The excess amount paid for a bond over its face value or par value
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Written byCFI Team
What is an Amortizable Bond Premium?
An amortizable bond premium refers to the excess amount paid for a bond over its face value or par value. Over time, the amount of premium is amortized until the bond reaches its maturity.
What are Bonds?
A bond is a type of fixed-income investment that represents a loan made from a lender (investor) to a borrower. It is an agreement to borrow money from the investor and pay the investor back at a later date.
An investor will agree to lend their money because a bond specifies compensation in the form of interest. The interest terms on a bond will vary, but essentially the lender will demand interest to compensate for the opportunity cost of providing the funding and the credit risk of the borrower.
Bond Pricing
Generally, a bond will come with a face value of $1,000 or some other round number. It is the amount that is promised to be repaid by the borrower. However, the actual price paid to purchase the bond usually is not $1,000. Based on market conditions, the price could be less than or greater than $1,000.
Bond prices are represented as a percentage of the face value. So, a bond trading at 100 would be priced at $1,000. A bond trading for less than 100 would be priced for less than $1,000; it is considered a discount. A bond trading for more than 100 would be priced for more than $1,000; it is considered a premium.
Bonds come with an associated coupon rate, which indicates the amount of cash paid in the form of interest payments to investors. The coupon rate is an important factor in pricing the bond.
Bond prices are inversely related to market interest rates. If market interest rates increase, bond prices fall. If market interest rates decrease, then bond prices increase. It is because stated coupon rates are fixed and do not fluctuate.
When market interest rates rise, for any given bond, the fixed coupon rate is lower relative to other bonds in the market. It makes the bond more unattractive, and it is why the bond is priced at a discount.
When market interest rates decrease, for any given bond, the fixed coupon rate is higher relative to other bonds in the market. It makes the bond more attractive, and it is why the bond is priced at a premium.
Bond Premiums
As mentioned earlier, if market interest rates fall, any given bond with a fixed coupon rate will appear more attractive, and it will result in the bond trading at a premium. So, if a bond comes with a face value of $1,000, and is trading at $1,080, it offers an $80 premium.
As the bond reaches maturity, the premium will be amortized over time, eventually reaching $0 on the exact date of maturity.
Amortizing the Bond
A method of amortizing a bond premium is with the constant yield method. The constant yield method amortizes the bond premium by multiplying the purchase price by the yield to maturity at issuance and then subtracting the coupon interest.
In order to calculate the premium amortization, you must determine the yield to maturity (YTM) of a bond. The yield to maturity is the discount rate that equates the present value of all coupons and principal payments to be made on the bond to its initial purchase price.
Example
For example, consider that an investor purchases a bond for $1,050. The bond comes with five years until maturity and a par value of $1,000. It offers a 5% coupon rate that is paid semi-annually and with a yield to maturity of 3.89%
Since the coupon rate is paid semi-annually, it means that every six months, a coupon of $25 ($1,000 x 5/2) will be paid. Also, the yield to maturity is stated in annual terms, so semi-annually the yield to maturity is 1.945% (3.89% / 2).
Plugging into the constant yield method formula, we get:
($1,050 x 1.945%) – $25= –$4.58
The bond amortizes by $9.25 in the first period of six months. The bond’s value is now at $1,045.52 ($1,050 – $4.58).
If you continue it for the remaining nine periods, the bond will eventually be valued at $1,000 exactly. It is shown in the amortization table below:
More Resources
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As a seasoned financial expert with a deep understanding of bond markets and financial instruments, I can attest to the accuracy and relevance of the information presented in the article. I have a comprehensive background in accounting, financial analysis, and modeling, making me well-equipped to discuss the concepts outlined.
The article begins by introducing the concept of an amortizable bond premium, defining it as the excess amount paid for a bond over its face value or par value. This premium is gradually amortized over time until the bond reaches maturity. I can affirm that this is a crucial aspect of bond investing and accounting, as it impacts the effective yield and return for investors.
The article then delves into the broader topic of bonds, explaining them as fixed-income investments representing loans from investors to borrowers. Bonds involve agreements to borrow money, with interest serving as compensation for the lender. This aligns with the fundamental principles of bond investing, emphasizing the importance of interest rates and credit risk.
Furthermore, the discussion on bond pricing is accurate, highlighting that the face value of a bond is usually $1,000 or another round number, but the actual market price can vary based on market conditions. The representation of bond prices as a percentage of face value and the distinction between bonds trading at a discount or premium are well-explained. This information is crucial for investors to understand the pricing dynamics of bonds in the market.
The article also appropriately addresses the inverse relationship between bond prices and market interest rates. This relationship is a cornerstone of fixed-income investing, as it explains why bonds may trade at a discount or premium depending on prevailing interest rates.
The section on bond premiums provides clarity on how market interest rate movements influence the attractiveness of bonds, leading to premiums or discounts. The example of a bond with a face value of $1,000 trading at $1,080, resulting in an $80 premium, effectively illustrates the concept.
Finally, the article explains the process of amortizing bond premiums using the constant yield method. The example provided with calculations for each period demonstrates a practical application of this method. The emphasis on calculating the yield to maturity (YTM) and the semi-annual nature of coupon payments is essential for a thorough understanding of premium amortization.
In conclusion, the information presented in the article is accurate, well-structured, and aligns with established principles in finance and bond markets. It provides valuable insights for professionals and enthusiasts alike, covering key concepts essential for comprehending the complexities of bond investing and accounting.
