# Bond Discount

## What Is a Bond Discount?

Bond discount is the amount by which the market price of a bond is lower than its principal amount due at maturity. This amount, called its par value, is frequently $1,000.

The primary highlights of a bond are its coupon rate, face value, and market price. An issuer makes coupon payments to its bondholders as compensation for the money loaned over a fixed period.

At maturity, the principal loan amount is repaid to the investor. This amount is equivalent to the par or face value of the bond. Most corporate bonds have a par value of $1,000. A few bonds are sold at par, at a premium, or at a discount.

## Understanding Bond Discount

A bond sold at par has its coupon rate equivalent to the overarching interest rate in the economy. An investor who purchases this bond has a return on investment that is determined by the periodic coupon payments.

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

A bond issued at a discount has its market price below the face value, making 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 instance, a bond with a par value of $1,000 that is trading at $980 has a bond discount of $20. The bond discount is likewise utilized in reference to the bond discount rate, which is the interest used to price bonds by means of present valuation computations.

Bonds are sold at a discount when the market interest rate surpasses the coupon rate of the bond. To grasp this concept, recollect that a bond sold at par has a coupon rate equivalent to the market interest rate. At the point when the interest rate increments past the coupon rate, bondholders presently hold a bond with lower interest payments.

These existing bonds reduce in value to mirror the way that fresher issues in the markets have more appealing rates. On the off chance that the bond's value falls below par, investors are bound to purchase it since they will be repaid the par value at maturity. To compute the bond discount, the present value of the coupon payments and principal value must be determined.

## Model

For instance, 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 somewhat 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%. Utilizing this data, the current value of the principal repayment at maturity is:

PV_{principal} = $1,000/(1.025^{6}) = $862.30

Presently we want to compute the current 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) + (17.50/1.025^{2}) + (17.50/1.025^{3}) + (17.50/1.025^{4}) + (17.50/1.025^{5}) + (17.50/1.025^{6})

PV_{coupon} = 17.07 + 16.66 + 16.25 + 15.85 + 15.47 + 15.09 = $96.39

The sum of the current 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, hence, $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 gets a similar coupon, the bond is discounted to match winning market yields.

Discounts likewise happen when the bond supply surpasses demand when the bond's credit rating is brought down, or when the perceived risk of default increments. On the other hand, falling interest rates or a superior credit rating might make a bond trade at a premium.

Short-term bonds are frequently issued at a bond discount, particularly on the off chance that they are zero-coupon bonds. Be that as it may, bonds on the secondary market might trade at a bond discount, which happens when supply surpasses demand.

## Features

- Various bonds trade at a discount for various reasons â€” for instance, bonds on the secondary market with fixed coupons trade at discounts when interest rates rise, while zero-coupon bonds short-term bonds are frequently issued at a bond discount when supply surpasses demand.
- Bond discount is the amount by which the market price of a bond is lower than its principal amount due at maturity.
- A bond issued at a discount has its market price below the face value, making a capital appreciation upon maturity since the higher face value is paid when the bond matures.