Question

You are the manager of an all-equity firm whose stock has a beta of 1.13, volatility of 13.09%, and market capitalization of $769 million. You decide to acquire another firm. The all-equity firm you acquire has stock with a beta of 0.69, volatility of 25.98%, and market capitalization of $644 million. The stock returns of your firm and the firm you are acquiring have a correlation of 0.04. The current market risk premium is 4.81% and the current risk free rate is 2.8%. What is the new standard deviation of your firm's stock returns after this acquisition? Express your answer as a percentage rounded to two decimal places (e.g., 11.25% not 0.1125).

Answer 1

Acquirer Firm:

Beta = B1 = 1.13, Volatility = V1 = 13.09 % and Market Value = V1 = $ 769 million

Risk Free Rate = Rf = 2.8 % and Market Risk Premium = Rm = 4.81 %

Expected Return = r1 = Rf + B1 x Rm = 8.2355 %

Target Firm:

Beta = B2 = 0.69, Volatility = V2 = 25.98 % and Market Value = V2 = $ 644 million

Risk Free Rate = Rf = 2.8 % and Market Risk Premium = Rm = 4.81 %

Expected Return = r2 = Rf + B2 x Rm = 2.8 + 0.69 x 4.81 = 6.1189 %

Correlation = p = 0.4

Weight of Acquirer in the combined firm = w1 = V1 / (V1+V2) = 769 / (769+644) = 0.544

Weight of Target in the combined firm = w2 = V2 / (V1+V2) = 644 / (769+644) = 0.456

Therefore, standard deviation post-acquisition = [{(V1 x w1)^(2)} + {(V2 x w2)^(2)} + 2 x w1 x w2 x V1 x V2 x p]^(1/2) = [{(.1309 x 0.544)^(2)} + {(0.2598 x 0.456)^(2)} + 2 x 0.544 x 0.456 x 0.1309 x 0.2598 x 0.4]^(1/2) = 0.16079 or 16.079 %