Amortizable Bond Premium

Last Updated: 2 Jan 2024

Bonds are among the popular financial securities issued by the government and big corporations to borrow money from the general public. bonds compensate investors with the interest in addition to principal repayment. Depending on the interest rates prevailing in the market, the price of bonds fluctuates. Investors may purchase bonds at a discount or premium.

This article highlights what is an Amortizable bond premium, the methods to calculate it and the constant yield method.

Amortizable Bond Premium

When the interest rate of a particular bond is higher than the market interest rates, it attracts investors. The higher demand leads the bond to trade at a higher market value than the par value. The bond premium is that additional portion of the market value of a bond other than the face value. For instance, a bond with a face value of Rs. 100 is traded in the market at Rs. 110, the Rs. 10 is bond premium. Amortization is the practice of writing off the initial cost gradually in regular periods.

Amortization of the bond premium is the practice of gradually writing off the bond premium over the life of the bond. Amortizable bond premium reduces the cost basis of the bond for each accrual. Cost basis means the adjusted purchase price of the bond, which holds importance for tax purposes. Bond premium forms a part of the cost basis of the bond. For each tax period, the cost basis is reduced by the amortized premium.

The amortizable bond premium is tax-deductible in the case of taxable bonds. The key benefit of amortizing the bond premium is that the amortized bond premium can set off the interest income from the bond. This aids in reducing the taxable income of the bondholder. Though in the case of tax-exempt bonds, amortized bond premium is not allowed to be set off against the taxable income.

Methods of Amortization of Bond premium calculation

Popularly there are two methods to calculate the amortization of bond premium. They are as under:

• Straight-line method

  According to the straight-line method, the amortized bond premium is constant for each accrual period. The amortized bond premium is calculated by dividing the total bond premium by the number of years.

  For example, if 100 bonds are purchased at Rs. 2600, which has a face value of Rs. 2500. The bond has a 10 years maturity period. Here, total bond premium is Rs. 10,000 (Rs. 100 premium/bond). The bond premium amortized each year will be Rs. 1000.

• Effective interest rate method

  The effective interest rate method of calculating amortized bond premium is relatively complex. This method considers the market interest rate. The amortized bond premium is calculated by the following formula.

  (Bond price * market interest rate) – (face value * coupon rate)

  For example, an investor purchased a bond for Rs. 2550. The maturity period is 5 years, and the face value of the bond is Rs. 2500. The coupon rate for bonds is 10% and the market rate of interest is 7%.

  The amortized bond premium = (2550 * 7%) – (2500 * 10%)
  = 178.5 – 250
  = -71.5

  For the next period, the bond premium will be calculated at Rs. 2478.5 (2550 – 71.5) price.

Amortizing Bond Premium with the Constant Yield

The constant yield method is used to amortize the bond premium for all the accrual periods. The constant yield method involves calculating the yield to maturity of the bond. Yield to maturity is the rate that equates the present value of the security’s future cash flow to its market value.

According to this method, the bond premium is amortized by multiplying the cost basis of the bond with the yield to maturity at the time of issuance and then subtracting the coupon payment.

For instance, An investor purchases a bond that is currently traded at Rs. 1100 in the market. Though, it was issued at Rs. 1000. On this bond, the yearly interest payout is Rs. 80. The coupon rate for the bond is 8%. The bond has a 10 years maturity period. The bond has a YTM of 6.67%.

As the bond pays interest annually, the first accrual period is at the end of the first year. The amortizable bond premium for the first accrual can be calculated as follows.

Amortizable bond premium = (1100 * 6.67%) – 80
= 73.37 – 80
= – 6.63

For the next period, the basis will equal the purchase price plus the amortized bond premium for the first year (1100 – 6.63 = 1093.37). The amortizable bond premium for the next accrual can be calculated as follows.

Amortizable bond premium = (1093.37 * 6.67%) – 80
= 72.93 – 80
= – 7.07

This process is continued for the next eight years. Ultimately, the amount of premium will be amortized at the end of maturity and equal to 1000 i.e. the face value.

To sum up, an amortizable bond premium is an additional price paid for the bond above its face value. Amortization of premiums is important for reducing tax. Various methods help to arrive at an amortizable bond premium amount for all accrual periods. For higher bond premium effective interest rate method is preferred and vice versa.