Calculating WACC correctly should preclude its use to optimize capital structure. In this post we’ll see why.
Traditional WACC Calculation
There was a time when WACC was used to find an “optimal capital structure”, which meant a debt/equity ratio that minimized the cost of capital. Charts like this were part of the argument:
This violates the capital structure irrelevance proposition of Modigliani and Miller: without taxes, leverage does not alter the cost of capital; with taxes, the cost of capital declines with leverage. How was the chart above produced?
An Apparent Mistake
The mistake above is made evident by adding a calculation of enterprise value, which produces the following chart:
We’ve expanded the Y axis a bit, but the blue curve is unchanged. We’ve added the enterprise value line, which increases monotonically instead of peaking at the point of minimum WACC. Here are the complete calculations:
A few important notes here:
- Notice the relevering formula for equity beta: it includes a term for debt beta, which is often assumed to be zero. This is the single most popular mistake we have seen in the study of “optimal capital structure”, and is the point of this whole post.
- The value of assets is the present value of the stream of earnings they produce. This doesn’t change with leverage.
- EV is the sum of the values of the operating assets (assumed 100.0) and the present value of the tax shield that we realize by reducing tax leakage by deducting interest payments. EV is sometimes calculated as the present value of the operating profits after tax; these two calculations will yield the same value unless a mistake has been made.
- The tax shield is the present value of the tax savings afforded by paying interest. You’ll notice we have discounted these flows at the cost of assets. There is considerable discussion about the riskiness of tax savings; we have taken a somewhat middle ground by discounting at asset risk. Feel free to switch the denominator to Ke or Kd.
- m, the market risk premium, is 6%; the risk-free rate is 4% and the tax rate is 50%.
You’ll notice that we bumped up the cost of debt as leverage increases, which is often done to generate the characteristic WACC “smile”.
Fixing the WACC Calculation
A proper calculation of debt beta, and then properly calculating equity beta, fixes the above problem. Here we show the calculations:
..and the resulting curves:
- WACC is minimized where EV is maximized
- Cost of capital decreases monotonically with increasing leverage, which aligns with our intuitions.
- Compared with the incorrect calculations, the cost of equity is lower. If we assume debt beta is always zero, we derive equity beta values that are too high.
- Debt beta is calculated using CAPM. Recall that CAPM can be used to price any asset, so if we are given an assumed cost of debt, we can impute a debt beta.
Why Not 100% Debt?
We have fixed our [download id=”4″] and now the numbers suggest maximizing leverage. Why don’t firms fund with 100% debt? The problem with this argument isn’t the risk of insolvency, at least not within the (unrealistic) assumptions of the Modigliani-Miller and CAPM frameworks: default doesn’t reduce enterprise value.
The problem lies with the ancillary costs of financial distress. Most firms, when approaching a default boundary, experience knock-on impacts on operating cash flows; for example, vendor or customer runs. (The Modigliani-Miller framework does not allow for these “business disruption costs”.) If we allowed for these costs, then the constant “100.0” value of assets above would begin to decline under large amounts of leverage. In this way one can produce a maximum EV at less than 100% leverage.
We casually turned to CAPM to calculate debt beta. Other approaches are discussed by Kaplan and Stein (How risky is the debt in highly leveraged transactions, 1990), Cooper and Davydenko (The cost of debt, 2001), and Groh and Gottschalg ( The risk-adjusted performance of US buyouts, 2006). The CAPM approach is slightly unusual, but we see no reason to not to use it if we are comfortable using CAPM to determine cost of equity.
Cornell and Green (The investment performance of low-grade bond funds, 1991) present a slightly distressing finding: the beta of long-term Treasury bonds from 1960-1989 was measured as 0.2. CAPM of course suggests the beta of a risk-free asset should be 0.