Definition of Yield Equivalence

A yield to be offered by a taxable investment which should be equal to the tax free yield on a municipal bond.

The formula to calculate yield equivalence for a taxable security is:

Yield equivalence = Taxable Yield x (1 – Tax Rate)

The formula to calculate yield equivalence for a tax-exempt security is:

Yield Equivalence = Tax-Exempt Yield / (1 – Tax Rate)

Explanation of Yield Equivalence 

Suppose there is an investor who is trying to decide if to invest in the bonds of Company XYZ or in municipal bonds by City ABC. Yielding for Company XYZ bonds are 7% and 6% are yielding for City ABC. Tax bracket for him is 35%.

At first sight, we can be of the view that investor should go for the Company XYZ bonds (all else being equal). After all, the yield is higher, and the investor stands to make more money.

But there might be another answer once the investor accounts for the fact that he must pay taxes on the 7% he earns on those Company XYZ bonds and no taxes on the 6% earned from City ABC. Using the yield equivalence formula, we can calculate what the Company XYZ bond is really yielding after taxes:

Yield Equivalence = .07 x (1 – 0.35) = 0.0455 or 4.5%

Therefore, we can say that the Company XYZ bond yields 4.5% after taxes, and the City ABC bonds yield 6% after taxes. All else being equal, the City ABC bonds turn out to be the better option for the deal.

On the contrary, if we shall compare the two bonds on a taxable basis, we can apply the formula to the tax-exempt City ABC bonds in order to determine what they would have to yield if they were taxable:

Yield Equivalence = .06 / (1 – 0.35) = 0.0923 or 9.23%

Hence, the City ABC bonds would have to pay 9.23% if they were taxable (and that would compare favorably to the taxable 7% Company XYZ is offering). Also the investor’s tax bracket makes a big difference in these calculations. The higher it is, the bigger the disparity between the taxable and tax-free yields.