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Athletes Case

Decent Essays

1. In looking at my calculations in this hypothetical case, I have concluded that the athlete whose contract was the better deal was the individual who received a deal with equal installments. The equal installments over the 10 years is a better deal for an athlete then the contract that will pay $100 million in installments with the installments increasing 5% per year. This is due to the fact that the contract with equal installments has a better time-value of money. To solve this problem we need to find the athlete who maximizes the present value of the amount signed in the 10-year contract of $100 million dollars. The present value=future value/(1+r)n. In the first contract the athlete receives $100 million in 10 equal installments. Therefore, there will be $10 million paid to the athlete every year. …show more content…

The annuity present value would be PV=C{1-[1/(1/1+r)2]}/r. To speed things up as taught in our lesson, one can turn to page 364 to find the Annuity Present Value factor. Since the period is over 10 years and we are plugging in 10% for both contracts, the Annuity PV Factor would equal 6.1446. If we wanted to stick with the initial formula for the first contract, we would say C=10,000,000. Therefore, C x {1-[1/(1.1)10]}/.1. This gets messy, so we should go back to the shortcut as described in our lecture. The Annuity PV Factor is 6.1446. the Annuity PV=$10 million times 6.1446. This would result in 61.446 million dollars. The second contract stipulates that 100 million will be paid in 10 installments, but the installments will increase 5% per year. In doing math we find should let x be the first installment in year one. Therefore, x(1+1.051+1.052+1.053+1.054+1.055+1.056+1.057+1.058+1.059)=100 million. In plugging in the formula, you would divide 100 by the parenthesis to separate x. X would result in

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