Calculate the rate of return .

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Answer 1

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Chapter 7, Problem 21P

To determine

Calculate the rate of return.

Expert Solution & Answer

Explanation of Solution

Initial cost (C) is -$210,000. First year cost (C1) is -$150,000. Second year saving (S) is $100 and savings increases (SI) by 60,000 thereafter. Time period (n) is 4.

Rate of return (i) for infinitive time period can be calculated as follows:

−C=C1(1+i)1+(S((1+i)n−1i(1+i)n)+SI1i((1+i)n−1i(1+i)n−n(1+i)n))(1(1+i)n)210,000=−150,000(1+i)1+(100,000((1+i)4−1i(1+i)4)+60,000×1i((1+i)4−1i(1+i)4−1(1+i)4))(1(1+i)1)

Substitute the rate of return as 24% by trial and error method in the above Equation.

210,000=−150,000(1+0.24)1+(100,000((1+0.24)4−10.24(1+0.24)4)+60,000×10.24((1+0.24)4−10.24(1+0.24)4−4(1+0.24)4))(1(1+0.24)1)210,000=−150,0001.24+(100,000(2.364214−10.24(2.364214))+60,000×10.24(2.364214−10.24(2.364214)−42.364214))(11.24)

210,000=−120,967.74+(100,000(1.3642140.567144)+60,000×4.1667(1.3642140.567144−42.364214))(0.806452)210,000=−120,967.74+(100,000(2.40541)+60,000×4.1667(2.40541−1.69187))(0.806452)210,000=−120,967.74+(240,541+60,000×4.1667(0.71354))(0.806452)210,000=−120,967.74+(240,541+178,386.43)(0.806452)210,000=−120,967.74+337,877.86210,000<216,877.12

When the rate of return is substituted as 24%, the calculated value is greater than the initial cost. Thus, the rate of return increases to 24.7%.

210,000=−150,000(1+0.247)1+(100,000((1+0.247)4−10.247(1+0.247)4)+60,000×10.247((1+0.247)4−10.247(1+0.247)4−4(1+0.247)4))(1(1+0.247)1)210,000=−120,288.69+(100,000(2.418053−10.247(2.418053))+60,000×10.247(2.418053−10.247(2.418053)−42.418053))(11.247)210,000=−120,288.69+(100,000(1.4180530.597259)+60,000×4.048583(1.4180530.597259−42.418053))(0.801925)

210,000=−120,288.69+(100,000(2.374268)+60,000×4.048583(2.374268−1.654223))(0.801925)210,000=−120,288.69+(237,426.8+60,000×4.048583(0.720045))(0.801925)210,000=−120,288.69+(237,426.8+174,909.72)(0.801925)210,000=−120,288.69+330,662.96210,000=210,374.27

The calculated value is nearly equal to the initial cost with rate of return 24.7%. Thus, it is confirmed that the rate of return is 24.7%.

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