Hamada's equation
In corporate finance, Hamada’s equation, named after Robert Hamada, is used to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani–Miller theorem with the capital asset pricing model. It is used to help determine the levered beta and, through this, the optimal capital structure of firms. Hamada’s equation relates the beta of a levered firm (a firm financed by both debt and equity) to that of its unlevered (i.e., a firm which has no debt) counterpart. It has proved useful in several areas of finance, including  capital structuring, portfolio management and risk management, to name just a few. This formula is commonly taught in MBA Corporate Finance and Valuation classes. It is used to determine the cost of capital of a levered firm based on the cost of capital of comparable firms. Here, the comparable firms would be the ones having similar business risk and, thus, similar unlevered betas as the firm of interest. Equation. The equation is where "β" and "β" are the levered and unlevered betas, respectively, "T" the tax rate and formula_2 the leverage, defined here as the ratio of debt, "D", to  equity, "E", of the firm. The importance of Hamada's equation is that it separates the risk of the business, reflected here by the beta of an unlevered firm, "β", from that of its levered counterpart, "β", which contains the financial risk of leverage. Apart from the effect of the tax rate, which is generally taken as constant, the discrepancy between the two betas can be attributed solely to how the business is financed. The equation is often wrongly thought to hold in general. However, there are several key "assumptions" behind the Hamada equation: Derivation. This simplified proof is based  on Hamada's original paper (Hamada, R.S. 1972). We know that, the beta of a company is : We also know that, the return on equity of a nonleveraged and a leveraged firm is: Where formula_6 is sum of the net capital expenditure and the change in net working capital. If we substitute the (3) and (4) equation into the (2), then we get these formulas (5), if we suppose that the covariances between the market and the components of equity cash flow are zero (hence "β=β=β=0"), except the covariance between EBIT and the market: To get  the well-known equation, suppose that the value of a firm's assets and the value of firm's equity are equal, if the firm is completely financed by equity and tax rate is zero. Mathematically this means the value of an unleveraged firm, when tax rate is zero: "V=V=E". If we fix the value of the unleveraged firm, and change some equity to debt ("D>0"), the value of the firm is still the same, because there is no corporate tax. In this situation the value of the leveraged firm is (6): If the tax rate  is bigger than zero ("T>0") and there is financial leverage ("D>0"), then the leveraged and the unlevaraged firm are not equal because the value of the leveraged firm is bigger by the present value of the tax shield: so (7): Where "V" is the value of the unleveraged firm's assets, which we fixed in above. From the (7) equation "E" is (8) Combine the (5) and (8) equation to get the well-known formula for the leveraged and non leveraged equity beta: Where "I" is the sum of interest payments, "E" is Equity, "D" is Debt, "V" is the  value of a firm category (leveraged or non leveraged), "A" is assets, "M" is referred to the market, "L" means leveraged, "U" means non leveraged category, "r" is the return rate and "T" denotes the tax rate.