A promising college football talent has to decide whether or not to enter this y
ID: 3365465 • Letter: A
Question
A promising college football talent has to decide whether or not to enter this year's NFL draft. If he enters, he expects that there is a 50% chance that he is a first round pick and a 50% chance that he is picked in a later round. As a first round pick, he would secure a 5 million dollar contract, if he is picked in a later round, his contract would only be worth $500 000.
If he does not enter the draft this year and continues to play in college, his chance of being a first round pick next year will increase to 75% (the contracts for first and later round picks are the same as in the previous year, $5 million and $500 000 respectively). However, there is a 20% chance that he suffers a career ending injury next season, in which case he could make $50 000 as an assistant coach for a college team.
What should the player do? What is the EMV of his optimal choice?
He should enter now and the EMV of his choice is 2.75 million.
He should enter next year and the EMV of his choice is 3.11 million.
He should enter this year, as the expected loss in case of an injury is too high.
He should enter next year and the EMV of his choice is 3.695 million.
a.He should enter now and the EMV of his choice is 2.75 million.
b.He should enter next year and the EMV of his choice is 3.11 million.
c.He should enter this year, as the expected loss in case of an injury is too high.
d.He should enter next year and the EMV of his choice is 3.695 million.
Explanation / Answer
For first year : P(first round pick up) = P(later round pick up) = 0.5
expected mean value i.e EMV for first year = 5,000,000*0.5+50,000*0.5 = 2.75 million
For second year : P(first round pick up) = 0.75 P(later round pick up) = 0.25
P(career ending injusry session) = 0.20
EMV =( 5 mn * 0.75 + 0.5mn * 0.25)*0.8 + 0.05*0.2
as in 20% of the cases player will get 0.05mn and for rest 80% ( 5 mn * 0.75 + 0.5mn * 0.25)
= 3.11 mn
so, option b He should enter next year and the EMV od his choice is 3.11 million
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