Kim Davis is in the 40% personal tax bracket. She is considering investing in HCA (taxable) bonds that carry a 12% interest rate.

a. What is her after-tax yield (interest rate) on the bonds?
b. Suppose Twin Cities Memorial has issued tax exempt bonds that have an interest rate of 6%. With all else the same, should Kim 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 Kim indifferent between these bonds and the HCA bonds?
Please help I am lost

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a. Kim's after-tax yield on the bonds is 7.2%. This is calculated by taking the 12% interest rate and subtracting 40% of that (4.8%) to get the after-tax yield.

b. Kim should buy the Twin Cities bonds, since the after-tax yield on the tax-exempt bonds is 6%, which is higher than the after-tax yield on the HCA bonds (7.2%).

c. Kim would be indifferent between the two bonds if the interest rate on the Twin Cities bonds was 8.4%. This is calculated by taking the 12% interest rate on the HCA bonds and subtracting 40% of that (4.8%) to get the after-tax yield (7.2%), and then adding the difference between the two yields (1.2%) to the Twin Cities bond rate (6%).

a. To calculate Kim's after-tax yield on the HCA bonds, we need to find out how much of the interest she will be able to keep after paying taxes. Assuming that the 40% personal tax bracket refers to the marginal tax rate, we can calculate her after-tax yield using the following formula:

After-tax yield = Interest rate * (1 - Tax rate)

After-tax yield = 12% * (1 - 40%) = 12% * 0.6 = 7.2%

Therefore, Kim's after-tax yield on the HCA bonds is 7.2%.

b. To determine which bonds Kim should buy, we need to compare the after-tax yield of both options. The HCA bonds have an after-tax yield of 7.2%, while the Twin Cities tax-exempt bonds have an interest rate of 6%. Since the interest on the Twin Cities bonds is tax-exempt, the after-tax yield is equivalent to the interest rate.

Comparing the two options, the HCA bonds offer a higher after-tax yield (7.2% > 6%). Therefore, Kim should buy the HCA bonds.

c. To find the interest rate on the Twin Cities tax-exempt bonds that would make Kim indifferent between the two options, we need to set the after-tax yield of the Twin Cities bonds equal to the after-tax yield of the HCA bonds. Let the interest rate on the Twin Cities bonds be x%.

After-tax yield of Twin Cities bonds = After-tax yield of HCA bonds
x% = 7.2%

To solve for x, we divide both sides of the equation by 100:
0.01 * x = 0.072

Dividing both sides by 0.01:
x = 0.072 / 0.01

x = 7.2%

Therefore, an interest rate of 7.2% on the tax-exempt Twin Cities bonds would make Kim indifferent between the two options.

To calculate Kim's after-tax yield on the HCA bonds, we need to determine the amount of taxes she would owe on the interest earned. The first step is to understand how the tax bracket works. The 40% personal tax bracket means that any income Kim earns above a certain threshold will be taxed at a rate of 40%.

a. To calculate the after-tax yield on the HCA bonds, we can use the following formula:

After-tax yield = Interest rate on bonds x (1 - Tax rate)

In this case, the interest rate on the HCA bonds is 12% and the tax rate is 40%. Plugging these values into the formula, we get:

After-tax yield = 12% x (1 - 40%) = 12% x 0.6 = 7.2%

So, Kim's after-tax yield on the HCA bonds is 7.2%.

b. To determine whether Kim should buy the HCA or the Twin Cities bonds, we need to compare their after-tax yields. The Twin Cities bonds are tax-exempt, meaning Kim would not owe any taxes on the interest earned from these bonds.

Comparing the after-tax yield of the HCA bonds (7.2%) to the interest rate of the Twin Cities bonds (6%), we can see that the HCA bonds have a higher after-tax yield. This means Kim would earn more money after taxes by investing in the HCA bonds.

Therefore, with all else the same, Kim should buy the HCA bonds rather than the Twin Cities bonds.

c. To find the interest rate on the tax-exempt Twin Cities bonds that would make Kim indifferent between the two options, we need to set the after-tax yield of the HCA bonds equal to the interest rate on the Twin Cities bonds.

Let's denote the interest rate on the tax-exempt Twin Cities bonds as "x".

Using the same formula as before:

After-tax yield on HCA bonds = Interest rate on Twin Cities bonds x (1 - Tax rate)

7.2% = x% x (1 - 40%)

Rearranging the equation and solving for x, we get:

x% = 7.2% / (1 - 40%)
x% = 7.2% / 0.6
x% ≈ 12%

So, in order for Kim to be indifferent between the HCA bonds and the tax-exempt Twin Cities bonds (meaning she would earn the same amount after taxes), the interest rate on the Twin Cities bonds would need to be approximately 12%.

I hope this helps clarify the calculations and answers to your questions!