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 12P

(a)

To determine

Calculate the rate of return.

(a)

Expert Solution
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Explanation of Solution

Investment is (I) is $650,000. Equivalent annual revenue (A) is $105,000. Salvage value (SV) is 50,000. Time period (n) is 5.

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

I=A((1+i)n1i(1+i)n)+SV(1+i)n650,000=105,000((1+i)51i(1+i)5)+50,000(1+i)5

The normal revenue is $575,000 ((105,000×5)+50,000) which is less than the investment. Thus, rate of return is negative. Substitute the rate of return as -3% by trial and error method in the above Equation.

650,000=105,000((1+(0.03))51(0.03)(1+(0.03))5)+50,000(1+(0.03))5650,000=105,000((0.97)51(0.03)(0.97)5)+50,000(0.97)5650,000=105,000(0.8587341(0.03)(0.858734))+50,0000.858734650,000=105,000(0.1412660.025762)+58,225.25650,000=105,000(5.483503)+58,225.25650,000=575,767.82+58,225.25650,000>633,993.07

When the rate of return as -3% is substituted, the calculated value is less than the investment and thus, the rate of return is reduced to 3.742%.

650,000=105,000((1+(0.03742))51(0.03742)(1+(0.03742))5)+50,000(1+(0.03742))5650,000=105,000((0.96258)51(0.03742)(0.96258)5)+50,000(0.96258)5650,000=105,000(0.8263881(0.03742)(0.826388))+50,0000.826388650,000=105,000(0.1736120.030923)+60,504.27650,000=105,000(5.614332)+60,504.27650,000=589,504.86+60,504.27650,000650,009.13

The calculated value is nearly equal to investment with rate of return 3.742%. Thus, it is confirmed that the rate of return is 3.742%.

(b)

To determine

Calculate the equivalent annual value.

(b)

Expert Solution
Check Mark

Explanation of Solution

Investment is (I) is $650,000. Salvage value (SV) is 50,000. Time period (n) is 5. Rate of return (i) is 15%.

Equivalent annual value (A) can be calculated as follows:

I=A((1+i)n1i(1+i)n)+SV(1+i)n650,000=A((1+0.15)510.15(1+0.15)5)+50,000(1+0.15)5650,000=A(2.01135710.15(2.011357))+50,0002.011357650,000=A(1.0113570.301704)+24,858.84650,000=A(3.35215)+24,858.84A(3.35215)=650,00024,858.84A=625,141.63.35215=186,489.61

The equivalent annual value is $186,489.61.

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