Question

Integral Industries, Inc. (III) has three subsidiaries, A, B, and C. You are negotiating to buy subsidiary C. Subsidiary A and B each contribute to 40% of III's market value and have betas of 0.9 and 1.4, respectively. The company as a whole has a beta of 1.2. What is the beta of subsidiary C? If you end up buying it, what would be C's opportunity cost of capital? The current risk-free rate is 3.0% and the market risk premium is 7.0%.

Answer 1

A). Beta_{Integral Industries, Inc.} = [W_A x $\beta$ _A] + [W_B x $\beta$ _B] + [W_C x $\beta$ _C]

1.2 = [0.4 x 0.9] + [0.4 x 1.4] + [0.2 x $\beta$ _C]

[0.2 x $\beta$ _C] = 1.2 - [0.4 x 0.9] - [0.4 x 1.4]

  [0.2 x $\beta$ _C] = 1.2 - 0.36 - 0.56

[0.2 x $\beta$ _C] = 0.28

$\beta$ _C = 0.28/0.2 = 1.4

b). According to the CAPM,

C's Ke = Rf + $\beta$ [E(Rm) - Rf]

= 0.03 + 1.4[0.07]

= 0.03 + 0.098 = 0.128, or 12.80%