Intro to Finance: Capital Structure - Tradeoff Theory, Tax Shield vs. Financial Distress Costs

What This Is

The trade-off theory in finance suggests that companies face a trade-off between two costs when deciding on their capital structure: tax shields and financial distress costs. Tax shields arise from the use of debt financing, which reduces taxable income and thus lowers the company's tax liability. However, high levels of debt can increase the risk of financial distress, which can lead to costly bankruptcy and liquidation. For example, consider Apple Inc., which has a market value of $2 trillion and a debt-to-equity ratio of 0.2. If Apple were to increase its debt-to-equity ratio to 0.5, it would reduce its tax liability by $100 million (assuming a 21% tax rate) but also increase its risk of financial distress.

Key Formulas & Symbols

• Tax Shield (TS) = Interest Expense × (1 - Tax Rate) where TS = tax shield, Interest Expense = interest paid on debt, Tax Rate = corporate tax rate.
• Financial Distress Costs (FDC) = Probability of Distress × Expected Loss where FDC = financial distress costs, Probability of Distress = probability of bankruptcy, Expected Loss = expected loss in case of bankruptcy.
• Weighted Average Cost of Capital (WACC) = (Debt / (Debt + Equity)) × (Interest Rate on Debt / (1 - Tax Rate)) + (Equity / (Debt + Equity)) × Cost of Equity where WACC = weighted average cost of capital, Debt = market value of debt, Equity = market value of equity, Interest Rate on Debt = interest rate on debt, Tax Rate = corporate tax rate, Cost of Equity = cost of equity capital.
• Debt-to-Equity Ratio = Total Debt / Total Equity where Debt-to-Equity Ratio = debt-to-equity ratio, Total Debt = market value of debt, Total Equity = market value of equity.
• Interest Coverage Ratio = EBIT / Interest Expense where Interest Coverage Ratio = interest coverage ratio, EBIT = earnings before interest and taxes, Interest Expense = interest paid on debt.
• Probability of Distress = (Debt / (Debt + Equity)) / (1 + (Debt / (Debt + Equity))) where Probability of Distress = probability of distress, Debt = market value of debt, Equity = market value of equity.

Step-by-Step Calculation

1. Calculate the tax shield: TS = Interest Expense × (1 - Tax Rate)
2. Calculate the financial distress costs: FDC = Probability of Distress × Expected Loss
3. Calculate the weighted average cost of capital (WACC): WACC = (Debt / (Debt + Equity)) × (Interest Rate on Debt / (1 - Tax Rate)) + (Equity / (Debt + Equity)) × Cost of Equity
4. Calculate the debt-to-equity ratio: Debt-to-Equity Ratio = Total Debt / Total Equity
5. Calculate the interest coverage ratio: Interest Coverage Ratio = EBIT / Interest Expense
6. Calculate the probability of distress: Probability of Distress = (Debt / (Debt + Equity)) / (1 + (Debt / (Debt + Equity)))

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value of debt and equity to calculate WACC, as market value reflects the current market price of the company's securities.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR (Internal Rate of Return) is the rate at which the NPV (Net Present Value) of a project is zero, while NPV ranking is based on the absolute value of NPV, not IRR.
• Mistake: Ignoring financial distress costs when calculating WACC.
• Correction: Include financial distress costs in the calculation of WACC to reflect the true cost of debt.

Exam / CFA Tips

• Tip: When calculating WACC, make sure to use market value of debt and equity, and include financial distress costs.
• Tip: Be careful when using IRR and NPV ranking, as they are often confused.
• Tip: Pay attention to the question's wording, as it may require you to calculate WACC with or without financial distress costs.

Quick Practice Problem

Apple Inc. has a market value of $2 trillion, a debt-to-equity ratio of 0.2, and an interest rate on debt of 5%. If the corporate tax rate is 21%, what is the tax shield?

Answer: TS = $100 million (Interest Expense × (1 - Tax Rate))

Last-Minute Cram Sheet

• The tax shield is calculated using interest expense, not interest paid on debt.
• Financial distress costs are calculated using probability of distress, not debt-to-equity ratio.
• WACC = (Debt / (Debt + Equity)) × (Interest Rate on Debt / (1 - Tax Rate)) + (Equity / (Debt + Equity)) × Cost of Equity
• Debt-to-Equity Ratio = Total Debt / Total Equity
• Interest Coverage Ratio = EBIT / Interest Expense
• Probability of Distress = (Debt / (Debt + Equity)) / (1 + (Debt / (Debt + Equity)))
• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• The weighted average cost of capital (WACC) is calculated using market value of debt and equity, not book value.
• Financial distress costs are included in the calculation of WACC.