Final answer:
The student's question involves calculating the expected NPV, standard deviation, and coefficient of variation of a project considering different scenario outcomes, as well as applying the concept of present discounted value in a business investment context.
Step-by-step explanation:
The student is asking how to calculate the expected net present value (NPV), standard deviation (SD), and coefficient of variation (CV) for a project with different scenario outcomes. To find the expected NPV, probabilities of each scenario occurring are multiplied by their respective NPV values and then summed up. The formula for this would be: Expected NPV = (probability of base case × NPV of base case) + (probability of worst case × NPV of worst case) + (probability of best case × NPV of best case). Using the provided probabilities and NPV values, the expected NPV calculation is as follows: (0.5 × $5M) + (0.25 × -$2M) + (0.25 × $9M) = $4.25M.
The standard deviation can be calculated by taking the square root of the variance, which involves finding the squared deviations from the expected NPV, each weighted by its probability. Once the SD is found, the coefficient of variation is calculated by dividing the standard deviation by the expected NPV. This provides a normalized measure of risk related to the expected return.
The information provided in the latter part of the question integrates the concept of present discounted value (PDV), which determines the value of future cash flows in today's dollars at a specific discount rate. For instance, dividing the PDV of total profits by the number of shares to determine the price per share is an application of this concept.