Financial Leverage and Cost of Capital Analysis
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Financial Leverage and Cost of Capital
1. Financial Leverage: Effect on Risk and Return
The capital structure that produces the highest firm value is the one that maximizes shareholder wealth.
Example: Trans Am Corporation currently has no debt in its capital structure and is considering issuing debt to buy back some of its equity.
For an all-equity firm, assets equal equity, meaning Return on Assets (ROA) is equal to Return on Equity (ROE):
- ROA = EBIT / Assets
- ROE = (EBIT - Interest) / Equity
Earnings per share (EPS) is calculated as:
EPS = Earnings / Number of shares outstanding
ROA is identical across economic states because it is calculated before interest. The effect of financial leverage depends on the company’s earnings before interest (EBIT). If EBIT is $1,200, the ROE is higher under the proposed debt structure; if EBIT is $400, the ROE is higher under the current all-equity structure.
Probability of Solvency
Based on the estimated distribution of EBIT, the probability of solvency for a given amount of debt is defined as:
Prob (EBIT > Interest expenses)
2. The Cost of Debt
The cost of debt refers to the effective rate a company pays on its current debt or new debt issuance, adjusted for the tax deductibility of interest expense.
The cost of debt is generally easier to estimate than the cost of equity. For bonds with a low risk of default, the current yield to maturity serves as a reliable estimate of investor expected returns and the cost of borrowing.
After-Tax Cost of Debt
The after-tax cost of debt is calculated as:
After-tax cost of debt = (1 - Tax rate) × Borrowing rate
Note: We tax-adjust the cost of debt because firms can deduct interest payments before paying taxes, whereas dividends are not tax-deductible.
Calculating Borrowing Costs
Banks determine the interest rate by ensuring the amount lent equals the present value of future payments. However, the nominal interest rate (i) often differs from the true cost of debt to the borrower due to additional fees, such as screening fees, transaction costs, or specific taxes.
The true cost of debt to the borrower (RB) is computed by solving:
C - Fees = I = Σ (Pj / (1 + RB)j)