a. The price of a bond is the present value of all the interest and payment payable on the bond.
b. Consider the following timeline of payments and how their respective present values:
c. The present value is calculated by discounting each payment with the required interest rate. Thus, the equation for the calculation of the price of the fixed income security at the time of its inception is:
Where, PV = Present Value PMT = Coupon Payment FV = Future Value r = Market Discount Rate or Required Rate of Return |
d. The bonds are quoted on a 100-point system. Thus, if a $ 2,000 bond is quoted at 95, then it implies a price of 95% of its face value, i.e. $ 1,900. And, if it is quoted at 105, then it means a premium of 5%, i.e. $ 2,100.
e. If the coupon rate is less than the market discount rate, then the present value is less than 100, and it is a discount bond.
If, however, the coupon rate is more than the market discount rate, then the present value is more than 100, and it is a premium bond.
If the coupon rate equals the market discount rate, then the present value equals 100, and it would be a par bond.
f. There is an inverse relationship between bond prices and interest rates. Thus, when the interest rate increases, the bond price decreases.