
(a)
Calculate the
(a)

Explanation of Solution
Installation cost is (IN) $4,970,000. Saving per year (A) is $1,300,000. Time period is 10.
Rate of return (i) can be calculated as follows:
S((1+i)n−1i(1+i)n)=IN1,300,000((1+i)10−1i(1+i)10)=4,970,000((1+i)10−1i(1+i)10)=4,970,0001,300,000((1+i)10−1i(1+i)10)=3.8231
Substitute the rate of return as 22% by trial and error method in the above Equation.
((1+0.22)10−10.22(1+0.22)10)=3.8231(7.304631−10.22(7.304631))=3.8231(6.3046311.607019)=3.82313.9231>3.8231
When the rate of return is substituted as 22%, the calculated value is greater than the 3.8231. Thus, the rate of return increases to 22.8%.
((1+0.228)10−10.228(1+0.228)10)=3.8231(7.798008−10.228(7.798008))=3.8231(6.7980081.777946)=3.82313.8235≈3.8231
The calculated value is nearly equal to initial cost with rate of return 22.8%. Thus, it is confirmed that the rate of return is 22.8%.
The interest rate can be calculated through spreadsheet function that given below:
=RATE(10,1300000,-4970000)
The above functions gives the value of 22.8%.
(b)
Calculate the rate of return.
(b)

Explanation of Solution
Length of the G (G) is 113. Cost of G (PG) per unit is $72,000. Saving per year (A) is $1,100,000. Time period is 10.
Rate of return (i) can be calculated as follows:
S((1+i)n−1i(1+i)n)=G×PG1,100,000((1+i)10−1i(1+i)10)=113×72,000((1+i)10−1i(1+i)10)=8,136,0001,100,000((1+i)10−1i(1+i)10)=7.3964
Substitute the rate of return as 6% by trial and error method in the above Equation.
((1+0.06)10−10.06(1+0.06)10)=7.3964(1.790848−10.06(1.790848))=7.3964(0.7908480.107451)=7.39647.3601<7.3964
When the rate of return is substituted as 6%, the calculated value is less than the 7.3964. Thus, the rate of return decreases to 5.896%.
((1+0.05896)10−10.05896(1+0.05896)10)=7.3964(1.773354−10.05896(1.773354))=7.3964(0.7733540.104557)=7.39647.3965<7.3964
The calculated value is nearly equal to the value 7.3964t with rate of return 5.896%. Thus, it is confirmed that the rate of return is 5.896%.
The interest rate can be calculated through spreadsheet function that given below:
= RATE(10,1100000,-72000*113)
The above functions gives the value of 5.896%.
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Chapter 7 Solutions
Engineering Economy
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