Calculating Debt in the Capital Structure of a Levered Firm

What is the approximate amount of debt in the capital structure of a levered firm?

If a levered firm is worth $5 million more than an identical unlevered firm, and the corporate tax rate is 34%, what is the approximate amount of debt in the capital structure?

Answer:

The approximate amount of debt in the capital structure is approximately $9,705,882.35.

To calculate the amount of debt in the capital structure of a levered firm, we can use the concept of the tax shield. The tax shield is the reduction in taxable income due to deductible expenses, such as interest payments on debt.

Given that the levered firm is worth $5 million more than the unlevered firm, this difference in value represents the present value of the tax shield provided by the debt. The tax shield can be calculated using the formula: TS = (Difference in firm value) / (1 - T).

Substituting the given values into the formula, we can calculate the tax shield to be approximately $3,300,000. This tax shield represents the present value of the tax savings from the interest expense.

Since the tax shield is equal to the interest expense multiplied by the corporate tax rate, we can then calculate the amount of debt in the capital structure by dividing the tax shield by the corporate tax rate. This calculation yields an approximate amount of debt in the capital structure of approximately $9,705,882.35.