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 12, Problem 29P
To determine

Calculate the internal rate of return.

Expert Solution & Answer
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Explanation of Solution

The first cost (FC) is $400,000. Annual operating cost (AC) is $75,000. Annual savings (AS) is $192,000. Salvage value (SV) is 20% of the first cost. Profitability index (i) is 12%. Time period (n) is 5 years.

The internal rate of return (ir) can be calculated using the following formula:

FC=(ASAC)((1+ir)n1ir(1+ir)n)+FC×SV(1+ir)n400,000=(192,00075,000)((1+ir)51ir(1+ir)5)+400,000×0.2(1+ir)5400,000=(117,000)((1+ir)51ir(1+ir)5)+80,000(1+ir)5

Substitute ir as 0.12 by trial and error method in the above calculation.   

400,000=(117,000)((1+0.12)510.12(1+0.12)5)+80,000(1+0.12)5400,000=(117,000)(3.6048)+80,0001.7623400,000=421,761.6+45,395.22400,000<467,156.82

The calculated value is less than the first cost. Thus, increase the ir value to 0.1809.

400,000=(117,000)((1+0.1809)510.1809(1+0.1809)5)+80,000(1+0.1809)5400,000=(117,000)(3.1211)+80,0002.2965400,000=365,168.7+34,835.62400,000400,00.32

Since the calculated value is equal to the first cost, the value of ir is confirmed as 18.09%.

The value PI can be calculated as follows:

PI=(ASAC)((1+ir)n1ir(1+ir)n)+FC×SV(1+ir)nFC=(117,000)((1+0.12)510.12(1+0.12)5)+80,000(1+0.12)5400,000=(117,000)(3.6048)+80,0001.7623400,000=421,761.6+45,395.22400,000=467,156.82400,000=1.17

The value of PI is 1.17.

The value PW can be calculated as follows:

PW=FC+(ASAC)((1+ir)n1ir(1+ir)n)+FC×SV(1+ir)n=400,000+(117,000)((1+0.12)510.12(1+0.12)5)+80,000(1+0.12)5=400,000+(117,000)(3.6048)+80,0001.7623=400,000+421,761.6+45,395.22=67,156.82

The present wroth (PW) is $67,156.82.

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