## Calculating the Cost of Capital

In order to evaluate projects of average risk, we must know the overall cost of capital. Cost of Capital is calculated as the weighted average of each component of capital - debt, common stock, preferred stock, and retained earnings. Each component is calculated as follows:**Cost of Debt (Cd)**: Calculate the after tax cost of debt based on the effective interest rate. The following formula is used to calculate the cost of debt:

Cd = I ( 1 - TR) where I is Interest Rate on Debt and TR is the Tax Rate.

Example 5 - Calculate the Cost of Debt

Cantor Corporation borrowed $ 100,000 at 8% interest. The amount of the loan proceeds was $ 96,000 and the tax rate is 35%.

Cost of Debt = ($ 100,000 x .08) / $ 96,000 x ( 1 - .35) = 8.3% x .65 = 5.4%.

**Cost of Common Stock (Ccs)**: Three different methods can be used to calculate the Cost of Common Stock. The three methods are:

1. Dividend Growth - Dividends paid to common shareholders along with the overall expected growth rate is used to calculate a cost for the common stock. The formula for calculating the cost of common stock is: (Dividends in Year 1 / Market Value of Stock) + Overall Growth Rate.

Example 6 - Calculate the Cost of Common Stock based on Dividend Growth

Cantor Corporation expects to pay a $ 6.00 dividend this year to common shareholders. Historically, dividends have grown by 2% each year. Cantor's common stock is currently selling for $ 45.00 per share.

Cost of Common Stock = ($ 6.00 / $ 45.00) + .02 = 15.3%.

2. Capital Asset Pricing Model (CAPM) - The CAPM is the most widely used approach to calculating the cost of common stock. The CAPM uses three components to calculate the cost of common stock - (1)

**rf**is the risk free rate earned by investors (such as U.S. Treasury Bonds; (2)

**b**is the beta coefficient which expresses the risk of the common stock in relation to the market; and (3)

**rm**is the rate earned in the market (such as the Standard & Poor’s 500 Composite Index). The CAPM formula is Ccs =

**rf + b ( rm - rf )**.

Example 7 - Calculate the Cost of Common Stock based on CAPM

Cantor Corporation has common stock with a listed beta of 1.35. The estimated market return is 12% and the risk free rate based on Treasury Bonds is 6.5%.

Ccs = 6.5% + 1.35 ( 12% - 6.5% ) = 13.9%

3. Bond Plus - A simple approach to calculating the cost of common stock is to add a risk premium to the cost of debt. The formula is Ccs = Cd + risk premium. The risk premium is the additional rate that must be paid to common shareholders above what is paid to bond holders.

Example 8 - Calculate the Cost of Common Stock based on Bond Plus

Referring back to Example 5, we calculated a cost of debt of 5.4%. We have estimated a market risk premium on common stock of 4%.

Ccs = 5.4% + 4.0% = 9.4%

**Cost of Preferred Stock (Cps)**: If your capital structure includes preferred stock, the cost of preferred stock is calculated by the amount of dividends in relation to the market price of the preferred stock. The formula is Cps = Dividends / Market Price of Stock.

Example 9 - Calculate the Cost of Preferred Stock

Assume we have preferred stock selling for $ 80 per share and dividends per share are $ 10. The cost of preferred stock is:

Cps = $ 10 / $ 80 = 12.5%

**Cost of Retained Earnings**: The cost of retained earnings (internal funds) within a capital structure is similar to the cost of common stock. We can think of the cost of retained earnings in relation to the opportunity cost of how we can use these funds. Generally, the cost of retained earnings is slightly less than the cost of common stock since no issuance costs is incurred.

After we have calculated each component cost of capital, we will calculate a weighted average based on the relative market values of each component. The following example will illustrate how weighted average cost of capital is calculated.

Our overall cost of capital is calculated as a weighted average based on the relative market values of each component of capital. If market values are not available, use %’s derived from the targeted or forecasted capital structure. If worse comes to worse, you can fall back on book values. In any event, the weighted average cost of capital is the overall cost of capital that will be used to evaluate capital investments.

### Cost of Equity and Risk

The Cost of Equity is the rate of return required by those who invest in equity securities. The expected return can be broken down into two components - Risk Free Rate and Risk Premium. A good benchmark for establishing the Risk Free Rate is the rate paid on 30 year U.S. Treasury Bonds since the risk of default is virtually non-existent. The Risk Premium can be established by understanding two forms of risk - Business Risk and Financial Risk. In the absence of debt, shareholders are confronted with one form of risk, business risk. Business Risk is the risk of changes to operating income from numerous factors that influence business. When we introduce debt, we have to include financial risk. Financial Risk is the risk of changes to earnings from the use of increased debt. More debt results in higher interest payments, which impacts earnings. Consequently, the Risk Premium consists of Business Risk + Financial Risk. The following graph summarizes these relationships:In the above graph, we have a total risk free rate of 5%. The addition of business risk increases the required rate on stock to 10%. When we introduce debt, this adds financial risk and increases the required return on stock. The final total rate of return on stock with all forms of risk climbs from 12% to 16% over a range of Debt to Equity Ratios. Since the cost of capital represents the rate that must be paid to investors for the use of long-term funds, higher risk to investors will increase the cost of capital.

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