Levered Beta and Unlevered Beta
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Levered Beta and Unlevered BetaModigliani and Miller (1963) with Corporate Tax (marginal tax-rate = T):VL = VU + T*DLDL + EL = VU + T*DLDL (1-T) + EL = VU Assume that T=30% and Debt:Equity Ratio DL/EL = 50% [pic 1][pic 2]ASSETS LIABILITIES VU EL (1-T)*DLWhich implies that the Beta of the assets must equal the weighted average of Beta for EL and Beta for DL (1-T). Therefore,
βU= βe [EL / {(1-T)DL + EL}] + βd [{(1-T)*DL } / {EL + (1-T) DL}]IF βd = 0 (as is implicitly assumed in textbooks), THEN βe = βU [{1+ (1-T)} * (DL/EL)]OTHERWISE,βe = βU [{1+ (1-T)} * (DL/EL)] − βd {(1-T)*(DL/EL)}Let us consider two cases:CASE 1:-βU = 1.2 βd = 0THEN,βe= 1.2 {1+(0.7*0.5) = 1.2*1.35 = 1.62Let us assume that Risk-free Rate is 5% and the Market Risk Premium is 6% Then, Cost of Equity in the Levered Firm, KeL= Rf + βL (RM − Rf) = 5 + 1.62*6 = 14.72 %Since debt has zero beta, therefore Cost of Debt = 5%