6.4 The “Levered” Beta
Here we shall return to and continue with the M&M (Modigliani and Miller) argument that the firm’s worth is a function of its EBIT (and ROA), i.e., its ability to produce operating profits rather than how its capital is structured in one or another proportion. Thus, it does not matter how one leverages the company, as its basic earnings power (EBIT or EBITDA) drives its worth.
Stocks and Bonds may both be said to have Betas, i.e., “relative risk.” The firm’s overall Beta is, again, a function of the size of its EBIT (or EBITDA) and the volatility thereof. Thus, it may also be viewed simply as the weighted average of the respective stock and bond Betas, where the weights are the relative values of the Debts and Equity with respect to the firm’s total assets. While mathematically the bond and equity Betas may change, the overall firm Beta does not. This is especially true if you accept M&M’s theory that firm risk, and hence valuation, are not a function of the firm’s capital structure and magnitude of leverage, but of its basic earnings power, EBIT and ROA, as determined by the extent and nature of its assets and the efficiency with which the assets are employed (or lack thereof).
As debts are senior to equity, the Betas of debt (“Debt Betas”) tend to be relatively low, while Equity Betas are higher. There may be occasional periods of interest rate volatility (e.g., the late 1990s and 1994-5), when Debt Betas too can be significant. A firm’s overall Beta is affected by the strength of its operating cash flows (EBITDA) which are not influenced by financial leverage (i.e., debt to equity ratios), but by its business and operating risks. Thus, a restructuring of the firm’s debt ratios (financial leverage), due to IPOs, re-financings, or otherwise, will affect only the Betas of its stocks and bonds, but not the firm’s overall riskiness, the firm’s Beta. The firm’s valuation will thus be unaffected by capital structural changes.
As new equity is issued, the firm’s debt Beta is reduced (and vice versa) because the equity tends to buffer the debt risk. What happens to the Equity Beta as debt is reduced?
| Initial Structure | After Debt Financing | |
| Debt/TA | 40% | 50% |
| Equity/TA | 60% | 50% |
| Debt Beta | 0.1 | 0.2 |
| Equity Beta | 1.35 | ? |
| Overall Firm Beta |
Find: The firm’s overall Beta (pre- and post-financing), and its new Equity Beta.
Initial: β Firm = (.4× 0.1) + (.6 ×1.35) = 0.85
Post Financing: 0.85 = (.5 × 0.2) + (.5 × βEquity)
βEquity= 1.5
Issuing more debt raises the firm’s equity Beta (βquity)! (The effect would be similar for using Free Cash Flow to increase debt.) This may not hold if the size of the “firm pie” increases.
Moral of the story: This does not prove that the firm’s value is a function of its EBIT and ROA risks/volatility. It does confirm, however, that the firm’s operating risk (EBIT volatility), on the one hand, and, on the other hand, the respective risks of its individual capital components (bonds and stocks) are somewhat interdependent.
