# 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).

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 βis 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)

3.4. Estimating β

The estimation of β is based on the statistical calculate the standard error which show the extent of possible mismeasurement. Next step is to set up a confidence interval of the estimated value plus or minus standard errors. Fortunately, the estimation error in our case is impossibly. That is why we turn to industry betas. Notice that the estimated industry β is somewhat reliable. This shows up in the lower standard error. The industry betas provide a rough guide to the risk in various lines of business.[5] Sometime we are going to invest or to have a deal with new kind of business not as usual to justify using a company cost of capital. In this case we should remember some things before we are making decision.

1. We have to avoid fudge factors. Don’t add fudge factors to discount rate to offset things could go wrong with the proposed investment. Firstly we have to adjust forecasted cash flows.

2. Do not forget about the determinants of asset risk. The characteristics of high-beta and low-beta assets can be observed when the β itself cannot be.

3. Do not forget diversifiable risk

3.4.1. Operating leverage and β

Sometime we do not have a β, or we get β estimates that are statistical garbage. In those cases, we can assess project’s operation leverage (its ratio of fixed to variable cost) and we can ask whether the project’s future cash flows will be unusually sensitive to the business cycle. Cyclical projects with high operating leverage have high betas. But it is important not to confuse diversifiable risk with market risk. Diversifiable risk does not increase the cost of capital. Many businesspeople associate risk with the variability of book, or accounting, earnings. But much of this variability reflects unique or diversifiable risk. What really counts is the strength of the relationship between the firm’s earnings and the aggregated on all real assets. We can measure this either by the accounting β or by the cash-flow β. We would predict that firms with high accounting or cash-flow betas should also have high project (contract) betas. There are firms whose revenues and earning are strongly dependent on the state of the business cycle – tend to be high-beta firms.

A business facility with high fixed costs, relative to variable cost, is said to have the high operating leverage. High operating leverage means high risk. The cash flows generated by any productive asset can be broken down into revenue, fixed costs, and variable cost:

Cash flow = revenue – fixed cost – variable cost (2.7)

We can break down the asset’s present value in the same way:

PV (asset) = PV (revenue) – PV (fixed cost) – PV (variable cost) (2.8)

We can figure out how the asset’s β is related to the betas of the values of revenue and costs. The β of PV (revenue) is weighted average betas of its component parts:

(2.9)