Amortization Calculations in the Constant Interest Method

Amortization is an accounting technique to convert certain assets and liabilities into expenses or income over a period of years. Companies use amortization for a number of applications, such as amortizing premium on bond investments. You can calculate the annual amortization in a few different ways, including the constant yield method, sometimes called the constant interest method or the yield-to-maturity method.

The Internal Revenue Service requires you to use the constant yield method to amortize bond premium, which is the excess of bond price over face value. You pay the bond price and, if you hold the bond until maturity, receive the face value. This creates a loss, but you can’t deduct the loss all at once. Instead, you amortize the bond over its remaining lifetime to expense part of the loss each year. The amortized amount reduces the interest income you receive for investing in the bond.

The first step is to determine your yield to maturity, which is the discount rate that equates the present value of the bond to the price you paid. You need a financial calculator or spreadsheet to figure the yield, using the bond interest rate, face value, price and years to maturity as inputs. Select an “accrual period,” which is how long you accumulate amortization before recognizing it as an expense. You normally set the accrual period equal to the time interval between interest payments. You’re now ready to calculate the amortization for the period.

Start with the cost basis of the bond. In the first period, this is the purchase price, but in each subsequent period, it’s the original price reduced by the amount already amortized. Multiply the cost basis by the yield to maturity adjusted for the length of the period. For example, if your yield is 12 percent annually, use 6 percent for a semi-annual accrual period. Subtract the result from the interest payment for the period to find the accrual amount.

Your company buys a newly issued $100,000 bond that matures in exactly seven years and pays 10 percent interest once per year. You pay $110,000, resulting in a $10,000 premium to amortize. You determine your yield to maturity to be 8.07439 percent, and you set your accrual period to one year, coinciding with the interest payment date. Multiply the yield by the adjusted cost basis, which in the first year is $110,000. The result is $8,881.83, which you subtract from the annual interest payment of $10,000, giving an amortization amount of $1,118.17. Use this amount to reduce the cost basis and to offset interest income.