The question is missing the requirement. The complete question is,
A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2 million a year for 5 years. Who is better paid? The interest rate is 10%.
Answer:
The less famous receiver is better paid.
Explanation:
To calculate who is better paid, we need to calculate the present value of the amount the famous quarterback and less famous receiver will receive.
The present value is the sum of future cash flows discounted back to today's terms using the discount rate or interest rate.
<u>PV of $15m for famous quarterback:</u>
The famous quarter back will receive the 15 million in equal payments for five years. We consider the payments are received at the end of period. We calculate the 5 year discount factor for such annuity at 10%.
- Discount factor = (1 - (1 + 10%)^-5) / 10% = 3.79079
- The discount factor is calculated using the simple formula for Present value of ordinary annuity
- The PV = $3 million * 3.79079 = $11.37237 million
<u>PV of $14 million for less famous receiver:</u>
The less famous receiver is receiving $4 million today which are worth exactly the same that is $4 million. Apart from that, the remaining payments of $10 million is received in ordinary annuity of $2 million a year. We calculate the PV of $4 million today and $2 million annuity for five years to calculate the value of $14 million today
- The annuity discount factor is same as the interest rate and time period is same.
- The PV = $4 million + $2 million * 3.79079 = $11.58158 million
