ISEN6935, Decision Analysis. Test #1 Spring 2017 Name: ................................................ Date ............................... Question #: 1 2 3 Test Grade Grade: Note: 1). This is a 2.5 hours exam (%:30 -8:00 PM). Please make sure that you return the test on time. 2). If in answering a question, you need to make an assumption (may be to make the concept more clear), your assumption must be logical, and you need to state your assumption 3). You are free to answer the questions with or without a computer software (Excel or other Decision Analysis software). 4). Please do not submit your answers in a format (like jpeg, ..) that I can not download or can not write on it when I grde them.. Problem #1 ( 15 Points) Suppose you were going to make an investment into only one of three investment vehicles: stock, mutual fund, or certificate of deposit (CD). Further suppose, that the market has a 50% chance of increasing, a 30% chance of staying even, and a 20% chance of decreasing. If the market increases the stock investment will earn $1500 and the mutual fund will earn $900. If the market stays even the stock investment will earn $300 and the mutual fund will earn $600. If the market decreases the stock investment will lose $800 and the mutual fund will lose $200. The certificate of deposit will earn $500 independent of the market's fluctuation. Part 1A: A) Show a rough influence diagram or a decision tree for the problem B) What is the expected value of perfect information? C) List all paths and all strategies. Part 1B If all the gains or losses happens every year for the next two years (we are investing for two years), and the interest rate is 6%. Which decision is the optimum. Problem #2 ( 25 Points) Product Switching Problem: A company needs to decide whether to switch to a new product or not. The product that the company is currently making provides a fixed payoff of $150,000. If the company switches to the new product, its payoff depends on the level of sales. It is estimated that there are about 30% chance of high-level sales ($300,000 payoff), 50% chance of medium-level sales ($100,000 payoff), and 20% chance of low-level sales (losing $100,000). A survey which costs $20,000 can be performed to provide information regarding the sales to be expected. If the survey shows high-level sales, then there are about 60% chance of high-level sales and 40% chance of medium-level sales when the company sells the product. On the other hand, if the survey shows low-level sales, then there are about 60%chance of medium-level sales and 40% chance of low-level sales when the company sells the product. A)- Develop the decision tree for the problem and determine the optimum course of action the company should take B)- List all the possible decision strategies C)- Develop risk profile and cumulative risk profile for each strategy D)- Indicate which strategy dominate the others and explain why. Indicate type of the dominance Problem #3 ( 20 Points) An Investor must decide whether to his $3.5 Mil savings in Industry (A), Stock market (B) or do nothing (C) . The payoff for alternatives A and B depends on the economic improvement in the next few years. The probability of different levels of economic improvement are given as X, 0.15, and Y (Strong, Modest, and Weak) as shown on the decision tree. Payoff ($Mil) (Strong) 9 X (Modest) .15 1 B (Modest) Do Nothing 0.15 2 3.5 FIGURE 1 Compare the strategies on the basis of EMV, by conduct a sensitivity analysis, assuming the probabilities, X and Y, can take different values. Graph the output and explain on what conditions (values of X and Y) each strategy is preferred