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Let me first read and analyze the image.The problem in the image asks you to determine the firm's after-tax cost of debt capital, using the debt ratings and credit spreads provided. Here is a breakdown of the key points and the dataThe problem in the image asks you to determine the firm's after-tax cost of debt capital, using the debt ratings and credit spreads provided. Here is a breakdown of the key points and the 

1. **Premise**: The firm’s debt is unrated, but you can assign a synthetic rating based on the table of spreads for known debt ratings.
2. **Risk-free rate**: Given as **6.06%**.
3. **Credit spreads by debt rating**:
   - AAA: **40 bp (basis points)**
   - A-: **65 bp**
   - BBB: **100 bp**
   - B: **150 bp**

4. **Corporate tax rate**: **30%**.

### Steps to calculate the after-tax cost of debt:

1. **Determine the debt rating**: Select the relevant rating from the table. This depends on what the problem is asking or what assumption you're instructed to make.
   
2. **Calculate the cost of debt before tax**:
   \[
   \text{Cost of debt (before tax)} = \text{Risk-free rate} + \text{Credit spread (in decimal form)}
   \]
   For instance, if you assume a BBB rating with a spread of 100 bp, the calculation is:
   \[
   6.06\% + 1.00\% = 7.06\%
   \]

3. **Apply the tax rate**:
   \[
   \text{After-tax cost of debt} = \text{Cost of debt (before tax)} \times (1 - \text{Tax rate})
   \]
   For example, for a BBB rating:
   \[
   7.06\% \times (1 - 0.30) = 4.942\%
   \]

### Answer:
Based on this, if the firm has a BBB rating, the **after-tax cost of debt** is approximately **4.94%**.

Would you like further details or clarification on this process?

### Follow-up questions:
1. What are the implications of the after-tax cost of debt for a firm's overall weighted average cost of capital (WACC)?
2. How does the corporate tax rate affect the cost of debt?
3. What happens to the after-tax cost of debt if the credit rating changes to A- or B?
4. Why is the risk-free rate used in calculating the cost of debt?
5. How would a change in the risk-free rate affect the overall cost of debt?

### Tip:
Always check the assumptions regarding the debt rating when calculating cost of debt, as small differences in credit spread can have significant impacts on the final result.

Determine the firm's after-tax cost of debt capital using debt ratings and credit spreads from the table. Risk-free rate: 6.06%, Corporate tax rate: 30%, Ratings: AAA (40 bp), A- (65 bp), BBB (100 bp), B (150 bp).

Learn how to calculate the after-tax cost of debt for a firm using debt ratings, credit spreads, and the risk-free rate. With a 6.06% risk-free rate and a 30% corporate tax rate, this guide explains step-by-step how to use credit spreads for AAA, A-, BBB, and B ratings to determine the cost of debt.

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