Final answer:
When a bond's coupon rate is below market interest rates, it sells at a discount. The bond's value is determined by discounting its future interest payments and face value using the market interest rate. Calculations require the present value of an annuity and a single amount formula.
Step-by-step explanation:
When a bond's coupon rate is lower than the prevailing market interest rates, the bond will sell at a discount. This is because investors can find alternative investments with a better return. The value of the bond is calculated by discounting the future cash flows, which are the interest payments and the face value at maturity, back to the present using the current market interest rate as the discount rate.
To calculate the present value of the bond in question, we would use the present value of an annuity formula for the semiannual interest payments and the present value of a single amount for the maturity value. Assuming you have the present value tables or a financial calculator, you would multiply the semiannual interest payment of $30,000 (which is 12% / 2 = 6% of $500,000) by the annuity factor for a 14% semiannual rate for 20 periods (10 years semiannually). Add the product to the present value of $500,000, which is multiplied by the single sum present value factor for 14% semiannual rate for 20 periods.
Should the market rate of interest increase, the present value of these cash flows would decrease, and the bond will sell for a lower price. This exemplifies the inverse relationship between bond prices and market interest rates.