Question

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?

Answer 1

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.