John Doe is in the 40 percent personal tax bracket. He is considering
investing in HCA bonds that carry a 12 percent interest rate.
a. What is his after-tax yield (interest rate) on the bonds?
b. Suppose Twin Cities Memorial Hospital has issued tax-exempt bonds
that have an interest rate of 6 percent. With all else the same, should
John buy the HCA or the Twin Cities bonds?
c. With all else the same, what interest rate on the tax-exempt Twin Cities bonds would make John indifferent between these bonds and
the HCA bonds?
a.
At 12% yield, with 40% going back to IRA, he nets 12%(1-0.4)=7.2%
b. and c
dependent on answer of a, will give you a chance to try them.
Sorry, meant
"going back to IRS"
4 Jane Smith currently holds tax-exempt bonds of Good Samaritan Healthcare that pay 7 percent interest. She is in the 40 percent tax bracket. Her broker wants her to buy some Beverly Enterprises taxable bonds that will be issued next week. With all else the same, what rate must be set on the Beverly Bond to make Jane interested in making a switch?
a. To calculate John Doe's after-tax yield on the HCA bonds, we need to calculate the amount of interest he will receive after taxes.
i. Calculate the after-tax interest by multiplying the interest rate (12%) by (1 - tax rate). The tax rate is the complement of John's personal tax bracket, which is 1 - 0.40 = 0.60.
After-tax interest = 12% * (1 - 0.40)
After-tax interest = 12% * 0.60
After-tax interest = 0.12 * 0.60
After-tax interest = 0.072 or 7.2%
Therefore, John's after-tax yield on the HCA bonds is 7.2%.
b. To determine whether John should buy the HCA or Twin Cities bonds, we need to compare their after-tax yields.
The after-tax yield on Twin Cities bonds is equal to the interest rate (6%) multiplied by (1 - tax rate). In this case, the tax rate is also 0.40.
After-tax yield on Twin Cities bonds = 6% * (1 - 0.40)
After-tax yield on Twin Cities bonds = 6% * 0.60
After-tax yield on Twin Cities bonds = 0.06 * 0.60
After-tax yield on Twin Cities bonds = 0.036 or 3.6%
Comparing the after-tax yields, we can see that the HCA bonds have a higher yield (7.2%) compared to the Twin Cities bonds (3.6%). Therefore, John should buy the HCA bonds.
c. To determine the interest rate on the tax-exempt Twin Cities bonds that would make John indifferent between the HCA and Twin Cities bonds, we need to find the point where their after-tax yields are equal.
Let's assume the interest rate on the Twin Cities bonds is x%.
Then the after-tax yield on the Twin Cities bonds would be x% * (1 - tax rate), which should be equal to the after-tax yield on the HCA bonds (7.2%).
x% * (1 - 0.40) = 7.2%
x% * 0.60 = 7.2%
x% = 7.2% / 0.60
x% = 12%
Therefore, a tax-exempt Twin Cities bond with an interest rate of 12% would make John indifferent between the HCA bonds and the Twin Cities bonds.