Problem 3 (20 points): Thomas Bayes had long been promised a graduation present

Question

Problem 3 (20 points): Thomas Bayes had long been promised a graduation present of S10,000 by his father, to be received on graduation day, 3 months hence. His father had recently offered an alternative gift, and Bayes was trying to decide between the two gifts, since his father had asked for a decision by the following day. The alternative gift would be 1,000 shares of stock in Satisficing Systems, Inc., a strategic consulting firm. On the day he was deciding the stock was selling for S12 per share. Thus, it looked to Bayes as if he would be wise to take the stock, since its value was $12,000. He would not receive the stock until graduation day, however, and he recognized that the stock price 3 months in the future was uncertain. With these facts in mind, Bayes reached the following conclusions (probability assessments): He thought that the stock price was He thought that there was only He thought that there was only more likely to rise than fall in the intervening 3 months, and that it wak would drop to S6 per share, and a l below $10, and there was I chance likely to be above $14 per share as chance in 100 that the price would be in 5 that it would be above SI6 below $14 when he would receive the more than twice its current price on when he received it. stock chance in 100 that the stock price chance in 5 that the price would be aduation day 1.0 08 0,7 03 s1 15 1 17 IN221 24 3s Sdock Price, 5 per share Draw a decision tree of Bayes' decision. Use the extended Swanson-Megill to model the stock price. Compute the expected value for each alternative. What is the preferred course of action?

Explanation / Answer

Option 1 $10000 Option 2 Shares Share Price 12 6 10 16 14 Probability 0.01 0.01 0.2 0.2 0.58 Total shares 1000 1000 1000 1000 1000 Payoffs $ 120 60 2000 3200 8120 EMV in $ 13500 (best option is accept $ 1000 shares not $10,000 amount)

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