Understanding Bond Discount vs. Premium Bond: Definitions and Examples

What Is a Bond Discount?

A bond discount occurs when a bond’s market price falls below its par value at maturity, often $1,000. Bondholders benefit from capital appreciation as the bond matures at its higher face value. This article explains how different bonds can be traded at a discount or premium, focusing on key factors like interest rates and market demand.

How Bond Discounts Impact Investors

If a bond is sold at par, its coupon rate matches the current interest rate. Investors earn a return based on these regular coupon payments.

A premium bond is one for which the market price of the bond is higher than the face value. If the bond’s stated interest rate is greater than those expected by the current bond market, this bond will be an attractive option for investors.

A bond issued at a discount has its market price below the face value, creating a capital appreciation upon maturity since the higher face value is paid when the bond matures. The bond discount is the difference by which a bond’s market price is lower than its face value.

For example, a bond with a par value of $1,000 that is trading at $980 has a bond discount of $20. The bond discount is also used in reference to the bond discount rate, which is the interest used to price bonds via present valuation calculations.

Bonds sell at a discount if the market interest rate is higher than the coupon rate. A bond at par means its coupon rate matches the market rate. When the interest rate increases past the coupon rate, bondholders now hold a bond with lower interest payments.

Existing bonds lose value when new bonds offer better rates. If a bond’s value drops below par, investors are drawn in, knowing they’ll receive the par value at maturity. To find the bond discount, calculate the present value of both the coupon payments and the principal.

Calculating a Bond Discount: An 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.

The Bottom Line

The article concludes by explaining that bond discount occurs when a bond’s market price is below its par value due to higher market interest rates or increased risk factors. This offers investors capital appreciation potential, as they can purchase bonds at a discount and receive the full par value at maturity. It’s crucial for investors to understand that varying factors, such as market interest rates and credit ratings, affect bonds’ trading status as either at a discount or premium. Navigating these differences can help investors make informed decisions when purchasing bonds.