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Proof: Recall that $$\beta_{i} = \frac{\mathrm{Cov}(r_{i},r_{m})}{\mathrm{Var}(r_{m})}.$$ Now, the returns on unlevered and levered equity are given by $$r_{U} = \frac{\mathrm{EBIT}(1-\tau) - \mathrm{CAPEX} + \mathrm{Depreciation}}{E_{U}}$$ $$r_{L} = \frac{\mathrm{EBIT}(1-\tau) - \mathrm{CAPEX} + \mathrm{Depreciation} + \mathrm{Net\ Debt} - ... 0 Say that you did the calculations in the classic regression way. If you stick the returns of your 4 asset returns in a (T\times 4) matrix Y, and your 3 factor returns in a (T\times 3) matrix X, then your betas would solve the multiple regressions, collected in a (3\times 4) matrix$$Y = X\cdot \beta + \epsilon You could also add a column of ones ...