3.2. Wacc and opportunity cost of capital
The cost of capital is estimated as blend of the cost of debt and cost of equity. To calculate it, we just take weighted average of the expected returns on the debt and the equity:
Company cost of capital = r (assets) =
(2.1)
Note that the value of dept and equity add up to the firm value (D+E=V) and that the firm value equals the asset value. This formula to show as the market values, not book values. The market value of firm’s equity is often very different from its book value. If the firm contemplating investment in a project that has the same risk as firm’s existing business, the opportunity cost of capital for this project is the same as the firm’s cost of capital. Other words, company cost of capital is not cost of debt, and not the cost equity, but an average. Thus blend is called the weighted-average cost of capital (WACC).
When the firm changes its mix of debt and equity, the risk and expected returns changes too, but the company’s overall cost of capital does not change. We must note remarkable things that interest paid on a firm’s borrowing can be deducted from taxable income. Thus the after-tax cost of debt is (r (1 – T)), where T is the marginal corporate tax rate. When companies discount an average-risk project they use the after-tax cost of debt to compute the after-tax weighted-average cost of capital (WACC):
After-tax WACC =
(2.2)2
We may see it the right discount rate for the projects that have the same risk as the company’s business. But if the project riskier than the firm as it stands, the cost of capital for the project should be higher. The project cost of capital for the safe project is lower.
Suppose that we are considering an across-the-board expansion. Such an investment would have the same degree of risk as the existing business. Therefore we should discount projected cash flows at a WACC. To calculate the WACC, we need an estimate of the cost of equity. We may use the capital asset pricing model (CAPM). Most large companies do use the CAPM to estimate the cost of equity. The CAPM is not the last word on risk and return we should pay attention to other models such an arbitrage pricing theory (APT).
3.3. Capm and apt
Then we estimate the company cost of capital the hardest part is figuring out the expected rate of return for investment. Most of firm turn to the capital asset pricing model (CAPM) for estimate expect rate of return. The CAPM states that expected return equals the risk-free interest rate (rf) plus a risk premium that depends on β and the market risk premium (rm – rf):
Expected return =
(2.3)
What is the expected risk premium when β is not 0 or 1? In the mid-1960s three economists – William Sharpe, John Lintner, and Jack Treynor – produced an answer to this question. Their answer is known as the capital asset pricing model or CAPM. The model’s message is that expected risk premium varies in direct proportion to β. We can write this relationship as
Expected risk premium = β x expected risk premium on market
(2.4)3
The capital asset pricing model begins with an analysis how to invest properly. Stephen Ross’s arbitrage pricing theory, or APT, starts with assuming that return depends partly on pervasive macroeconomic “factors” and partly on “nose” – events that are unique to that company. The returns are assumed to obey the following relationship:
Return =
(2.5)4
The theory does not say what the factors are: there could be an oil price factor, an interest-rate factor, and so on. Arbitrage pricing theory states that the expected risk premium depends on the risk premium associated with each factor and sensitivity to each factor.
The formula is:
Risk premium =
(2.6)