Full solution

Q. 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. 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

Present value

\square

million

Identify Variables: To find the present value (PV) of the quarterback's contract, we need to discount each of the $\$3$ million payments back to the present value using the formula for the present value of an ordinary annuity. The formula for the present value of an ordinary annuity is $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$ , where $PMT$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.
Plug Values into Formula: First, we identify the variables needed for the calculation: $\newline$ $PMT$ (annual payment) = $\$3$ million $\newline$ $r$ (interest rate per period) = $10\%$ or $0.10$ $\newline$ $n$ (number of periods) = $5$ years
Calculate Present Value: Now we can plug these values into the present value of an ordinary annuity formula: $\newline$ $PV = \$3 \text{ million} \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]$
Round Present Value: Next, we calculate the present value: $\newline$ $PV = (\$)3 \text{ million} \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]$ $\newline$ $PV = (\$)3 \text{ million} \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]$ $\newline$ $PV = (\$)3 \text{ million} \times \left[\frac{1 - 0.620921323059155}{0.10}\right]$ $\newline$ $PV = (\$)3 \text{ million} \times \left[\frac{0.379078676940845}{0.10}\right]$ $\newline$ $PV = (\$)3 \text{ million} \times 3.79078676940845$ $\newline$ $PV = (\$)11.37236030822535 \text{ million}$
Round Present Value: Next, we calculate the present value: $\newline$ PV = $\$3$ million * $\left[1 - (1 + 0.10)^{-5}\right] / 0.10$ $\newline$ PV = $\$3$ million * $\left[1 - (1.10)^{-5}\right] / 0.10$ $\newline$ PV = $\$3$ million * $\left[1 - 0.620921323059155\right] / 0.10$ $\newline$ PV = $\$3$ million * $\left[0.379078676940845 / 0.10\right]$ $\newline$ PV = $\$3$ million * $3$ . $79078676940845$ $\newline$ PV = $\$11.37236030822535$ millionFinally, we round the present value to two decimal places as instructed: $\newline$ PV = $\left[1 - (1 + 0.10)^{-5}\right] / 0.10$ $0$ million