Complete Guide To Corporate Finance

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Cost Of Capital - Cost Of Equity

The cost of equity is the return that stockholders require for their investment in a company. The traditional formula for cost of equity (COE) is the dividend capitalization model:



A firm's cost of equity represents the compensation that the market demands in exchange for owning the asset and bearing the risk of ownership. (Learn more about investing in Hate Dealing With Money? Invest Without Stress and Investment Options For Any Income.)

Here's a very simple example: let's say you require a rate of return of 10% on an investment in TSJ Sports. The stock is currently trading at $10 and will pay a dividend of $0.30. Through a combination of dividends and share appreciation you require a $1.00 return on your $10.00 investment. Therefore the stock will have to appreciate by $0.70, which, combined with the $0.30 from dividends, gives you your 10% cost of equity.

A company that earns a return on equity in excess of its cost of equity capital has added value. (For more on ROE, read Keep Your Eyes On The ROE.)



Calculating the Cost of Equity
The cost of equity can be a bit tricky to calculate as share capital carries no "explicit" cost. Unlike debt, which the company must pay in the form of predetermined interest, equity does not have a concrete price that the company must pay, but that doesn't mean no cost of equity exists.

Common shareholders expect to obtain a certain return on their equity investment in a company. The equity holders' required rate of return is a cost from the company's perspective because if the company does not deliver this expected return, shareholders will simply sell their shares, causing the price to drop. The cost of equity is basically what it costs the company to maintain a share price that is theoretically satisfactory to investors. (For further reading on share price, see Top 5 Stocks Back From The Dead and The Highest Priced Stocks In America.)

On this basis, the most commonly accepted method for calculating cost of equity comes from the Nobel Prize-winning capital asset pricing model (CAPM): The cost of equity is expressed formulaically below:

Re = rf + (rm – rf) * β

Where:

  • Re = the required rate of return on equity
  • rf = the risk free rate
  • rm – rf = the market risk premium
  • β = beta coefficient = unsystematic risk

But what does this mean?

  • Rf – Risk-free rate - This is the amount obtained from investing in securities considered free from credit risk, such as government bonds from developed countries. The interest rate of U.S. Treasury Bills is frequently used as a proxy for the risk-free rate.
  • ß – Beta - This measures how much a company's share price reacts against the market as a whole. A beta of one, for instance, indicates that the company moves in line with the market. If the beta is in excess of one, the share is exaggerating the market's movements; less than one means the share is more stable. Occasionally, a company may have a negative beta (e.g. a gold-mining company), which means the share price moves in the opposite direction to the broader market. (Learn more in Beta: Know The Risk.)
    For public companies, you can find database services that publish betas. Few services do a better job of estimating betas than BARRA. While you might not be able to afford to subscribe to the beta estimation service, this site describes the process by which they come up with "fundamental" betas. Bloomberg and Ibbotson are other valuable sources of industry betas.
  • (Rm – Rf) = Equity Market Risk Premium (EMRP) - The equity market risk premium (EMRP) represents the returns investors expect to compensate them for taking extra risk by investing in the stock market over and above the risk-free rate. In other words, it is the difference between the risk-free rate and the market rate. It is a highly contentious figure. Many commentators argue that it has gone up due to the notion that holding shares has become more risky.
    The EMRP frequently cited is based on the historical average annual excess return obtained from investing in the stock market above the risk-free rate. The average may either be calculated using an arithmetic mean or a geometric mean. The geometric mean provides an annually compounded rate of excess return and will in most cases be lower than the arithmetic mean. Both methods are popular, but the arithmetic average has gained widespread acceptance.

Once the cost of equity is calculated, adjustments can be made to take account of risk factors specific to the company, which may increase or decrease a company's risk profile. Such factors include the size of the company, pending lawsuits, concentration of customer base and dependence on key employees. Adjustments are entirely a matter of investor judgment, and they vary from company to company. (Learn more in The Capital Asset Pricing Model: An Overview.)

Cost of Newly Issued Stock
Cost of newly issued stock (Rc) is the cost of external equity, and it is based on the cost of retained earnings increased for flotation costs (cost of issuing common stock). For a constant-growth company, this can be calculated as follows:

Rc = D1__ + g
P0 (1-F)
where:
F = the percentage flotation cost, or (current stock price - funds going to company) / current stock price


Example: Cost of Newly Issued Stock
Assume Newco's stock is selling for $40, its expected ROE is 10%, next year's dividend is $2 and the company expects to pay out 30% of its earnings. Additionally, assume the company has a flotation cost of 5%. What is Newco's cost of new equity?

Answer:
Rc = 2 + 0.07 = 0.123, or 12.3%
40(1-0.05)

It is important to note that the cost of newly issued stock is higher than the company's cost of retained earnings. This is due to the flotation costs. (For more on newly issued stock, see Why Investors Can't Get Enough Of Social Media IPOs and 5 Signs That Social Media Is The Next Bubble.)

Weighted Average Cost of Equity

Weighted average cost of equity (WACE) is a way to calculate the cost of a company's equity that gives different weight to different aspects of the equities. Instead of lumping retained earnings, common stock and preferred stock together, WACE provides a more accurate idea of a company's total cost of equity.

Here is an example of how to calculate WACE:

First, calculate the cost of new common stock, the cost of preferred stock and the cost of retained earnings. Let's assume we have already done this and the cost of common stock, preferred stock and retained earnings are 24%, 10% and 20% respectively.

Now, calculate the portion of total equity that is occupied by each form of equity. Again, let's assume this is 50%, 25% and 25%, for common stock, preferred stock and retained earnings, respectively.

Finally, multiply the cost of each form of equity by its respective portion of total equity, and sum of the values to get WACE. Our example results in a WACE of 19.5%.

WACE = (.24*.50) + (.10*.25) + (.20*.25) = 0.195 or 19.5%

Determining an accurate cost of equity for a firm is integral in order to be able to calculate the firm's cost of capital. In turn, an accurate measure of the cost of capital is essential when a firm is trying to decide if a future project will be profitable or not.

Cost Of Debt And Preferred Stock


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  3. How do I use the CAPM (capital asset pricing model) to determine the cost of equity?

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