Question

# A baseball player is offered a 5-year contract that pays him the following amounts: Year 1:...

A baseball player is offered a 5-year contract that pays him the following amounts:

Year 1: \$1.28 million

Year 2: \$1.83 million

Year 3: \$2.19 million

Year 4: \$2.74 million

Year 5: \$3.20 million

Under the terms of the agreement all payments are made at the end of each year. Instead of accepting the contract, the baseball player asks his agent to negotiate a contract that has a present value of \$1.73 million more than that which has been offered. Moreover, the player wants to receive his payments in the form of a 5-year ANNUITY DUE. All cash flows are discounted at 11.00 percent. If the team were to agree to the player's terms, what would be the player's annual salary (in millions of dollars)? (Express answer in millions. \$1,000,000 would be 1.00)

 Calculation of Present Value of the Cash Flows Year Cash Flow Discount Factor@11% Discounted Cash Flows A B C = 1/(1+11%)^A D = B*C 1 1.28 0.900900901 1.153153153 2 1.83 0.811622433 1.485269053 3 2.19 0.731191381 1.601309125 4 2.74 0.658730974 1.804922869 5 3.2 0.593451328 1.89904425 Present Value of Cash Flows 7.94369845 Amount need as contract in Present Value terms = \$7.94369845 million + \$1.73 million = \$9.67369845 million P = Annual Salary n = 5 years r = interest rate = 11% Present Value needed = P * [1 - (1+r)^-n] / r \$9.67369845 million = P * [1 - (1+11%)^-5] / 11% \$1.064106829 million = P * 0.406548672 P = \$2.617416 million Therefore, annual amount needed for 5 years annuity is \$2.62 million

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