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Truck Corp. evaluated a project. The project will generate a net present value (NPV) of $19,800, 70 percent of the time. Additionally, 10 percent of the time, the NPV will be $20,100, and 20 percent of the time, the NPV will be $31,500.

What is the project's coefficient of variation?

A. 12,559
B. 15,559
C. 257
D. 363
E. 747

Answer :

Final answer:

The project's coefficient of variation is approximately 21.02%.

Explanation:

To calculate the coefficient of variation for the project's net present value, we need to find the standard deviation and the mean net present value.

Step 1: Calculate the mean net present value:

Mean = (Value1 * Probability1) + (Value2 * Probability2) + (Value3 * Probability3)

Mean = ($19,800 * 0.70) + ($20,100 * 0.10) + ($31,500 * 0.20)

Mean = $13,860 + $2,010 + $6,300

Mean = $22,170

Step 2: Calculate the standard deviation:

Standard Deviation = sqrt((Value1 - Mean)^2 * Probability1 + (Value2 - Mean)^2 * Probability2 + (Value3 - Mean)^2 * Probability3)

Standard Deviation = sqrt(($19,800 - $22,170)^2 * 0.70 + ($20,100 - $22,170)^2 * 0.10 + ($31,500 - $22,170)^2 * 0.20)

Standard Deviation = sqrt((-$2,370)^2 * 0.70 + (-$2,070)^2 * 0.10 + ($9,330)^2 * 0.20)

Standard Deviation = sqrt($5,616,090 * 0.70 + $4,288,490 * 0.10 + $86,832,090 * 0.20)

Standard Deviation = sqrt($3,931,263 + $428,849 + $17,366,418)

Standard Deviation = sqrt($21,726,530)

Standard Deviation ≈ $4,659.68

Step 3: Calculate the coefficient of variation:

Coefficient of Variation = (Standard Deviation / Mean) * 100

Coefficient of Variation = ($4,659.68 / $22,170) * 100

Coefficient of Variation ≈ 21.02%

Learn more about calculating the coefficient of variation for a project's net present value here:

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