A \(\$ 5,000\) process improvement project is expected to increase annual expenses for the next 3 years by an average of \(\$ 20,000\), with a standard deviation of \(\$ 3,000\). The annual savings generated over the 3 years will average \(\$ 24,000\) with a standard deviation of \(\$ 4,000\). MARR is 20 percent. Assume independent cash flows.

For the following questions, determine an analytical solution:

a. Assuming that present worth is normally distributed, determine the probability that the process improvement will result in a loss.

b. Assuming that present worth is normally distributed, determine the probability that the process improvement will result in a present worth of \(\$ 10,000\) or greater.
For the following questions, determine a simulation solution using @RISK:

c. Using a Latin hypercube simulation with 10,000 iterations, estimate the probability that the process improvement will result in a loss and the probability that the present worth is \(\$ 10,000\) or greater.

d. Using a Monte Carlo simulation with 10,000 iterations, estimate the probability that that process improvement will result in a loss and the probability that the present worth is \(\$ 10,000\) or greater.