# Cost of Capital

### Definition of Cost of Capital

The costs of raising capital for a business include the cost of debt and the cost of equity.

Cost of capital is the required return that is necessary to make a capital budgeting project make sense to take on. Big Systems Inc. wants to buy a new building for its operations. The company would need to consider all of the costs associated with financing a project, including both the costs of debt and the costs of equity. These costs depend on the financing Big Systems Inc. uses to fund the project. If only equity, or securities representing ownership in the company, is used to finance an upgrade, for example, the required return is referred to as the cost of equity. If a project is financed through debt, then the required return is referred to as the cost of debt.

When a company is thinking about implementing a project or buying an asset, the actual cost of capital is the hurdle rate, the minimum rate of return required by an investor or management to proceed with a project. If the project is not going to make more money than it costs, then it may not be justifiable to investors unless another factor makes the project necessary or worthwhile. Legal and customer obligations sometimes fall into this category.

### Calculating the Cost of Each Component of Capital with Examples

The cost of capital can be calculated for each component of capital, such as the cost of equity and the cost of debt.
The cost of capital is the required return necessary for a company to take on a capital budgeting project. Two calculations are considered to analyze the cost of capital: the cost of equity and the cost of debt. These components will help determine the return stockholders require before they will invest in a company. One formula for determining the cost of equity is calculated by using the capital asset pricing model (CAPM). The CAPM formula shows that the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security or a dividend capitalization model, which is used for companies that pay out dividends.
${\text{Cost of Equity}=\text{Risk-Free Rate of Return}+\text{Beta}\times(\text{Market Rate of Return} -\text{Risk-Free Rate of Return})}$
The risk-free rate is the rate of return paid on risk-free investments, such as Treasury bills. Beta is a measure of risk calculated as a regression on the company's stock price. For example, if the risk-free rate is 5 percent, the market return is 10 percent, and the stock's beta is 2, then the expected return on the stock will be 15 percent.
${\text{Cost of Equity}}=0.05+2\;(0.10-0.05)=15\%$
The cost of debt is the effective rate a company pays on its current debt. To calculate the cost of debt, interest expense is multiplied by 1 minus the tax rate and then divided by the total amount of debt. Jim loans Big Systems Inc. $200,000 at an interest rate of 15 percent ($\200{,}000\times0.15=\30{,}000$), and this business has a 25 percent average tax rate. Here, Big Systems Inc. would have$22,500 in interest for this loan in its first year ($\30{,}000\times(1-0.25)=\22{,}500$). Thus, Big System Inc.'s cost of debt would be 11.25 percent ($\22{,}500/\200{,}000=11.25\%$), which means its rate of return would need to be higher than 11.25 percent for this to be a favorable transaction.

### WACC Formula

The WACC formula can be used to calculate the cost of capital and guide management decision-making.

The weighted average cost of capital (WACC) is a formula for determining the relative average a company is expected to pay to all its security holders to finance its assets. The WACC represents the total costs of all capital ("total capital," or TC), weighted in proportion to their balance sheet percentages held by the business. The WACC measures the current cost of a particular component of capital used by the business to fund operations including working capital and long-term investments. WACC will not inform management of the weighted average cost of capital a company is expected to pay to equity and debt holders to acquire additional capital from them because the current market costs may be different than the historical costs paid by the business. But the current WACC will help managers determine whether they should raise new debt or equity based on current market costs in order to decide whether they should refinance to reduce their capital costs.

The WACC is a calculation of the firm's cost of capital in which each category of capital is proportionately weighted. This would include items such as common stock, preferred stock, bonds, and any other long-term debt.
$\text{WACC}=\frac{\rm {E}}{\rm {D}+{E}}(r_{\rm e})+\frac{\rm {D}}{\rm {D}+{E}}(r_{\rm d})(1-{\rm {t}})$
Where:
\begin{aligned}{\rm {E}}=\;&\text{Market Value of Equity}\\\ {\rm {D}}=\;&\text{Market Value of Debt}\\r_{\rm e}=\;&\text{Cost of Equity}\\r_{\rm d}=\;&\text{Cost of Debt}\\t=\;&\text{Corporate Tax Rate}\end{aligned}
To calculate WACC, the first step is to determine the current cost of each capital component, that is, the cost of debt, common equity, and preferred equity. One other important use of the WACC is as a guide or hurdle rate for making future long-term investment decisions. A hurdle rate is the minimum rate of return required by investors to proceed with a project. Managers will use the current WACC to decide whether to approve a new investment by requiring that all such investments must have a return on investment (ROI) greater than the WACC rate. In other words, the ROI on any new long-term capital investment must cover the cost of capital (WACC) plus earn a gross profit above that amount in order to be considered a viable economic alternative.

For example, Big Systems Inc. holds total debt and equity of $100 million. Big Systems Inc.'s total debt is$50 million and is comprised of long-term debt and bonds. Big Systems Inc. also has 50 million in equity from common stock and preferred stock. Assume Big Systems Inc.'s equity is comprised of 50 percent common stock and 50 percent preferred stock. Next, the cost of common equity is determined. Capital Amount Proportional % TC Costs TC Component Costs Common $\{25{,}000{,}000}$ ${25}\times{10}\%$ ${2.50}\%$ Preferred $\{25{,}000{,}000}$ ${25}\%\times{5}\%$ ${1.25}\%$ 10-year bond $\{50{,}000{,}000}$ ${50}\%\times{4}\%$* ${2.00}\%$ WACC = $5.75\%\;{\text{or}}\;0.025+0.0125+0.02$ * Note that the 4 percent debt costs are after-tax using the bond's pretax coupon rate of 6 percent and given a corporate tax rate of 33.3 percent. Weighted average cost of capital (WACC) is the weighted average rate cost of capital a company is expected to pay to all its security holders to finance its assets. CAPM is used to determine the current cost of common equity as this is the accepted formula used to describe the relationship between systematic risk and expected return for assets, particularly stocks. The cost of equity is the risk-adjusted return required by an investor from Big Systems Inc.'s common stock. To calculate the investor's required return, the CAPM formula can be used. $\text{CAPM}:\;r_s=r_{rf}+(r_M-r_{rf})b=r_{rf}+(rp_m)b$ The rate of stock (rs) derives the calculation of the risk-free rate of return (rrf) which is the rate of return paid on investments that are considered "risk-free," such as Treasury bonds. The risk-free rate is added to the difference of the market return (rm) and the risk-free rate (rrf) times beta (b). Once this is calculated, the risk-free rate of return (rrf) is added to (rpm), the risk of the market minus risk premium, times beta (b). Beta is a measurement used to calculate risk based on a company's stock price and we can assume that with a beta of 1 the security will be less volatile than the market. When a company's stock price is more volatile, its beta will generally be higher. For Big Systems Inc., beta is designated as 1, the risk-free rate is 3 percent, and the market return is 10 percent. Thus, using these values, the cost of equity can be calculated using a formula and is 10 percent. ${\text{Cost of Equity}}=0.03+(0.10-0.03)\times1=0.10\;{\text{or}}\;10\%$ The Internal Revenue Service (IRS) allows for U.S. businesses to deduct the cost of debt from their reported tax liabilities. The cost of debt is the interest rate charged on a particular debt. Since a business is allowed to deduct all debt interest, the after-tax cost of such cost depends on the income tax rate of that business. For example, assume a company has a 33 percent federal tax rate and pays 6 percent interest on one loan. Since interest expense is tax-deductible, the after-tax cost of debt can be calculated. Thus, the actual cost of a company’s debt is multiplied by their before and assumed tax rates. Before tax rate is the rate of tax on gains and losses and the assumed tax rate is the highest effective marginal combined U.S. federal, state, and local income tax rate for a fiscal year. $r_d\;{\rm{AT}}=r_d\;{\rm{BT}}(1-{\rm {T}})$ Where: \begin{aligned}r_d=\;&\text{Cost of Debt}\\\rm{AT}=\;&\text{After-Tax Cost of Debt}\\\rm{BT}=\;&\text{Before-Tax Rate}\\{\rm {T}}=\;&\text{Assumed Tax Rate}\end{aligned} To determine its after-tax cost of debt (AT), the assumed tax rate (T) must be subtracted from 1, and then multiplied by the before-tax rate (BT). Big Systems Inc.'s after-tax cost of debt is 4.02 percent. $\text{After-Tax Cost of Debt}=0.06\times(1-0.33)=4.02\%$ When thinking of WACC, it is often useful to imagine a pool of money. Cash pooling is a cash management strategy wherein a company consolidates the cash balances of its subsidiaries. Cash pooling allows a company to pull all of its resources together. Big Systems Inc. went public by issuing 1 million shares of common stock at25 per share, which are now trading at $30 per share. The current risk-free rate is 4 percent, the market risk premium is 8 percent, and the company has a beta coefficient (the amount of systematic risk an asset or portfolio has with respect to the market) of 1.2. During the last year, it issued 50,000 bonds of$1,000 each, paying a 10 percent coupon rate in 20 years. The bonds are currently trading at \$950. The tax rate is 30 percent. With this information, using the WACC formula, WACC can be calculated.
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The cost of equity, or the risk-free rate plus the beta times the market risk premium, can be calculated.
${\text{Cost of Equity}}=4\%+1.2\times8\%=13.6\%$
Next, the yield to maturity (YTM), or rate of maturity, can be calculated.
${\text{YTM}}=\frac{\rm {C}+\frac{\rm {F}-{P}}n}{\frac{\rm F-\rm P}2}$
Where:
\begin{aligned}{\rm {C}}&=\frac{\text{Coupon}}{\text{Interest Payment}}\\{\rm F}&=\text{Face Value}\\\rm P&=\text{Price}\\n&=\text{Years to Maturity}\end{aligned}
${\text {YTM}}=\;\frac{0.10+\frac{(\1,000-\950)}{20}}{\frac{(\1,000-\950)}2}=10.40\%$
The yield to maturity is then taken from the after-tax cost of debt.
$10.40\%\times(1-30\%)=7.28\%$
Finally, WACC can be calculated.
$\text{WACC}=38.71\%\times13.6\%+61.29\%\times7.28\%=9.73\%$