3. DTS has Same Risk as the Firm's Debt

3.2. WACC Estimation

It is important to note that the WACC expressions are the same for the two financing policies. Once we have estimated the relevered beta under the target capital structure, we can therefore proceed in the exact same way as in the previous chapter to estimate the firm's WACC.

With the available information, and maintaining the assumptions from the previous chapter, we can estimate the relevant ingredients of the WACC expression. Let us first estimate the resulting WACC when we use the "correct" equations from the previous page:

  • Cost of equity, kE* = RF + βE* × MRP = 0.02 + 1.93 × 0.05 = 11.65%
  • Cost of debt, kD* = RF + βD* × MRP = 0.02 + 0.6 × 0.05 = 5.0%
  • Target debt level (D*) = 6'000
  • Target equity level (E)* = 5'200
  • Marginal tax rate, τ = 30%.

 

Consequently, the firm's WACC is 7.3%:

 

WACC = \( k_D^* \times(1- \tau_C ) \times \big(\frac{D}{D+E}\big)^*+k_E^* \times \big(\frac{E}{D+E}\big)^* \)

WACC = \( 0.05 \times (1 - 0.3) \times \frac{6'000}{6'000 + 5'200} + 0.1165 \times \frac{5'200}{6'000 + 5'200} \) = 7.3%.

  

In contrast, if we use the simplified equations from the previous section to estimate the WACC under the new capital structure, the result is as follows: The relevered equity beta according to the simplified equations is 2.31. Consequently, the cost of equity under the target capital structure is 13.54% instead of 11.65%:

  

k*E,simplified = RF + β*E,simplified × MRP = 0.02 + 2.31 × 0.05 = 13.54%

  

When we plug this value in the WACC expression above, the resulting WACC is 8.2% instead of 7.3%:

  

WACCsimplified  = \( 0.05 \times (1 - 0.3) \times \frac{6'000}{6'000 + 5'200} + 0.1354 \times \frac{5'200}{6'000 + 5'200} \) = 8.2%.

  

Again, using the simplified equations to unlever and relever the firm's beta leads to a considerable bias in the resulting WACC (8.2% vs. 7.3%). And again, this bias is systematic:

  • If a firm increases its debt ratio, the simplifying equations will systematically overestimate the firm's cost of capital (WACC).
  • In contrast, if the firm decreases its debt ratio, the simplifying equations will systematically underestimate the firm's cost of capital (WACC).

This bias can be avoided easily: Use the full equation from before (or the provided excel file).

  

Taken together, the recommended procedure is as follows:

1) Estimate the unlevered beta using the following equation:

\( \beta_A = \beta_D \times \frac{D \times (1-\tau) }{D \times (1-\tau)+E} + \beta_E \times \frac{E}{D \times (1-\tau)+E} \).

 

2) If you do not "know" the current βD, extract it from the current cost of debt as follows: 

\( \beta_{D, implied} = \frac{k_D - R_F}{MRP} \). 

 

3) Estimate βE* under the target capital structure (relevered beta):

\( \beta_E^* = \beta_A + (\beta_A - \beta_D^*) \times \big(\frac{D \times (1-\tau)}{E}\big)^* \).

  

4) Think about how the new financing policy will affect the cost of borrowing. If the cost of borrowing change, use the expression from (2) to extract the new beta of debt (βD*).

 

5) Use the betas from (3) and (4) to estimate the respective costs of capital using the CAPM:

kj = RF + βj × MRP

 

6) Use these values to estimate the firm's WACC under the target financing policy.

WACC = \( k_D^* \times(1- \tau_C ) \times \big(\frac{D}{D+E}\big)^*+k_E^* \times \big(\frac{E}{D+E}\big)^* \)