Problem 1:

Hologram Corporation is a holding company with four main subsidiaries. The percentage of its business coming from each of the subsidiaries, and their respective betas, are as follow: 

Subsidiary

Percentage of Business

Beta

Water Company 60% , .70

Cable Company 25% , .90

Real estate 10% , 1.30

Technology companies 5% , 1.50

Part 1: What is the company's beta? 

Portfolio Beta = (percentage of water company x beta of water company) + (percentage of cable company x beta of cable company) + (percentage of real estate x beta of real estate) + (percentage of technology companies x beta of technology companies)

Portfolio Beta = (.60 x .70) + (.25 x .90) + (.10 x 1.30) + (.05 x 1.50)

Portfolio Beta = .42 + .225 + 0.13 + .075

Portfolio Beta = 0.85

Part 2: Assume that the risk-free rate is 6% and that the market risk premium is 5%. What is the holding company's required rate of return?

Beta (B) = .85

Risk Premium (RP) = .05

Risk Free Rate (RF) = .06

Rate of Return = RF + B(RP) 

Rate of Return = .06 + .85(.05)

Rate of Return = .06 + .0425

Rate of Return = .1025 or 10.25%