Question

You are considering a 10-year investment project. At present, the expected cash flow each year is $10,000. Suppose, however, that each year's cash flow is normally distributed with mean equal to last year's actual cash flow and standard deviation $1000. For example, suppose that the actual cash flow in year 1 is $12,000. Then year 2 cash flow is normal with mean $12,000 and standard deviation $1000. Also, at the end of year 1, your best guess is that each later year's expected cash flow will be $12,000. Round all your answers to a whole dollar amount.

a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year.

Answer 1

To estimate the mean and standard deviation of the NPV of the 10-year investment project, we can perform a Monte Carlo simulation. This simulation involves generating random cash flows each year based on a normal distribution and calculating the NPV for each simulated cash flow. The mean and standard deviation of the NPV can then be calculated from the distribution of values.

Step-by-step explanation:

To estimate the mean and standard deviation of the NPV (Net Present Value) of the 10-year investment project, we need to perform a Monte Carlo simulation. In this simulation, we would generate random cash flows each year based on a normal distribution with a mean equal to the previous year's actual cash flow and a standard deviation of $1000. We would then calculate the NPV for each simulated cash flow and repeat this process multiple times to get a distribution of NPV values.

With the distribution of NPV values, we can calculate the mean and standard deviation. The mean of the NPV represents the expected value of the investment project, while the standard deviation indicates the volatility or risk associated with the project.

It's important to note that this estimation assumes a discount rate of 10% per year. Additionally, rounding all the answers to a whole dollar amount may introduce some approximation error.