Assume that John Richards pays income taxes at a 30 percent rate. He currently owns a not-for-profit (municipal) bond that pays 5 percent interest. What interest rate would have to be set on a for-profit (corporate) bond to produce the same amount of usable (after-tax) income?

• A. 5 percent
• B. 7.1 percent
• C. 6.0 percent
• D. 7.5 percent

Answer: (B)

When comparing a tax-exempt municipal bond to a taxable corporate bond, you must account for taxes. The municipally issued 5% interest is tax-exempt, so its after-tax income is 5%. To match that with a taxable corporate bond, the yield must be high enough that after paying taxes you still get 5%: after-tax yield = yield × (1 − tax rate) = y × 0.70. Set 0.70y = 0.05 and solve for y: y = 0.05 / 0.70 ≈ 0.07143, or about 7.14%. The closest option is 7.1%, which yields about 4.97% after tax, very close to 5%.