An investor purchases a 10-year U.S. government bond for $800. The bond's coupon rate is 10 percent and,? at time of purchase, it still had five years remaining until maturity. If the investor holds the bond until it matures and collects the $1,000 par value from the Treasury and his marginal tax rate is 28 percent, what will his after-tax yield to maturity be?
To calculate the after-tax yield to maturity, we need to take into account the coupon payments and the tax implication on those payments. Here's how you can calculate it:
Step 1: Calculate the annual coupon payment:
The coupon rate is given as 10 percent, and the par value is $1,000. Therefore, the annual coupon payment is 10% * $1,000 = $100.
Step 2: Calculate the total coupon payments over the remaining five years:
Since the bond has five years remaining until maturity, the total coupon payments will be 5 * $100 = $500.
Step 3: Calculate the after-tax coupon payments:
The investor's marginal tax rate is 28 percent. To calculate the after-tax coupon payments, we will subtract the tax amount from the total coupon payments. The tax amount is 28% * $500 = $140.
Step 4: Calculate the after-tax yield to maturity:
To calculate the after-tax yield to maturity, we need to incorporate the tax amount into the bond's purchase price. The investor paid $800 for the bond, but we need to subtract the tax amount from the purchase price since that amount is effectively paid in taxes. The adjusted purchase price is $800 - $140 = $660.
Now, we can calculate the after-tax yield to maturity using the formula:
After-tax yield to maturity = (Total after-tax coupon payments + After-tax par value) / Adjusted purchase price
The total after-tax coupon payments are $500 - $140 = $360.
The after-tax par value is $1,000 - ($1,000 * 0.28) = $720.
The adjusted purchase price is $660.
Therefore, the after-tax yield to maturity is ($360 + $720) / $660 = 1.818 (approximately 181.8%).
The after-tax yield to maturity for the investor is approximately 181.8%.