# Cost of capital

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In Economics and Accounting, the cost of capital is the cost of a company's funds (both debt and equity), or, from an investor's point of view "the required rate of return on a portfolio company's existing securities". [1] It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.

Economics is the social science that studies the production, distribution, and consumption of goods and services.

Accounting or accountancy is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. The modern field was established by the Benedikt Kotruljevic in 1458, merchant, economist, scientist, diplomat and humanist from Dubrovnik (Croatia), and Italian mathematician Luca Pacioli in 1494. Accounting, which has been called the "language of business", measures the results of an organization's economic activities and conveys this information to a variety of users, including investors, creditors, management, and regulators. Practitioners of accounting are known as accountants. The terms "accounting" and "financial reporting" are often used as synonyms.

Debt is when something, usually money, is owed by one party, the borrower or debtor, to a second party, the lender or creditor. Debt is a deferred payment, or series of payments, that is owed in the future, which is what differentiates it from an immediate purchase. The debt may be owed by sovereign state or country, local government, company, or an individual. Commercial debt is generally subject to contractual terms regarding the amount and timing of repayments of principal and interest. Loans, bonds, notes, and mortgages are all types of debt. The term can also be used metaphorically to cover moral obligations and other interactions not based on economic value. For example, in Western cultures, a person who has been helped by a second person is sometimes said to owe a "debt of gratitude" to the second person.

## Basic concept

For an investment to be worthwhile, the expected return on capital has to be higher than the cost of capital. Given a number of competing investment opportunities, investors are expected to put their capital to work in order to maximize the return. In other words, the cost of capital is the rate of return that capital could be expected to earn in the best alternative investment of equivalent risk; this is the opportunity cost of capital. If a project is of similar risk to a company's average business activities it is reasonable to use the company's average cost of capital as a basis for the evaluation or cost of capital is a firm's cost of raising funds. However, for projects outside the core business of the company, the current cost of capital may not be the appropriate yardstick to use, as the risks of the businesses are not the same. [2]

Return on capital (ROC), or return on invested capital (ROIC), is a ratio used in finance, valuation and accounting, as a measure of the profitability and value-creating potential of companies after taking into account the amount of initial capital invested. The ratio is calculated by dividing the after-tax operating income (NOPAT) by the book value of both debt and equity capital less cash/equivalents.

In economics, capital consists of assets that can enhance one's power to perform economically useful work. For example, in a fundamental sense a stone or an arrow is capital for a caveman who can use it as a hunting instrument, while roads are capital for inhabitants of a city.

In microeconomic theory, the opportunity cost, or alternative cost, of making a particular choice is the value of the most valuable choice out of those that were not taken. When an option is chosen from alternatives, the opportunity cost is the "cost" incurred by not enjoying the benefit associated with the best alternative choice. The New Oxford American Dictionary defines it as "the loss of potential gain from other alternatives when one alternative is chosen."

A company's securities typically include both debt and equity, one must therefore calculate both the cost of debt and the cost of equity to determine a company's cost of capital. Importantly, both cost of debt and equity must be forward looking, and reflect the expectations of risk and return in the future. This means, for instance, that the past cost of debt is not a good indicator of the actual forward looking cost of debt.

Once cost of debt and cost of equity have been determined, their blend, the weighted average cost of capital (WACC), can be calculated. This WACC can then be used as a discount rate for a project's projected free cash flows to the firm.

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Importantly, it is dictated by the external market and not by management. The WACC represents the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

The annual effective discount rate expresses the amount of interest paid/earned as a percentage of the balance at the end of the (annual) period. This is in contrast to the effective rate of interest, which expresses the amount of interest as a percentage of the balance at the start of the period. The discount rate is commonly used for U.S. Treasury bills and similar financial instruments.

## Example

Suppose a company considers taking on a project or investment of some kind, for example installing a new piece of machinery in one of their factories. Installing this new machinery will cost money; paying the technicians to install the machinery, transporting the machinery, buying the parts and so on. This new machinery is also expected to generate new profit (otherwise, assuming the company is interested in profit, the company would not consider the project in the first place). So the company will finance the project with two broad categories of finance: issuing debt, by taking out a loan or other debt instrument such as a bond; and issuing equity, usually by issuing new shares.

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. The most common types of bonds include municipal bonds and corporate bonds.

In accounting, equity is the difference between the value of the assets and the value of the liabilities of something owned. It is governed by the following equation:

In financial markets, a share is a unit used as mutual funds, limited partnerships, and real estate investment trusts. The owner of shares in the corporation/company is a shareholder of the corporation. A share is an indivisible unit of capital, expressing the ownership relationship between the company and the shareholder. The denominated value of a share is its face value, and the total of the face value of issued shares represent the capital of a company, which may not reflect the market value of those shares.

The new debt-holders and shareholders who have decided to invest in the company to fund this new machinery will expect a return on their investment: debt-holders require interest payments and shareholders require dividends (or capital gain from selling the shares after their value increases). The idea is that some of the profit generated by this new project will be used to repay the debt and satisfy the new shareholders.

Interest, in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

A dividend is a payment made by a corporation to its shareholders, usually as a distribution of profits. When a corporation earns a profit or surplus, the corporation is able to re-invest the profit in the business and pay a proportion of the profit as a dividend to shareholders. Distribution to shareholders may be in cash or, if the corporation has a dividend reinvestment plan, the amount can be paid by the issue of further shares or share repurchase. When dividends are paid, shareholders typically must pay income taxes, and the corporation does not receive a corporate income tax deduction for the dividend payments.

A capital gain refers to profit that results from a sale of a capital asset, such as stock, bond or real estate, where the sale price exceeds the purchase price. The gain is the difference between a higher selling price and a lower purchase price. Conversely, a capital loss arises if the proceeds from the sale of a capital asset are less than the purchase price.

Suppose that one of the sources of finance for this new project was a bond (issued at par value) of $200,000 with an interest rate of 5%. This means that the company would issue the bond to some willing investor, who would give the$200,000 to the company which it could then use, for a specified period of time (the term of the bond) to finance its project. The company would also make regular payments to the investor of 5% of the original amount they invested ($10,000), at a yearly or monthly rate depending on the specifics of the bond (these are called coupon payments). At the end of the lifetime of the bond (when the bond matures), the company would return the$200,000 they borrowed.

Par value, in finance and accounting, means stated value or face value. From this come the expressions at par, over par and under par.

Suppose the bond had a lifetime of ten years and coupon payments were made yearly. This means that the investor would receive $10,000 every year for ten years, and then finally their$200,000 back at the end of the ten years. From the investor's point of view, their investment of $200,000 would be regained at the end of the ten years (entailing zero gain or loss), but they would have also gained from the coupon payments; the$10,000 per year for ten years would amount to a net gain of $100,000 to the investor. This is the amount that compensates the investor for taking the risk of investing in the company (since, if it happens that the project fails completely and the company goes bankrupt, there is a chance that the investor does not get their money back). This net gain of$100,000 was paid by the company to the investor as a reward for investing their money in the company. In essence, this is how much the company paid to borrow $200,000. It was the cost of raising$200,000 of new capital. So to raise $200,000 the company had to pay$100,000 out of their profits; thus we say that the cost of debt in this case was 50%.

Theoretically, if the company were to raise further capital by issuing more of the same bonds, the new investors would also expect a 50% return on their investment (although in practice the required return varies depending on the size of the investment, the lifetime of the loan, the risk of the project and so on).

The cost of equity follows the same principle: the investors expect a certain return from their investment, and the company must pay this amount in order for the investors to be willing to invest in the company. (Although the cost of equity is calculated differently since dividends, unlike interest payments, are not necessarily a fixed payment or a legal requirement)

## Cost of debt

When companies borrow funds from outside lenders, the interest paid on these funds is called the cost of debt. The cost of debt is computed by taking the rate on a risk-free bond whose duration matches the term structure of the corporate debt, then adding a default premium. This default premium will rise as the amount of debt increases (since, all other things being equal, the risk rises as the cost of debt rises). Since in most cases debt expense is a deductible expense, the cost of debt is computed on an after-tax basis to make it comparable with the cost of equity (earnings are taxed as well). Thus, for profitable firms, debt is discounted by the tax rate. The formula can be written as

${\displaystyle K_{D}=(R_{f}+{\text{credit risk rate}})(1-T)}$,

where ${\displaystyle T}$ is the corporate tax rate and ${\displaystyle R_{f}}$ is the risk free rate.

## Cost of equity

The cost of equity is inferred by comparing the investment to other investments (comparable) with similar risk profiles. It is commonly computed using the capital asset pricing model formula:

Cost of equity = Risk free rate of return + Premium expected for risk
Cost of equity = Risk free rate of return + Beta × (market rate of return – risk free rate of return)

where Beta = sensitivity to movements in the relevant market. Thus in symbols we have

${\displaystyle E_{s}=R_{f}+\beta _{s}(R_{m}-R_{f})}$

where:

Es is the expected return for a security;
Rf is the expected risk-free return in that market (government bond yield);
βs is the sensitivity to market risk for the security;
Rm is the historical return of the stock market; and
(Rm – Rf) is the risk premium of market assets over risk free assets.

The risk free rate is the yield on long term bonds in the particular market, such as government bonds.

An alternative to the estimation of the required return by the capital asset pricing model as above, is the use of the Fama–French three-factor model.

### Expected return

The expected return (or required rate of return for investors) can be calculated with the "dividend capitalization model", which is

${\displaystyle K_{cs}={\frac {{\text{Dividend}}_{\text{Payment/Share}}(1+{\text{Growth}})}{{\text{Price}}_{\text{Market}}}}+{\text{Growth}}_{\text{rate}}}$.

The models state that investors will expect a return that is the risk-free return plus the security's sensitivity to market risk (β) times the market risk premium.

The risk premium varies over time and place, but in some developed countries during the twentieth century it has averaged around 5% whereas in the emerging markets, it can be as high as 7%. The equity market real capital gain return has been about the same as annual real GDP growth. The capital gains on the Dow Jones Industrial Average have been 1.6% per year over the period 1910-2005. [3] The dividends have increased the total "real" return on average equity to the double, about 3.2%.

The sensitivity to market risk (β) is unique for each firm and depends on everything from management to its business and capital structure. This value cannot be known "ex ante" (beforehand), but can be estimated from ex post (past) returns and past experience with similar firms.

#### Cost of retained earnings/cost of internal equity

Note that retained earnings are a component of equity, and, therefore, the cost of retained earnings (internal equity) is equal to the cost of equity as explained above. Dividends (earnings that are paid to investors and not retained) are a component of the return on capital to equity holders, and influence the cost of capital through that mechanism.

Cost of internal equity = [(next year's dividend per share/(current market price per share - flotation costs)] + growth rate of dividends)]

## Weighted average cost of capital

The weighted cost of capital (WACC) is used in finance to measure a firm's cost of capital. WACC is not dictated by management. Rather, it represents the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere. [4]

The total capital for a firm is the value of its equity (for a firm without outstanding warrants and options, this is the same as the company's market capitalization) plus the cost of its debt (the cost of debt should be continually updated as the cost of debt changes as a result of interest rate changes). Notice that the "equity" in the debt to equity ratio is the market value of all equity, not the shareholders' equity on the balance sheet. To calculate the firm's weighted cost of capital, we must first calculate the costs of the individual financing sources: Cost of Debt, Cost of Preference Capital, and Cost of Equity Cap.

Calculation of WACC is an iterative procedure which requires estimation of the fair market value of equity capital [ citation needed ] if the company is not listed. The Adjusted Present Value method (APV) is much easier to use in this case as it separates the value of the project from the value of its financing program.

## Factors that can affect cost of capital

Below are a list of factors that might affect the cost of capital [5] [6]

### Capital Structure

Because of tax advantages on debt issuance, it will be cheaper to issue debt rather than new equity (this is only true for profitable firms, tax breaks are available only to profitable firms). At some point, however, the cost of issuing new debt will be greater than the cost of issuing new equity. This is because adding debt increases the default risk - and thus the interest rate that the company must pay in order to borrow money. By utilizing too much debt in its capital structure, this increased default risk can also drive up the costs for other sources (such as retained earnings and preferred stock) as well. Management must identify the "optimal mix" of financing – the capital structure where the cost of capital is minimized so that the firm's value can be maximized.

The Thomson Financial league tables show that global debt issuance exceeds equity issuance with a 90 to 10 margin.

The structure of capital should be determined considering the weighted average cost of capital.

### Accounting Information

Lambert, Leuz & Verrecchia (2007) have found that the quality of accounting information can affect a firm's cost of capital, both directly and indirectly. [7]

## Modigliani–Miller theorem

If there were no tax advantages for issuing debt, and equity could be freely issued, Miller and Modigliani showed that, under certain assumptions (no tax), the value of a levered firm and the value of an unlevered firm should be the same.

## Related Research Articles

In finance, the net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

To invest is to allocate money in the expectation of some benefit in the future.

The Modigliani–Miller theorem is an influential element of economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. Since the value of the firm depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt, the Modigliani–Miller theorem is often called the capital structure irrelevance principle.

In finance, a convertible bond or convertible note or convertible debt is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features. It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering.

The APV was introduced in 1974 bij Stewart Myers. According to Myers, the value of the levered firm is equal to the value of the firm with no debt plus the present value of the tax savings due to the tax deductability of interest payments, the so called value of the tax shield (VTS). Myers proposes calculating the VTS by discounting the tax savings at the cost of debt (Kd). The argument is that the risk of the tax saving arising from the use of debt is the same as the risk of the debt. The method is to calculate the NPV of the project as if it is all-equity financed. Then the base-case NPV is adjusted for the benefits of financing. Usually, the main benefit is a tax shield resulted from tax deductibility of interest payments. Another benefit can be a subsidized borrowing at sub-market rates. The APV method is especially effective when a leveraged buyout case is considered since the company is loaded with an extreme amount of debt, so the tax shield is substantial.

In finance, the yield on a security is the amount of cash that returns to the owners of the security, in the form of interest or dividends received from it. Normally, it does not include the price variations, distinguishing it from the total return. Yield applies to various stated rates of return on stocks, fixed income instruments, and some other investment type insurance products.

Preferred stock is a form of stock which may have any combination of features not possessed by common stock including properties of both an equity and a debt instrument, and is generally considered a hybrid instrument. Preferred stocks are senior to common stock, but subordinate to bonds in terms of claim and may have priority over common stock in the payment of dividends and upon liquidation. Terms of the preferred stock are described in the issuing company's articles of association or articles of incorporation.

Capital structure in corporate finance is the way a corporation finances its assets through some combination of equity, debt, or hybrid securities.

In corporate finance, the return on equity (ROE) is a measure of the profitability of a business in relation to the equity, also known as net assets or assets minus liabilities. ROE is a measure of how well a company uses investments to generate earnings growth.

In finance, the cost of equity is the return a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire capital from others to operate and grow. Individuals and organizations who are willing to provide their funds to others naturally desire to be rewarded. Just as landlords seek rents on their property, capital providers seek returns on their funds, which must be commensurate with the risk undertaken.

Share repurchase is the re-acquisition by a company of its own stock. It represents a more flexible way of returning money to shareholders.

The following outline is provided as an overview of and topical guide to finance:

A financial ratio or accounting ratio is a relative magnitude of two selected numerical values taken from an enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Financial analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.

Dividend policy is concerned with financial policies regarding paying cash dividend in the present or paying an increased dividend at a later stage. Whether to issue dividends, and what amount, is determined mainly on the basis of the company's unappropriated profit and influenced by the company's long-term earning power. When cash surplus exists and is not needed by the firm, then management is expected to pay out some or all of those surplus earnings in the form of cash dividends or to repurchase the company's stock through a share buyback program.

Corporate finance is an area of finance that deals with sources of funding, the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value. Although it is in principle different from managerial finance which studies the financial management of all firms, rather than corporations alone, the main concepts in the study of corporate finance are applicable to the financial problems of all kinds of firms.

## References

1. Brealey, Myers, Allen. "Principles of Corporate Finance", McGraw Hill, Chapter 10
2. Fernandes, Nuno. 2014, Finance for Executives: A Practical Guide for Managers, p. 17.
3. Fred's Intelligent Bear Site Archived 2004-12-09 at the Wayback Machine
4. Fernandes, Nuno. 2014, Finance for Executives: A Practical Guide for Managers, p. 32.
• Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment". American Economic Review . 48 (3): 261–297. JSTOR   1809766.
• Rosenbaum, Joshua; Joshua Pearl (2009). Investment Banking: Valuation, Leveraged Buyouts, and Mergers & Acquisitions. Hoboken, NJ: John Wiley & Sons. ISBN   978-0-470-44220-3.
• Yee, Kenton K. (2000). "Aggregation, Dividend Irrelevancy, and Earnings-Value Relations". Contemporary Accounting Research . 22 (2): 453–480. doi:10.1506/GEH4-WNJR-G58F-UM0U. SSRN  .