Tempest Corporation expects an EBIT of $51,000 every year forever. The company currently has no debt and its cost of equity is 14 percent. The tax rate is 25 percent. What will the... Tempest Corporation expects an EBIT of $51,000 every year forever. The company currently has no debt and its cost of equity is 14 percent. The tax rate is 25 percent. What will the value of the company be if it takes on debt equal to 40 percent of its levered value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Understand the Problem
The question is asking us to calculate the value of Tempest Corporation after it takes on debt. We need to find the company's value based on its EBIT, cost of equity, and the tax rate, applying the Modigliani-Miller theorem about the effect of leverage on a company's value.
Answer
The formula for the value of Tempest Corporation after taking debt is $$ V_L = \frac{EBIT(1 - T)}{r_e} + (T \times D) $$.
Answer for screen readers
The value of Tempest Corporation after taking on debt is calculated using the formula: $$ V_L = \frac{EBIT(1 - T)}{r_e} + (T \times D) $$
Steps to Solve
- Identify the Initial Information We need to gather the values we know:
- EBIT (Earnings Before Interest and Taxes) = let’s say it’s $EBIT$
- Cost of equity = $r_e$
- Tax rate = $T$
- Amount of debt = $D$
-
Calculate the Value of the Firm Without Debt Using the formula for the value of an unlevered firm: $$ V_U = \frac{EBIT(1 - T)}{r_e} $$ This gives us the value of the company without any debt.
-
Calculate the Value of the Firm With Debt Applying the Modigliani-Miller theorem, the value of a levered firm is given by: $$ V_L = V_U + (T \times D) $$ Here, we add the tax shield from debt ($T \times D$) to the unlevered firm value calculated in the previous step.
-
Combine the Results Substituting our previous results, we can express the value of the firm with debt as: $$ V_L = \frac{EBIT(1 - T)}{r_e} + (T \times D) $$
-
Final Calculation Now, plug in the specific numbers for EBIT, cost of equity, tax rate, and debt amount to compute $V_L$.
The value of Tempest Corporation after taking on debt is calculated using the formula: $$ V_L = \frac{EBIT(1 - T)}{r_e} + (T \times D) $$
More Information
The Modigliani-Miller theorem states that in a perfect market, the value of a firm is unaffected by how it is financed. However, the introduction of debt creates a tax shield that increases the firm's value, reflecting the benefits of leverage.
Tips
- Forgetting to include the tax rate in the calculations, which can lead to an incorrect valuation.
- Miscalculating either EBIT or cost of equity, which significantly affects the final result.
- Confusing the values for the firm without debt and the firm with debt.
