WACC, Modigliani–Miller and the Hamada Beta Formula

Calculate WACC

Use a capital structure consistent with the cash flows and valuation horizon. Cost of equity is commonly estimated with CAPM. The after-tax debt term assumes the tax saving is available; this assumption may fail for a loss-making or deduction-constrained borrower.

WACC = E/(D+E) × r_e + D/(D+E) × r_d × (1 − T)
CAPM cost of equity = Risk-free rate + equity beta × equity risk premium

Worked example: market-value weights

Equity is worth $60m and debt $40m. With cost of equity of 12%, cost of debt of 7% and tax rate of 25%, WACC is 60% × 12% + 40% × 7% × 75% = 9.3%. Book equity is not a substitute for market equity just because it is easier to obtain.

Unlever and relever beta

Remove financing effects from comparable-company betas before applying the target leverage ratio. Hamada assumes a particular tax-shield framework and ignores material debt beta. Risky debt, unstable debt policies and operating leases can require a more complete approach.

β_U = β_L / [1 + (1 − T) × D/E]
β_L = β_U × [1 + (1 − T) × D/E]

Worked example: a change in leverage

A comparable has levered beta 1.3, D/E of 0.5 and tax rate 25%. Its unlevered beta is 1.3 / 1.375 = 0.9455. Relevering to D/E of 0.8 gives 0.9455 × 1.6 = 1.5127. At a 4% risk-free rate and 5% equity risk premium, indicated cost of equity is approximately 11.56%.

What Modigliani–Miller does and does not imply

In the ideal no-tax, frictionless case, financing does not change operating asset value and leverage raises equity risk. Adding corporate taxes introduces a debt tax benefit under specified assumptions; distress, personal taxes and agency effects complicate the result. More leverage does not create unlimited real-world value.

Practical valuation checks

Match nominal cash flows with nominal discount rates and maintain currency consistency. A rapidly amortizing LBO may be better explained with APV or changing discount rates than a single unexplained WACC. diophos has cost-of-capital inputs and financing-derived calculations; these formulas are educational, not a claim that the app estimates peer betas or market risk premia automatically.