How to Calculate the Break-Even Interest Rate on Bonds

By Markets

Bond investors routinely have to make judgment calls about expectations on future conditions in the credit markets, including changes in prevailing interest rates and inflation. Using a break-even calculation can help assist investors to make those judgment calls in a more informed way. In particular, there are two situations that often come up where knowing a break-even interest rate can help you make better decisions.

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Situation 1: Comparing short-maturity bonds with long-maturity bonds
One common situation involves deciding the maturity of the bond you want to buy. Typically, bonds that mature further into the future offer higher rates than those that mature sooner. But if you think interest rates will rise, then you might prefer to take a lower rate now in exchange for being able to reinvest at a higher rate sooner in the future. In this case, the break-even interest rate will tell you how far prevailing rates would need to rise by the time the shorter-term bond matures in order to make up for its smaller interest payments.

To calculate the break-even interest rate, you need to know the yields to maturity, and the number of years left before the bonds mature. Take each bond's yield to maturity, add one to the yield, and then use an exponential calculation, raising the sum to the power of the number of years before maturity.

You'll have two results: one for the longer-term bond, and one for the shorter-term bond. Divide the longer-term bond result by the shorter-term bond result, and then do another exponential calculation, raising the number to the power of one divided by the difference in years of the two maturities. Subtract one from the result, and that gives you the break-even interest rate.

An example will make this clearer. Say you can invest in a five-year bond yielding 2%, or a 10-year bond yielding 3%. To calculate the break-even interest rate, take (1 + 0.02) ^ 5 for the five-year bond, and (1 + 0.03) ^ 10 for the 10-year bond. The resulting numbers are 1.10408 and 1.34392, respectively. Divide 1.34392 by 1.10408 to get 1.21723, and then take 1.21723 ^ (1 / (10-5)) to get 1.04010. Subtract one, and the final break-even interest rate is 4.01%.

This means that, in five years, you'd have to be able to buy another five-year bond yielding 4.01% in order to do as well as you would have buying the 10-year bond at 3% now.

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Situation 2: Inflation-indexed bonds
The other typical situation involves comparing a traditional bond with a bond with the same maturity date whose principal value automatically adjusts for inflation. In this case, you're calculating the break-even interest rate of inflation for which buying the inflation-indexed bond will provide a larger return.

Here, the calculation is simpler because the maturities are the same. Take the yield to maturity for each bond, and add one to it. Then divide the traditional bond's number by the inflation-indexed bond's number, and subtract one from the result. The final answer is the break-even inflation rate.

Again, for example, say you can choose between a 10-year traditional bond paying 3%, and a 10-year inflation-indexed bond yielding 1%. Divide 1.03 by 1.01, and subtract one, and the break-even rate of 1.98% represents the average annual inflation rate that would leave the two bonds equal at maturity.

Knowing the break-even interest rate is important in comparing bonds. With it, you can make your own predictions about what the future will bring, and then make a decision accordingly.

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