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Answer to Question #52024 in Microeconomics for khalid

Question #52024
Robert Ryan General manger Chicago stars professional football team is currently negotiating a new contract with Ronnie smith, the team's star running back. Under league rules smith is now a free agent, which means that he is free to negotiate a contract with any other team in the league. Smith has presented Ryan with a final contract demand consisting of alternatives for a five year contract. If Ryan does not agree to one of these, smith will sign contract with another team. The alternative contract demands are:
A) A $2000, 000 bonus payment immediately, a payment of 500,000 dollars at the end of each of the next five years, and a deferred payment of 1000,000 at the end of fifth year of the contract.
B) A $500,000 bonus payment immediately, a payment of 300,000 dollars at the end of each of the next five years, and a deferred payment of 200,000 each payable at the end of years 11 through 20.
Ryan has determined that smith's value to the team over the next five years is about 3000,000 dollars (in terms of present value of additional revenue from gate receipts and television discounted at 12% per year) should Ryan accept one of smith's contract demands, if so, which one? Explain fully.
Expert's answer
A) A $2,000,000 bonus immediately, $500,000 at the end of each of 5 years, $1,000,000 at the end of fifth year.
In this case present value will be:
PV = 2,000,000+500,000/1.12+ 500,000/1.12^2+500,000/1.12^3+ 500,000/1.12^4+1,500,000/1.12^5 = $4,369,814.96
B) A $500,000 bonus immediately, $300,000 at the end of each of 5 years, $200,000 at the end of years 11-20.
PV = 500,000+300,000/1.12+ 300,000/1.12^2+300,000/1.12^3+ 300,000/1.12^4+300,000/1.12^5+ 200,000/1.12^11+ 200,000/1.12^12+ 200,000/1.12^13+ 200,000/1.12^14+ 200,000/1.12^15+ 200,000/1.12^16+ 200,000/1.12^17+ 200,000/1.12^18+ 200,000/1.12^19+ 200,000/1.12^20 = $1,945,276.98
Smith's value over the next 5 years is about $3,000,000 (r =12%), so Ryan should accept smith's contract B, as its present value is less than the Smith's value over the next 5 years.

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