You are working as an intern at Coral Gables Products, a privately owned manufacturing company. Shortly after you read Chapter 13 in this book, you got into a discussion with the chief financial officer (CFO) at Coral Gables about weighted average cost of capital calculations. She pointed out that, just as the beta of the assets of a firm equals a weighted average of the betas for the individual assets, as shown in Equation 7.13:

β n Asset portfolio = Σ

i=1 n

x i β i = x 1 β 1 + x 2 β 2 + x 3 β 3 + ⋯ + x n β n the beta of the assets of a firm also equals a weighted average of the betas for the debt, preferred stock, and common stock of a firm:

β n Asset portfolio = Σ

i=1 n

x i β i = x Debt β Debt + x ps β ps + x cs β cs Why must this be true?