4. The Weighted Average Cost of Capital (WACC)

The valuation approach that we have considered so far incorporates the side-effects of financing in the cash flow estimation. In our main example, we have seen that debt financing increases the annual cash flow to the providers of capital by 87.5 each year. To find the ajdusted present value of the company, we have then capitalized the future expected interest tax savings using the appropriate cost of capital.

 

An alternative, and sometimes more practical approach, is to incorporate the side-effects of financing directly in the cost of capital. The idea is very simple:

  • The cost of debt (kD) indicates the firm's pre-tax cost of borrowing. In our example, that pre-tax cost is 10%.
  • Assuming a tax rate (τ) of 35%, the firm saves 35 cents in taxes for reach dollar in interest expenses.
  • Factually, this lowers the cost of borrowing by 35%. 
  • Therefore, the net cost of borrowing is not the pre-tax cost of debt (kD) but the after-tax cost of debt, which is kD × (1-τ). In our example, the after-tax cost of debt is therefore 6.5% [= 0.1 × (1 - 0.35)].

 

Instead of using the pre-tax cost of capital, we can use the after-tax cost of capital to estimate the so-called Weighted Average Cost of Capital (WACC). Formally, the WACC is defined as:

 

WACC = \( k_D \times (1-\tau) \times \frac{D}{D+E} + k_E \times \frac{E}{D+E} \)

 

The only difference to the expression for the cost of assets (kA) from before is that the cost of debt is reflected on an after-tax basis instead of a pre-tax basis. Also, it is important to note that the WACC-expression is the same for the two financing policies that we have considered before (target debt ratios vs. target debt levels).

 

To estimate the value of the levered firm directly, we can capitalize the firm's free cash flows with the WACC. In our simplified example, we can use the firm's operating net income, which is:
 

Free cash flow = Operating net income = NOPLAT = EBIT × (1 - τ) = 600 × 0.65 = 390.

 

Let us now apply this approach to our simple example firm.

  

Application 1: Example firm with target debt levels (in currency)

In the first version of our sample firm, we have assumed that the firm pursues a target debt level of 2'500 of debt. We have collected the following information about the firm:

  • Debt outstanding (D) = 2'500
  • Equity value (E) = 1'625
  • Cost of debt (kD) = 10% (pre-tax)
  • Tax rate (τ) = 35%
  • Cost of equity (kE) = 14%.

 

With this information, we can compute the firm's WACC:

 

WACC = \( 0.10 \times (1-0.35) \times \frac{2'500}{2'500+1'625} + 0.14 \times \frac{1'625}{2500+1'625} \) = 9.45%

  

The firm's WACC is 9.45%. When we use this discount rate to capitalize the firm's free cash flows, we directly obtain the levered value of the company (VL):

 

VL = \( \frac{\text{Free cash flow}}{WACC} = \frac{390}{0.0945} \) = 4'125.

 

Note that the adjusted present value approach from before has produced the exact same levered value of the company.

 

Application 2: Example with target debt ratio

The alternative version was that the firm pursues a target debt ratio. Under this scenario, the information that we have collected was as follows:

  • Cost of equity (kE) = 15.38%
  • Equity value (E) = 1'479
  • All other elements had the same value as in the first application.

 

With this information, we can also compute the WACC under the alternative financing policy:

  

WACC = \( 0.10 \times (1-0.35) \times \frac{2'500}{2'500+1'479} + 0.1538 \times \frac{1'479}{2500+1'479} \) = 9.8%

 

Under this financing policy, the firm's WACC is 9.8%. If we use this WACC to capitalize the firm's free cash flow of 390, the resulting firm value is 3'979:

 

VL = \( \frac{\text{Free cash flow}}{WACC} = \frac{390}{0.098} \) = 3'979.

 

Again, this valuation is identical to the one from the preceding section with the adjusted present value approach.