Weighted Average Cost of Capital





Kerry Back

Weighted Average Cost of Capital

\[ \text{WACC} = \text{% Equity} \times \text{Cost of Equity} \]

\[+ \text{% Debt} \times \text{After-tax Cost of Debt}\]

  • After-tax cost of debt:
    • Suppose $100 interest and 30% tax rate
    • Taxes are reduced by $30, so after-tax interest cost is only $70.
    • After-tax cost of debt = debt yield \(\times\) (1 - tax rate).

Example

  • A company has perpetual expected earnings before interest and taxes (EBIT) of 76 2/3.
  • Interest expense is projected to be 10 forever.
  • The company’s bond yield is 5%.
  • Market value of the debt is 10 / 0.05 = 200.

  • The company’s tax rate is 40%.
  • Invested capital is expected to be constant forever.
  • Required return on equity is 20%.
  • We want to value the equity.
    • Method 1: discount equity cash flows at the cost of equity.
    • Method 2: discount free cash flows at the WACC and then subtract value of debt.

Method 1: Discount equity cash flows

  • Pre-tax income is 66 2/3. Taxes are 26 2/3. Net income is 40.
  • Equity cash flow is 40.
  • Equity value is 40/0.2 = 200.
  • Company is 50% debt and 50% equity by market value.

Method 2: Discount free cash flows

  • Apply tax rate to EBIT as if there were no interest: taxes = 30 2/3.
  • Income = 76 2/3 - 30 2/3 = 46.
  • Free cash flow = 46.
  • WACC is

\[\frac{1}{2} \times \text{20%} + \frac{1}{2} \times (1-\text{40%}) \times \text{5%} = \text{11.5%}\]

  • Enterprise value is 46/0.115 = 400.
  • Subtract 200 debt value to get 200 equity value.