Decision Making Under Uncertainty You are the manager of the Cleveland Cavaliers

Question

Decision Making Under Uncertainty You are the manager of the Cleveland Cavaliers (a professional basketball team in the NBA) and you are considering a trade with another team. You have the opportunity to sign a great young player, Isaiah Thomas, who formerly played for the Boston Celtics. Answer the following questions. I. You expect that signing Thomas will increase your team's profits by S12 million per year, and you expect him to play for another 10 years. Assuming that the team 's profits are earned at the end of each year, and that the interest rate is 690, what is the most you should be willing to pay Isaiah Thomas today for a ten-year contract to play for your team? a. b. Suppose now that there is the possibility that Thomas has a serious injury. This introduces some uncertainty about how well he plays, and thus how he will impact your team's profits. There is a 25% chance that his hip injury is so severe that he will increase your profits by just $5 million for the nextfive years, and then will have no impact on the team's profits during the second half of the contract. There is a 50% chance that he increases your team's profits by $12 million per year as he did in (a) above. There is a 25% chance that he does even better than expected, and he increases the team's profits by S20 million for each of the next five years and then S10 million for the five after that. Given this uncertainty, how much should you be willing to pay for Thomas' 10-year contract if you use the expected value criterion? Assume the interest rate is still 6%.

Explanation / Answer

a. The most that could be paid to Thomas for signing Thomas is the present value of the increased earnings due to Thomas.

Present value = $12 million * 7.36

= $88.32 million

P.S. 7.36 is the cumulative present value of $1 payable at the end of each year

b. We calculate the present value of each of the three probable situations and then multiply with the respective probabilities.

PV of 25% chance of increasing profits by $5 million in first five years = 5 million * 4.212 = $21.06 million

PV of 50% chance of increasing profits by $12 million in ten years = 12 million * 7.36 = $88.32 million

PV of 25% chance of increasing profits by $20 million in first five years and 10 million for another five years = 20 million * 4.212 + 10 million * 3.147 = $115.71 million

Now the present value with probabilities is calculated below:

Therefore, in the above case, Thomas should get at the most $78.35 million considering the above probabilities.

Probability 25% 50% 25% Total Present value of earnings $21.06 $88.32 $115.71 Present value with probability $5.27 $44.16 $28.93 $78.35

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