Calculating interest expense on a payable bond should be relatively straightforward, but then the accountants got involved. Generally accepted accounting principles, or GAAP, turn what is ordinarily a simple multiplication problem into something slightly more complicated.

With some examples, I'll show how to calculate interest expense under three scenarios: bonds sold at a discount, at premium, and at face value.

Calculating interest expense for bonds sold at a discount
Let's start first with bonds issued at a discount. Assume XYZ Corp. sells $100,000 of five-year bonds with a semiannual coupon of 5%, or 10% per year. Investors think the company is risky, so they demand a 12% yield to maturity for buying these bonds.

The first step is to use a finance calculator to calculate how much the company will receive from selling these bonds by entering the following information into a financial calculator:

Future value: $100,000 (The face value of the bonds).
Number of periods: 10 (5 years of semiannual payments).
Payment: $5,000 (5% semiannual coupon multiplied by the face value).
Rate: 6% (12% yield-to-maturity divided by two semiannual periods).

Solve for the present value.

The result is that the company receives only $92,639.91 from selling these bonds. Thus, the bonds are sold at a discount of $7,360.09 ($100,000 in face value minus proceeds of $92,639.91).

Interest expense calculations
Every six months, XYZ Corp. will naturally have to pay its bondholders cash coupons of $5,000. This is clearly interest expense. However, it isn't the only amount recorded as interest expense on a bond sold at a discount.

The discount on the bonds of $7,360.09 is an additional cost of financing. GAAP requires that the discount is amortized into interest expense over time.

To calculate the interest expense for the first period, we take the $92,639.91 carrying value of the bonds and multiply it by half the yield-to-maturity. This results in $92,639.91*(0.12/2)=$5,558.39 of interest expense for the first semiannual period.

The actual cash interest paid was only $5,000 -- the coupon multiplied by the bond's face value. However, interest expense also includes the $558.39 of amortized discount in the first six months.

To calculate interest expense for the next semiannual payment, we add the amount of amortization to the bond's carrying value and multiply the new carrying value by half the yield to maturity. Here's what the math looks like for the full five-year period.

Discount Amortization

Bonds sold at a premium
Whereas the discount on a bond is recorded as additional interest expense, the premium on a bond is recorded as a reduction in interest expense.

Let's use the same example. Suppose XYZ Corp. issues $100,000 of bonds that pay a semiannual coupon of 5%, or 10% per year. These bonds are seen to be very attractive, and investors think the borrower is too good of a risk to pay 10% per year. Thus, the bonds sell at a yield to maturity of 8%, resulting in a premium.

The first step is to use a finance calculator to calculate how much the company will receive from selling these bonds by entering the following information into a financial calculator:

Future value: $100,000 (the face value of the bonds).
Number of periods: 10 (five years of semiannual payments).
Payment: $5,000 (5% semiannual coupon multiplied by the face value).
Rate: 4% (8% yield to maturity divided by two semiannual periods).

Solve for the present value.

You should find that the present value is $108,110.90. Thus, the bonds were sold at a premium of $8,110.90 ($108,110.90 in proceeds minus $100,000 in face value).

Interest expense calculations
To calculate interest expense on these bonds, we take the carrying amount of the bonds ($108,110.90) and multiply it by half the annual yield to maturity (8%/2=4%) to get $4,324.44 in interest expense.

Of course, the actual cash interest expense is still $5,000. However, the premium is amortized as a reduction to interest expense. Thus, interest expense is recorded as $4,324.44 for the first period, while $675.56 is recorded as premium amortization.

To calculate interest expense for the next semiannual payment, we subtract the amount of amortization from the bond's carrying value and multiply the new carrying value by half the yield to maturity. Here's what that looks like over the full five-year period.

Premium Amortization

Bonds sold at face value
You're in luck. When bonds are sold at face value, the amount of interest expense is simply the coupon for each payment multiplied by the face value. Thus, using our previous example of $100,000 in XYZ Corp. bonds with a 5% semiannual coupon, the company would record interest expense of $5,000 ($100,000*5%) for every period. There is no premium or discount to amortize, and thus interest expense should equal the coupon rate multiplied by the face value of the bond.

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