Weighted Average Cost of Capital
Posted by D Nathan Meehan October 8, 2011

There is a lot more to this subject than is covered here in one blog post. Essentially this is what I think the petroleum engineer as an analyst needs to know. It is far from the level of understanding needed to calculate WACC and many of its applications.

## Conceptual Framework

Several concepts of financial theory are used to determine the weighted average cost of capital (WACC). This cost is the weighted return an investor requires from all sources of funding for a corporation including both debt and equity. This approach makes the most sense for publicly traded firms and underlying assumptions include these concepts.

The first of these assumptions is that the value of a firm at any point in time is equal to the market value of its debt and equity capital. That is, the whole is equal to the sum of its parts. The value of any part of a corporation’s capital structure, whether it be a bond, commercial paper, common stock, or any other component of the capital structure is determined by the current financial parameters such as the prime interest rate, level of economic activity, etc.
The second concept of financial theory used to determine cost of capital is that the cost of capital is the after-tax weighted average marginal cost of debt and equity capital. Weighted COC means that the weights are the percentage of debt or equity capital in the total corporate structure. The marginal cost of debt capital is the interest rate to be paid on the next dollar of borrowed funds; the marginal cost of equity is the return that the next shareholder expects from the purchase of a corporation’s stock. Marginal costs (and not historical costs) of debt or equity are used because marginal costs determine the market value of the total debt or equity components of the capital structure.

In an algebraic form, the after-tax weighted average cost of capital (WACC) is:

D = the market value of all interest-bearing liabilities in the capital structure
E = the market value of all equity securities
V = the value of the firm or D+E hence
= D/V + E/V
rd = the marginal cost of debt
MTR = the marginal tax rate
re = the marginal cost of equity

While the marginal cost of debt is fairly easily obtained from financial markets for publicly traded, the marginal cost of equity is somewhat elusive.
This brings us to the third financial concept used to determine the weighted average cost of capital; it is in the Capital Asset Pricing Model (CAPM).
Through CAPM, the marginal cost of equity can be calculated. The model uses historical and readily available current information in the calculation. (There are other models for calculating the cost of equity.)

Algebraically, CAPM is: where,
re = is the marginal cost of equity
rf = the risk-free interest rate, usually defined as the interest rate on l3-week T-Bi11s
rm = the expected return on the market current return on some stock index such as the S&P 500 or the DJIA
β = a coefficient which measures the tendency of a security’s return to move in parallel with the overall markets return

A value of β equal to 1.0 means that the security’s return precisely mirrors the market movement. A β of 0.0 would be completely uncorrelated. A value of β greater than 1 would suggest higher volatility than the market (up and down). In principle a negative β is possibly means that a stock tends to rise when the market falls and vice versa. β *(rm – rf) is the market’s evaluation of the variability in the expected return, or in other words, the risk premium for that security.

## Value of a Corporation

An estimate of the market value of a corporation can be done by determining the market value of its capital elements. Pertinent information can be obtained from various filings and market information. This value is not the same as what the company might sell for to a potential buyer! It is essentially what it is selling for today.

### Market Value of Debt

The various components of a company’s interest-bearing liabilities have varying types of instruments, maturity dates, and coupon rates. Market values for listed securities may be obtained from public sources while the market values for other debt instruments can be estimated from direct bid/asked information or yield information for similar securities.

Example securities include equipment obligations, debentures, notes, refunding mortgage bonds, commercial paper, pollution control bonds, convertible debentures, sinking fund debentures, private placement notes, current portion of long term debt (LTD) and a bewildering array of other options. The book and market value of these securities are used to estimate the market value of debt.

### Market Value of Equity

The market value of equity can be estimated by multiplying the number of outstanding common shares by the price per share. In many cases a company’s stock may be selling at a substantial premium (or discount) over book value while total debt may be worth a discount (or less frequently a premium) from book value. The effect of valuing each component of capital structure on a market value basis is to lower (or raise) the market debt to capitalization ratio when compared to its value on a book value basis. For some companies there is less debt due to inflation and more equity due to expectations of financial performance.

### Value of the Firm

Taking the value of the firm as the sum of the market value of its Debt and Equity, we can estimate the market and book value of the firm. Typically there is a large disparity and most firms trade well above book value.

## Marginal Cost of Debt and Equity

To determine the marginal cost of debt, the assumption is typically made that the next dollar of borrowed capital would come from the mix of debt instruments currently in the debt capital structure. The costs of such debt are typically weighted in current proportions with advice from corporate financial expertise as to future debt funding plans.

The CAPM is one method of calculating the marginal cost of equity. While others are typically used in establishing a value of WACOC for a corporation, CAPM is sufficient to illustrate the concept. We have the following formula for the calculation. T-Bills typically can be used to establish (rf). Assuming that the historical relationship of (rm – rf) remains fixed during rapidly changing financial conditions, all that is needed to calculate the marginal cost of equity is β.

Several values for β were available. These include public sources and regression correlation coefficients of stock price and market prices over time frames ranging from a month to several years.

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