Given the planned rise in marginal tax rates it’s a sure bet that interest in tax-free investments will also be rising. Comparing of taxable vs. other taxable rates of return is quite simple and the same for comparing tax-free instruments against each other but how do we compare taxable vs. non-taxable products? The answer is by converting one side to it’s equivalent rate. In other words, if we want to know how a 4% tax-free municipal bond relates to taxable bonds then we must first convert the tax-free rate to it’s equivalent taxable rate. This short article will demonstrate the methods for converting either rate to it’s equivalent.

Conversion of tax-free rate to it’s equivalent taxable value.

The mathematics are quite simple and there is a nice general formula you may use.

Tax-equivalent yield = return rate / (1 – your tax rate)

As an example if your marginal tax rate is 25% and you are considering a 4% municipal bond then to earn the same return from a taxable bond would require:

Y_taxable = 4 %/ (1 –.25) = 4%/0.75 = 5.33%

So it would take a coupon of 5.33% on a taxable corporate bond to give you the same income. Notice the direct relationship between your tax rate and the taxable return needed to equal the tax-free rate. Using the same example but changing the person’s top marginal rate to 40% the equivalent rate now becomes:

Y_taxable = 4 %/ (1 –.40) = 4%/0.60 = 6.67%

Conversion of a taxable rate to equivalent tax-free value.

This is just as simple but our formula is now:

Tax free yield = return rate * ( 1 – your tax rate)

Using our previous example to double check. If you have top marginal rate of 40% then a 6.67% taxable bond would be equivalent to

Y_tax-free = 6.67% * ( 1 – 0.40) = 6.67% * 0.6 = 4%

As promised at the club discussion here is a quick review of the most common properties of working with exponents that you will need to remember. If you took notes when we were talking these will match your notes. There are many exponent properties but these few will get you through most problems. Feel free to let me know if you would like a more through review, some more complicated examples, etc. Our goal to provide information at the level the club needs.

Property 1:

Example: 2²2³ = (2 • 2) • (2 • 2 • 2) = 32 = 2⁵

Property 2:

Example: 2⁴/2² = 2^4-2 = 2² = 4

Property 3:

Example: (2⁴)² = 2^{4 • 2} = 2⁸

Property 4:

Example: 5⁰ = 1

Property 5:

Example: 2^-2 = 1/2² = 1/4

Property 6:

Example: (2 • 3)³ = 2³ • 3³

Property 7:

Example: (2/3)³ = 2³/3³