Roger Cuddy

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%