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Recently an NFL quarterback agreed to an eight-year, $50 million contract that at the time made him one of the highest paid players in professional football history. The contract included a signing bonus of $11 million. The agreement called for annual salaries of $2.5 million in 2005, $1.75 million in 2006, $4.15 million in 2007, $4.90 million in 2008, $5.25 million in 2009, $6.2 million in 2010, $6.75 million in 2011, and $7.5 million in 2012. The $11 million signing bonus was prorated over the course of the contract, so that an additional $1.375 million was paid each year over the eight-year contract period. Table ST3.8 shows the net annual payment schedule, with the salary paid at the beginning of each season.
(a) How much was the quarterbacks contract actually worth at the time of signing?
(b) For the signing bonus portion, suppose that the quarterback was allowed to take either the prorated payment option as just described or a lump-sum payment option in the amount of $8 million at the time he signed the contract. Should he have taken the lump-sum option instead of the prorated one? Assume that his interest rate is 6%.

Beginning
of Season

Prorated
Contract
Salary

Actual
Signing
Bonus

Annual
Payment

2005

$2,500,000

$1,375,000

$3,875,000

2006

1,750,000

1,375,000

3,125,000

2007

4,150,000

1,375,000

5,525,000

2008

4,900,000

1,375,000

6,275,000

2009

5,250,000

1,375,000

6,625,000

2010

6,200,000

1,375,000

7,575,000

2011

6,750,000

1,375,000

8,125,000

2012

7,500,000

1,375,000

8,875,000

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