Ninja Lines is considering a purchase of a new bulk carrier for $10 million. Ninja has forecasted that yearly revenues follow normal distribution with expected value of the previous years realized cash flow ($5 million for the first year), and a standard deviation of $1 million. The yearly operating cost follows normal distribution with expected value of $4 million and a standard deviation of $0.5 million. In addition there is a major refit that will be required after both the fifth and tenth year, where the cost follows uniform distribution between $1.5 million and $2.5 million. After 15 years the ship can be sold for a value that has a uniform distribution between $0 and $3 million. You can use the NORMINV function in Excel to simulate the values from normal distribution.

a. Using a simulation with 500 replications estimate the probability distribution for total profit after 15 years. Present its graph. How often buying the ship is profitable (profit>0)?

b. Estimate the expected profit, standard deviation of the profit and standard error of the mean. Estimate the 5 % percentile for the profit and interpret it. Also give the 95% confidence interval for the expected profit.

c. The company wants a required rate of return of 8 %. Estimate the expected net present value (NPV) of the ship with the same statistics as in part b. Show the estimated probability distribution of the NPV graphically.

d. How much would Ninja Lines be willing to pay for the ship?