Assignment 3 Decision-Making Under Conditions of Uncertainty
There are three problems associated with “Decision Making Under Uncertainty” lectures and readings. The grading weights for the three problems are: 1) 10%, 2) 60% and 3) 30%.
Assignment 3 Decision Making Template
1) A potentially huge hurricane is forming in the Caribbean and there is some chance that it might make a direct hit on Isle of Palms, South Carolina where you are director of emergency preparedness. You have made plans for evacuating everyone from the island but such a strategy is obviously costly and upsetting for everyone and the evacuation decision should not be made lightly. Based on input from staff and meteorologists, you developed the following data. Calculate the EMV for each decision and determine the optimal payoff. Explain the EMV for each decision and the relationship of the EMV values across each decision. Explain your final decision and explain all factors that you used to make it.
Probabilities p=.2 p=.5 p=.3
Outcomes O1 O2 O3
Decisions (Miss) (Indirect Hit) (Direct Hit)
D1 (Don’t evacuate) 0 -100K -200K
D2 (Recommend evacuate) -10K -75K -125K
D3 (Mandate evacuate) -25K -50K -100K
2) An investor has $10,000 to invest and several options: (1) Invest in risk-free savings account with guaranteed 3% annual return rate; (2) Invest in safe stick with possible rate of returns of 6, 8 or 10%; or (3) invest in risky stock with annual return rates of 1, 9 or 17%. The investor can place all funds in any one option or split $10,000 into two $5,000 investments in any two of the options. The joint probability distributions of the possible return rates for the two sticks is given in the provided data file below. A payoff table has been created for you in the provided Template. You must use DecisionTree to identify the maximum strategy, and perform a sensitivity analysis on the optimal decision.
- a) A payoff table has been created for you and is provided in the Assignment 3 template. Review the payoff table to fully understand the investor’s return in dollars in one year for each possible year and each outcome with respect to the stock returns. It would be wise for you to print the payoff table and have it handy before proceeding with the next step.
- b) Using the detailed procedures provided in Chapter 6 beginning on page 280 (PrecisionTree instructions begin on p. 290), use Palisades PrecisionTree to develop a decision tree that identifies the strategy that maximizes the investor’s expected earning in one year from the given investment opportunities. Be sure to document your work. (NOTE THAT THE STEPS FOR DEVELOPING A DECISION TREE USING PALISADES ARE ALSO REVIEWED IN THE YOUTUBE LECTURE FOR THIS WEEK … A GREAT WAY TO FIGURE OUT HOW TO GET THROUGH THE ACTIVITY!)
- c) After developing the decision tree perform a sensitivity analysis on the optimal decision, letting the amount available to invest and the risk-free return rate both vary, one at a time, plus or minus 100% from their base values.
- d) Answer the following questions about your results:
1) What is the best decision and associated EMV?
2) Does this make sense from an intuitive perspective? Explain.
3) Describe the results of your sensitivity analysis. What impact did varying the amount to invest have on the decision? What impact did varying the risk-free return rate have on the decision?
My objective this semester is to minimize feelings of frustration with the analytical tools we are exploring. Since this problem has often been a source of frustration in the past I developed and am providing a template so that you no longer have to develop the payoff table. Focus on learning how to create a decision tree. I offer some items of assistance. First is a “Help Sheet” (or go to Files Directory) that I prepared. It might be helpful if you read it before doing the problem. Second is a useful example. This assignment is similar to Problem 39 on p. 334 (4th edition). If you need help with Problem 41 review Problem 39 and the associated solution set.
3) Pizza Shack (PS) and Doug’s Brick Oven (DBO) are competitive pizza chains.
The PS owner wants a recommendation from you regarding the price that it should charge for a pizza. The owner has done some preliminary analysis and is providing you with her results:
- In investigating how much DBO will charge for a pizza she has come up with the following probabilities:
- 25% chance that DBO will charge $6 per pizza
- 50% chance that DBO will charge $8 per pizza, and
- 25% chance that DBO will charge $10 per pizza.
- Patty, the owner of PS, has determined a demand formula based on how much she charges for a pizza in relation to how much DBO charges. Here is the formula:
- If PS charges p1 and DBO charges price p2 …
- PS will sell 100 + 25(p2 – p1) pizzas.
- It costs PS $4 to make a pizza.
- Patty would like to analyze five alternatives in terms of how much she should charge for a pizza in order to maximize her expected profit.
- PS is considering charging $5, $6, $7, $8 or $9 per pizza.
- Using the provided tab on the Assignment 3 Template, use the preceding information to make a recommendation in terms of which of the five pricing options would yield the maximize expected profit.
Use the Assignment 3 Decision Making Template for this problem. Part 3 (Pizza Shack) uses Excel only – this is not a decision tree problem. The problem uses a number of concepts learned during the first three weeks.
In order to tackle this problem you are provided an Excel Workbook to help in making the pricing decision. As you probably have figured out by now, we need to use formulas in every possible case in these spreadsheets. We also need to use the Data/What-if Analysis/Data Table function that we learned in our Spreadsheet Modeling: An Introduction handout from weeks 1 to 3 (see content starting on A-14).
For this problem you are given prices and probabilities in terms of what DBO will charge, so you probably should enter that data. These data are not based on formula so you just type in the values. You also know PS’s unit cost ($4) and price ($5) so you should enter these values.
The next part gets a bit tricky. An array is provided in the Template depicting PS’s price depending on DBO’s price. Since this is tricky, I have saved you some headaches by filling in the formulas in this section so you really don’t have to do anything.
But please note some things: Patty’s demand function (100+25(p2-p1)) is used to determine PS’s demand. The final column depicts PS’s profit for each of NG’s prices.
Ah, but we CANNOT forget about those probabilities for each of DBO’s prices (the 25%, 50% and 25%). We take these into account when calculating the Expected Value using our handy-dandy SUMPRODUCT feature. This gives you the number that you need to do the final step described next.
Now you need to use the What-if Analysis/Data Table function to create a table that depicts Expected PS Profit as a Function of PS Price. Some help for this. The table will have two columns: PS Price and Exp Profit. The first entry in the Exp Profit column will be the cell (pointed to) where we used the SUMPRODUCT feature (see above). The rest of this column has to be generated using the Data Table feature. The first entry in the PS Price column is blank. Below that cell you will list a range of PK prices: $5, $6, $7, $8 and $9 – recall that these are the alternatives that you have been asked to evaluate. This is how you set up the table so that you can use the Data Table feature.
Once you define the Data Table and populate the Exp Profit values you will be able to pick the value that answers the question for this problem. This should get you across the finish line.
