A rookie quarterback is in the process of negotiating his first contract. The team's general manager has offered him three possible contracts. Each contract lasts for four years. All of the money is guaranteed and is paid at the end of each year. The payment terms of the contracts are as follows: (dollars in millions)
Year Contract 1 Contract 2 Contract 3
1 $1.50 1.0 3.5
2 $1.50 1.5 0.5
3 $1.50 2 0.5
4 $1.50 2.5 0.5
The quarterback discounts all the cash flows at 12%. Which of the three contracts offers the most value? (Hint: Calculate the present value of future cash flows)

Contract 2 offers the most value.

Explanation:

a) Data and Calculations:

Payment terms of the contracts:

(dollars in millions)

Year Contract 1   Contract 2   Contract 3

1            $1.50           1.0                 3.5

2           $1.50           1.5                 0.5

3           $1.50           2                   0.5

4           $1.50           2.5                0.5

Discount rate = 12%

Present value of Contract 1:

PV annuity factor at 12% for 4 years = 3.037

PV annuity of $1.50 = $1.50 * 3.037 = $4.5555 or $4,555,500

Present value of Contract 2:

$1.0 * 0.893 = $0.893

$1.5 * 0.797 =   1.1955

$2 * 0.712 =     1.424

$2.5 * 0.636 = 1.59

Total =          $5.1025 or $5,102,500

Present value of Contract 3:

$3.5 * 0.893 = $3.1255

$0.5 * 0.797 =   0.3985

$0.5 * 0.712 =    0.356

$0.5 * 0.636 =   0.318

Total =          $4.198 million or $4,198,000

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order: