Reference no: EM13819499

1. Who Wants to be a Millionaire. You are a contestant on Who Wants to be a Millionaire. You have already answered the $250,000 question, and now must decide if you would like to answer the $500,000 question.

You can choose to walk away at this point with $250,000 in winnings, or you may decide to answer the $500,000 question. If you answer the $500,000 question correctly, you can then choose to walk away with $500,000 in winnings, or go on and try to answer the $1,000,000 question. If you answer the $1,000,000 question correctly the game is over, and you win $1,000,000. If you answer either the $500,000 or the $1,000,000 question incorrectly, the game is over immediately and you take home "only" $32,000.

A feature of the game Who Wants to be a Millionaire is that you have three lifelines-namely 50-50, ask the audience, and phone a friend. At this point (after answering the $250,000 question), you have already used two of them, but you have the phone a friend lifeline remaining. With this option, you may phone a friend to get their advice on the correct answer to a question before answering it. You may use this option only once (i.e., you can use it on either the $500,000 question or the $1,000,000 question, but not both). Since your friends are all smarter than you are, phone a friend improves your odds for answering a question correctly. Without phone a friend, if you choose to answer the $500,000 question you have a 65% chance of answering correctly, and if you choose to answer the $1,000,000 question you have a 50% chance of answering correctly (the questions get progressively harder). With phone a friend, you have an 80% chance of answering the $500,000 question correctly, and a 65% chance of answering the $1,000,000 question correctly.

a. Use TreePlan to construct and solve a decision tree to decide what to do. Should you answer the $500,000 question? Should you use "phone a friend"? Should you save "phone a friend" for the $1,000,000 question?

Should you even answer the $1,000,000 question if you get to it? Is that your final answer? State (in words below the tree) what is the best course of action, assuming your goal is to maximize your expected winnings.

b. Use the equivalent lottery method discussed in class to determine your utility function (in particular, your utility values for all of the possible payoffs in the game). Include on the spreadsheet a brief description of how you obtained each of your utility values (e.g., describe the lotteries you considered to determine your utility value of the various payoffs). Copy the worksheet from part a (hold down control (PC) or option (Mac) and drag the tab for 1a to create a copy of that tab, and then relabel the new tab 1b). Re-solve the tree, replacing the expected payoffs with your utility values, to maximize your expected utility. Does the best course of action change?

2. UW Toys and the Professor Hillier Action Figure. UW Toys has developed a brand new product-a Professor Hillier Action Figure (PHAF). They are now deciding how to market the doll.

One option is to immediately ramp up production and launch an ad campaign throughout the state of Washington. This option would cost $100,000. Based on past experience, new action figures either take off and do well, or fail miserably. Hence, they predict one of two possible outcomes- total sales of 100,000 units or total sales of only 2000 units. The net profit per unit sold is $2.

Another option is to test market the product in Yakima. This would require less capital for the production run, and a much smaller ad campaign. Again, they predict one of two possible outcomes for Yakima. The product will either do well (sell 1000 units) or do poorly (sell 100 units). The cost for this option is estimated to be $5000. The net profit per unit sold is $2 for the test market as well. Once the test market is complete, University Toys would then use these results to help decide whether to market the toy statewide.

University Toys has test marketed similar toys in the Yakima market 50 times in the past, with the results shown in the table below. Since University Toys thinks PHAF is similar to these other toys, they plan to estimate the probabilities of the various outcomes based on these historical results. For example, ignoring the test-market results, 30 out of 50 of the previous toys sold well statewide, so without a test market they estimate a 60% probability for PHAF to sell well statewide as well. If a test market is done, these same data should be used to estimate the probabilities of the various outcomes.

There is a complication with the Yakima test market option, however. A rival toy manufacturer is rumored to be considering the development of a Dean Jiambalvo Action Figure (DJAF). After doing the test market in Yakima, if University Toys decides to go ahead and ramp up production and market throughout the state, the cost of doing so would still be $100,000. However, the sales prospects depend upon whether DJAF has been introduced into the market or not. If DJAF has not entered the market, then the sales prospects will be the same as before (i.e., 100,000 units if PHAF does well, or 2000 units if PHAF does poorly, on top of any units sold in the test market). However, if DJAF has entered the market, the increased competition will diminish sales of PHAF. In particular, they expect to sell 50,000 if PHAF does well, and 1000 units if it does poorly, on top of any units sold in the test market. Note that the probability of PHAF doing well or doing poorly is not affected by DJAF, just the final sales totals of each possibility. If a test market is done, DJAF would enter before the completion of the test market with 20% probability. On the other hand, if UW Toys markets PHAF immediately, they are guaranteed to beat DJAF to market (thus making DJAF a nonfactor).

a. Use TreePlan to develop a decision tree to help UW Toys decide the best course of action and the expected payoff. In words below the tree, state the best course of action assuming your goal is to maximize the expected payoff.

b. Now suppose UW Toys is uncertain of the probability that DJAF will enter the market before the end of the test market in Yakima would be completed (if it were done). How does the expected payoff vary as the probability that the DJAF would enter the market changes? On the same worksheet used for part a, generate a data table that shows how the expected payoff and the initial decision changes as the probability that DJAF enters varies from 0% to 100% (at 10% increments). At what probability does the decision change?

3. Aberdeen Resort Hotel. The Aberdeen Development Corporation (ADC) is considering the Aberdeen Resort Hotel project. It would be located right on the picturesque banks of Grays Harbor, and have its own championship-level golf course.

The cost to purchase the land would be $3 million, payable right now. Construction costs would be approximately $2 million, payable at the end of year 1. However, the construction costs are uncertain-they could be up to 20% higher or lower than the estimate. Assume the construction costs would follow a triangular distribution.

ADC is very uncertain about the annual operating profits (or losses) that would be generated once the hotel was constructed. Their best guess for the annual operating profit that would be generated in years 2, 3, 4, and 5 is $700,000. Due to their great uncertainty, they guess the standard deviation to also be about $700,000. Assume each year is independent and follows the normal distribution. (For calculating NPV, assume all profits are received at year end.)

At the end of year 5, they plan to sell the hotel. The selling price is likely to be somewhere between $4 and $8 million (all values in this range are equally likely).

a. Assume ADC uses a 10% discount rate, and use Crystal Ball to generate a distribution of the NPV of the project over 1000 trials. What is the mean NPV? What is the probability that the project will yield a positive NPV?

b. ADC is also concerned about operating profits in years 2, 3, 4, and 5. Use Crystal Ball to forecast what ADC should expect the worst of the four years (i.e., the year with the lowest operating profit of the four) to look like. What is the mean value of the lowest annual operating profit over the four years? What is the probability that the lowest annual operating profit over the four years will at least be greater than $0?