Question

Let's see if we can figure this one out. Actually, it is pretty easy. There are two one-year discount bonds in the market. One of them is a municipal bond issued by a city government to raise money to invest in a desalination plant. This bond is tax-free. The other is a Treasury bond issued by the U.S. Treasury Department to finance the government's spending on various programs. This bond is NOT tax-free. You have to pay a tax on the interest you earn from this bond. So, for example, if you earn $100 from this bond in interest and the tax rate is 20%, then you will have to pay 0.20 x $100 = $20 to the government and will get to pocket only $80. Obviously, you care about the after-tax interest income. Both bonds are risk-free. Suppose the interest rate on the tax-free municipal bond is 7.5% and the average tax rate is 25%. Then, arbitrage will ensure that the interest rate on the Treasury bond equals percent.

Answer 1

arbitrage will ensure that the interest income of the two bonds should be equal.

interest rate of municipal bond is 7.5%

tax rate is 25%, investor has to give 25% of the interest earned on the Treasury bond as tax to the government.

lets assume the investor has 100$ with him, arbitrage will ensure that the interest income on both the bonds are equal.

investment of 100$ in municipal bond will yield him 107.5$ after a year

similarly if he invests in Treasury bond, he only gets 75% of the interest earned,

100(1+7.5)= 100+ (75/100) * 100(x)

107.5 = 100 + (3/4) * 100x

7.5 = (3/4) * 100x

x = (7.5 * 4) / (100*3)

x = 0.10

x = 10%.

Arbitrage will ensure that the interest rate on Treasury Bond equals 10%