Finance help please homework?

Question

Kim Davis is in the 40% person 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 bonds?

b.  Suppose Twin Cities Memorial Hospital 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?

The book gives a AT=BT x (1-t) formula but I do not understand this at all if someone could please explain

Prof · Answer

The formula means that the After tax return = Before tax return * (1 - tax rate). but you don't need the formula to solve the problem.

Assume an investment amount, e.g. $10,000. Then the Before tax return is $10,000 * .12 = $1,200. But you have to pay 40% in tax, $1,200 * .40 = $480, leaving you $720 of interest income.

In the formula AT = $1,200 * (1 - .4) = $1,200 * .6 = $720. In other words, the after tax yield on the bonds is $720.

Now when you divide $720 by the $10,000 investment, you have a return of 7.2 percent ($720 / $10,000 = .072). The tax exempt bonds yield 6% tax free, but that is only $600 on the $10,000 investment. Now you should be able to answer b and c parts of the problem.

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Finance help please homework?

2 Answers