Finance: Bond Question?

Question

The yield on a corporate bond is 7.5 percent, while the yield on a municipal bond with the same risk is 5.4 percent. At what tax rate would you be indifferent between the two bonds? The answer is 28%, but I do not know how to get that specifically.

Answer 1

The bond with the 7.5% yield will pay you $75, but 28% of it ($21) will go to Uncle Sam, leaving you with only $54.

The bond with the 5.4% yield will pay you $54. Since municipal bonds are not taxable by the IRS, you will get to keep the whole $54.

Now which bond is better? The one that leaves you with $54. or the one that leaves you with $54?

Answer 2

The formula for determining the "Taxable Equivalent Yield"  is Tax Exempt Yield/(1-tax rate)

In this case

.054/(1-.28)

.054/.72 =.075 (or 7.5%)

If you want to find out the tax rate for the problem, it is

1-(Tax Exempt Yield/Taxable Yield)

1-.(054/.075)

1-(.72) =.28  (your tax rate!)