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2 February, 04:57

A famous quarterback just signed a contract for $16 mil, providing $3.6 million a year for 4 years. A less famous receiver signed a contract for $15.0, providing $3 mil now and $3.0 a year for 4 years. The interest rate is 9%. What are the present value of their contract?

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  1. 2 February, 05:07
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    The PV of the famous quarterback is $11,662,991.56, while the PV of less famous receiver is $12,719,159.63.

    Explanation:

    Present value (PV) refers to the valuation date value of a stream of income expected to be received in the future.

    The PV for each of the two contracts can calculated by using the interest rate of 9%% (i. e. 0.12) as the discounting factor (r) to calculate the PV for each year. The discounting formula to use is (1+r) ^n where n represents each relevant year. The calculations are done as follows:

    1. For a famous quarterback

    Step 1. Calculation of the PV for year

    Year 1 PV = $3,600,000 : (1.09) ^1 = $3,302,752.29

    Year 2 PV = $3,600,000 : (1.09) ^2 = $3,030,047.98

    Year 3 PV = $3,600,000 : (1.09) ^3 = $2,779,860.53

    Year 4 PV = $3,600,000 : (1.09) ^4 = $2,550,330.76

    Step 2. Calculation of the total PV

    This is obtained by adding the PVs of year 1 - 4 calculated above, and this is equal to $11,662,991.56.

    2. For a less famous receiver

    Step 1. Calculation of the PV for year

    Year 1 PV = $3,000,000 : (1.09) ^1 = $2,752,293.58

    Year 2 PV = $3,000,000 : (1.09) ^2 = $2,525,039.98

    Year 3 PV = $3,000,000 : (1.09) ^3 = $2,316,550.44

    Year 4 PV = $3,000,000 : (1.09) ^4 = $2,125,275.63

    Step 2. Calculation of the total PV

    This is obtained by adding the PVs of year 1 - 4 calculated above, and this is equal to $9,719,159.63.

    In addition, the $3,000,000 is to receive now is added to the $9,719,159.63 as follows:

    PV of less famous receiver = $9,719,159.63 + $3,000,000

    = $12,719,159.63

    Conclusion

    Therefore, the PV of the famous quarterback is $11,662,991.56, while the PV of less famous receiver is $12,719,159.63.
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