How to Calculate Premium on Bonds Payable

Bonds payable are a significant form of long-term debt used by corporations and governmental entities to raise capital. An organization issues bonds to borrow money from investors, promising regular interest payments and repayment of the principal on a specified future date. This financial instrument is recorded as a liability on the issuer’s balance sheet.

A bond premium occurs when a bond is issued for a price greater than its face (par) value. This situation arises because the bond’s stated interest rate, also known as the coupon rate, is higher than the prevailing market interest rate for similar bonds at the time of issuance. Investors are willing to pay more for the bond to secure the higher periodic interest payments it offers compared to current market alternatives.

Understanding Key Bond Terminology

Understanding bond terminology is fundamental for comprehending bond premium calculations.

The face value, also called par value or maturity value, is the principal amount the bond issuer promises to repay to the bondholder at maturity. This value, typically $1,000, serves as the basis for calculating cash interest payments. The face value is the amount that will be returned to the investor when the bond reaches the end of its life.

The stated interest rate, or coupon rate, is the fixed annual interest rate printed on the bond. This rate calculates the cash interest payments the issuer pays to bondholders. For example, a $1,000 face value bond with a 5% stated rate pays $50 in cash interest annually.

The market interest rate, or yield to maturity, is the prevailing interest rate that investors demand for bonds of similar risk and maturity in the financial markets at a given time. This rate fluctuates based on economic conditions and the creditworthiness of the issuer. The relationship between the stated interest rate and the market interest rate determines whether a bond is issued at a premium, discount, or par value. If the stated rate exceeds the market rate, the bond sells at a premium.

The maturity date is when the bond’s face value is due to bondholders. The interest payment frequency dictates how often payments are made, commonly semi-annually or annually. This frequency is important for calculating the number of interest periods.

Initial Calculation of Bond Premium

Calculating the initial bond premium involves determining the bond’s issue price, the present value of its future cash flows, and comparing it to the bond’s face value. A premium arises when the stated interest rate leads investors to pay more than face value, as the bond’s future cash interest payments are more appealing than market alternatives.

The issue price of a bond is calculated by discounting two components: the present value of the bond’s face value and the present value of its future interest payments. Both components are discounted using the market interest rate, not the stated interest rate. The market rate reflects the true return investors demand for similar risk at the time of issuance.

To begin the calculation, determine the present value of the bond’s face value, which is a single lump-sum payment received at maturity. This requires using a present value of a single amount factor, based on the market interest rate and the number of interest periods. For instance, a $100,000 face value bond maturing in five years with semi-annual interest payments would involve 10 periods (5 years 2 payments/year) and the semi-annual market interest rate.

Next, calculate the present value of the series of future interest payments, which constitutes an annuity. The cash interest payment for each period is determined by multiplying the bond’s face value by its stated interest rate and adjusting for the payment frequency (e.g., dividing the annual stated rate by two for semi-annual payments). This periodic cash interest payment is then multiplied by the present value of an ordinary annuity factor, again using the market interest rate and the total number of interest periods.

Once both present values are determined, sum them to arrive at the bond’s issue price. The bond premium is the difference between this issue price and the bond’s face value. For example, if a $100,000 face value bond is issued for $106,000, the premium is $6,000.

Consider a bond with a $1,000 face value, a 6% stated annual interest rate paid semi-annually, and a five-year maturity. If the market interest rate is 4% annually (2% semi-annually), the semi-annual cash interest payment is $30 ($1,000 0.06 / 2). The present value of the $1,000 face value, discounted at 2% over 10 periods, is $820.35, and the present value of the 10 semi-annual $30 interest payments is $269.45. Summing these, the issue price is $1,089.80, resulting in a bond premium of $89.80.

Amortization of Bond Premium

After a bond is issued at a premium, the initial premium amount must be systematically reduced over the bond’s life through a process called amortization. The purpose of amortizing a bond premium is to adjust the bond’s carrying value on the balance sheet and to ensure the interest expense recognized each period accurately reflects the effective interest rate. By the bond’s maturity date, the premium will be fully amortized, and the bond’s carrying value will equal its face value.

Two primary methods are used for bond premium amortization: the straight-line method and the effective interest method. The choice of method impacts the amount of interest expense recognized each period. Both methods systematically reduce the premium.

Straight-Line Method

The straight-line method is a simpler approach where the total bond premium is divided equally by the number of interest periods over the bond’s life. This results in a constant amortization amount each period. For example, if a $6,000 premium is amortized over 10 semi-annual periods, $600 ($6,000 / 10) would be amortized each period. This constant amortization amount leads to a constant reduction in the recorded interest expense over the bond’s life.

Effective Interest Method

The effective interest method is generally required under accounting standards such as Generally Accepted Accounting Principles (GAAP) and International Financial Reporting Standards (IFRS) because it provides a more accurate reflection of the true cost of borrowing. This method calculates interest expense based on the bond’s carrying value and the market interest rate at the time of issuance. The premium amortization amount then represents the difference between the cash interest paid and the calculated interest expense.

To apply the effective interest method:
Calculate cash interest paid (face value stated rate).
Determine interest expense (bond’s carrying value market rate).
Premium amortization is the difference between cash interest paid and interest expense.
Update the bond’s carrying value by subtracting the amortization.
This results in varying amortization but ensures a constant effective interest rate.

For instance, if cash interest paid is $3,000 and the calculated interest expense is $2,800, the premium amortization for that period is $200. This $200 reduces the premium on bonds payable account, and also effectively reduces the interest expense reported. This process systematically aligns the bond’s carrying value with its face value by maturity.