Most notes, bonds, and other debt that companies offer to investors pay interest on a regular basis. However, some debt issues are structured as non-interest-bearing notes or zero-coupon bonds. These securities don't pay regular interest, but they're priced at a substantial discount to their face value. The difference between the discounted price and the eventual maturity value represents the interest the investor will earn over the life of the bond, and both for tax purposes and to determine your return, you need to know how to calculate imputed interest on such securities.
Determining the rate of return
The first step in imputing interest on non-interest-bearing notes is to figure out the rate of return. To do so, you'll need to know the initial price of the bond, the length of the term until maturity, and the face value representing the final payment that investors receive at maturity.
To calculate the rate of return, divide the face value by the initial price of the bond. Then take that number and raise it to the power of 1 divided by the number of years of the bond's term. Subtract 1 from the final answer, and that will give you the annual rate of return.
For instance, say a zero coupon bond is issued for $800 and will pay $1,000 at maturity 10 years from now. Dividing $1,000 by $800 gives 1.25, and 1.25 raised to the 1/10th power gives 1.0226. Subtract 1, and you're left with 0.0226, or 2.26%.
Imputing interest with the constant-interest method
Once you have the rate of return, imputing interest is simple if you use the constant-interest method. Essentially, all you have to do is apply the rate of the return to the bond's imputed balance as of the year in question to come up with that year's imputed interest.
Again taking the previous example, in year 1, imputed interest would be $800 x 2.26% or about $18. You don't actually receive that money, though, so the imputed value of the bond as of the end of year 1 would be $800 plus $18 or $818. For year 2, take the new $818 value and multiply it by 2.26%, getting about $18.50. Repeat this method for the full 10-year period, and you'll eventually get imputed interest amounts that add up to $200 -- the difference between the initial price and the face value.
Knowing imputed interest is important not just to get a sense of whether a non-interest-bearing note is a good investment but also because the IRS will require you to treat imputed interest as taxable income. Calculating imputed interest in advance will help you avoid surprises down the road.
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