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# How To Calculate the Cost of Capital Published

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Many companies make decisions to build new facilities, invest in new machinery, or expend sums for other large projects without any idea of whether the return to be expected from these projects will exceed the cost of capital needed to fund them. As a result, a company may find that it is working furiously on any number of new projects but seeing its ability to generate cash flow to repay debt or pay stockholders decline over time. To avoid this situation, it is necessary to calculate the return on investment. This post discusses the second part of the investment decision, which is the calculation of the cost of capital against which investment decisions must be compared. The post describes the primary components of a company’s capital, how the cost of each kind is combined to form a weighted cost of capital, and how this information should be most appropriately used when evaluating the return on new projects that require funding, as well as for discounting the cash flows from existing projects.

### Components Of The Cost Of Capital

Before determining the amount of a company’s cost of capital, it is necessary to determine its components. The following two sections describe in detail how to arrive at the cost of capital for these components. The weighted average calculation that brings together all the elements of the cost of capital is then described in the section that follows these.

• The first component of the cost of capital is “DEBT”. This is a company’s commitment to return to a lender both the interest and principal on an initial or series of payments to the company by the lender. This can be shortterm debt, which is typically paid back in full within one year, or long-term debt, which can be repaid over many years, either with continual principal repayments, large repayments at set intervals, or a large payment when the entire debt is due, which is called a balloon payment. All these forms of repayment can be combined in an infinite number of ways to arrive at a repayment plan that is uniquely structured to fit the needs of the individual corporation.
• The second component of the cost of capital is “PREFERRED STOCK”. This is a form of equity that is issued to stockholders and carries a specific interest rate. The company is obligated to pay only the stated interest rate to shareholders at stated intervals, but not the initial payment of funds to the company, which it may keep in perpetuity, unless it chooses to buy back the stock. There may also be conversion options, so that a shareholder can convert the preferred stock to common stock in some predetermined proportion. This type of stock is attractive to those companies that do not want to dilute earnings per share with additional common stock or to incur the burden of principal repayments. Although there is an obligation to pay shareholders the stated interest rate, it is usually possible to delay payment if the funds are not available; however, the interest will accumulate and must be paid when cash is available.
• The third and final component of the cost of capital is “COMMON STOCK”. A company is not required to pay anything to its shareholders in exchange for the stock, which makes this the least risky form of funding available. Instead, shareholders rely on a combination of dividend payments, as authorized by the board of directors (and which are entirely at the option of the board—authorization is not required by law), and appreciation in the value of the shares. However, because shareholders indirectly control the corporation through the board of directors, actions by management that depress the stock price or lead to a reduction in the dividend payment can lead to the firing of management by the board of directors. Also, since shareholders typically expect a high return on investment in exchange for their money, the actual cost of these funds is the highest of all the components of the cost of capital.

As will be discussed in the next two sections, the least expensive of the three forms of funding is debt, followed by preferred stock and common stock. The main reason for the differences between the costs of the three components is the impact of taxes on various kinds of interest payments. This is of particular concern when discussing debt, which is covered the next sections. Read on…

### How to Calculate the Cost Of Debt

This section covers the main factors to consider when calculating the cost of debt and also notes how these factors must be incorporated into the final cost calculation. We also note how the net result of these calculations is a form of funding that is less expensive than the cost of equity, which is covered in the next section.

When one is calculating the cost of debt, it is important to remember that the interest expense is tax deductible. This means that the tax paid by the company is reduced by the tax rate multiplied by the interest expense.

An example is shown below, where it is assumed that \$1 million of debt has a basic interest rate of 9.5 percent, and the corporate tax rate is 35 percent.

Calculating the Interest Cost of Debt, Net of Taxes

Net after-tax interest expense:

= (Interest expense) × (1 – tax rate) / Amount of debt

= \$95,000 × (1 – 0.35) / \$1,000,000

= \$61,750 / \$1,000,000

= 6.175%

Calculating the Interest Cost of Debt, Net of Taxes, Fees, and Discounts

Net after-tax interest expense:

= (Interest expense) × (1  tax rate) / (Amount of debt) – (Fees) – (Discount on sale of debt)

= \$95,000 × (1 – 0.35) / \$1,000,000 – \$25,000 – \$20,000

= \$61,750 / \$955,000

= 6.466%

Note: There can also be a premium on sale of debt instead of a discount, if investors are willing to pay extra for the interest rate offered. This usually occurs when the rate offered is higher than the current market rate or if the risk of nonpayment is so low that this is perceived as an extra benefit by investors.

It clearly shows that the impact of taxes on the cost of debt significantly reduces the overall debt cost, thereby making this a most desirable form of funding. If a company is not currently turning a profit, and therefore not in a position to pay taxes, one may question whether the company should factor the impact of taxes into the interest calculation. The answer is still yes, because any net loss will carry forward to the next reporting period, when the company can offset future earnings against the accumulated loss to avoid paying taxes at that time. Thus, the reduction in interest costs caused by the tax deductibility of interest is still applicable even if a company is not currently in a position to pay income taxes.

Another issue is the cost of acquiring debt and how this cost should be factored into the overall cost of debt calculation. When obtaining debt, either through a private placement or simply through a local bank, there are usually extra fees involved, which may include placement or brokerage fees, documentation fees, or the price of a bank audit. In the case of a private placement, the company may set a fixed percentage interest payment on the debt but find that prospective borrowers will not purchase the debt instruments unless they can do so at a discount, thereby effectively increasing the interest rate they will earn on the debt. In both cases, the company is receiving less cash than initially expected but must still pay out the same amount of interest expense. In effect, this raises the cost of the debt. To carry forward the first example above to second example, it is assumed that the interest payments are the same but that brokerage fees were \$25,000 and that the debt was sold at a 2 percent discount. The result is an increase in the actual interest rate.

When compared to the cost of equity that is discussed in the following section, it becomes apparent that debt is a much less expensive form of funding than equity. However, though it may be tempting to alter a company’s capital structure to increase the proportion of debt, thereby reducing the overall cost of capital, there are dangers involved in incurring a large interest expense.

### How to Calculate the Cost Of Equity

This section shows how to calculate the cost of the two main forms of equity: preferred stock and common stock. These calculations, as well as those from the preceding section on the cost of debt, are then combined in the following section to determine the weighted cost of capital.

Preferred stock stands at a midway point between debt and common stock. It requires an interest payment to the holder of each share of preferred stock but does not require repayment to the shareholder of the amount paid for each share. There are a few special cases in which the terms underlying the issuance of a particular set of preferred shares will require an additional payment to shareholders if company earnings exceed a specified level, but this is a rare situation. Also, some preferred shares carry provisions that allow delayed interest payments to be cumulative, so that they must all be paid before dividends can be paid out to holders of common stock.

The main feature shared by all kinds of preferred stock is that, under the tax laws, interest payments are treated as dividends instead of interest expense, which means that these payments are not tax deductible. This is a key issue, because it greatly increases the cost of funds for any company using this funding source. By way of comparison, if a company has a choice between issuing debt or preferred stock at the same rate, the difference in cost will be the tax savings on the debt. In the following example, a company issues \$1 million of debt and \$1 million of preferred stock, both at 9 percent interest rates, with an assumed 35 percent tax rate:

Debt cost = Principal × (Interest rate × (1 – Tax rate))
Debt cost = \$1,000,000 × (9% × (1 – 0.35))
\$58,500 = \$1,000,000 × (9% × 0.65)

If the same information is used to calculate the cost of payments using preferred stock, the result is:

Preferred stock interest cost = Principal × interest rate
Preferred stock interest cost = \$1,000,000 × 9%
\$90,000 = \$1,000,000 × 9%

This example shows that the differential caused by the applicability of taxes to debt payments makes preferred stock a much more expensive alternative. This being the case, why does anyone use preferred stock?

The main reason is that there is no requirement to repay the stockholder for the initial investment, whereas debt requires either a periodic or balloon payment of principal to eventually pay back the original amount. Companies can also eliminate the preferred stock interest payments if they include a convertibility feature into the stock agreement that allows for a conversion to common stock at some preset price point for the common stock. Thus, in cases in which a company does not want to repay principal any time soon, but does not want to increase the amount of common shares outstanding, preferred stock provides a convenient but expensive alternative.

The most difficult cost of funding to calculate by far is common stock, because there is no preset payment from which to derive a cost. Instead, it appears to be free money, because investors hand over cash without any predetermined payment or even any expectation of having the company eventually pay them back for the stock. Unfortunately, the opposite is the case.

Because holders of common stock have the most at risk (they are the last ones paid off in the event of bankruptcy), they want the most in return. Any management team that ignores its common stockholders and does nothing to give them a return on their investments will find that these people will either vote in a new board of directors that will find a new management team, or else they will sell off their shares at a loss to new investors, thereby driving down the value of the stock and opening up the company to the attention of a corporate raider, who will also remove the management team.

One way to determine the cost of common stock is to make a guess at the amount of future dividend payments to stockholders and discount this stream of payments back into a net present value. The problem with this approach is that the amount of dividends paid out is problematic, because they are declared at the discretion of the board of directors. Also, there is no provision in this calculation for changes in the underlying value of the stock; for some companies that do not pay any dividends, this is the only way in which a stockholder will be compensated.

A better method is called the “Capital Asset Pricing Model (CAPM)“. Without going into the very considerable theoretical detail behind this system, it essentially derives the cost of capital by determining the relative risk of holding the stock of a specific company as compared to a mix of all stocks in the market. This risk is composed of three elements.

The first is the return that any investor can expect from a risk-free investment, which is usually defined as the return on a U.S. government security. The second element is the return from a set of securities considered to have an average level of risk. This can be the average return on a large “market basket” of stocks, such as the Standard & Poor’s 500, the Dow Jones Industrials, or some other large cluster of stocks. The final element is a company’s beta, which defines the amount by which a specific stock’s returns vary from the returns of stocks with an average risk level. This information is provided by several of the major investment services, such as Value Line. A beta of 1.0 means that a specific stock is exactly as risky as the average stock, while a beta of .8 would represent a lower level of risk and a beta of 1.4 would be higher. When combined, this information yields the baseline return to be expected on any investment (the risk-free return), plus an added return that is based on the level of risk that an investor is assuming by purchasing a specific stock. This methodology is totally based on the assumption that the level of risk equates directly to the level of return, which a vast amount of additional research has determined to be a reasonably accurate way to determine the cost of equity capital. The main problem with this approach is that a company’s beta will vary over time, since it may add or subtract subsidiaries that are more or less risky, resulting in an altered degree of risk. Because of the likelihood of change, one must regularly recompute the equity cost of capital to determine the most recent cost.

A major problem with the use of beta for calculating a company’s cost of equity capital is that it is based on past results, which may not accurately reflect a company’s future prospects. Also, the beta calculation can result in drastically different results if the calculation period varies by as little as a few days, sometimes resulting in changes in beta of more than 100 percent. Given these problems, it has been proposed that the traded price of a company’s equity options be used instead as the foundation for the beta calculation, since these prices are based on the market’s best estimate of the future price volatility of the stock. This alternative method will only work if a company’s equity options are publicly traded, though it may be possible to impute option data by using similar options issued by comparable companies.

The calculation of the equity cost of capital using the CAPM methodology” is relatively simple, once one has accumulated all the components of the equation. For example: if the risk-free cost of capital is 5 percent, the return on the Dow Jones Industrials is 12 percent, and ABC Company’s beta is 1.5, the cost of equity for ABC Company would be:

Cost of equity capital:
= Risk-free return + Beta × (Average stock return – Risk-free return)
= 5% + 1.5 (12% – 5%)
= 5% + 1.5 × 7%
= 5% + 10.5%
= 15.5%

Although the example uses a rather high beta that increases the cost of the stock, it is evident that, far from being an inexpensive form of funding, common stock is actually the most expensive, given the size of returns that investors demand in exchange for putting their money at risk with a company. Accordingly, this form of funding should be used the most sparingly in order to keep the cost of capital at a lower level.

### How To Calculate The Weighted Cost Of Capital

Now that we have derived the costs of debt, preferred stock, and common stock, it is time to assemble all three costs into a weighted cost of capital. This section is structured in an example format, showing the method by which the weighted cost of capital of the Lie Dharma Corporation is calculated.

Following that, there is a short discussion of how the cost of capital can be used. The chief financial officer [CFO] of the Lie Dharma Corporation, Mr. Lie, is interested in determining the company’s weighted cost of capital, to be used to ensure that projects have a sufficient return on investment, which will keep the company from going to seed.

There are two debt offerings on the books. The first is \$1 million that was sold below par value, which garnered \$980,000 in cash proceeds. The company must pay interest of 8.5 percent on this debt. The second is for \$3 million and was sold at par but included legal fees of \$25,000. The interest rate on this debt is 10 percent. There is also \$2.5 million of preferred stock on the books, which requires annual interest (or dividend) payments amounting to 9 percent of the amount contributed to the company by investors. Finally, there is \$4 million of common stock on the books. The risk-free rate of interest, as defined by the return on current U.S. government securities, is 6 percent, while the return expected from a typical market basket of related stocks is 12 percent. The company’s beta is 1.2, and it currently pays income taxes at a marginal rate of 35 percent.

What is the Lie Dharma Company’s weighted cost of capital?

The method we will use is to separately compile the percentage cost of each form of funding, and then calculate the weighted cost of capital, based on the amount of funding and percentage cost of each of the above forms of funding. We begin with the first debt item, which was \$1 million of debt that was sold for \$20,000 less than par value, at 8.5 percent debt. The marginal income tax rate is 35 percent. The calculation is as follows:

Net after-tax interest percent is:
= ((Interest expense) × (1 – tax rate)) x Amount of debt / (Amount of debt) – (Discount on sale of debt)
= ((8.5%) × (1 – 0.35)) × \$1,000,000 / \$1,000,000 – \$20,000
= 5.638%

We employ the same method for the second debt instrument, for which there is \$3 million of debt that was sold at par. Legal fees of \$25,000 were incurred to place the debt, which pays 10 percent interest. The marginal income tax rate remains at 35 percent. The calculation is:

Net after-tax interest percent:
= ((Interest expense) × (1 – tax rate)) x Amount of debt / (Amount of debt) – (Legal expense)
= ((10%) × (1 – 0.35)) × \$3,000,000 / \$3,000,000 – \$25,000
= 7.091%

Having completed the interest expense for the two debt offerings, we move on to the cost of the preferred stock. As noted above, there is \$2.5 million of preferred stock on the books, with an interest rate of 9 percent. The marginal corporate income tax does not apply, because the interest payments are treated like dividends, and are not deductible. The calculation is the simplest of all, for the answer is 9 percent, since there is no income tax to confuse the issue.

Weighted Cost of Capital Calculation

Type of Funding      Amount of-     %         Cost Dollar Cost
Funding

Debt number 1       \$980,000      5.638%    \$55,252
Debt number 2       2,975,000     7.091%    210,957
Preferred stock       2,500,000     9.000%    225,000
Common stock      4,000,000   13.200%     528,000
Totals                \$10,455,000      9.75%  \$1,019,209

To arrive at the cost of equity capital, we take from the example a return on risk-free securities of 6 percent, a return of 12 percent that is expected from a typical market basket of related stocks, and a beta of 1.2. This information is plugged into the following formula to arrive at the cost of equity capital:

Cost of equity capital:
= Risk-free return + Beta × (Average stock return ? Risk-free return)
= 6% + 1.2 (12% ? 6%)
= 13.2%

Now that we know the cost of each type of funding, it is a simple matter to construct a table such as the one shown in above that lists the amount of each type of funding and its related cost, which we can quickly sum to arrive at a weighted cost of capital. When combined into the weighted average calculation shown in figure, we see that the weighted cost of capital is 9.75 percent. Though there is some considerably less expensive debt on the books, the majority of the funding is comprised of more expensive common and preferred stock, which drives up the overall cost of capital. Thus far, we have discussed the components of the cost of capital, how each one is calculated, and how to combine all the various kinds of capital costs into a single weighted cost of capital. Now that we have it, what do we use it for? That is the subject of my next post Incremental Cost of Capital“.

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