Chapter 11, Problem 62P

An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors:

• The fixed cost of developing the Racer is triangularly distributed with parameters $3, $4, and $5, all in billions.
• Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000.
• The selling price in year 1 is $25,000. The year 2 selling price will be 1.05[year 1 price + $50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50(− 10)] = $25,725. Similarly, the year 3 price will be 1.05[year 2 price + $50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales.
• The variable cost in year 1 is triangularly distributed with parameters $ 10,000, $ 12,000, and $ 15,000, and it is assumed to increase by 5% each year.

Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.