Question

Question 3
Explain the following equation and what it denotes.

ko = 672) ku(1 – 1) + 6 + E) *

Answer 1

Measuring the Cost of Capital The cost of capital (discount rate) used should reflect both the riskiness and the type of cash flows under consideration. If the cash flows are cash flows due to E (D), then the appropriate cost of capital is the cost of equity, ke (cost of debt, ka). In general, firms use both E & D to finance projects. We will use weighted average cost of capital (WACC). WACC: ke=D/(E+D) ka (1-t) + E/(E+D) ke • Cost of debt (kd) The cost of debt of a project (ka): The interest a firm has to pay to borrow from a bank or the bond market to fund a project. Sometimes ka is called pre-tax cost of debt. It is easy to determine for a firm: A firm calls a bank/investment bank to find out the interest rate it has to pay to borrow capital. It is also easy to determine for companies that borrow from debt markets, which are rated. If the company is not rated or most of the debt is old bank debt, it is more difficult to calculate a current kd. In these cases, we benchmark ka with similar companies (similar size, similar industry, similar D/V, etc.) Q: How does a bank set the interest rate for a given firm? A: Base rate (say, a risk free rate like T-bills, kf) + spread (reflecting the risk of the company/project, which includes CR). We will see this in Chapter 18. Note: Interest payments are tax deductible = After-tax cost of debt = kd*(1-t) • Cost of equity (ke) The cost of equity of a project (ke): The required (expected) return on equity a firm has to pay to investors. This is an equilibrium result. A model is needed to determine required rates of return on equity. We can use the CAPM or other risk-return models, for example a multifactor model, with the 3 Fama-French factors. (Recall that only undiversifiable risk is priced in expected returns.) We will use the CAPM, which produces the required rate of return on equity, to value the cost of equity: ke = kr + B (km - kf) kr: Risk-free rate (in practice, short-term government security rates, say 90-day T-bill rates). km: Expected return on a market portfolio (in practice, the long-run return on a well-diversified market index). B: Systematic Risk of the project/firm = Cov(ke,km)/Var(km) (in practice, a coefficient estimated by a regression against excess market returns or risk premium, (km - kf), using 5 years of data).