1. A Step-by-Step Guide to Estimating the WACC in Practice

1.2. Situation B: Traded Shares; Firm has Different Target Capital Structure

Now suppose Coffee's shares are traded on the exchange but the firm wants to change its capital structure in the future by increasing the debt ratio from 40% to 50%. What is its WACC under this new capital structure?

 

With additional debt, Coffee's cost of equity will increase. Its cost of debt might increase as well. Hence Coffee's current \( k_E \) and (possibly) \( k_D \) will change. The only thing that remains the same is Coffee's \( k_A \), since the overall cost of capital is dictated by the operating risk of Coffee. As long as the change in the firm's capital structure does not affect its operating activities, \( k_A \) is independent of the firm's capital structure. Let's assume Coffee's debt tax shield has the same risk as its assets. If so, we can use the preceding information to compute:

 

\( k_A=k_D \times \frac{D}{D+E}+k_E \times \frac{E}{D+E}=0.06 \times 0.4+0.124 \times 0.6 \) = 9.84%.

 

We can refer to this computation as the "unlevering” of the firm's cost of equity (in other words, we compute the cost of equity the firm would have if it had no debt outstanding). With this information at hand, we can now compute the WACC under the new capital structure (denoted with *):

 

\( WACC=k_A-k_D^* \times \tau_C \times \big(\frac{D}{D+E}\big)^* \).

 

Suppose the new capital structure can be described with the following information:

 

New proportion of debt in the capital structure, D/(D+E)

50%

Risk-free rate of return, \( R_F \)

4%

Coffee's new debt rating

A-

Premium for A- rated debt above the risk-free rate

3%

 

As a first approximation, we can write:

 

\( k_D^*=R_F+0.03 = 0.04 + 0.03 \) = 7%.

 

With this, we compute:

 

\( WACC =k_A-k_D^* \times \tau_C \times \big(\frac{D}{D+E}\big)^* = 0.0984 - 0.07 \times 0.3 \times 0.5\) = 8.79%.

 

We obtain the same estimate by first calculating the cost of equity under the new capital structure:

 

\( k_E = k_A +(k_A - k_D^* \times \big(\frac{D}{E}\big)^* = 0.0984 + (0.0984 - 0.07) \times 1 \) = 12.68%,

 

where we use the fact that (D/E)* = 1 under the new capital structure. Note that, in this expression, we are de facto "relevering” the cost of the firm's assets (in other words, we compute the cost of equity the firm has under the new leverage). With that information, we can compute:

 

\( WACC = 0.07 \times (1-0.3) \times 0.5 + 0.1268 \times 0.5 \) = 8.79%.

 

This section has shown how we can estimate the WACC of a listed company that will change its capital structure in the future. The trick was to identify the firm's overall cost of capital \( k_A \), which is driven by the firm's operating risk and therefore independent of the capital structure. Once we "know" \( k_A \), we can estimate the WACC under the new financing policy by adjusting \( k_A \) with the debt tax shield under that new policy.