[beta]l is the leveraged beta
; [beta][mu] is the unleveraged beta, the unleveraged beta of each American sector compared to the Brazilian; t is the current tax rate, which is 34%; D is the debt and E is equity.
(1) Deb minus cash over market cap;(2) Obtained as the slope coefficient of regressing each country's credit risk factor against the average risk factor (see Table 4, sample 2012-2013); (3) See Table 5 sample 2012-2013-(4) Assumes Beta of Debt equal to zero and is obtained as (Leveraged Beta
)/(1+D-E), where D-E net debt to equity; (5) Obtained as: (Country Debt Lambda)*(D/E)-(1+D/E) + (Leveraged Lambda)*(1/(1 + (D/E)); (6) Uses the premia from Table 5; (7) Beta and Lambda are re-leveraged assuming an average D-E equal to 0.44; (8) Calculated with re-leveraged parameters and uses premia from Table 5.
Table 1 The unchanged WACC according to Modigliani and Miller's theory FCF 100 100 Perpetuity growth = g 3.00% 3.00% Risk free rate = r 2.00% 2.00% Market risk premium 7.00% 7.00% Unleveraged beta = [beta] * 0.90 0.90 Cost of debt Pretax cost of debt 3.40% 5.50% Post tax @ 36.1% 2.17% 3.51% Beta of the debt 0.20 0.50 Leveraged beta = [beta] 1.20 1.07 Cost of equity = k 10.38% 9.49% WACC = K 7.11% 7.11% P 8.30% 8.30% Adjusted cost of capital 7.11% 7.11% EV 2,509 2,509 Debt 1,000 1,000 Equity 1,509 1,509 For a FCF which is equal to 100, a risk free rate of 2%, a market risk premium of 7% and an unleveraged beta of 0.9, 2 assumptions regarding the pretax cost of debt are taken into account: 3.40%, based on a debt's beta of 0.20 and 5.50% based on debt's beta of 0.50.
The WACC calculation is a bit subjective as a lot of assumptions have to be taken into account: the market risk premium depends on a assumption regarding the perpetuity growth rate of the listed firms' dividends; when the firm is listed, the cost of equity can either include its beta (which is different according to the data provider) or a leveraged beta based on the industry's unleveraged beta, which depends on the peers which have been included in the sample; the weighting coefficients can correspond to a target--or normative--financial structure or be based on an iterative calculation.
The perception that that asset class is predominantly leveraged beta
will gain more credibility among its institutional clients.
In this way, leveraged beta (beta for investment in shareholders' equity or own capital beta) is determined both by the risk of the sector where the company operates and by the amount of assumed financial leverage risk.
Concerning the investigation of the company's systematic risk variation, the beta of leveraged companies, according to Rai (2005), under the assumption of non-existence of risk-free rates and assets, leveraged beta and non-averaged beta may be related by the equation (1):