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 7, Problem 17P
To determine

Calculate the rate of return.

Expert Solution & Answer
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Explanation of Solution

Initial cost (C) is $130,000. Repayment in year 1 (R1) is 78,000 and increases (I) by $1,000 per year thereafter. Equivalent annual cost (AC) is $49,000. Time period (1) is 8.

Rate of return (i) can be calculated as follows:

C=(AC((1+i)n1i(1+i)n)+R1((1+i)n1i(1+i)n)+I×1i((1+i)n1i(1+i)nn(1+i)n)+SV(1+i)n)130,000=(49,000((1+i)81i(1+i)8)+78,000((1+i)81i(1+i)8)+1,000×1i((1+i)81i(1+i)8n(1+i)8)+23,000(1+i)8)

Substitute the rate of return as 19% by trial and error method in the above Equation.

130,000=(49,000((1+0.19)810.19(1+0.19)8)+78,000((1+0.19)810.19(1+0.19)8)+1,000×10.19((1+0.19)810.19(1+0.19)88(1+0.19)8)+23,000(1+0.19)8)130,000=(49,000(4.02138510.19(4.021385))+78,000(4.02138510.19(4.021385))+1,000×5.263158(4.02138510.19(4.021385)84.021385)+23,0004.021385)130,000=(49,000(3.0213850.764063)+78,000(3.0213850.764063)+5,268.158(3.0213850.7640631.989364)+5,719.42)130,000=(49,000(3.954573)+78,000(3.954573)+5,268.158(3.9545731.989364)+5,719.42)130,000=(193,774.08+308,456.69+1,000×5.263158(1.965209)+5,719.42)130,000=(193,774.08+308,456.69+10,343.21+5,719.42)130,000=130,745.24

When the rate of return is substituted as 19%, the calculated value is greater than the initial cost. Thus, the rate of return increases to 19.17%.

130,000=(49,000((1+0.1917)810.1917(1+0.1917)8)+78,000((1+0.1917)810.1917(1+0.1917)8)+1,000×10.1917((1+0.1917)810.1917(1+0.1917)88(1+0.1917)8)+23,000(1+0.1917)8)130,000=(49,000(4.06757410.1917(4.067574))+78,000(4.06757410.1917(4.067574))+1,000×10.1917(4.06757410.1917(4.067574)84.067574)+23,0004.067574)130,000=(49,000(3.0675740.779754)+78,000(3.0675740.779754)+1,000×5.216584(3.0675740.77975484.067574)+5,654.48)130,000=(49,000(3.934028)+78,000(3.934028)+1,000×5.216584(3.9340281.966734)+5,654.48)130,000=(192,767.37+306,854.18+1,000×5.216584(1.967294)+5,654.48)130,000=(192,767.37+306,854.18+10,262.55+5,654.48)130,000130,003.84

The calculated value is nearly equal to initial cost with rate of return 19.17%. Thus, it is confirmed that the rate of return is 19.17%.

The spreadsheet function to calculate the rate of return is given below:

Engineering Economy, Chapter 7, Problem 17P

The rate of return is 19.17%.

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