Question

26. Solve each of the following independent cases using the present value tables: The following actual contracts signed by athletes: a. $28,000,000 contract, payable at $2,000,000 per year for 14 years. b. $31,500,000 contract, payable at $1,575,000 per year for 20 years. c. $24,000,000 contract, payable at $2,400,000 per year for 10 years. Determine the present value of each contract and indicate (with explanation) which contract you would prefer to have. Assume an 8% interest rate.

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
	Option-1	Option-2	Option-3
Annual Payment	2,000,000	1,575,000	2,400,000
No of payments	14	20	10
Contract value-Annual Payments * No of payment	28,000,000	31,500,000	24,000,000
Interest Rate	8%	8%	8%
PV of such payments	=PMT x (((1-(1 + r) ^- n)) / i)	=PMT x (((1-(1 + r) ^- n)) / i)	=PMT x (((1-(1 + r) ^- n)) / i)
PV of such payments	=2000000* (((1-(1 + 8%) ^- 14)) / 8%)	=1575000* (((1-(1 + 8%) ^- 20)) / 8%)	=2400000* (((1-(1 + 8%) ^- 10)) / 8%)
PV of such payments	16,488,474	15,463,582	16,104,195
Since the PV is highest in option 1 so we will prefer option 1