Question

Today is January 1, 2017. Your friend Pat has just signed a contract to play for a professional football team. He will receive $2,500,000 for 2017, $3,500,000 for 2018, $3,700,000 for 2019, and $4,200,000 for 2020. All payments are made at the end of the year. Assume a 5% annual interest rate (EAR). a) What is the present value of his contract? b) Instead of receiving annual payments, Ted wants to receive equal-dollar-amount-quarterly cheques (first cheque today, last cheque at the end of 2020), how large is his quarterly pay (assuming the present value of his contract remains the same)?

Answer 1

a)
					AMOUNT IN $
DATE		RECEIPT		PRESENT VALUE FACTOR		PRESENT VALUE
31-Dec-17		2,500,000		0.952		2380000
31-Dec-18		3,500,000		0.907		3174500
31-Dec-19		3,700,000		0.864		3196800
31-Dec-20		4,200,000		0.823		3456600
		Present value of contract				12207900
b)
Let x be amount of quarterly payment
Total number of payments to be received is 16 (4*4)
It is given that present value is same
Therefore
present value annuity factor(5%, 16 installments) is 10.055
	=	x*10.055	=	12207900
		x	=	1214112.38	(12207900/10.055)
Thus quarterly payment should be 1214112