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?
Twin Cities bond, a non-profit corporation, the investor would have to pay no taxes on the interest and would be able to keep the entire amount.
To calculate John Doe's after-tax yield on the HCA bonds, we need to consider his personal tax bracket.
a. After-tax yield on the HCA bonds:
1. Calculate the taxable interest earned on the bonds: 12% interest rate on the HCA bonds.
Taxable Interest = (12% * Amount Invested)
2. Calculate the tax paid on the interest earned:
Tax Paid = Taxable Interest * Tax Bracket (40%)
3. Calculate the after-tax yield:
After-tax Yield = 12% - Tax Paid
b. To compare the HCA bonds with tax-exempt Twin Cities bonds, we need to calculate the after-tax yield on the Twin Cities bonds as well. Since the Twin Cities bonds are tax-exempt, the after-tax yield will be the same as the stated interest rate.
c. To calculate the interest rate on the Twin Cities bonds that would make John indifferent between the two options, we need to set the after-tax yield on the Twin Cities bonds equal to the after-tax yield on the HCA bonds:
After-tax Yield on Twin Cities bonds = After-tax Yield on HCA bonds
Now, let's proceed with the calculations:
a. After-tax yield on the HCA bonds:
Taxable Interest = 12% * Amount Invested
Tax Paid = Taxable Interest * Tax Bracket (40%)
After-tax Yield = 12% - Tax Paid
b. After-tax yield on the Twin Cities bonds = Interest rate of the Twin Cities bonds
c. Set After-tax Yield on Twin Cities bonds equal to After-tax Yield on HCA bonds:
After-tax Yield on Twin Cities bonds = After-tax Yield on HCA bonds
Now, solve the equation for the interest rate on the Twin Cities bonds that would make John indifferent between the two options.