A project under consideration has a 10-year projected life. The initial investment for the project is estimated to have a mean of \(\$ 10,000\) and a standard deviation of \(\$ 1,000\). The annual receipts are independent, with each year's expected return having a mean of \(\$ 1,800\) and a standard deviation of \(\$ 200\). MARR is 12 percent.

For the following question, determine an analytical solution:

a. Determine the probability that the present worth is negative.

For the following questions, determine a simulation solution using @RISK:

Assume the initial investment and annual receipts are independent and normally distributed.

b. Using a Latin hypercube simulation with 10,000 iterations, estimate the probability that the present worth is negative.

c. Using a Monte Carlo simulation with 10,000 iterations, estimate the probability that the present worth is negative.