The costs of debt and equity capital are crucial components in a company's financial structure. After-tax cost of debt factors in tax benefits, while equity cost estimation methods like CAPM and DGM consider market risk and dividend growth.

Weighted Average Cost of Capital (WACC) combines these costs to determine a company's overall capital cost. This metric is essential for evaluating investment opportunities and optimizing the balance between debt and equity financing.

The Costs of Debt and Equity Capital

After-tax cost of debt

Represents the effective cost of debt financing for a company, considering the tax deductibility of interest payments
Calculated using the formula: $r_d(1-t)$ $r_{d} (1 - t)$
- $r_d$ denotes the before-tax cost of debt (yield to maturity on the company's debt)
- $t$ represents the company's marginal tax rate (tax rate applied to the last dollar of income)
Accounts for the fact that interest payments on debt reduce a company's taxable income, thus lowering the effective cost of debt (interest tax shield)
Plays a crucial role in determining the overall cost of capital for a company

Return to debt holders vs cost of debt

Return to debt holders (before-tax cost of debt) is the yield to maturity ( $r_d$ $r_{d}$ ) on the company's debt
- Represents the return required by debt holders to lend money to the company (coupon payments and principal repayment)
Cost of debt to the firm (after-tax cost of debt) is lower than the return to debt holders due to the tax deductibility of interest payments
- Calculated as $r_d(1-t)$ , taking into account the company's marginal tax rate ( $t$ )
- Reflects the effective cost of debt financing for the company after considering tax benefits (interest tax shield)
The level of debt in a company's capital structure affects its financial leverage and potential for financial distress

After-tax cost of debt, Risky tax shields and risky debt: an exploratory study

Methods for estimating equity cost

Capital Asset Pricing Model (CAPM) estimates the cost of equity based on the stock's sensitivity to market risk
- Formula: $r_e = r_f + \beta_e(r_m - r_f)$ $r_{e} = r_{f} + β_{e} (r_{m} - r_{f})$
  - $r_e$ represents the cost of equity
  - $r_f$ denotes the risk-free rate (yield on government bonds)
  - $\beta_e$ is the stock's beta, measuring its systematic risk relative to the market
  - $r_m$ represents the expected return on the market portfolio
- Accounts for the stock's exposure to non-diversifiable market risk and the risk premium demanded by investors
- The difference between $r_m$ and $r_f$ represents the equity risk premium
Dividend Growth Model (DGM) estimates the cost of equity based on expected dividend growth
- Formula: $r_e = \frac{D_1}{P_0} + g$ $r_{e} = \frac{D _{1}}{P _{0}} + g$
  - $r_e$ represents the cost of equity
  - $D_1$ denotes the expected dividend per share in the next period
  - $P_0$ is the current stock price
  - $g$ represents the expected dividend growth rate (assumed to be constant)
- Assumes that the stock's value is the present value of all future dividends, growing at a constant rate
- Suitable for companies with stable dividend growth and a long history of paying dividends (mature companies)

Weighted Average Cost of Capital (WACC)

Represents the overall cost of capital for a company, considering both debt and equity financing
Calculated by weighting the costs of debt and equity based on their proportions in the company's capital structure
Used to evaluate investment opportunities and determine the minimum required return for new projects
Reflects the company's optimal mix of debt and equity financing to minimize its cost of capital