A bond that has a $1,000 par value (face value) and a contract or coupon interest rate of 10.6%. The bonds have a current market value of $1,125 and will mature in 10 years. The firm's marginal rate is 34%.

To calculate the annual interest payment on the bond, you need to multiply the par value by the coupon interest rate. In this case, the annual interest payment would be $1,000 (par value) multiplied by 10.6% (coupon interest rate), which equals $106.

Next, to calculate the after-tax interest payment, you need to multiply the annual interest payment by (1 - marginal tax rate). In this case, the marginal tax rate is 34%. Therefore, the after-tax interest payment would be $106 multiplied by (1 - 0.34), which equals $69.96.

Finally, to calculate the yield to maturity (YTM), you need to use the current market value of the bond, which is $1,125. There are various online calculators or financial software that can help you find the YTM. Alternatively, you can use trial and error by inputting different interest rates until you reach a value close to the market price. Using an online calculator or financial software will make this process quicker and easier.

To summarize:
1. Multiply the par value ($1,000) by the coupon interest rate (10.6%) to find the annual interest payment ($106).
2. Multiply the annual interest payment ($106) by (1 - marginal tax rate, 34%) to find the after-tax interest payment ($69.96).
3. Use an online calculator or financial software to determine the yield to maturity (YTM) by inputting the current market value of the bond ($1,125).

Please note that this explanation provides a general understanding of how to approach the problem, but it's always recommended to consult with a financial professional or utilize specialized tools for accurate calculations.