You own a bond that has an 8 percent coupon and matures 8 years from now. You purchased this bond at par value when it was originally issued. If the current market rate for this type and quality of bond is 8.25 percent, then you would expect
To calculate the expected price of the bond, we need to compare the coupon rate (8%) with the market rate (8.25%).
If the coupon rate and market rate are the same, the bond will be priced at par value. In this case, since the market rate (8.25%) is higher than the coupon rate (8%), the bond is expected to be priced lower than par value.
The relationship between interest rates and bond prices is inverse: when interest rates rise, bond prices fall, and vice versa. So, with the market rate higher than the coupon rate, the bond is less attractive, and its price is expected to be discounted below par value.
To determine the expected price of the bond, you can use the present value formula:
PV = C/(1 + r)^n
Where:
PV = Present value or expected price of the bond
C = Coupon payment per period (8% of par value)
r = Market interest rate per period (8.25%)
n = Total number of periods (8 years)
Using this formula, you can calculate the present value of the coupon payments for the bond over the 8-year period. The sum of these present values plus the present value of the par value will give you the expected price of the bond.