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The rate of return required by equity investors in the firmAPPROACHES TO VALUATION Analysts use a wide range of models to value assets in practice, ranging from the simple to the sophisticated. These models often make very different assumptions about pricing, but they do share some common characteristics and can be classified in broader terms. There are several advantages to such a classification -- it makes it easier to understand where individual models fit into the big picture, why they provide different results and when they have fundamental errors in logic. In general terms, there are three approaches to valuation. The first, discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. The second, relative valuation, estimates the value of an asset by looking at the pricing of comparable assets relative to a common variable such as earnings, cashflows, book value or sales. The third, contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics. Some of these assets are traded financial assets like warrants, and some of these options are not traded and are based on real assets - projects, patents and oil reserves are examples. The latter are often called real options. There can be significant differences in outcomes, depending upon which approach is used. One of the objectives in this book is to explain the reasons for such differences in value across different models and to help in choosing the right model to use for a specific task. Discounted Cashflow Valuation While discounted cash flow valuation is one of the three ways of approaching valuation and most valuations done in the real world are relative valuations, we will argue that it is the foundation on which all other valuation approaches are built. To do relative valuation correctly, we need to understand the fundamentals of discounted cash flow valuation. To apply option pricing models to value assets, we often have to begin with a discounted cash flow valuation. This is why so much of this book focuses on discounted cash flow valuation. Anyone who understands its fundamentals will be able to analyze and use the other approaches. In this section, we will consider the basis of this approach, a philosophical rationale for discounted cash flow valuation and an examination of the different sub-approaches to discounted cash flow valuation. Basis for Discounted Cashflow Valuation This approach has its foundation in the present value rule, where the value of any asset is the present value of expected future cashflows that the asset generates. The cashflows will vary from asset to asset -- dividends for stocks, coupons (interest) and the face value for bonds and after-tax cashflows for a real project. The discount rate will be a function of the riskiness of the estimated cashflows, with higher rates for riskier assets and lower rates for safer projects. You can in fact think of discounted cash flow valuation on a continuum. At one end of the spectrum, you have the default-free zero coupon bond, with a guaranteed cash flow in the future. Discounting this cash flow at the riskless rate should yield the value of the bond. A little further up the spectrum are corporate bonds where the cash flows take the form of coupons and there is default risk. These bonds can be valued by discounting the expected cash flows at an interest rate that reflects the default risk. Moving up the risk ladder, we get to equities, where there are expected cash flows with substantial uncertainty around the expectation. The value here should be the present value of the expected cash flows at a discount rate that reflects the uncertainty. The Underpinnings of Discounted Cashflow Valuation In discounted cash flow valuation, we try to estimate the intrinsic value of an asset based upon its fundamentals. What is intrinsic value? For lack of a better definition, consider it the value that would be attached to the firm by an all-knowing analyst, who not only knows the expected cash flows for the firm but also attaches the right discount rate(s) to these cash flows and values them with absolute precision. Hopeless though the task of estimating intrinsic value may seem to be, especially when valuing young companies with substantial uncertainty about the future, we believe that these estimates can be different from the market prices attached to these companies. In other words, markets make mistakes. Does that mean we believe that markets are inefficient? Not quite. While we assume that prices can deviate from intrinsic value, estimated based upon fundamentals, we also assume that the two will converge sooner rather than latter. Categorizing Discounted Cash Flow Models There are literally thousands of discounted cash flow models in existence. Oftentimes, we hear claims made by investment banks or consulting firms that their valuation models are better or more sophisticated than those used by their contemporaries. Ultimately, however, discounted cash flow models can vary only a couple of dimensions and we will examine these variations in this section. . Equity Valuation, Firm Valuation and Adjusted Present Value (APV) Valuation There are three paths to discounted cashflow valuation -- the first is to value just the equity stake in the business, the second is to value the entire firm, which includes, besides equity, the other claimholders in the firm (bondholders, preferred stockholders, etc.) and the third is to value the firm in pieces, beginning with its operations and adding the effects on value of debt and other non-equity claims. While all three approaches discount expected cashflows, the relevant cashflows and discount rates are different under each. The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, reinvestment needs, tax obligations and net debt payments (interest, principal payments and new debt issuance), at the cost of equity, i.e., the rate of return required by equity investors in the firm. The dividend discount model is a specialized case of equity valuation, where the value of the equity is the present value of expected future dividends. The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses, reinvestment needs and taxes, but prior to any payments to either debt or equity holders, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions. The value of the firm can also be obtained by valuing each claim on the firm separately. In this approach, which is called adjusted present value (APV), we begin by valuing equity in the firm, assuming that it was financed only with equity. We then consider the value added (or taken away) by debt by considering the present value of the tax benefits that flow from debt and the expected bankruptcy costs. Value of firm = Value of all-equity financed firm + PV of tax benefits + Expected Bankruptcy Costs In fact, this approach can be generalized to allow different cash flows to the firm to be discounted at different rates, given their riskiness. While the three approaches use different definitions of cashflow and discount rates, they will yield consistent estimates of value as long as you use the same set of assumptions in valuation. The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm. In the illustration that follows, we will show the equivalence of equity and firm valuation. Later in this book, we will show that adjusted present value models and firm valuation models also yield the same values. 2.1: Effects of mismatching cashflows and discount rates Assume that you are analyzing a company with the following cashflows for the next five years. Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) The current market value of equity is $1,073 and the value of debt outstanding is $800. YearCashflow to EquityInterest (1-t)Cashflow to Firm1$ 50$ 40$ 902$ 60$ 40$ 1003$ 68$ 40$ 1084$ 76.2$ 40$ 116.25$ 83.49$ 40$ 123.49Terminal Value$ 1603.008$ 2363.008 The cost of equity is given as an input and is 13.625%, and the after-tax cost of debt is 5%. Cost of Debt = Pre-tax rate (1 - tax rate) = 10% (1-.5) = 5% Given the market values of equity and debt, we can estimate the cost of capital. WACC = Cost of Equity (Equity / (Debt + Equity)) + Cost of Debt (Debt/(Debt+Equity)) Method 1: Discount CF to Equity at Cost of Equity to get value of equity We discount cash flows to equity at the cost of equity: Note that the value of equity is $1073 under both approaches. It is easy to make the mistake of discounting cashflows to equity at the cost of capital or the cashflows to the firm at the cost of equity. 1: Discount CF to Equity at Cost of Capital to get too high a value for equity PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 + (83.49+1603)/1.09945 = $1248 2: Discount CF to Firm at Cost of Equity to get too low a value for the firm PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 + (123.49+2363)/1.136255 = $1613 effects of using the wrong discount rate are clearly visible in the last two calculations. When the cost of capital is mistakenly used to discount the cashflows to equity, the value of equity increases by $175 over its true value ($1073). When the cashflows to the firm are erroneously discounted at the cost of equity, the value of the firm is understated by $260. We have to point out that getting the values of equity to agree with the firm and equity valuation approaches can be much more difficult in practice than in this example. We will return and consider the assumptions that we need to make to arrive at this result. A Simple Test of Cash Flows There is a simple test that can be employed to determine whether the cashflows being used in a valuation are cashflows to equity or cashflows to the firm. If the cash flows that are being discounted are after interest expenses (and principal payments), they are cash flows to equity and the discount rate that should be used should be the cost of equity. If the cash flows that are discounted are before interest expenses and principal payments, they are usually cash flows to the firm. Needless to say, there are other items that need to be considered when estimating these cash flows, and we will consider them in extensive detail in the coming chapters. II. Total Cash Flow versus Excess Cash Flow Models The conventional discounted cash flow model values an asset by estimating the present value of all cash flows generated by that asset at the appropriate discount rate. In excess return (and excess cash flow) models, only cash flows earned in excess of the required return are viewed as value creating, and the present value of these excess cash flows can be added on to the amount invested in the asset to estimate its value. To illustrate, assume that you have an asset in which you invest $100 million and that you expect to generate $12 million per year in after-tax cash flows in perpetuity. Assume further that the cost of capital on this investment is 10%. With a total cash flow model, the value of this asset can be estimated as follows: Value of asset = $12 million/0.10 = $120 million With an excess return model, we would first compute the excess return made on this asset: Excess return = Cash flow earned - Cost of capital * Capital Invested in asset = $12 million - 0.10 * $100 million = $2 million then add the present value of these excess returns to the investment in the asset: Value of asset = Present value of excess return + Investment in the asset = $2 million/0.10 + $100 million = $120 million Note that the answers in the two approaches are equivalent. Why, then, would we want to use an excess return model? By focusing on excess returns, this model brings home the point that it is not earning per se that create value, but earnings in excess of a required return. Later in this book, we will consider special versions of these excess return models such as Economic Value Added (EVA). As in the simple example above, we will argue that, with consistent assumptions, total cash flow and excess return models are equivalent. |
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