-14,292
Challenger-10,349

The challenger can be replaced if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender with challenger.

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