A famous quarterback just signed a $\$ 15$ million contract providing $\$ 3$ million a year for $5$ years. A less famous receiver signed a million $5$ -year contract providing $\$ 4$ million now and $\$ 2$ million a year for $5$ years. The interest rate is $10 \%$ . $\newline$ a. What is the PV of the quarterback's contract? $\newline$ Note: Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places. $\newline$ Hint $\newline$ Print $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline Present value & million \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ b. What is the PV of the receiver's contract?

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Q. A famous quarterback just signed a

\$ 15

million contract providing

\$ 3

million a year for

5

years. A less famous receiver signed a million

5

-year contract providing

\$ 4

million now and

\$ 2

million a year for

5

years. The interest rate is

10 \%

\newline

a. What is the PV of the quarterback's contract?

\newline

Note: Do not round intermediate calculations. Enter your answer in millions rounded to

2

decimal places.

\newline

Hint

\newline

\newline

\begin{tabular}{|c|c|}

\newline

\hline Present value & million \\

\newline

\hline

\newline

\end{tabular}

\newline

b. What is the PV of the receiver's contract?

Calculate Present Value: To find the present value of the quarterback's contract, we need to discount each annual payment of $\$3$ million back to the present value using the formula for present value of an annuity: $\newline$ $PV = Pmt \times \left(1 - \left(1 + r\right)^{-n}\right) / r$ $\newline$ where $Pmt$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods. $\newline$ In this case, $Pmt = \$3$ million, $r = 0.10$ , and $n = 5$ years.
Calculate PV Factor: First, we calculate the present value factor for an annuity: $\newline$ PV factor = $[\frac{1 - (1 + 0.10)^{-5}}{0.10}]$
Compute PV Factor: Now, we compute the actual present value factor: $\newline$ PV factor = $[\frac{1 - (1 + 0.10)^{-5}}{0.10}] = [\frac{1 - (1.10)^{-5}}{0.10}] = [\frac{1 - 0.620921323059155}{0.10}] \approx 3.79079$
Multiply for QB Contract PV: Next, we multiply the annual payment by the present value factor to get the present value of the quarterback's contract: $\newline$ $PV = \$3 \text{ million} \times 3.79079 \approx \$11.37237 \text{ million}$
Calculate Receiver's PV: To find the present value of the receiver's contract, we need to calculate the present value of the immediate payment of $\$4$ million and the present value of the annuity of $\$2$ million a year for $5$ years. $\newline$ For the immediate payment, the present value is simply the payment itself, since it is already in present terms: $\newline$ $PV_{\text{immediate}} = \$4$ million
Calculate Immediate PV: For the annuity part, we use the same present value of an annuity formula as before, but with $Pmt = \$2$ million. $PV_{\text{annuity}} = \$2$ million $* 3.79079 \approx \$7.58158$ million
Calculate Annuity PV: Now, we add the present value of the immediate payment to the present value of the annuity to get the total present value of the receiver's contract: $\newline$ PV_{\text{total}} = PV_{\text{immediate}} + PV_{\text{annuity}} = \$($4 \text{ million}) + \$(\(7$.$58158$ \text{ million}) = \$($11$.$58158$ \text{ million})