Answer:
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.
