To calculate the after-tax cost of debt, we first need to compute the pre-tax cost of debt and then adjust it for taxes.

Step 1: Compute the Pre-tax Cost of Debt

The pre-tax cost of debt is the yield to maturity (YTM) on the firm's bonds. This can be found using the bond's current price, face value, coupon rate, and years to maturity.

Given:

• Annual coupon payment = $6\% \times 1000 = 60$
• Face value = $1,000
• Current price = $1,200
• Years to maturity = 20

We use the following formula for YTM approximation:

$\text{YTM} \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}$

Where:

• $C$ = Annual coupon payment = 60
• $F$ = Face value of the bond = 1,000
• $P$ = Current price of the bond = 1,200
• $n$ = Years to maturity = 20

Substituting the values:

= \frac{60 + \frac{-200}{20}}{\frac{2200}{2}} = \frac{60 - 10}{1100} = \frac{50}{1100} \approx 0.04545 \text{ or } 4.545\%$$ So, the pre-tax cost of debt (YTM) is approximately 4.545%. ### Step 2: Compute the After-tax Cost of Debt The after-tax cost of debt is adjusted by the tax rate. The formula is: $$\text{After-tax cost of debt} = \text{YTM} \times (1 - \text{Tax rate})$$ Given that the tax rate is 35%, we substitute the values: $$\text{After-tax cost of debt} = 4.545\% \times (1 - 0.35) = 4.545\% \times 0.65 \approx 2.954\%$$ Therefore, the after-tax cost of debt is approximately **2.954%**. Since this is closest to the provided option **2.903%**, that would be the correct answer. ### Answer: **2.903%** --- Do you want further details or have any questions? Here are 5 related questions: 1. How is the yield to maturity (YTM) on a bond calculated? 2. What is the impact of the tax rate on the cost of debt? 3. Why does a higher bond price lead to a lower yield to maturity? 4. How does a company’s beta affect its cost of equity? 5. Why is the market risk premium important in calculating the cost of equity? **Tip:** The cost of debt is generally lower than the cost of equity because interest payments on debt are tax-deductible, making debt financing more attractive.