EBK ENGINEERING ECONOMY
EBK ENGINEERING ECONOMY
8th Edition
ISBN: 8220103675437
Author: Blank
Publisher: YUZU
Question
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Chapter 13, Problem 37P

(a):

To determine

Calculate the payback period with interest rate (i) 0%.

(a):

Expert Solution
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Explanation of Solution

SA: First cost (FC) is $40,000. Net annual income (NI) is $10,000.

AU: First cost (FC) is $90,000. Net annual income (NI) is $15,000.

Payback period (n) for SA can be calculated as follows:

Payback period=FCAI=40,00010,000=4

Payback period is 4 years.

Payback period (n) for AU can be calculated as follows:

Payback period=FCAI=90,00015,000=6

Payback period is 6 years. Since the payback period for the alternative SA is less than 5 years, select the alternate SA.

(b):

To determine

Calculate the payback period with interest rate (i) 10%.

(b):

Expert Solution
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Explanation of Solution

Payback period (n) for alternate SA can be calculated as follows:

AI((1+i)n1i(1+i)n)=I10,000((1+0.1)n10.1(1+0.1)n)=40,000((1+0.1)n10.1(1+0.1)n)=40,00010,000((1+0.1)n10.1(1+0.1)n)=4

Substitute n as 5 by trial and error method to verify the time period in the above calculation.

(1+0.1)510.1(1+0.1)5=4(1.6105110.1(1.61051))=40.610510.161051=43.7907<4

Since the calculated present value factor to the annual value is less than the given value, the payback period is more than 5 years.

Payback period (n) for alternate AU can be calculated as follows:

AI((1+i)n1i(1+i)n)=I15,000((1+0.1)n10.1(1+0.1)n)=90,000((1+0.1)n10.1(1+0.1)n)=90,00015,000((1+0.1)n10.1(1+0.1)n)=6

Substitute n as 5 by trial and error method to verify the time period in the above calculation.

(1+0.1)510.1(1+0.1)5=6(1.6105110.1(1.61051))=60.610510.161051=63.7907<6

Since the calculated present value factor to the annual value is less than the given value, the payback period is more than 5 years. Since both the alternate’s payback periods are greater than 5 years, both the alternates should not be selected.

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