BONDS

 

Example

For example, consider a bond with a par value of $1,000 set to mature in 3 years. The bond has a coupon rate of 3.5%, and interest rates in the market are a little higher at 5%. Since interest payments are made on a semi-annual basis, the total number of coupon payments is 3 years x 2 = 6, and the interest rate per period is 5%/2 = 2.5%. Using this information, the present value of the principal repayment at maturity is:

PV_principal = $1,000/(1.025⁶) = $862.30

Now we need to calculate the present value of coupon payments. The coupon rate per period is 3.5%/2 = 1.75%. Each interest payment per period is 1.75% x $1,000 = $17.50.

PV_coupon = (17.50/1.025) + (17.50/1.025²) + (17.50/1.025³) + (17.50/1.025⁴) + (17.50/1.025⁵) + (17.50/1.025⁶)

PV_coupon = 17.07 + 16.66 + 16.25 + 15.85 + 15.47 + 15.09 = $96.39

The sum of the present value of coupon payments and principal is the market price of the bond.

Market Price = $862.30 + $96.39 = $958.69.

Since the market price is below the par value, the bond is trading at a discount of $1,000 - $958.69 = $41.31. The bond discount rate is, therefore, $41.31/$1,000 = 4.13%.

Bonds trade at a discount to par value for a number of reasons. Bonds on the secondary market with fixed coupons will trade at discounts when market interest rates rise. While the investor receives the same coupon, the bond is discounted to match prevailing market yields.

Discounts also occur when the bond supply exceeds demand when the bond's credit rating is lowered, or when the perceived risk of default increases. Conversely, falling interest rates or an improved credit rating may cause a bond to trade at a premium.

Short-term bonds are often issued at a bond discount, especially if they are zero-coupon bonds. However, bonds on the secondary market may trade at a bond discount, which occurs when supply exceeds demand.