Dord Motors is considering whether to introduce a new model called the Racer. The profitability of the Racer will depend on the following factors:

■ The fixed cost of developing the Racer is equally likely to be $3 or $5 billion.

■ 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 $13,000. The year 2 selling price will be 1.05[year 1 price  $30(% diff1)]

where % diff1 is the percentage 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%

below the expected year 1 sales, then the year 2 price will be 1.05[13,000  30(10)]
$13,335 Similarly, the year 3 price will be 1.05[year 2 price  $30(% diff2)]

where % diff 2 is the percentage by which actual year 2 sales differ from expected year 2 sales.

■ The variable cost is equally likely to be $5000,

$6000, $7000, or $8000 during year 1 and is assumed to increase by 5% each year.

a. Your goal is to estimate the NPV of the new car during its first 3 years. Assume that cash flows are discounted at 10%. Simulate 1000 trials and estimate the mean and standard deviation of the NPV for the first 3 years of sales. Also, determine an interval so that you are 95% certain that the NPV of the Racer during its first 3 years of operation will be within this interval.

b. Rerun the simulation from part

a, but now assume that the fixed cost of developing the Racer is triangularly distributed with minimum, most likely, and maximum values $3, $4, and $5 billion. Also, assume that the variable cost per car in year 1 is triangularly distributed with minimum, most likely, and maximum values $5000, $7000, and $8000.