# Bond Issue Calculation ## Given Data: - Face value of bonds = \$275,000 - Coupon rate = 10% - Bond term = 5 years - Interest rate (market rate) = 9% - Interest payment dates = June 30 and December 31 - Issue date = January 1, 2019 --- ## 1. Present Value of Principal (Face Value) Since the bonds are issued at a discount or premium based on market rate, the present value of the principal (face value) is discounted at the market rate over 5 years: \[ PV_{principal} = 275,000 \times \frac{1}{(1 + .09)^5} \] \[ PV_{principal} = 275,000 \times \frac{1}{1.53862} \approx 275,000 \times .64993 \approx \mathbf{\$178,730.87} \] --- ## 2. Present Value of Interest (Coupon Payments) Coupon payment each period: \[ C = 275,000 \times 10\% / 2 = 13,750 \] Number of periods: \[ n = 5 \text{ years} \times 2 = 10 \text{ periods} \] Market rate per period: \[ i = 9\% / 2 = 4.5\% \] Present value of annuity of interest payments: \[ PV_{interest} = 13,750 \times \left(1 - \frac{1}{(1 + .045)^{10}}\right) / .045 \] Calculate denominator: \[ (1 + .045)^{10} \approx 1.045^{10} \approx 1.553 \] Then: \[ PV_{interest} = 13,750 \times \left(1 - \frac{1}{1.553}\right) / .045 \] \[ PV_{interest} = 13,750 \times (1 - .643) / .045 \] \[ PV_{interest} = 13,750 \times .357 / .045 \approx 13,750 \times 7.933 \approx \mathbf{\$109,084.36} \] --- ## 3. Selling Price of the Bonds \[ \text{Selling Price} = PV_{principal} + PV_{interest} \approx \$178,730.87 + \$109,084.36 = \boxed{\$287,815.23} \] --- ## **Final Answers:** | **Present value of principal** | **Present value of interest** | **Selling price** | |--------------------------------|------------------------------|------------------| | **\$178,730.87** | **\$109,084.36** | **\$287,815.23** | *Note: Rounding to two decimal places as instructed.*