Bond break-even calculator

[kmiklas]

Anyone know of a calculator that will tell me if it makes sense to sell a bond at current market price? That the market price of the bond has “broken even,” and market price is >= holding to maturity, including taxes and the time value of money?

Simple example: BOT 1yT bill with a 5% yield; i.e. at 95. Assuming a tax bracket of 32%, that only Federal tax will be paid, and that the bond will be taxed marginally (?) the after-tax return will be around 3.5%(?).

Now if rates drop and the market price (after taxes) of the bond is equal to the keep-to-maturity yield, then it makes sense to sell and take profit sooner, so that the dollars can be reinvested.

This of course is a highly simplified example with just a T-bill—not a muni, corp, etc. It also has no coupon payments and associated reinvestment risk, FX risk for foreign bonds, etc.

The math gets complex quite fast.

Any good calculator recommendations?

My guess is that these formulae are proprietary… and I’ve got some Python coding ahead of me.

Ty, Keith

 

[ph1l]

I couldn't find a specific Bond break-even calculator, but I found some information on how to calculate the break-even interest rate on bonds. Would you like me to explain how to do this calculation? ¹

Source: Conversation with Bing, 6/17/2023
(1) How to Calculate the Break-Even Interest Rate on Bonds. https://www.fool.com/knowledge-center/how-to-calculate-the-break-even-interest-rate-on-b.aspx.
(2) How to Calculate the Break-Even Interest Rate on Bonds. https://www.nasdaq.com/articles/how-calculate-break-even-interest-rate-bonds-2016-02-21.

Sure! 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.

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.

For example, 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.

 

[kmiklas]

Thank you!!!