Question

A baseball player is offered a 5-year contract that pays him the following amounts: Year 1: $2.7 million Year 2: $1.1 million Year 3: $1.6 million Year 4: $2.3 million Year 5: $1.4 million Under the terms of agreements all payments are made at the end of each year. Instead of accepting the contract, the basketball player asks his agent to negotiate a contract that has a present value of $2 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 13.5. Percent. If the team were to agree to the player’s terms, what would be the player’s annual salary (in millions of dollars)

Answer 1

Present value of given cash flows=Cash flows*Present value of discounting factor(rate%,time period)

=2.7/1.135+1.1/1.135^2+1.6/1.135^3+2.3/1.135^4+1.4/1.135^5

=$6.45624616 million(Approx)

Hence required present value of contract=6.45624616+2

=$8.45624616 million(Approx)

Present value of annuity due=(1+rate)*Annuity[1-(1+interest rate)^-time period]/rate

8.45624616=1.135*Annuity[1-(1.135)^-5]/0.135

8.45624616=Annuity*3.94383293

Annuity=8.45624616/3.94383293

=$2.14 million(Approx)