If we solve this equation for βS, we get
βS = βA(1+B/S).
By inspection, if a firm has debt in its capital structure, its equity beta will always exceed its asset beta. As long as βS is greater than βB, even if the bond beta does not equal zero, this observation will be true; i.e., βS > βA.
In other words, when we add debt to a firm's capital structure, we increase the risk of the stock, βS. The relationship is linear, and can be drawn as follows:
B/S = Bonds/Stock, or Debt/Equity Ratio
Therefore, an important determinant of equity betas is the amount of debt, or financial leverage, a firm has in its capital structure. We’ll say more about this concept later.
V. A Project’s Discount Rate with Debt in the Financial Structure:
Recall that the E(Rp) is just the weighted sum of the E(Ri) of all of the securities in the portfolio. The same can be said for the E(R) on a portfolio consisting of all of the firm’s financial securities, or the securities that make up a firm’s financial structure.
E(Rp) = Xi * E(Ri), where
i = 1
E(Rp) = the expected return on the portfolio of financial securities,
Xi = the weight of security i in the portfolio,
E(Ri) = the expected return on Security i, and
N = the number of different securities in the firm’s financial structure.