The Cost of Capital

1

KIERULFF’S NOTES ON THE COMPONENT COSTS OF CAPITAL

The cost of capital is the rate of return required to induce sufficient investment in a given project or company by suppliers of capital. You use it to discount cash flows in present value analyses and in comparison with the internal rate of return (IRR) or modified IRR (MIRR) of an investment. The term “cost of capital” is generally used to refer to the discount rate for the company as a whole. The term “hurdle rate” is used for project, division, department, or other asset valuations.

This cost is a future oriented, incremental concept—what will be the cost of debt andthe required rate of return on equity for the next investment. Often, you estimate it by using some average of past data assuming an efficient market (where companies are fairly valued). If you use past data, remember that you are assuming that the required rate of return = expected rate of return = average actual (past) rate of return unless you make adjustments to reflect your view of the future. Also, you should recognize that the further back you go into the past to obtain data, the more data points you have; the more data points you have the greater is the statistical accuracy. On the other hand, the further back you go, the less relevant to a forecast are the data points and the more likely they are to mislead.

The cost of capital must be sufficient to support the following:

1. An inducement to forego liquidity. Investors tend to prefer liquidity since it gives them the options to save, spend now on consumer goods, or invest in another (presumably better) future opportunity. Historically, investors have required a one to three percent real return on capital (non-inflationary) as encouragement to invest. This factor is often referred to as liquidity preference or as the real rate of interest—real because it does not include inflation or risk.

1. The rate of inflation expected over the investment’s life assuming the cash flow estimate includes inflation.

1. Maturity or investment rate risk. Risk is most often understood as variation in returns. The greater the expected variation, the greater is the risk. Since the prices of government bonds vary slightly over time as interest rates change, even these “safe” bonds are subject to risk. Longer-term government bond prices vary more than short-term government bonds.

1. Market risk, expressed as a percentage and added to the above three factors.

Factors a, b, and c are termed the “risk free” rate of return even though c denotes risk.The proxy for the risk free rate is generally the current Treasury bond yield that matches the maturity of the project (current rule of thumb, 20 years for a company). Factor d is termed the risk premium (RP) or the market return less the risk free rate (Rm – Rf).

The liquidity and inflation factors in the riskless rate are multiplicative because they are independent of one another; the maturity or investment rate risk is additive:

Risk free rate = {[(1+Liquidity %) * (1+Expected Inflation %)] – 1} + Maturity (Investment Rate) Risk.

This is important because sometimes cash flows are forecast in constant rather than current values, leaving out the effect of inflation. If that is the case, you must adjust the risk free rate by dividing out expected inflation from the risk free rate rather than subtracting it: (1 + Treasury bond yield) / (1+Expected Inflation) - 1

Capitalization and the cost of capital

The capitalizationor Enterprise Value of the company (its total operating capital) is made up of all interest bearing debt associated with operations, preferred stock, common stock, and retained earnings. Retained earnings belong to the common stockholders so is a part of common equity and included inthe return to equity (Ke). Actually, the required return on (cost of) retained earnings is less than the required return on new common stock because it costs to float a stock issue—five to ten percent of the issue itself to pay for lawyers, investment bankers, printers to print the offering materials and distribute them, etc.

The currency value of the capitalization (interest bearing debt + equity) exactly equals the value of the operating assets of the company minus the operating current liabilities. Otherwise the balance sheet will not balance. A balance sheet T account can demonstrate this. On the left hand side is net operating working capital (current operating assets minus current operating liabilities), fixed operating tangible assets, and operating intangible assets such as patents, copyrights, trademarks and the like. Current operating working capital excludes such non-operating items as excess cash, loans to employees, and current interest bearing debt. On the right hand side of the T account balance sheet are all interest bearing debt + equity. Equity includes preferred stock, common stock, retained earnings (cumulative profit and losses after taxes, cumulative after tax gains and losses on the sale of assets, and cumulative gains and losses on currency transactions), and the repurchase of stock by the company (treasury stock) with after tax cash flows. Keep in mind that valuators are analyzing the value of an operating company, division, joint venture, etc. not counting the assets and liabilities that do not contribute to operations. Non-operating assets and liabilities are valued separately. Since the balance sheet in this form must balance, you can value the assets by valuing the operating debt + equity.

It is important to note the distinction between market value and book value. The value of the assets on the books of the company often does not reflect the market value of the assets because of the difficulty in estimating intangible value. Most valuation authorities recommend using the market value of the debt and equity. However, some academics have suggested that market values fluctuate radically and may be poor measures of value at times. Also, they note that executives setting policy using ratio measures such as debt to equity do so in book value terms. When terms such as Enterprise Value, Market Value of Invested Capital (MVIC), Total Enterprise Value (TEV), and Market Cap are used market instead of book value is meant.

When estimating the cost of capital, the weighted average cost of capital (WACC) approach has you weighing the debt and equity components by the percentage each makes up of the total. WACC represents the discount factor (i, or sometimes r) in discounted cash flow using the Income Method. Including the cost of preferred stock that most writers exclude or treat as debt for simplicity:

WACC = [(Kd * D/V * (1 – T)] + (Kp * P/V) + (Ke * E/V) = i.

Where:Kd = cost of debt (the interest rate)

D = amount of debt in the capital structure

V = value of the operating assets as measured by debt + equity

T = expected tax rate

Kp = required return on preferred stock

P = value of preferred stock

Ke = required return on equity

E = value of common stock

As you add debt, the cost of capital will begin to decline at the point investors realize the risk of adding debt. It will continue to decline at least up to the point where debt becomes so burdensome that risk begins to increase disproportionately. This phenomenon is due to the tax deductibility of debt and was explained in a groundbreaking article by Modigliani and Miller (now known as M&M).

The M & M insight

Does it matter whether you use debt, preferred stock, common stock or some combination to finance a company or project? The returns to holders of these securities have to cover their liquidity preference, inflation, maturity risk, and market risk. These four factors stay the same regardless of the form of financing—so long as the risk associated with the assets does not change. Another way of looking at it is this: the way assets, including intangible assets, are used determines the value of a firm or division or business unit and the risk associated with it. The market value of a set of assets is not dependent upon how those assets are financed.

On the other hand, debt is typically less expensive than preferred stock, which is less expensive than common stock. In the event of financial difficulties, holders of these securities are paid off in the above order, so creditors are more likely than equity holders to get their money back if the balance sheet is restructured or the company is liquidated. Furthermore, debt principal and interest must be paid when due or creditors can take legal action. The rules on common stock and common stock dividends are not so strict. It follows that when you add debt to a capital structure, you might expect that the overall cost of capital would drop rather than stay the same because debt is less expensive than equity.

So you are faced with a dilemma. Does adding debt not matter because the risks associated with the way the assets are deployed in the market determines their required rate of return? Or will adding debt reduce the overall cost of capital because debt is less expensive than equity?

Modigliani and Miller (now nicknamed M&M) came up with an answer by demonstrating that as you add debt, the risk to both debt holders and stockholders increases because the requirement to pay principal and interest may cripple the company and depress its stock in hard times when cash is limited. This risk is called financial risk to distinguish it from market risk and operating risk. The company is said to be adding financial leverage (called gearing in the UK), and as the risk associated with this leverage increases with the addition of debt, so must the cost of equity. Similar reasoning applies to the addition of preferred stock since it has many of the characteristics of debt.

M&M showed that the reduction in capital costs coming about by using more debt is exactly offset by the increase in the cost of debt and equity. This makes sense, since the market risk remains constant at a point in time no matter how the company is financed. Financing has nothing to do with market risk. If the cost of equity capital (its price in the market) is below the rate needed to satisfy liquidity preference, inflation, investment risk, and market risk, the demand for the equity will increase. Eventually, this will drive the cost of equity up following the law of supply and demand. The same reasoning holds true for suppliers of debt and investors in preferred stock. The reverse happens if the cost of capital is too high. In other words, arbitrage will happen.

However, M&M’s proof only works in the absence of taxes. In practice, the government participates in the market risk to the extent of the tax deductibility of interest. Dividends on preferred and common stock are not so blessed. As a result, the more debt you use, the cheaper the overall cost of capital, but the greater the financial risk. At some point, the increasing cost of debt and equity offsets the advantage of tax deductibility and the cost of capital rises. Sadly enough, there is no formula to tell you where this debt/equity point is for any given company or industry at any given time. Expected economic conditions and changes in the structure and strategic use of company assets influence this point.

The components of the cost of capital

1. Cost of Debt: Kd

1. Debt includes all interest bearing securities. Some theorists would exclude short-term debt, i.e., debt that must be paid off in a year or less and is not rolled over (extended) on a routine basis.

1. You may estimate the cost as a percentage by finding: (1) the required yield (IRR) on the interest bearing debts of the subject company assuming the yield will stay the same; or (2) the interest rate paid on similar debt instruments by companies with similar risk characteristics; or (3) CAPM (see below).

1. The Kd is usually shown as the interest rate charged by the lender. It does not take account of taxes; it is a pre-tax number. But the company does not pay the pre-tax cost of debt—it pays the after tax rate because interest is tax deductible. This lower cost should be recognized by the (1 – T) factor where T is the federal and state income tax.

1. Debt is cheaper than preferred stock and common stock because of the tax factor, but also because debt-holders get paid off before the others in the case of bankruptcy. Also, interest must be paid and principal repaid on schedule or the firm faces serious difficulties. There are many different kinds of debt and repayment arrangements, and you should be familiar with the differences.

1. Cost of Preferred Stock: Kp

1. The cost of preferred stock may be estimated by dividing the expected (or past) preferred dividend per share by the expected price of the preferred stock per share (or the total preferred dividend by the total value of the preferred stock). Again, the past doesn’t necessarily reflect the future.

1. Although there are significant differences between preferred stocks and corporate bonds, you usually treat preferred stocks as bonds for the purpose of determining cost of capital.

1. Cost of Equity (COE or Ke) measures the required return to holders of common stock. The numerous measures of this factor all have strengths and drawbacks. The most well known and practical measures are shown here:

1. (D1+P1-Po) / Po: Shareholder Return Model, i.e., dividends expected for the next period plus expected change in stock price (capital gains) divided by beginning stock price. This is referred to as return on shareholders’ equity or investment. You use the next period if the dividend for this period has already been paid. You may estimate this equity cost by using previous periods’ data, if you realize that you are violating the incremental, future value concept—i.e., the future may not be like the past. If a stock split occurs before the end of a given period being measured, the formula becomes, for an X for Y split (say 2 for 1):

(x/y*D1) + [((x/y*P1)-Po)]

Ke = Po

1. Dividend growth model: Ke = (D1 / Po) + g.

Where D1 equals the next expected dividend (or free cash flow) to equity per share, Po the current price of the stock, and g, the expected equity dividend (or free cash flow to equity) growth forever. You estimate dividend or free cash flow to equity growth (g) by (1) a time series analysis of past data using regression, (2) a compound growth forecast based upon past data, (3) a subjective estimate, and / or (4) the following sustainable growth rate (SGR) formula based upon ROE:

SGR = Rate the company can grow without increasing the debt / equityratio.

SGR = ROE * [1- (Dividends per share / Earnings per share)]

1. Equity build-up models (BUM), including the capital asset pricing model (BUMCAPM). Measures of market risk, specific industry and/or company risk, and country risk are added to the risk free rate to produce Ke. Market risk measures have in common some form of beta, explained below.

Measuring Market Risk with Beta

Market risk is measured as the difference between the return on investments (ROI) generated by a proxy market index such as the Standard and Poor’s (S&P) 500Index or various stock exchanges such as the New York Stock Exchange (NYSE) Index shown as market risk (Rm) and the risk free rate (Rf). Market risk is often noted as(Rm- Rf) or ERP (Equity Risk Premium). These indexes are assumed to reflect the entire market for investments (a notion currently under challenge by practitioners and academics). However, in using Duff & Phelps (D&P) data you need to distinguish between the ERP and Rmor Rm–Rf (usually total market risk minus the risk free rate), and RP (risk premium). The latter three usually refer to past data that may or may not have a factor added for the expected future depending upon the author’s definition. In D&P, ERP refers to the past actual Rm plus an ERPadjustment to reflect your estimate of what the future may bring. RP refers to historical data in D&P.

Variations, both down and up, in this index over time constitute market risk—referred to as systematic risk. Systematic risks are those that affect all companies more or less equally and require a risk premium (RP or ERP) as part of the cost of capital. The business cycle, interest rate changes, social upheavals, and similar events and trends qualify as systematic risks. Since each company will react differently to these risks, a special qualifier called beta, signified by β, is multiplied by the ERP in the D&P data. A beta larger than one indicates that the company is riskier than the average company in the proxy market; a beta smaller than one indicates that the company is less risky. It is important to remember that systematic risks do not cover all risks faced by a firm.

Unsystematic or unique risks associated with individual companies or industries will also affect future company returns. Unsystematic risks are specific to a firm or industry, examples being the sudden death of the CEO, the unexpected acquisition of a large order, a lawsuit, positive and negative events that affect one industry more than others, and similar events. Unsystematic risks must be captured separately to develop total company risk.