A tax-exempt municipal bond has a yield of 2.19%. What should be the yield (in %

Question

A tax-exempt municipal bond has a yield of 2.19%. What should be the yield (in %, to the nearest 0.01%) on an otherwise similar corporate bond to make an investor with the 34% marginal tax rate indifferent between the two bonds? E.g., if your answer is 7.145%, record it as 7.15.

You invested in a one-year debt security and realized a pre-tax return of 6.99% for the year. You happen to be in the 43% tax bracket. Inflation during the year was 0.3%. What is your realized after-tax real return, in %, to the nearest 0.01%? E.g., if your answer is 2.254%, record it as 2.25.

Explanation / Answer

1.required yield on similar corporate bond = yield on tax exempt / (1 - tax rate)

=> 2.19% / (1-0.34)

=>3.32%.

at yield of 3.32% for corporate bond the investor will be indifferent between two bonds.

2.after tax return = pre tax return *(1 - tax rate)

=>6.99% *(1- 0.43)

=>3.9843%.

after tax real return =[ (1+after tax return) / (1+inflation rate)] - 1

=>[(1.039843) / (1.003)]-1

=>3.67%

after tax real return = 3.67%.

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