Calculate the expected NPV for both projects. Can the question be resolved with this information alone?

To calculate the expected NPV for both projects, you can multiply each possible NPV by its corresponding probability, and then add up the results:

Expected NPVA = (-$34,000)(0.15) + (-$8,500)(0.20) + ($17,000)(0.30) + ($42,500)(0.20) + ($68,000)(0.15) = $22,250 Expected NPVB = (-$12,750)(0.15) + ($2,125)(0.20) + ($17,000)(0.30) + ($31,785)(0.20) + ($46,750)(0.15) = $19,838

The expected NPV for Project A is $22,250 and for Project B is $19,838. But with this information alone, it is difficult to say which project is better to choose.

b) To calculate the variance and standard deviation of the NPVs for both projects, you can use the following formulas:

Variance = ∑(NPV – Expected NPV)^2 * Probability Standard deviation = √ Variance

For Project A: Variance = (-$34,000 – $22,250)^2 * 0.15 + (-$8,500 – $22,250)^2 * 0.20 + ($17,000 – $22,250)^2 * 0.30 + ($42,500 – $22,250)^2 * 0.20 + ($68,000 – $22,250)^2 * 0.15 = $3,016,250 Standard deviation = √$3,016,250 = $5,499.08

For Project B: Variance = (-$12,750 – $19,838)^2 * 0.15 + ($2,125 – $19,838)^2 * 0.20 + ($17,000 – $19,838)^2 * 0.30 + ($31,785 – $19,838)^2 * 0.20 + ($46,750 – $19,838)^2 * 0.15 = $1,622,031.25 Standard deviation = √$1,622,031.25 = $1272.13

The standard deviation for Project B is lower than that of project A, indicating that Project B is less risky.

c) The coefficient of variation (CV) is a ratio of the standard deviation to the expected NPV, expressed as a percentage. The formula is: CV = (Standard deviation / Expected NPV) * 100% For Project A: CV = ($5,499.08 / $22,250) * 100% = 24.74% For Project B: CV = ($1,272.13 / $19,838) * 100% = 6.4%

As we can see that Project B has a much lower CV, which can be interpreted as being less risky than Project A.

d) To calculate the probability of a negative NPV for both projects, you can add up the probabilities for all the scenarios where the NPV is negative: Probability of a negative NPVA = 0.15 + 0.20 = 0.35 or 35% Probability of a negative NPVB = 0.15 = 0.15 or 15%