# Understanding Bond Discounts: Definition, Calculation, and Real-Life Examples

Summary:

Bond discount refers to the amount by which the market price of a bond falls below its face value, commonly set at \$1,000. When a bond is issued at a discount, it has a market price lower than its face value, leading to capital appreciation at maturity. Various factors, such as changing interest rates and supply-demand dynamics, can influence why bonds are sold at a discount. In this article, we’ll delve deeper into the concept of bond discounts, explaining the reasons behind them and providing a practical example of how to calculate bond discounts and their rates.

## What is a bond discount?

A bond discount is the difference between the market price of a bond and its principal amount due at maturity. The principal amount, often known as the par or face value, typically stands at \$1,000. It’s essential to grasp the key features of a bond, including its coupon rate, face value, and market price. The issuer makes periodic coupon payments to bondholders as a form of interest on the money borrowed over a specified period.

At the bond’s maturity, the investor receives the principal amount, which equals the par or face value of the bond. Most corporate bonds have a par value of \$1,000. However, bonds can be sold at par, at a premium, or at a discount.

### Bond sold at par

A bond sold at par has a coupon rate that matches the prevailing interest rate in the economy. Investors who purchase such bonds receive a return on investment determined by the periodic coupon payments.

A premium bond is one with a market price exceeding its face value. These bonds become attractive to investors when the bond’s stated interest rate is higher than what the current bond market expects.

## Bond issued at a discount

A bond issued at a discount has its market price below the face value, resulting in capital appreciation at maturity since the higher face value is paid when the bond matures. The bond discount represents the difference between a bond’s market price and its face value.

For instance, consider a bond with a par value of \$1,000 trading at \$980. In this case, the bond discount amounts to \$20, as the market price is \$20 lower than the par value.

## Why do bonds trade at a discount?

Bonds are sold at a discount when the market interest rate surpasses the coupon rate of the bond. To understand this, remember that a bond sold at par has a coupon rate equal to the market interest rate. When the market interest rate rises above the coupon rate, existing bondholders find themselves with a bond that offers lower interest payments.

In such situations, the value of existing bonds decreases because newer issues in the market offer more attractive interest rates. When a bond’s value falls below par, it becomes more appealing to investors because they will be repaid the par value at maturity. Calculating the bond discount requires determining the present value of coupon payments and the principal value.

## Example of calculating bond discount

Let’s illustrate this with an 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%, while market interest rates are slightly higher at 5%. Since interest payments occur semi-annually, there will be a total of six coupon payments. The interest rate per period is 5%/2, which is 2.5%. We’ll calculate the present value of the principal repayment at maturity:

PVprincipal = \$1,000 / (1.025^6) = \$862.30

Next, we need to determine the present value of coupon payments. The coupon rate per period is 3.5%/2, which is 1.75%. Each interest payment per period amounts to 1.75% of \$1,000, which is \$17.50.

PVcoupon = (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)

PVcoupon = \$17.07 + \$16.66 + \$16.25 + \$15.85 + \$15.47 + \$15.09 = \$96.39

The sum of the present value of coupon payments and the principal value gives us the market price of the bond:

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

In this example, 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 \$41.31 / \$1,000, which is 4.13%.

## Reasons for bond discounts

Bonds are traded at a discount to par value for various reasons. Bonds with fixed coupons in the secondary market trade at discounts when market interest rates rise. While investors receive the same coupon, the bond’s market price decreases to align with the prevailing market yields.

Discounts may also occur when there’s an excess supply of bonds compared to demand, when the bond’s credit rating is downgraded, or when the perceived risk of default increases. Conversely, falling interest rates or an improved credit rating can lead to a bond trading at a premium.

WEIGH THE RISKS AND BENEFITS

Here is a list of the benefits and the drawbacks to consider.

##### Pros
• Pay back less than what you owe
• Become debt-free in less time
• Avoid bankruptcy
##### Cons
• Negative impact on credit score
• Remains on your credit history for 7 years

### Why are some bonds sold at a discount?

Bonds are sold at a discount when the market interest rate exceeds the coupon rate of the bond. When newer bonds offer higher interest rates, existing bonds may lose value, making them more attractive to investors.

### How is the bond discount calculated?

The bond discount is calculated by determining the present value of both the coupon payments and the principal value of the bond. The market price of the bond is the sum of these present values.

### What factors can lead to a bond trading at a discount?

Bonds can trade at a discount due to various factors, including rising market interest rates, excess supply compared to demand, credit rating downgrades, and increased perceptions of default risk.

### How do bond discounts impact investors?

Bond discounts can affect investors in several ways. Investors who purchase bonds at a discount may benefit from potential capital appreciation at maturity. However, they may receive lower interest payments during the bond’s lifespan. It’s essential for investors to carefully consider the trade-offs and their specific financial goals.

### Are all bonds with discounts a good investment?

Not necessarily. While a bond discount can present an opportunity for capital gains, it’s crucial to assess the bond’s credit quality, maturity, and your own investment objectives. A discounted bond from a financially unstable issuer may carry a higher risk of default, so it’s important to conduct due diligence.

### What are zero-coupon bonds, and why are they often issued at a discount?

Zero-coupon bonds are bonds that do not make periodic interest payments. They are typically issued at a discount because the investor receives the face value at maturity. The discount is a way for investors to earn a return on their investment, despite not receiving regular interest payments.

### Can a bond be issued with a premium and later trade at a discount?

Yes, it’s possible for a bond initially issued at a premium to later trade at a discount. This can happen if market interest rates rise significantly, causing the bond’s market price to fall below its face value. In such cases, investors who purchased the bond at a premium may face capital losses.

### How can I calculate the yield to maturity (YTM) for a bond with a discount?

Calculating the yield to maturity for a bond with a discount involves considering both the present value of the bond’s future cash flows (coupon payments and principal repayment) and the current market price. The YTM reflects the annualized return you can expect if you hold the bond until it matures.

### What are the tax implications of buying bonds at a discount?

The tax treatment of bonds purchased at a discount varies by jurisdiction. In some cases, you may need to report the annual accretion of the discount as interest income, even though you don’t receive the interest until maturity. It’s advisable to consult with a tax professional to understand the specific tax rules applicable to your situation.

### Can a bond discount turn into a premium over time?

Yes, a bond that was initially issued at a discount can turn into a premium over time if market interest rates decrease significantly. As market rates fall, the bond’s coupon rate may become more attractive, causing its market price to rise above the face value.

## Key takeaways

• Bond discount is the difference between a bond’s market price and its principal amount due at maturity, often \$1,000.
• A bond issued at a discount has a market price lower than its face value, resulting in capital appreciation upon maturity.
• Bonds are sold at a discount when market interest rates surpass the coupon rate, making existing bonds less attractive.
• Calculating the bond discount involves finding the present value of coupon payments and principal value.
• Various factors, including rising interest rates and excess supply, can lead to bonds being sold at a discount.
###### View Article Sources
1. How to Price a Bond – Harvard Business School
2. Zero Coupon Bond – Securities and Exchange Commissions
3. What are Corporate Bond? – Securities and Exchange Commissions
4. Mastering Macaulay Duration: A Comprehensive Guide to Bond Investing – SuperMoney
5. What is Par Value in Stocks and Bonds? – SuperMoney