Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters $15, $17, and $20. The current selling price is $45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters $5 million, $7.5 million, and $12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t > 1) are determined as follows. Suppose that at the end of year t – 1, n competitors are present (including Play Things). Then during year t , a fraction 0.9 − 0.1 n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 − 0.04 n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISK’s output to find an interval such that you are 95% certain that the company’s actual NPV will be within this interval.

BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 11, Problem 61P
Textbook Problem

Play Things is developing a new Lady Gaga doll. The company has made the following assumptions:

  • The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely.
  • At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this.
  • The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this.
  • The variable cost of producing a doll during year 1 has a triangular distribution with parameters $15, $17, and $20.
  • The current selling price is $45.
  • Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year.
  • The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters $5 million, $7.5 million, and $12 million.
  • Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market.
  • Year t sales (for t > 1) are determined as follows. Suppose that at the end of year t – 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 − 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 − 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean.
    1. a. Use @RISK to estimate the expected NPV of this project.
    2. b. Use the percentiles in @ RISK’s output to find an interval such that you are 95% certain that the company’s actual NPV will be within this interval.

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Chapter 11 Solutions

Practical Management Science
Ch. 11.3 - In the cash balance model from Example 11.5, the...Ch. 11.3 - In the cash balance model from Example 11.5, is...Ch. 11.3 - Run the retirement model from Example 11.6 with a...Ch. 11.3 - The simulation output from Example 11.6 indicates...Ch. 11.3 - Modify the model from Example 11.6 so that you use...Ch. 11.3 - Referring to the retirement example in Example...Ch. 11.3 - A European put option allows an investor to sell a...Ch. 11.3 - Modify Example 11.8 so that the portfolio now...Ch. 11.3 - Change the new car simulation from Example 11.4 as...Ch. 11.3 - Based on Kelly (1956). You currently have 100....Ch. 11.3 - Amanda has 30 years to save for her retirement. At...Ch. 11.3 - In the financial world, there are many types of...Ch. 11.3 - Suppose you currently have a portfolio of three...Ch. 11.3 - If you own a stock, buying a put option on the...Ch. 11.3 - For the data in the previous problem, the...Ch. 11.3 - A stock currently sells for 69. The annual growth...Ch. 11.3 - A knockout call option loses all value at the...Ch. 11.3 - Suppose an investor has the opportunity to buy the...Ch. 11.4 - Suppose that Coke and Pepsi are fighting for the...Ch. 11.4 - Seas Beginning sells clothing by mail order. An...Ch. 11.4 - Based on Babich (1992). Suppose that each week...Ch. 11.4 - The customer loyalty model in Example 11.9 assumes...Ch. 11.4 - We are all aware of the fierce competition by...Ch. 11.4 - Suppose that GLC earns a 2000 profit each time a...Ch. 11.4 - The Mutron Company is thinking of marketing a new...Ch. 11.5 - A martingale betting strategy works as follows....Ch. 11.5 - The game of Chuck-a-Luck is played as follows: You...Ch. 11.5 - You have 5 and your opponent has 10. You flip a...Ch. 11.5 - Assume a very good NBA team has a 70% chance of...Ch. 11.5 - Consider the following card game. The player and...Ch. 11.5 - Based on Morrison and Wheat (1984). When his team...Ch. 11 - You now have 5000. You will toss a fair coin four...Ch. 11 - You now have 10,000, all of which is invested in a...Ch. 11 - Suppose you have invested 25% of your portfolio in...Ch. 11 - A ticket from Indianapolis to Orlando on Deleast...Ch. 11 - Based on Marcus (1990). The Balboa mutual fund has...Ch. 11 - Consider a device that requires two batteries to...Ch. 11 - Appliances Unlimited (AU) sells refrigerators. Any...Ch. 11 - The annual demand for Prizdol, a prescription drug...Ch. 11 - A company is trying to determine the proper...Ch. 11 - The DC Cisco office is trying to predict the...Ch. 11 - A common decision is whether a company should buy...Ch. 11 - Suppose you begin year 1 with 5000. At the...Ch. 11 - You are considering a 10-year investment project....Ch. 11 - Play Things is developing a new Lady Gaga doll....Ch. 11 - An automobile manufacturer is considering whether...Ch. 11 - It costs a pharmaceutical company 75,000 to...Ch. 11 - Suppose you buy an electronic device that you...Ch. 11 - Rework the previous problem for a case in which...Ch. 11 - Chemcon has taken over the production of Nasacure...Ch. 11 - The Tinkan Company produces one-pound cans for the...Ch. 11 - You are unemployed, 21 years old, and searching...Ch. 11 - In this version of dice blackjack, you toss a...Ch. 11 - It is January 1 of year 0, and Lilly is...Ch. 11 - It is January 1 of year 0, and Merck is trying to...Ch. 11 - Suppose you are an HR (human resources) manager at...Ch. 11 - You are an avid basketball fan, and you would like...Ch. 11 - Suppose you are a financial analyst and your...Ch. 11 - Software development is an inherently risky and...Ch. 11 - Health care is continually in the news. Can (or...

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