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The image shows a financial problem regarding the cost of debt based on the firm’s bond ratings. Here's a breakdown of the text and table:

### Problem Description:
You are tasked with determining your firm’s cost of debt capital. The only debt on the balance sheet is a series of bonds. The firm does not have frequent bond trades, so market prices are unavailable to determine the current yield. The firm has an AA credit rating, which affects the credit spread. 

The information given includes the following:
- The risk-free rate of return is **3.5%**.
- The corporate tax rate is **30%**.
- Credit spreads are given for different credit ratings.

### Table of Credit Ratings and Corresponding Credit Spreads:
| Debt Rating | Credit Spread (bp) |
|-------------|---------------------|
| AAA         | 80 bp               |
| AA          | 100 bp              |
| A           | 130 bp              |
| BBB         | 150 bp              |

### Question:
What is the firm’s after-tax cost of debt capital?

#### Formula:
The cost of debt is calculated using the following formula:
\[
\text{Cost of Debt} = (\text{Risk-Free Rate} + \text{Credit Spread}) \times (1 - \text{Tax Rate})
\]

#### Inputs for the Calculation:
- **Risk-Free Rate (RFR):** 3.5%
- **Credit Spread for AA Rating:** 100 basis points (or 1%)
- **Tax Rate:** 30% (or 0.30)

#### Step-by-Step Calculation:
1. **Determine the pre-tax cost of debt:**
   \[
   \text{Pre-Tax Cost of Debt} = \text{Risk-Free Rate} + \text{Credit Spread}
   = 3.5\% + 1.0\% = 4.5\%
   \]
2. **Calculate the after-tax cost of debt:**
   \[
   \text{After-Tax Cost of Debt} = \text{Pre-Tax Cost of Debt} \times (1 - \text{Tax Rate})
   = 4.5\% \times (1 - 0.30) = 4.5\% \times 0.70 = 3.15\%
   \]

### Conclusion:
The firm’s after-tax cost of debt is **3.15%**.

Would you like further details on the calculation or an explanation of any specific part?

### Five Related Questions:
1. How does the tax rate affect the cost of debt?
2. What is the relationship between the risk-free rate and the credit spread?
3. How would a change in the firm's credit rating impact its cost of debt?
4. Why is the cost of debt calculated on an after-tax basis?
5. What happens to the cost of debt if the tax rate increases?

### Tip:
Always account for the tax shield benefit when calculating the cost of debt, as it lowers the effective interest expense.

You are tasked with determining your firm’s cost of debt capital. The only debt on the balance sheet is a series of bonds. The firm does not have frequent bond trades, so market prices are unavailable to determine the current yield. The firm has an AA credit rating, which affects the credit spread. The risk-free rate of return is 3.5%, and the corporate tax rate is 30%. What is the firm’s after-tax cost of debt capital?

Learn how to calculate a firm's after-tax cost of debt capital using the risk-free rate, credit spreads, and tax rate. The firm's AA credit rating, risk-free rate of 3.5%, and corporate tax rate of 30% are key factors in determining the cost of debt.

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