Levered Beta and Unlevered Beta

Levered Beta and Unlevered Beta

Modigliani and Miller (1963) with Corporate Tax (marginal tax-rate  = T):

VL = VU + T*DL

DL + EL = VU + T*DL

DL (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)*DL

Which 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 = 0

THEN,

βe= 1.2 {1+(0.7*0.5)  = 1.2*1.35 = 1.62

Let 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%