a) ABC Corporation forecasts an annual EBIT of $300,000. With $800,000 in 8% bonds and a 10% cost of equity capital, along with a corporate tax rate of 25%, determine the firm's value.

To calculate the value of the firm, we can use the **Weighted Average Cost of Capital (WACC)** and the **Modigliani-Miller Proposition**. First, we need to calculate the firm's value using both the equity and debt components, taking into account the interest tax shield.

### Step 1: Calculate the cost of debt (after tax)
The cost of debt is the effective interest rate that the firm pays on its debt, adjusted for taxes:

\[
\text{Cost of debt (after tax)} = \text{Interest rate on debt} \times (1 - \text{Tax rate})
\]

Given:
- Interest rate on debt = 8% or 0.08
- Tax rate = 25% or 0.25

\[
\text{Cost of debt (after tax)} = 0.08 \times (1 - 0.25) = 0.08 \times 0.75 = 0.06 \text{ or } 6\%
\]

### Step 2: Calculate the value of the firm using the **Modigliani-Miller Proposition with taxes** (no growth):

The value of the firm in the presence of debt is given by the formula:

\[
V_L = V_U + \text{Tax shield}
\]

Where:
- $ V_L $ = Levered firm value
- $ V_U $ = Unlevered firm value (if there were no debt)
- Tax shield = Debt × Tax rate

First, we need to calculate the unlevered firm value, which assumes the firm is all-equity financed.

### Step 3: Calculate the Unlevered Firm Value

The value of an unlevered firm ($ V_U $) is the present value of the firm's expected EBIT, discounted by the cost of equity (since it has no debt):

\[
V_U = \frac{\text{EBIT}}{\text{Cost of equity}}
\]

Given:
- EBIT = $300,000
- Cost of equity = 10% or 0.10

\[
V_U = \frac{300,000}{0.10} = 3,000,000
\]

### Step 4: Calculate the Tax Shield

The tax shield is the benefit the company gets from the ability to deduct interest expenses from taxable income. This is equal to the debt times the tax rate:

\[
\text{Tax shield} = \text{Debt} \times \text{Tax rate}
\]

Given:
- Debt = $800,000
- Tax rate = 25%

\[
\text{Tax shield} = 800,000 \times 0.25 = 200,000
\]

### Step 5: Calculate the Levered Firm Value

Now, we can calculate the levered firm value using the formula:

\[
V_L = V_U + \text{Tax shield}
\]

\[
V_L = 3,000,000 + 200,000 = 3,200,000
\]

### Final Answer:

The value of the firm with debt is **$3,200,000**.

---

Would you like more details on any step, or have any further questions on this? 

Here are 5 related questions you may find interesting:

1. How does the value of the firm change if the company reduces its debt level?
2. What is the impact on the firm's value if the tax rate increases?
3. How would the value of the firm be calculated if there was perpetual growth in EBIT?
4. What other methods could be used to value a leveraged firm?
5. How does the presence of debt affect the firm's risk profile and cost of equity?

**Tip:** Understanding the relationship between leverage (debt) and the value of a firm is crucial in corporate finance, as using debt increases the potential tax shield but also adds financial risk.

ABC Corporation forecasts an annual EBIT of $300,000. With $800,000 in 8% bonds and a 10% cost of equity capital, along with a corporate tax rate of 25%, determine the firm's value.

Learn how to calculate the value of a firm using the Modigliani-Miller Proposition with taxes. This problem uses ABC Corporation's EBIT, cost of debt, and equity capital to determine its levered firm value. Key formulas and concepts include cost of debt, unlevered firm value, and tax shield. Suitable for advanced high school and college students studying finance.

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