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**Business Valuation Methods**

Prepared by Professor Kirby D. Cochran and Eric E. Anderson, PhD January 2014

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**Agenda Three Valuation Methods Comparison of Valuation Methods**

The Income Approach Time Value of Money Free Cash Flow Discounted Cash Flow (DCF) Analysis Internal Rate of Return (IRR) Discount Rate and Cost of Capital Models Cost of Capital Models Risk Premium Factors Equity Risk Premiums Exercises

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What is Valuation? Valuation is an unbiased process of determining the current worth of economic value of an asset or business It is an appraisal that takes into account both the positives and negatives of a business

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**3 Basic Valuation Methods**

Market Approaches (Comparable Approach) Uses The market for similar businesses, including comparable sales Ratio methods Direct Market Data Method (Guideline Transaction Method) Industry rule of thumb Asset Approaches Book Value Replacement Cost Liquidation Value Income Approaches Historical Earnings - including debt-paying ability, capitalization of earnings or cash flow (T0/(d-g)), gross income multipliers, and dividend-paying ability methods Future Earnings – the most appropriate for stable, profitable companies NPV, IRR Combination of Approaches (or Blended Approaches) Assets and Earnings (e.g., Excess earnings method) Market and Income

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**Which Valuation Method is Most Appropriate?**

Valuation Approach Typical Usage Pros Cons Market Approach Value based on Comparing Business with its Peers (Industry & Specific Companies) Most valuations in stock markets are market based. Also known as Relative Valuation Approach or Comparable Approach Simpler to compute Takes into account both supply and demand factors and current market climate Many businesses are unique Difficulty in finding comparable businesses Growth only implicitly considered Asset Approach Value based on adjusted net book value (Assets less Liabilities) Often used for Mature or Declining growth cycle businesses Used for Strong Asset Base companies Liquidation Valuation Easier to support valuation Good indicator of barriers to entry for asset intensive businesses Serves as Sanity Check on business value Results are often lower than fair-market-value because the method doesn’t consider ongoing business concerns and growth Income Approach Current value is function of Future value that an investor can expect to receive from purchasing some or all of business Use Discounted cash flow analysis to determine present value of future returns from a business (NPV, IRR) Used for valuing profitable businesses expected to continue operating for the foreseeable future (a going concern) Most accurately represents the economic value of a particular business Accurately models future growth Doesn’t require identification of comparable companies More difficult to compute Requires detailed financial model Early stage companies require forecast with no track record Must determine appropriate discount rate

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**Income Approach to Business Valuation**

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**The Income Approach to Business Valuation**

The Income Approach address 2 fundamental questions associated with valuation of a business: What are the potential economic benefits of investing time and money into a business? What are the risks involved in not obtaining all or part of the economic benefit on the prescribed time schedule? The Income Approach computes the current value of a business by discounting expected future economic benefits to current time based on the appropriate discount rate determined by quantifying the associated risks. In practice, current value of future earnings is calculated based on Historical Earnings using Capitalization of Earnings or Cash Flow method Models of Future Earnings using Discounted Cash Flow Analysis to calculate The Net Present Value (NPV) Internal Rate of Return (IRR) Applies to stable, profitable companies and accurately represents the value of a particular business model. Relies heavily on the ability to forecast future earnings and to quantify the risks associated with a business

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The Time Value of Money The Time Value of Money is the principle that a certain currency amount of money today has a different buying power (value) than the same currency amount of money in the future. The value of money at a future point of time must take account of interest earned and inflation accrued over a given period of time. There is an opportunity to earn interest on the money. Inflation will drive prices up, changing the "value" of the monetary benefit streams. Present Value is used to account for TVOM in the evaluation of future cash flows PV evaluates the current worth of a future sum of money or stream of cash flows discounted at the discount rate. The higher the discount rate, the lower the PV of the future cash flows. Several factors can be used to determine the appropriate discount rate including cost of capital and risk factors.

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**Discounted Cash Flow Analysis**

A Finite Sum of Cash Flows Business 3 In general a typical business will generate a series of cash flows, Y1, Y2, Y3, …, Yn in years 1, 2, 3,…, n Discounted Cash Flow (DCF) analysis computes the Net Present Value (NPV)1,2 which is the sum of all future cash flows, each discounted by the appropriate factor determined by the discount rate, r, and the year the cash is generated. In this case, the NPV is given by n NPV(n) = ∑ Yi / (1+r)i i = 1 where n is the number of years in which the future cash flows are generated Assume a business yields a series of cash flows of $100 each year for the next 20 years. How much would you pay today for this business? Assume a discount rate of 10% Use DCF analysis to evaluate the NPV of all future cash flows from the business and determine today’s value. Notes: 1. Karl Marx termed NPV, “fictitious capital” in his critique of political economy. It is introduced in chapter 29 of the third volume of Capital prepared by Friedrich Engels from notes left by Karl Marx and published in 1894. 2. NPV was formalized and popularized by Irving Fisher in his 1907 The Rate of Interest and became included in textbooks from the 1950s onwards, starting in finance texts

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**Discounted Cash Flow Analysis Example**

Reference the Riemann integral approximation. NPV of 20 year flow with a 10% discount rate is less than half of the total flows

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**Estimating Free Cash Flow**

Discounted Cash Flow Analysis typically is based on Free Cash Flow – not Earnings. A key measure value of a company is the amount of free cash (non-obligated) it generates for its owners. Net Income include non-cash items such as depreciation and amortization which can mask the long term cash generation potential of a company. Capital Expenditures and changes in Working capital necessary for the operation and growth can greatly affect cash flow and are not reflected in net income, and need taccounted for Calculating Free Cash Flow: Start with a model of the Income Statement Adjust Net Income (after tax) for non-cash items included on Income statement such as amortization and depreciation. Adjust for changes in necessary working capital items such as Accounts Payable (AP), Accounts Receivable (AR) and inventory to get Cash Flow from Operations Adjust for Capital Items such as Capital Expenditures and gains from salvage to get Free Cash Flow Typically model Free Cash Flow on a yearly basis for 5-10 years. Notes: Often times interest payments are removed from (i.e., added back into) Net Income to remove from affect of a company’s debt load on earnings. In this manner, Discounted cash flow analysis estimates total Enterprise Value. To arrive at Equity Value, balance sheet cash must be added to and total debt subtracted from EV.

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**Modeling Cash Flows to Equity**

Value from Operations Value from investments Enterprise Value Value Generated Business Value to Equity Debt and Other Liabilities Equity

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**Discounted Cash Flow Analysis**

Performing DCF Analysis: Start with a model of free cash flow (FCF) typically on a annual basis for 5-10 years. Evaluate the risks associated with business model and calculate the annual discount rate using one of several Cost of Capital or Build-up Methods Calculate the Net Present Value (NPV) of the Free Cash Flow over the model period using the discount rate from step 2. Estimate the annual growth in (FCF) as a constant value for all years beyond the model period. Calculate the “Terminal Value” which is an estimate of the value of all future cash flows beyond the model period. Appropriately discount the terminal value to the present time. Add the model NPV result from step 7 and the discounted terminal value from step 9 to arrive at the DCF Valuation. Notes: PV discount factors can be generalized to a mid-year convention using the appropriate fractional exponents. The model can be generalized to a finite number of growth periods, each with different values for growth, using multiple terminal value. For finite duration businesses, terminal value is not needed and business value includes liquidation value or assets and working capital.

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**Computing the DCF Value**

The Net Present Value (NPV) of cash flows is given by n NPV(n) = ∑ Yi / (1+r)i i = 1 where n is the number of years in which the future cash flows are generated, Y1, Y2, Y3, …, Yn is a series of cash flows in years 1, 2, 3,…, n, and r is the discount rate. The Terminal Value beyond year n is given by T0 = Yn (1 + g) / (r – g) where Yn is the cash flow in year n, g is the projected annual growth rate in free cash flow beyond year n, and Calculate the present value of the terminal value as PV(T0, n) = T0 / (1+r)n Finally compute the DCF value of the business as DCF(n) = NPV(n) + PV(T0 ,n) S = Sum {n=1,N-1} (r^n); s-rs = 1-r^N = s(1-r) for (r/=1); s = (1-r^N)/1-r; as N-> inf and r<1, s->1/(1-r)

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**DCF Valuation Analysis Example**

Cash flow is given below for years 1 to 5, including initial development investment in Yr 1 Assume discount rate, r = 25% Assume growth rate, g = 3%, for the period beyond Yr 5 NPV of cash from Yr 1 to 5 with (r = 25%) = $17.36M Terminal Value, T0 = 35*(1.03)/(0.22) = $163.8M Present value of T0 = T0/(1+0.25)^5 = $53.7M DCF valuation = 17.4M M = $71.5M 164 Y1 Y2 Y3 Y4 Y5 T0 -20 3 15 30 35 Growth Terminal NPV PV(T0,5) DCF Value DCF Analysis of Free Cash Flow ($M) Development

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**DCF Analysis for XYZ Genetics – Income Statement**

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**DCF Analysis for XYZ Genetics – Balance Sheet**

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**DCF Analysis for XYZ Genetics – Cash Flow**

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**DCF Analysis for XYZ Genetics – Cash Flow**

Example: Calculate the Discounted Cash Flow on the free cash flow of XYZ Genetics using a mid-year convention for PV discount factors. Assume discount rate, r = 40.0% Assume growth rate, g = 10.0%, beyond the model period

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**Internal Rate of Return**

Internal Rate of Return (IRR) or Economic Rate of Return (ERR)is the annual effective compound rate of return that yields zero net present value of future cash flows. I.e., the IRR is the value of the discount rate, r = IRR, such that, n NPV(n) = ∑ Yi / (1+r)i = 0 i = 1 where n is the number of years in which the future cash flows are generated, Y1, Y2, Y3, …, Yn is a series of cash flows in years 1, 2, 3,…, n, and r is the discount rate. The cash flows included in the IRR calculation, include all cash flows (including the investment, which is considered a negative cash flow). Specific, the IRR of an investment is the discount rate at which the NPV of costs (negative cash flows) of the investment equals the NPV of the benefits (positive cash flows) of the investment — In other words, the rate at which an investment breaks even. IRR calculations are commonly used to evaluate the desirability of investments or projects. The higher a project's IRR, the more desirable it is to undertake the project. A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Note: The solution of the IRR equation involves the finding roots to the expression, and requires the use of iterative numerical methods such as the secant method. See for example the Excel formula IRR(values, [guess])

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**Internal Rate of Return Analysis Example**

Continuing from the previous example: The Cash flow series is given below for years 1 to 5, and the terminal value in year 6 as calculated in the previous example. Using the Excel formula IRR(values,[guess]) = IRR({-20,3,15,30,35,164}) = 88.4% To check the answer we calculate the NPV of the cash flow series using r = IRR = 88.4% and verify that NPV = 0. 164 Y1 Y2 Y3 Y4 Y5 T0 -20 3 15 30 35 Growth Terminal IRR IRR of Free Cash Flow ($M) Development

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**Solar DCF Analysis – 4.0 kW-dc Typical Usage / 20% Down / 30% Fed Tax Credit**

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**Solar DCF Analysis – 4.0kW-dc Typical Usage / 100% Down / NO Fed Tax Credit**

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**Solar DCF Analysis – 4.0kW-dc Typical Usage / 100% Down / 30% Fed Tax Credit**

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**Solar DCF Analysis – 4.0kW-dc Typical Usage / 20% Down / 30% Fed Tax Credit**

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**Discount Rate and Cost of Capital Models**

The Discount Rate is used to calculate a company’s value using Discounted Cash Flow (DCF) analysis or similarly using the Capitalization of Earnings Method Capitalization of Earnings Method: Value = future earnings level / ( r – g ) where r = discount rate, and g = growth rate The Discount Rate is similar to the Capitalization Rate or Cap Rate which is used to estimate the investor's potential return on his investment based on a constant annual income: Cap Rate = Yearly Income / Total Value or Total Value = Yearly income / Cap Rate The Cap Rate is equivalent to the discount rate of a perpetuity. Several Cost of Capital Models are used to compute the Discount Rate Weighted Average Cost of Capital (WACC) Capital Asset Pricing Model (CAPM) Modified CAPM Build-Up Model Arbitrage Pricing Theory Model (APT) Fama-French Three Factor Model

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**Value is a Subjective Quantity**

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**Weighted Average Cost of Capital (WACC)**

The Discount Rate is used in Discounted Cash Flow (DCF) analysis to compute the Present Value of future returns. A company’s Weighted Average Cost of Capital (WACC) is often used as the discount rate WACC is the rate that a company is expected to pay (on average) to all its security holders to finance its assets In the case where the company is financed with only equity and debt, the average cost of capital is given by: WACC = D/(D + E) Kd + E/(D+E) Ke where D is the total debt, E is the total shareholder’s equity, Ke is the cost of equity, and Kd is the cost of debt. Tax effects reduce the effective cost of debt and can be incorporated into the formula by replacing Kd with Kd (1-t) where t is the effective tax rate.

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**Capital Asset Pricing Model**

Capital Asset Pricing Model (CAPM) is used to determine the expected rate of return of an asset investment given that assets “non-diversifiable” risk (or market risk) The CAPM rate can be used to compute the discount rate or capitalization rate for adding an asset investment to an already well-diversified portfolio. The CAPM dictates that the risk premium for an asset or individual security is proportional to the market risk premium, Ri – Rf = Bi ( Rm – Rf ) or Ri = Rf + Bi ( Rm – Rf ) where Ri = expected return of the capital asset (or an individual security in the market) Rm = expected return of the market as a whole Rf = the risk free interest rate (such as that of government bonds) Bi = “Beta” is the sensitivity of the expected excess asset returns to the expected excess market returns and is a measure of risk arising from exposure to a market. (Statistically, Bi = Cov(Ri, Rm) / Var (Rm))) Rm - Rf = known as the market risk premium Ri - Rf = risk premium for a given asset of individual security Security Market Line (SML) CAPM was introduced by Jack Treynor (1961, 1962),[2] William Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory.

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Average Return vs Beta

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**Modified Capital Asset Pricing Model**

The basic CAPM considers only the market risk to determine the discount or capitalization rate. The Modified CAPM extends the CAPM to consider other risks involved in an investment as: Ri = Rf + Bi ( Rm - Rf) + SCRP + CSRP , Where Ri = expected return of the capital asset (or an individual security in the market) Rf = Risk free rate of return (Generally taken as 10-year Government Bond Yield) Bi = Beta Value (Sensitivity of the stock returns to market returns) Rm = Market Rate of Return SCRP = Small Company Risk Premium, CSRP = Company specific Risk premium Build Up Method to determine after-tax net cash flow discount rate, which in turn yields the capitalization rate. Called a "build-up" method because it is the sum of risks associated with various classes of assets. It is based on the principle that investors would require a greater return on classes of assets that are more risky.

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**Risk Premiums and the Discount Rate**

Discount rates are adjusted to account for the various risks involved in the realization and timing of expected returns. The equity discount rate is built up by adding a risk premium for each risk element to risk free rate. Equity Risk Premium – The excess return that an individual stock or the overall stock market provides over a risk-free rate. This excess return compensates investors for taking on the relatively higher risk of the equity market. The size of the premium will vary as the risk in a particular stock, or in the stock market as a whole, changes; high-risk investments are compensated with a higher premium. Industry or Market Risk Premium – High risk industries result in higher risk premiums Company Size Premium – Generally, smaller companies are associated with higher investment risk. Hence small company investors demand higher returns. Company Specific Risk Premium – accounts for the unique attributes of the business itself. Business risk factors that lead to higher premium values include unstable earnings, high leverage, customer or product concentration and low quality of management or staff. Liquidity Risk Premium – included to account for lack of marketability of an asset. It is highest for lightly traded securities and small issues, as well as during a bear market.

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**Effect of Size on the Risk Premium**

Source: Duff and Felps, “Risk Premium Report 2013”

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**Annual Average Return Using 8 Measures of Company Size**

Source: Duff and Felps, “Risk Premium Report 2013”

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**Average Risk Premium vs Market Value**

Figure 13: Exhibit A-1 (abbreviated) Historical Equity Risk Premium: Average Since 1963 Data for Year Ending Dec 31, 2012 Companies Ranked by Market Value of Equity Portfolio Rank by Size Average Market Value ($M) Smoothed Average Risk Premium 1 136,859 2.63% 2 39,247 4.52% 3 25,711 5.15% … 24 288 11.95% 25 94 13.65% Source: Duff and Felps, “Risk Premium Report 2013”

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Discount Rate Build Up Example of a build up of the total equity discount rate for small business valuation: In this example, the total equity discount rate is 45%. A time varying discount profile can also be used that increases the discount rate for cash flows occurring further in the future. (This method can be used, for example, to account for the yield curve premium for long term debt.) Risk Risk Evaluation Risk Premium (e.g.) Risk Free Rate Long Term U.S. Treasury Bond 3% Equity Risk Publically traded equity investment 7% Size Risk Small privately-owned Company 20% Industry Risk Risk of investing in the particular industry the business operates 5% Company Specific Risk Risk of investing in particular business 10% Total Discount Rate 45%

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Equity Risk Premium Source:

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**Source: http://aswathdamodaran. blogspot**

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Equity Risk Premium

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**Are U.S. Equity Risk Premiums Reaching an Inflection Point?**

Rising US Treasury yields are putting pressure on US equity risk premiums, and if 10 year yields go up any more the ERP will fall below its historic average, making stocks look relatively expensive

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**US Equity and Bond Yield Correlation**

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**Company Valuation Exercises – Income Approach**

Exercise 2 – Performing DCF Analysis Compute DCF valuations for the cash flow series below Assume discount rate, r = 36% Assume growth rate, g = 10%, for the period beyond Yr 5 NPV of cash from Yr 1 to 5 with (r = 36%) = __________ Terminal Value, T0 = Y5 cash flow*(1+g)/(d-g) = _________ Present value of T0 = T0/(1+r)^5 = _________ DCF valuation = _________ ? Y1 Y2 Y3 Y4 Y5 T0 -100 25 60 100 110 Growth Terminal NPV PV(T0,5) DCF Value DCF Analysis of Free Cash Flow ($M) Development

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**Company Valuation Exercises – Income Approach**

Exercise 2 – Calculating the IRR Compute IRR of the cash flow series below with terminal value in year 6 as computed in the previous example. Assume discount rate, r = 36% and the growth rate, g = 10%, for the period beyond Yr 5 Using the Excel formula IRR(values,[guess]), calculate the IRR = _____% Check the answer by calculating the NPV of the cash flow series using r = IRR calculated above and verify that NPV = 0. If your companies Cost of Capital is 30%, would you invest in this company? ? Y1 Y2 Y3 Y4 Y5 T0 -100 25 60 100 110 Growth Terminal NPV PV(T0,5) DCF Value DCF Analysis of Free Cash Flow ($M) Development

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