You buy a 10 year $1,000 par 4% annual payment coupon bond priced to yield 6%.You do not sell the bond at year end.If you are in a 15% tax bracket at year end you will owe taxes on this investment equal to _______.

Question

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The bond pays an annual coupon payment of $40 ($1,000 par value x 4% coupon rate). The bond is priced at a yield of 6%, so the purchase price is $747.26 (PV of a 10-year, 4% bond with a 6% yield). At year end, you will receive $40 in coupon payments and owe taxes on the interest income of $60 ($40 x 1.5 since the tax bracket is 15%).

The tax owed will be $9 ($60 x 0.15). However, since the coupon payments are already after-tax payments (meaning the company has already paid taxes on the interest income before it's paid out as a coupon payment), the tax owed is actually only on the incremental interest income of $20 (the difference between the coupon payment and the yield to maturity).

Therefore, the tax owed on this investment is $7.68 ($20 x 0.384, which is the tax rate on the incremental income of $20 in a 15% tax bracket).

You Buy a 10 Year $1,000 Par 4% Annual Payment