Namratha has the choice between investing in a city of Watkinsville bond at 4.5 percent or a Moe's, Inc. bond at 7 percent. Assuming that both bonds have the same nontax characteristics and that Namratha has a 32 percent marginal tax rate, in which bond should she invest? What interest rate offered by Moe's, Inc. would make Namratha indifferent between investing in the two bonds?

Question

What will be an ideal response?

Answer 1

Namratha's after-tax rate of return on the tax-exempt city of Watkinsville bond is 4.5 percent. The Moe's, Inc. bond pays taxable interest of 7 percent. Namratha's after-tax rate of return on the Moe's, Inc. bond is 4.76 percent (i.e., 7% interest income ? (7% × 32%) tax = 4.76%). Namratha should invest in the Moe's, Inc. bond.

For Namratha to be indifferent between investing in the two bonds, the Moe's, Inc. bond should provide Namratha the same after-tax rate of return as the city of Watkinsville bond (4.5 percent). To solve for the required pretax rate of return we can use the following formula: After-tax return = Pretax return × (1 ? Marginal Tax Rate).

Moe's, Inc. needs to offer a 6.62 percent interest rate to generate a 4.5 percent after-tax return and make Namratha indifferent between investing in the two bonds.

4.5% = Pretax return × (1 ? 32%);
Pretax return = 4.5%/(1 ? 32%) = 6.62%