Definitions

# Weighted average cost of capital

The weighted average cost of capital (WACC) is the rate that a company is expected to pay to finance its assets. WACC is the minimum return that a company must earn on existing asset base to satisfy its creditors, owners, and other providers of capital.

Companies raise money from a number of sources: common equity, preferred equity, straight debt, convertible debt, exchangeable debt, warrants, options, pension liabilities, executive stock options, governmental subsidies, and so on. Different securities are expected to generate different returns. WACC is calculated taking into account the relative weights of each component of the capital structure. Calculation of WACC for a company with a complex capital structure is a laborious exercise.

## The formula for a simple case

The weighted average cost of capital is defined by:

$c = left\left(\left\{E over K\right\} right\right) cdot y + left\left(\left\{D over K\right\} right\right) cdot b \left(1-t_C\right)$

where

$K = D + E$

and the following table defines each symbol:

Symbol Meaning Units
$c$ weighted average cost of capital %
$y$ required or expected rate of return on equity, or ''cost of equity" %
$b$ required or expected rate of return on borrowings, or cost of debt %
$t_C$ corporate tax rate %
$D$ total debt and leases (including current portion of long-term debt and notes payable) currency
$E$ total market value of equity and equity equivalents currency
$K$ total capital invested in the going concern currency

This equation describes only the situation with homogeneous equity and debt. If part of the capital consists, for example, of preferred stock (with different cost of equity y), then the formula would include an additional term for each additional source of capital.

or

WACC = wd (1-T) rd + we re

wd = debt portion of value of corporation
T = tax rate
rd = cost of debt (rate)
we = equity portion of value of corporation
re = cost of internal equity (rate)

## How it works

Since we are measuring expected cost of new capital, we should use the market values of the components, rather than their book values (which can be significantly different). In addition, other, more "exotic" sources of financing, such as convertible/callable bonds, convertible preferred stock, etc., would normally be included in the formula if they exist in any significant amounts - since the cost of those financing methods is usually different from the plain vanilla bonds and equity due to their extra features.

WACC is a special way to measure the capital discount of the firms gaining and spending.

## Sources of information

How do we find out the values of the components in the formula for WACC? First let us note that the "weight" of a source of financing is simply the market value of that piece divided by the sum of the values of all the pieces. For example, the weight of common equity in the above formula would be determined as follows:

Market value of common equity / (Market value of common equity + Market value of debt + Market value of preferred equity).

So, let us proceed in finding the market values of each source of financing (namely the debt, preferred stock, and common stock).

• The market value for equity for a publicly traded company is simply the price per share multiplied by the number of shares outstanding, and tends to be the easiest component to find.
• The market value of the debt is easily found if the company has publicly traded bonds. Frequently, companies also have a significant amount of bank loans, whose market value is not easily found. However, since the market value of debt tends to be pretty close to the book value (for companies that have not experienced significant changes in credit rating, at least), the book value of debt is usually used in the WACC formula.
• The market value of preferred stock is again usually easily found on the market, and determined by multiplying the cost per share by number of shares outstanding.

Now, let us take care of the costs.

• Preferred equity is equivalent to a perpetuity, where the holder is entitled to fixed payments forever. Thus the cost is determined by dividing the periodic payment by the price of the preferred stock, in percentage terms.
• The cost of common equity is usually determined using the capital asset pricing model.
• The cost of debt is the yield to maturity on the publicly traded bonds of the company. Failing availability of that, the rates of interest charged by the banks on recent loans to the company would also serve as a good cost of debt. Since a corporation normally can write off taxes on the interest it pays on the debt, however, the cost of debt is further reduced by the tax rate that the corporation is subject to. Thus, the cost of debt for a company becomes (YTM on bonds or interest on loans) × (1 − tax rate). In fact, the tax deduction is usually kept in the formula for WACC, rather than being rolled up into cost of debt, as such:

WACC = weight of preferred equity × cost of preferred equity
+ weight of common equity × cost of common equity
+ weight of debt × cost of debt × (1 − tax rate).

And now we are ready to plug all our data into the WACC formula.

## Effect on valuation

Economists Merton Miller and Franco Modigliani showed in the Modigliani-Miller theorem that in a economy with no transaction costs or taxes, financing decisions are irrelevant to the company's value: all-equity financed company is worth the same as an all-debt one. However, many governments allow a tax deduction on interest, creating a bias towards debt financing to achieve the lowest WACC. In addition, there is a cost to financial distress (especially bankruptcy) which creates a bias towards debt to achieve the lowest WACC.

## References

• G. Bennet Stewart III (1991). The Quest for Value. HarperCollins.
• F. Modigliani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review (June 1958).
• M. Miller and F. Modigliani. "Corporate income taxes and the cost of capital: a correction." American Economic Review, 53 (3) (1963), pp. 433-443.
• J. Miles und J. Ezzell. "The weighted average cost of capital, perfect capital markets and project life: a clarification." Journal of Financial and Quantitative Analysis, 15 (1980), S. 719-730.