Toys For U is developing a new Hannah Montana doll.

The company has made the following assumptions:

■ It is equally likely that the doll will sell for 2, 4, 6, 8, or 10 years.

■ At the beginning of year 1, the potential market for the doll is 1 million. The potential market grows by an average of 5% per year. Toys For U is 95% sure that the growth in the potential market during any year will be between 3% and 7%. It uses a normal distribution to model this.

■ The company believes its share of the potential market during year 1 will be at worst 20%, most likely 40%, and at best 50%. It uses a triangular distribution to model this.

■ The variable cost of producing a doll during year 1 is equally likely to be $4 or $6.

■ Each year the selling price and variable cost of producing the doll will increase by 5%. The current selling price is $10.

■ The fixed cost of developing the doll (which is incurred right away, at time 0) is equally likely to be

$4, $8, or $12 million.

■ Right now, one competitor is in the market. During each year that begins with four or fewer competitors, there is a 20% chance that a new competitor will enter the market.

■ We determine year t sales (for t  1) as follows.

Suppose that at the end of year t  1, n competitors are present. Then we assume that during year t, a fraction 0.9  0.1n of the company’s loyal customers (last year’s purchasers) will buy a doll during the next year, and a fraction 0.2  0.04n of customers currently in the market who did not purchase a doll last year will purchase a doll from the company this year. We can now generate a prediction for year t sales. Of course, this prediction will not be exactly correct. We assume that it is sure to be accurate within 15%, however. (There are different ways to model this. You can choose any method that is reasonable.)

a. Use @RISK to estimate the expected NPV of this project.

b. Use the percentiles in @RISK’s output to find an interval so that you are 95% certain that the company’s actual NPV will be within this interval.