Question

CASE

Billy Wilson, All American

In his senior year at a major Midwestern university, Billy Wilson had been the third runner up for the famed Heismann Tophy. The trophy goes to the outstanding football player in America and is presented annually by the New York Athletic Club. During the past football season, Wilson had run for over 1,500 yards and scored 18 touchdowns. He also caught 41 passes coming out of the backfield. His time in running the 40-yard dash, which professional scouts consider to be extremely important, was 4.38 seconds. He was voted first team All American by the Associated Press and was a second team All American in the Coaches Poll selections.

On Monday morning, his agent, Joel Weinberg, called to say that he was looking at three different proposals that a major West Coast professional football team had made for Billy Wilson’s services. The team had drafted him in the first round of the National Football League draft as the sixth player to be selected out of the thousands of college football players that were eligible for that year. The Edmonton, Alberta, team of the Canadian Football League was also interested in Wilson’s services. The Canadian team had called his agent over the weekend to put its offer on the table. While the National Football League (NFL) team that had drafted Billy Wilson in the first round had exclusive rights overall other U.S. teams in signing Billy Wilson during the current year, the Canadian team was not bound by such an arrangement and could make any offer it wished and hope the outcome would be positive.

Actual Proposals:

The West Coast NFL team offered the following three proposals. The team’s general manager, who was in charge of contract negotiations, said his team would stand behind any of the three offers and it was up to Billy Wilson and his agent to choose which they preferred:

Contract offer 1:

• • $900,000 immediate signing bonus
• • $850,000 at the end of each year for the next five (5) YEARS

Contract offer 2:

• • $200,000 immediate signing bonus
• • $100,000 at the end of each year for the next four years.
• • $150,000 a year at the end of years 5 through 10
• • $1,000,000 a year at the end of years 11 through year 40.

Contract offer 3:

• • $1,000,000 immediate signing bonus
• • $500,000 at the end of year 1
• • $1,000,000 at the end of year 2
• • $1,500,000 at the end of year 3
• • $2,000,000 at the end of year 4

Canadian Football League:

• • $1,100,000 immediate signing bonus
• • $2,000,000 at the end of each year for the next three years.

Required Assignment

Assume that the cash flows will be discounted using a 10 percent interest rate.

4. Given your answers to #2, how much could Billy pay himself for the next 40 years assuming a 10% interest rate? Calculate the answer using all four (4) football conracts.

Answer 1

The PVs of the alternative offers are calculated below:
CONTRACT OFFER 1:		PV
Amount paid immediately		$   9,00,000
850000 t1 to t5 = 850000*(1.1^5-1)/(0.1*1.1^5)=		$ 32,22,169
PV of the offer		$ 41,22,169
CONTRACT OFFER 2:
Amount paid immediately		$   2,00,000
100000 t1 to t4 = 100000*(1.1^4-1)/(0.1*1.1^4) =		$   3,16,987
Discounted value at t4 of 150000 paid t5 to t10 = 150000*(1.1^6-1)/(0.1*1.1^6) =	$     6,53,289
PV of the above amount = 653289/1.1^4 =		$   4,46,205
Discounted value at t10 of 1000000 paid t11 to t40 = 1000000*(1.1^30-1)/(0.1*1.1^30) =	$   94,26,914
PV of the above amount = 9426914/1.1^10 =		$ 36,34,483
PV of the offer		$ 45,97,675
CONTRACT OFFER 3:
Immediate payment		$ 10,00,000
PV of other payments = 500000/1.1+1000000/1.1^2+1500000/1.1^3+2000000/1.1^4 =		$ 37,73,991
PV of the offer		$ 47,73,991
CANADIAN FOOTBALL LEAGUE:
Immediate payment		$ 11,00,000
PV of 2000000 t1 to t3 = 2000000*(1.1^3-1)/(0.1*1.1^3) =		$ 49,73,704
PV of the offer		$ 60,73,704
CHOICE:
The Canadian football offer is preferred as it has the highest PV.
AMOUNT THAT BILLY COULD PAY HIMSELF FOR THE NEXT 40 YEARS:
It is an annuity whose PV will be as those calculated above.
Contract Offer 1 = 4122169*0.1*1.1^40/(1.1^40-1) =	$     4,21,531
Contract Offer 1 = 4597675*0.1*1.1^40/(1.1^40-1) =	$     4,70,156
Contract Offer 1 = 4773991*0.1*1.1^40/(1.1^40-1) =	$     4,88,186
Contract Offer 1 = 6073704*0.1*1.1^40/(1.1^40-1) =	$     6,21,093