Question
An aspiring boxer hopes to win an important competition. He reckons that if he enters this year, his chance of winning is 35%, in which
An aspiring boxer hopes to win an important competition. He reckons that if he enters this year, his chance of winning is 35%, in which case the present value of his future earnings would be one million dollars ($1,000,000), but if he losses, then the present value of his future earning (boxing on the local circuit) would plummet to fifty thousand dollars ($50,000). However, he can delay his attempt for one year and enter the next round. He would then devote himself in the meanwhile to supervised practice at a cost of forty thousand dollars ($40,000). The prospects would then be as follows: If his skills improve, which will occur with a probability of 65%, his chances of winning would increase to 70% and the present value of his future earnings in that case would be Page 2 of 3 $1.75 million dollars ($1,750,000). If he fails to win the competition, the present value of his future earnings would be $60,000. If his skills remain the same, his chances of winning the contest would fall to only 15% and the present value of his future earnings in that case would be nine hundred thousand dollars ($900,000). Again, if he fails to win the competition, the present value of his future earnings would be $50,000 1. Using a decision tree, or otherwise, compute the strategy that maximizes the expected 15 present value of earnings. Write down this strategy in words and the expected monetary value. [Submit the decision tree or detailed calculations]
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