A famous quarterback just signed a $19.2 million contract providing $3.2 million a year for 6 years. A less famous receiver signed a $21.2 million 6-year contract providing $5 million now and $2.8 million a year for 6 years. The interest rate is 9%.
a. What is the PV of the quarterback's contract?
b. What is the PV of the receiver's contract?
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a. The present value (PV) of the quarterback's contract can be calculated using the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
where:
PMT = $3.2 million (annual payment)
r = 9% (interest rate)
n = 6 years (number of payments)
PV = $3.2 million * [(1 - (1 + 0.09)^-6) / 0.09]
PV = $3.2 million * 4.9173
PV = $15.735 million
So, the present value of the quarterback's contract is approximately $15.735 million.
b. The present value (PV) of the receiver's contract can be calculated by adding the present value of the $5 million received now and the present value of the annuity:
PV = $5 million + PMT * [(1 - (1 + r)^-n) / r]
where:
PMT = $2.8 million (annual payment)
r = 9% (interest rate)
n = 6 years (number of payments)
PV = $5 million + $2.8 million * [(1 - (1 + 0.09)^-6) / 0.09]
PV = $5 million + $2.8 million * 4.9173
PV = $5 million + $13.768 million
PV = $18.768 million
So, the present value of the receiver's contract is approximately $18.768 million.
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