# A Basic Introduction to the Methodology Used to Determine a Discount Rate

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1 A Basic Introduction to the Methodology Used to Determine a Discount Rate By Dubravka Tosic, Ph.D. The term discount rate is one of the most fundamental, widely used terms in finance and economics. Whether one is dealing with a business valuation or litigation involving allegations of lost profit or lost compensation, the financial and economic analysis performed typically involves the critical process of determining an appropriate discount rate. A discount rate is used to determine the present value of a stream of economic benefits expected to be generated in the future. Examples of such economic benefits are a stream of future cash flows for a business, asset, or an investment, or a stream of projected earnings for an individual. The present value of a stream of future cash flows must be determined for at least one simple reason, the time value of money. The concept of the time value of money answers questions such as whether \$1,000 today is worth more, less or the same as \$1,000 one year from today, and why? The time value of money reflects the simple idea that everyone would prefer to have one dollar today compared to receiving one dollar at a later date. According to this view, deferring receipt of money to a later date requires a return, i.e. interest. As such, the value today of money to be received in the future is less than the face value to be received in the future; i.e., a future receipt is discounted to arrive at today s value (or present value ). The present value of a future economic benefit can be calculated by using the following basic formula: PV FV 1 r t t Where: FV t is the future value of a cash payout a time t, r is the discount rate, and t is the length of time between the present and the future payout. 1

2 For example, if one anticipates receiving \$100,000 five years from now from a business venture, the present value of this amount is calculated as: PV = \$100,000 / (1 + r) 5 Where r is the discount rate to be used. If one assumes that a proper discount rate to use is a risk-free rate of 0.25%, the calculations would be: PV = \$100,000 / ( ) 5 = \$88, Based on this calculation, \$100,000 five years from now is worth \$88, today. Another way to interpret this calculation is that an investment of \$88, today, at an interest rate of 0.25%, will be valued at \$100,000 in five years (assuming simple interest). This example illustrates that the discount rate is just the interest rate used to determine the present value of a stream of future cash flows. Net present value ( NPV ) is a similar concept to present value. NPV is basically the present value of a stream of cash flows received at expected time intervals (e.g. received over several years). In calculating the present value of a stream of cash flows, NPV considers both inflows and outflows. When the NPV of a cash flow is positive, the economic benefit is thought to have a positive present value. Therefore, the determination of the present value of a cash flow in essence determines a discounted cash flow. Hence, one of the fundamental ways of determining value is to first estimate or forecast a future cash flow which is then discounted with an appropriate discount rate to convert this forecasted cash flow to present value. The basic formula for NPV is: NPV C 0 C 1 C2 1 r CT... 1 r 2 1 r T Where: C0, C1, C2..CT are the projected or forecasted cash flows at time 0, 1, 2 T, and r is the discount rate to be used in the calculation. 2

3 A common type of NPV analysis is called a discounted cash flow model ( DCF ). A DCF analysis is generally one method used to value an income producing asset or business. Chart 1 (below) shows the impact varied discount rates have on the present value of \$5,000,000 to be received five years from today. Chart 1 Present Value of \$5 Million Using Different Discount Rates Present Value \$5,000,000 \$4,500,000 \$4,000,000 \$3,500,000 \$3,000,000 \$2,500,000 \$2,000,000 \$1,500,000 \$1,000,000 \$500,000 \$0 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% Discount Rate Present Value From Chart 1 one can see that by applying a 2% discount rate, a cash flow of \$5 million received five years from now has a present value of about \$4.5 million. On the other hand, applying a discount rate of 30% reduces the present value of the \$5 million substantially to approximately \$1.3 million. Since a present value of \$4.5 million is drastically different from a present value of \$1.3 million, one can reach drastically different conclusions about the value of a forecasted economic benefit. Chart 1 demonstrates several key points: 1. There is an inverse relationship between the present value and the discount rate used. The higher the discount rate used, the lower the present value, and the lower the discount rate used, the higher the present value. 2. The present value of an economic benefit is sensitive to the discount rate chosen. For example, using a 12% discount rate above yields a present value of \$2.8 million, while choosing a 14% discount rate yields a present value of almost \$2.6 million. A 2% difference in the discount rate chosen results in over a \$200,000 difference in present value. 3

5 uncertain or riskier future cash flows are perceived to be, the higher the rate of return an investor will require, meaning that a higher discount rate would be required, leading to a lower present value. Conversely, the lower the perceived risk to an investment, the lower the required rate of return will be, leading to a higher present value. This implies that the discount rate for investments with risky cash flows should be higher than the discount rate for investments with risk free cash flows. Additionally, since a discount rate should consider the time value of money and the riskiness of the forecasted cash flows, it typically represents a company s cost of capital or an investor s required rate of return. Determining the present value of a forecast of future cash flows to a business requires an understanding of earnings generated by the business as well as returns for both debt and equity investors. Therefore, the cost of capital of a business is typically considered to be a combination of debt costs and equity costs, weighted by the relative proportion of each type of capital invested in the company. A methodology used to determine an appropriate discount rate is to calculate the Weighted Average Cost of Capital ( WACC ). WACC is the discount rate used to evaluate the NPV of stream of future cash flows. WACC is calculated as the weighted cost of the various components of a company s capital structure, typically consisting of debt and equity. The WACC equation can be expressed as: Where: E = market value of the company s equity V = total value of the company s equity and debt Re = the company s cost of equity D = the market value of the company s debt Rd = the company s cost of debt Tc = the company s corporate tax rate A balance sheet would show the company s capital structure and the value of assets owned by the company, both debt and equity. If a company s balance sheet shows \$40 million in assets, of which \$24 million is in debt and \$16 million is in equity, then the debt to equity ratio is (or 3-2). As a consequence, debt capital represents 60% of the company s assets, and equity capital represents 40% of 5

6 the company s assets. The WACC calculation, therefore, would weight debt capital by 60% and equity capital by 40%. In order to calculate WACC, one must first calculate the cost of debt capital, and then the cost of equity capital: 1. Cost of Debt The cost of debt may be calculated in various ways, and may be calculated by considering various types of debt. Most often, the cost of debt corresponds to the interest rate a company is paying on all of its debt, such as long-term bank debt, corporate bonds, leases, preferred stock, warrants, etc. Companies with higher risk will usually have a higher cost of debt. The cost of debt may be adjusted by the corporation s tax rate, to take into account that a reduction in taxable income also reduces the tax obligation. This adjustment is often referred to as tax-effecting the interest rate and involves the interest rate shield ( ITS ). While DCF analysis attempts to capture taxes and other financing effects in a WACC, other analysis such as the Adjusted Present Value ( APV ) analysis does not. 2. Cost of Equity The cost of equity can be considered the rate of return required by a company s common stockholders. If shareholders do not receive the return they expect on their investment, they may be inclined to sell their shares. Therefore, a company will want to ensure that it returns what its investors desire, through share appreciation and dividends. All methodologies used to calculate the cost of equity have three basic components in common: 5a. The risk-free rate This interest rate typically corresponds to what an investor expects to receive from an investment with zero risk. A U.S. Government bond is an example of such an investment instrument. In calculations, one would use the yield on a long-term U.S. Government security to approximate the risk-free rate. 5b. Beta or the Industry risk premium This measure quantifies a company s risk relative to the overall market, typically represented by the S&P 500. A company with a Beta greater than 1 would be considered riskier than the market, and a company with a Beta less than 1 would be considered less risky than the market. 5c. The equity risk premium This estimate is probably the most debated underlying figure used in the calculation of the cost of equity. Equity risk premium can be calculated using 6

9 The sum of the risk-free rate, equity risk premium and size premium are often referred to as systematic or uncontrollable risk, as these risks are associated with general market movements. The industry risk premium and the company specific premium are referred to as unsystematic or controllable risk as these risks are associated with a specific industry or specific company. And, through diversification, an investor may be able to control such risks. b. Capital Asset Pricing Model (CAPM) CAPM is the preferred method used by finance and economics professionals for determining an appropriate discount rate. CAPM was initially developed by William Sharpe in 1964, a financial economist and Nobel Prize winner in Economics, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. The general formula for CAPM is: CAPM compares market returns for a particular company or industry to the market as a whole. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (r f ) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (Beta) that compares the returns of the asset to the market over a period of time and to the market premium (r m -r f ). The CAPM asserts that the expected return of a security (r a ) equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return of an investor, then the investment may not be undertaken. For example, if one was analyzing a company in the retail industry, one may conclude that this company and industry are less consistent (or the company s stock price may be more volatile) than the overall market, and therefore have a Beta greater than 1. The CAPM method will take a riskfree rate and then add the equity return premium (ERP), adjusted by the retail industry s Beta and the company s Betas. 9

10 Despite the existence of more sophisticated and complex approaches to asset pricing (e.g. Arbitrage Pricing theory and Merton's Portfolio Problem), CAPM still remains popular due to its simplicity and usefulness. Once the cost of debt, the cost of equity, and the company s proportion of debt capital and equity capital are calculated, the WACC can then be determined. Using the previous example, where: - Debt capital represents 60% of a company total capital, - Equity capital represents 40% of the company s total capital, - Assuming the cost of debt is 6% (adjusted for the corporate tax rate), and - Cost of equity is 11.75% (as in Chart 2): WACC = (60% x 6%) + (40% x 11.75%) = 8.3% As one can see, WACC is the average of the discount rate for debt capital and the discount rate for equity capital, where the average is weighted by the relative proportions of debt capital and equity capital to total capital. In some calculations, it may be most appropriate to calculate not one discount rate for an entire period of analysis, but a separate discount rate for each year of analysis. In the calculation of the present value of projected lost profits, it may be that lost profits vary from year to year, and the discount rate varies from year to year. In this situation, the discounting is typically prepared for each year separately. Further, based on particular facts of the analysis, the financial and economic expert may determine that an appropriate discount rate would be based only on a specific cost of debt or based only on the cost of equity. Special Cases In certain calculations of the present value of future cash flows, financial and economic experts do not undertake the above process to calculate an appropriate discount rate. Due to legal precedent, there are special cases where the expert must use a risk-free rate to calculate the present value of a stream of future cash flows. For example, the calculation of the present value of economic damages in wrongful termination, employment discrimination, personal injury and wrongful death matters generally 10

12 References: Brealey, Richard, Stewart Myers, and Franklin Allen, Principles of Corporate Finance, 11 th Edition, McGraw-Hill Higher Education, January Damodaran, Aswath, Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2 nd Edition, Wiley, Damodaran, Aswath, Applied Corporate Finance: A User's Manual, Third Edition, Wiley, Fisher, Franklin M. and R. Craig Romaine, Janis Joplin s Yearbook and the Theory of Damages, Journal of Accounting, Auditing and Finance, Volume 5, Numbers ½, Winter/Spring 1990, pp Weil, Roman L., Peter B. Frank, Christian W. Hughes, and Michael J. Wagner, Litigation Services Handbook: The Role of the Financial Expert, Fourth Edition, Wiley, December

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