Bond Discount: Definition, Example, Vs. Premium Bond

A bond discount occurs when a bond is sold or traded for less than its face value, also known as its par value. The face value is the amount the bond issuer promises to pay the bondholder upon maturity. For example, a bond with a $1,000 face value sold for $950 is trading at a discount of $50. This discount reflects the difference between the bond’s market price and its par value.

Bonds trade at a discount for several reasons, primarily tied to the relationship between the bond’s coupon rate (the interest rate it pays) and prevailing market interest rates. When market interest rates rise above a bond’s coupon rate, the bond becomes less attractive to investors because newer bonds offer higher yields. To compensate, the bond’s price falls below par, creating a discount. Other factors, such as credit risk or changes in the issuer’s financial health, can also contribute to a bond trading at a discount.

The discount is not a loss in the traditional sense. Investors who purchase a discounted bond still receive the full face value at maturity, assuming the issuer does not default. The difference between the purchase price and the face value represents additional return, effectively increasing the bond’s yield to maturity (YTM) above its coupon rate.

Why Do Bonds Trade at a Discount?

To understand bond discounts, it’s crucial to grasp the inverse relationship between bond prices and interest rates. When market interest rates increase, the fixed coupon payments of existing bonds become less competitive. For instance, if a bond pays a 3% coupon while new bonds offer 5%, investors will demand a lower price for the older bond to align its yield with current rates. This price adjustment results in a discount.

Credit risk is another factor. If an issuer’s credit rating declines, investors may perceive the bond as riskier, demanding a higher yield to compensate for the increased likelihood of default. This pushes the bond’s price below par. Additionally, macroeconomic factors, such as inflation expectations or changes in monetary policy, can influence bond prices and contribute to discounts.

Calculating a Bond Discount

The bond discount is straightforward to calculate: it’s the difference between the face value and the market price. For example:

Face Value: $1,000
Market Price: $950
Discount: $1,000 – $950 = $50

However, understanding the financial implications requires calculating the bond’s yield to maturity, which accounts for both the coupon payments and the discount realized at maturity. The YTM is the internal rate of return (IRR) of the bond’s cash flows, factoring in the purchase price, coupon payments, and face value repayment. The formula for YTM is complex, but it can be approximated as follows for a bond with annual coupons:

YTM≈C+(F−P)n(F+P)2 YTM \approx \frac{C + \frac{(F – P)}{n}}{\frac{(F + P)}{2}} YTM≈2(F+P)C+n(F−P)

Where:

C = Annual coupon payment
F = Face value
P = Purchase price
n = Years to maturity

For precise calculations, financial calculators or software like Excel are often used, as the formula involves solving for the rate that equates the present value of future cash flows to the bond’s price.

Example of a Bond Discount

Let’s walk through a practical example to illustrate a bond discount and its impact on an investor.

Suppose you’re considering purchasing a corporate bond with the following characteristics:

Face Value: $1,000
Coupon Rate: 4% (paid annually, or $40 per year)
Maturity: 5 years
Market Price: $920

The bond is trading at a discount because its market price ($920) is less than its face value ($1,000). The discount is:

$1,000 – $920 = $80

Why is the bond discounted? Assume market interest rates for similar bonds have risen to 5%. The bond’s 4% coupon is less attractive, so its price adjusts downward to offer a competitive yield.

To calculate the yield to maturity, we consider the bond’s cash flows:

Annual Coupon Payments: $40 for 5 years
Face Value at Maturity: $1,000
Purchase Price: $920

Using a financial calculator or iterative methods, the YTM is approximately 5.6%. This yield is higher than the coupon rate because the investor benefits from both the annual $40 payments and the $80 gain when the bond matures at $1,000. The YTM reflects the total return if the bond is held to maturity, assuming no default.

Now, let’s consider the investor’s experience. By purchasing the bond for $920, they receive $40 annually for five years, totaling $200 in coupon payments. At maturity, they receive $1,000, resulting in an $80 capital gain. The total cash received is $1,200 ($200 in coupons + $1,000 face value), yielding a profit over the $920 investment. The YTM of 5.6% aligns with market rates, making the bond a viable investment despite its lower coupon.

Tax Implications of a Bond Discount

For taxable accounts, bond discounts have specific tax considerations. In the U.S., the IRS distinguishes between two types of discounts: market discount and original issue discount (OID).

Market Discount: When a bond is purchased at a discount in the secondary market (e.g., due to rising interest rates), the difference between the purchase price and the face value is treated as ordinary income when the bond matures or is sold. Investors can choose to accrue this income annually or report it at maturity.
Original Issue Discount: If a bond is issued at a discount (e.g., a zero-coupon bond), the discount is treated as interest income, accrued over the bond’s life. Investors report this income annually, even if no cash is received until maturity.

Tax rules vary by jurisdiction, so investors should consult a tax professional to understand their obligations.

Bond Discount vs. Premium Bond

To fully grasp bond discounts, it’s helpful to compare them with premium bonds, which trade above their face value. The key differences stem from the relationship between the bond’s coupon rate and market interest rates.

Premium Bond Definition

A premium bond is sold or traded for more than its face value. For example, a $1,000 face value bond trading at $1,050 has a $50 premium. Premiums occur when a bond’s coupon rate exceeds market interest rates, making it more attractive than newer bonds with lower yields. Investors are willing to pay extra for the higher coupon payments.

Example of a Premium Bond

Consider a bond with:

Face Value: $1,000
Coupon Rate: 6% (paid annually, or $60 per year)
Maturity: 5 years
Market Price: $1,080

The bond trades at a premium because its 6% coupon is higher than the market rate of, say, 4%. The premium is:

$1,080 – $1,000 = $80

The YTM for this bond, calculated similarly to the discount example, is approximately 4.2%, lower than the coupon rate because the investor pays $1,080 upfront but receives only $1,000 at maturity. The premium effectively reduces the yield, aligning it with market rates.

Key Differences

Coupon Rate vs. Market Rate:
- Discount Bond: Coupon rate is lower than market rates, causing the price to fall below par.
- Premium Bond: Coupon rate is higher than market rates, pushing the price above par.
Yield to Maturity:
- Discount Bond: YTM is higher than the coupon rate due to the capital gain at maturity.
- Premium Bond: YTM is lower than the coupon rate due to the capital loss at maturity.
Investor Perspective:
- Discount Bond: Appeals to investors seeking higher yields and potential capital gains, assuming they hold to maturity.
- Premium Bond: Attracts investors who value higher coupon payments, even if the overall yield is lower.
Price Behavior:
- Discount Bond: Price rises toward par as maturity approaches, assuming stable interest rates.
- Premium Bond: Price falls toward par as maturity nears, assuming stable rates.

Which Is Better?

The choice between discount and premium bonds depends on investor goals, tax considerations, and market outlook. Discount bonds may appeal to those anticipating stable or declining interest rates, as the bond’s price could rise. Premium bonds suit income-focused investors who prioritize higher cash flows. However, both can be profitable if aligned with the investor’s strategy and held to maturity.

Risks and Considerations

Investing in discounted or premium bonds carries risks:

Interest Rate Risk: Rising rates can further depress discount bond prices, while falling rates may reduce the value of premium bonds’ high coupons.
Credit Risk: Discounted bonds from issuers with poor credit ratings carry higher default risk.
Liquidity Risk: Some bonds, especially those trading at deep discounts, may be harder to sell.
Tax Complexity: As noted, discounts and premiums have unique tax treatments that can affect after-tax returns.

Practical Applications

Bond discounts and premiums are not just theoretical concepts—they impact real-world investing. For example:

Portfolio Diversification: Discount bonds can enhance yield in a fixed-income portfolio.
Retirement Planning: Premium bonds may suit retirees seeking steady income.
Market Timing: Savvy investors may buy discounted bonds during high-rate environments, anticipating price appreciation if rates fall.

Conclusion

Bond discounts and premium bonds are two sides of the same coin, driven by the interplay of coupon rates, market rates, and investor demand. A bond trading at a discount offers the potential for capital gains and higher yields, while a premium bond provides higher coupon payments at the cost of a lower overall return. By understanding these dynamics, investors can make informed decisions that align with their financial goals. Whether choosing a discounted bond for its yield or a premium bond for its income, the key is to evaluate the bond’s YTM, risks, and tax implications.