Comparing Tax-Free and Taxable Bonds

Here's a little calculator that allows you to compare municipal bond yields to those offered on taxable investments (thanks to Sound Money Tips for the link). However, in case you're interested, here's the math behind the calculations.

Let's assume that you are in the 25% marginal tax rate (to see your actual tax rate, look at the table at the bottom of the page where the calculator is located). This means that if you earn an additional dollar, the government takes $0.25 of it in taxes. So, if you're in this bracket, you "keep" 75% (i.e. 1 - 0.25) of any additional taxable income that you earn.

So, for any taxable interest rate TI and any tax rate t, your after-tax interest (ATI) would be:
TI x (1-t) = ATI
Since the interest on municipal bonds is tax exempt, their after tax interest rate is the same as their stated rate.

So, assuming this 25% marginal tax bracket. let's compare a taxable bond paying 6% to a municipal bond paying 5%. The after tax interest on the taxable bond is
6% (1-0.25) = 4.5%
Since this is lower than the interest rate on the municipal bond (5%), the municipal bond is a better investment, since it gives you a higher after tax yield.

Next, what would the taxable bond have to pay in order to make it as attractive as the municipal bond? To answer this, start with the same equation:
TI x (1-t) = ATI
With a little algebra, you can solve for the equivalent taxable interest:
ATI / (1-t) = TI

or, in our specific example,

5%/(1-.25) = 6.33%
So, in this case, in order for a taxable investment to be as attractive as the municipal bond, it would have to yield 6.33%. If it paid this interest rate, it would provide the same after-tax return (5%) as the taxable bond.

Finally, here's how you calculate the tax rate that would make you indifferent between the taxable and tax-free investments. Start with the same basic equation, and solve for "t":
TI x (1-t) = ATI;

solving for "t",

t = 1 - (ATI/TI)
Using the information from this example, t = 1 - 5/6 or 16.67%. So, if you were in the 16.67% tax bracket, the two investments would give you an identical after-tax return (in this case, of 5%). If your tax bracket is above this rate, the municipal bond would be preferred, and if your bracket is lower than this, you'd prefer the taxable bond.