
Selling bonds at a premium can be a double-edged sword for issuers. By selling bonds at a premium, issuers can reap the benefits of higher proceeds upfront.
However, this approach also comes with some drawbacks. Issuers who sell bonds at a premium may end up paying a higher interest rate to investors, which can increase their borrowing costs over time.
The premium also reduces the effective yield of the bond for investors, making it less attractive compared to other investment options. This can lead to reduced demand for the bond and potentially lower credit ratings for the issuer.
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What is Unamortized Premium?
The unamortized premium is the difference between a bond's face value and its sale price. This excess amount is what remains of the bond premium that the issuer has not yet written off as an interest expense.
If a bond is sold at a premium, the issuer must still repay the full face value at par. This means the unamortized premium becomes a liability for the issuer.
For example, let's say a bond sells for $1,090 after interest rates decline. The difference between the selling price and par value is the unamortized bond premium, which is $90.
The unamortized premium will eventually be amortized, or written off, against expenses in the future. This means it will be credited as an interest expense, and the bondholder can choose to amortize the premium to reduce the amount of interest income included for taxes.
Key Concepts
If an issuer sells bonds at a premium, it means they're offering higher coupon rates, which can provide a more stable income stream. This is because premium bonds typically offer higher coupon rates than discount bonds.
You'll usually pay more upfront for premium bonds, which might result in a lower yield to maturity than the coupon rate. This is a trade-off for the potential stability of the bond's price.
Premium bonds can be less sensitive to interest rate fluctuations, offering some price stability.
Calculating Issue Price
Calculating issue price is a crucial step in understanding the value of a bond. The issue price of a bond is based on the relationship between the interest rate that the bond pays and the market interest rate being paid on the same date.
To determine the issue price, you need to consider the basic steps required, which involve comparing the bond's interest rate to the market interest rate. The bond's interest rate will either be higher or lower than the market rate, resulting in either a premium or discount price.
If a bond is sold at a premium, the issuer must still repay the full face value at par, which is a liability for the issuer. This is known as an unamortized bond premium, and it can be calculated using the bond's face value and sale price.
For example, if a bond is sold at 90 cents on the dollar, the issuer must still repay the full 100 cents of face value at par. The unamortized bond premium in this case is the difference between the bond's face value and its sale price.
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To calculate the unamortized bond premium, you can use the following steps:
- Multiply the selling price of the bond by the yield to maturity (YTM)
- Subtract the result from the coupon amount
- The remaining amount is the amortizable amount
Here's an example of how this works:
As you can see, the unamortized bond premium decreases over time as the premium is amortized. This is an important consideration for investors who purchase premium bonds, as they will receive back the face value at maturity, which will be less than the premium price they initially paid.
Benefits of Premium
Premium bonds offer several benefits that make them appealing to investors. One of the main advantages is that they often have more price stability than other bond categories.
The tax implications for premium bonds can be favorable, allowing you to amortize the premium, which means gradually writing off the extra cost over the bond's life. This can help reduce your taxable income.
Premium bonds deliver more of their total cash flows through higher coupon payments before the bond reaches maturity. This typically serves to dampen price fluctuations in response to changes in the market interest rates.
By converging with their face value as the maturity date nears, premium bonds can provide a more stable market price. This gives them an advantage for investors looking to preserve their capital while earning investment income.
Tax and Liquidity
Treasury bonds are subject to federal taxes but are generally exempt from state and local taxes.
Municipal bonds are often exempt from federal income taxes and sometimes from state and local taxes, while corporate bonds are taxable at the federal and state levels.
If you sell a bond at a higher price than you paid, you could be subject to capital gains tax on the profit.
Premium bonds offer certain structural benefits in a rising rate environment and are not subject to the layers of discounting that par/discount bonds face.
Due to the tax implications and complexity of discount bonds, they are generally less liquid than premium bonds.
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Tax Treatment of Premiums
If you sell a bond at a higher price than you paid, you could be subject to capital gains tax on the profit.
Treasury bonds are subject to federal taxes but are generally exempt from state and local taxes, while municipal bonds are often exempt from federal income taxes and sometimes from state and local taxes.
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Corporate bonds are taxable at the federal and state levels. This means you'll have to pay taxes on the interest income you earn from these bonds.
The good news is that you may be able to amortize the premium on premium bonds, which means gradually writing off the extra cost over the bond's life. This can help reduce your tax liability.
For example, if the bond's face value is $1,000 and the bond sells for $1,090 after interest rates decline, the difference between the selling price and par value is the unamortized bond premium ($90).
Liquidity
Discount bonds are generally less liquid than premium bonds due to tax implications and complexity. As of September 30, 2022, 5 percent coupons were the most prevalent in the municipal market, making them more liquid.
The market discount embedded in the bond itself is the first layer of discounting that sellers must offer to entice investors to purchase discount bonds. This can be a significant issue for intermediate-term bonds.
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For intermediate-term bonds, the present value of the future tax liability can make a significant difference in where the bond can be sold. This is less of an issue for longer-term bonds in which this liability is spread out over longer time periods.
Sellers of par/discount bonds must also offer an amount to compensate investors for the lower liquidity of these bonds.
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Example and Considerations
If an issuer sells bonds at a premium, the buyer pays more than the face value of the bond. The premium is essentially an upfront fee for the buyer to purchase the bond.
The issuer receives the face value of the bond, while the buyer gets a higher yield than the coupon rate. This is because the buyer is paying more upfront, so they need a higher return to make the investment worthwhile.
To understand the implications of buying a bond at a premium, consider the example of XYZ Corporation selling $1,000 bonds at a 5% premium. The buyer pays $1,050, but the issuer receives only $1,000.
The buyer's yield on the bond will be higher than the coupon rate, which is typically the case when buying bonds at a premium.
Differences and Comparisons
Selling bonds at a premium can be beneficial for both the issuer and the investor. This occurs when the market value of a bond exceeds its face value, allowing investors to buy the bond for more than its par value.
A bond with a par value of $1,000 is considered to be selling at a premium if it can be bought for more than $1,000. For example, if the market value is $1,100, it's selling at a premium.
The premium can arise from various factors, including a higher coupon rate compared to the current market interest rates. If a bond pays a 5% coupon with a face value of $1,000 and the market interest rate is 3%, the bond is selling at a premium.
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Differences Between Premium and Discounted Prices
A bond's market value can vary from its face value, selling at a premium if it's more than its par value, or at a discount if it's less.
If a bond's value exceeds its face value, it's selling at a premium, meaning you can buy it for more than its par value. For example, a bond with a par value of $1,000 can be bought for more than $1,000.
Conversely, a bond selling for less than its par value is discounted. This can happen when the bond's coupon rate is lower than the current market interest rates.
When interest rates increase, a bond's market price will fall and vice versa. This is because the bond's value is associated with interest rates. If you purchased a bond that pays a 5% coupon with a face value of $1,000 when the market interest rate was 3%, you can sell it for a profit if interest rates decrease by 1% after your purchase.
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Shorter Duration
Premium bonds offer a shorter duration than par/discount bonds, allowing investors to build income faster.
This shorter duration can improve total return if interest rates go up, as investors can reinvest the funds and take advantage of higher rates.

The higher income generated by increased coupon payments can help offset some of the price declines as rates rise.
Premium bonds historically have retained their value more so than discount bonds, making them more liquid in rising rate environments.
Investors can take advantage of premium bonds as a defensive position when rates rise, thanks to their ability to retain value and provide a higher income stream.
Sources
- https://www.investopedia.com/terms/u/unamortized-bond-premium.asp
- https://www.investopedia.com/ask/answers/186.asp
- https://www.debtbook.com/learn/blog/what-is-premium/discount
- https://www.breckinridge.com/insights/details/premium-bonds-101-2/
- https://www.accountingtools.com/articles/how-to-calculate-the-issue-price-of-a-bond.html
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