\( 1 \leftarrow \begin{array}{l}\text { Ten years ago Salmon Acqua Farming Inc. issued twenty - five - year } 8 \% \text { annual coupon bonds with } \\ \text { a } \$ 1,000 \text { face value each. Since then, interest rates in general have fallen and the yield to maturity on } \\ \text { the Bacon bonds is now } 7 \% \text {. Given this information, what is the price today for such a bond? } \\ \text { A. } \$ 1,000 \\ \text { B. } \$ 914.41 \\ \text { C. } \$ 1,091.08 \\ \text { D. } \$ 1,116.54\end{array} \)

To determine the current price of the bond, we need to calculate the Present Value (PV) of the future cash flows, which consist of the annual coupon payments and the face value at maturity. The annual coupon payment is \( 8\% \) of \( \$1,000 \), which equals \( \$80 \). Since there are 15 years remaining (25 years - 10 years), we can use the formula for the price of a bond: \[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \] Where: - \( P \) = price of the bond - \( C \) = annual coupon payment = \( \$80 \) - \( F \) = face value of the bond = \( \$1,000 \) - \( r \) = yield to maturity = \( 0.07 \) - \( n \) = number of years remaining = 15 Calculating the present value of the coupons and the face value: 1. Present Value of Coupons: \[ PV_{coupons} = 80 \left( \frac{1 - (1 + 0.07)^{-15}}{0.07} \right) \approx 80 \cdot 9.107 = 728.56 \] 2. Present Value of Face Value: \[ PV_{face value} = \frac{1000}{(1 + 0.07)^{15}} \approx \frac{1000}{2.759} \approx 362.44 \] 3. Total Price of the Bond: \[ P = PV_{coupons} + PV_{face value} \approx 728.56 + 362.44 \approx 1,091.00 \] So the price today for the bond is approximately \( \$1,091.08 \), which corresponds to option C. Option C: \$1,091.08 is the right answer!