You are told by the finance section that a particular projects NPV is positive, but that the standard deviation of the NPV (after performing a monte carlo simulation) is exactly triple the expected NPV figure. If NPV is normally distributed, what is the probability that the project will increase your shareholders’ wealth?
To find the probability that the project will increase shareholders' wealth, given the information provided, we will use the concept of standard deviation and a normal distribution.
1. Start by calculating the coefficient of variation (CV), which is the ratio of the standard deviation to the expected NPV:
CV = standard deviation / expected NPV
2. In this case, it is given that the standard deviation of NPV is exactly triple the expected NPV:
CV = (3 * expected NPV) / expected NPV
Simplifying, CV = 3
3. The CV represents the relative variability of the NPV measurement. In finance, a higher CV generally implies greater risk, while a lower CV implies lower risk.
4. Now, we need to determine the probability that the NPV exceeds zero. Since it is mentioned that NPV follows a normal distribution, we can utilize the standardized normal distribution table.
5. The area under the curve in the standardized distribution corresponds to probabilities. We want to find the probability that NPV is greater than zero.
6. Since we are given the CV, we can use it to find the corresponding Z-score. The Z-score formula is:
Z = (X - μ) / σ
where X is the value we want to find the probability for
μ is the expected NPV
σ is the standard deviation of NPV
7. In this case, we want to find the probability of NPV being greater than zero, so X = 0. Plugging in the values, we get:
Z = (0 - μ) / (3 * μ)
Simplifying, Z = -1/3
8. Using the standardized normal distribution table, we can find the probability corresponding to the Z-score of -1/3. The area under the curve to the right of this Z-score gives the probability.
9. Consulting the table, we find that the area to the right of -1/3 is approximately 0.628. Therefore, the probability that the project will increase shareholders' wealth is approximately 0.628 or 62.8%.
By following these steps and using the concepts of standard deviation and a normal distribution, we were able to calculate the probability of the project increasing shareholders' wealth.