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1. Valuation Techniques 2. 3. 4. DCF Valuation Valuation Cost of Equity Terminal Value Value Valuation Date Adjustments Lecture 9 2 Discounted Cash Flow Valuation The Terminal Value Theoretically - the valuation of an equity security requires us to estimate and discount all the future cash distributions for the di th di th infinite future. FCFE t Equity Value Et t t 1 (1 re ) Represents the fact that value is based on ‘expectations’ of the future The terminal value of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. Remember that the present value of a growing perpetuity of payments, beginning with a $K one year from now and growing at rate g forever after, discounted at rate re, is given by the following formula: But, practically we use two main periods in our forecast: Forecasting (Finite) horizon - for which we make explicit forecasts for each year Terminal period - We assume that, after this point, the financial statement line items settle down to a constant growth rate growth rate.
Equity Value t 1 T 1 K (1 g ) K (1 g ) 2 K (1 g )3 K K ... 2 3 4 (1 re ) (1 re ) (1 re ) (1 re ) re g Replacing K with the FCFET – the free cash flows to equity at the first year of the terminal period we get the familiar at the first year of the terminal period, we get the familiar Gordon growth model:
TerminalValue To get the present value, it needs to be discounted to today by a factor of (1+re)-(T-1) FCFEt Terminal ValueT (1 re )t (1 re )T 1 FCFET re g The forecasting horizon should begin with the fiscal year that we are currently in and extend out to the point where we can no longer make a better forecast than to simply assume that all the financial statement line items will grow at the same rate as sales sales. If all the financial statement line items will grow at the same rate as sales, free cash flows to equity holders will also grow at this rate.
3 Note: to use this formula, the terminal value estimate has to be a perpetuity or have a constant growth rate. 4 Discounted Cash Flow Valuation Inputs to the model Thus, the value of equity is simply computed as follows: Equity Value T 1 FCFEt FCFET t (re g )(1 re )T 1 t 1 (1 re ) For Starbucks: The explicit forecast is 2008-2017 The terminal year begins in 2018:
2018 2019 2020 2021 2022 P.V. 100 100 100 100 100 The present value of the annuity due is for the end of 2017 5 Explicit FCFE forecasts using pro-forma financial statements. Forecasting Horizon (T) – will be determined based on the firm and its industry. Is a too long/short of a period a problem? Terminal Growth Rate (g) represent growth in abnormal earnings in perpetuity. Growth in GDP abnormal earnings in perpetuity. Growth in GDP is a good assumption for g because it assumes that, in steady state, the company’s growth keeps pace with growth in the economy. At a maximum, g cannot exceed the GDP growth rate or else the firm would subsume the entire economy. Note that the forecasted financial statements in year T should equal the projected accounts in year 10, growing at your projected terminal growth rate (g) – see SBUX spreadsheet. Cost of Equity Capital (re)
6 Terminal Value
Clothing and Footwear Industry Sales Growth Drivers The terminal values in DCF valuations can be substantial (in some cases, more than 100% of the total value of the firm). 7 8 Cost of Capital Estimating Cost of Equity Cost of capital is also variously referred to as opportunity cost of capital, discount rate, hurdle rate, expected return Systematic Risk Vs Idiosyncratic Risk Systematic risk: Risk of a decline in the value of a stock or portfolio due to market-wide movements or general economic conditions. Example: The decline in NASDAQ and DJIA, increase in energy prices, and current economic slow down. Idiosyncratic Risk: Risk of a decline in the value of a stock Risk: of decline in the value of stock or portfolio due to firm-specific events such as (a) accounting irregularities, (b) union problems, (c) product defects, etc. Which risk is relevant for cost of capital? risk is relevant for cost of capital? In perfect markets, only systematic risk should matter in computing cost of capital. This is because the securities market will compensate an investor only for the systematic risk borne by him risk borne by him. High systematic risk High cost of capital. As we focus on the FCFE – we will use the cost of equity. There are two approaches to estimating the cost of equity of a firm: The asset pricing approach: The asset pricing approach relies on asset pricing models provided by financial theory. In particular: The Capital Asset Pricing Model (CAPM). The discounted cash flow (DCF) approach: This approach estimates cost of equity as the internal rate of return that equates the present value of projected free cash flows to equity (FCFE) to current stock price. The cost of equity estimated from the DCF approach is referred to as the ex ante cost of equity. 9 10 CAPM model
The cost of capital/expected return of an asset ‘i’ is: E(ri) = rf + “Risk Premium” rf is the risk-free rate and “Risk Premium” is an appropriate risk premium. CAPM computes the risk premium for the stock/asset as a linear function of the market risk premium: Implementing the CAPM th CAPM
re rf E (rm ) rf The risk free interest rate. Use long term US bond yield for long horizon projects The systematic risk of a stock, estimated using time series regressions The expected risk premium for the market index over long-term bonds. re r f e E rm r f
rf = E(rm)-rf = e = rf and can be taken straight from Yahoo. For long-term projects, it is customary to use the long-term US long projects it is customary to use the long US government bond yield as the risk-free rate. We will use a 10-year U.S. Treasury Bond for rf. As for the risk premium, 5.77% is the arithmetic mean from 1968 1968-2007, so use this amount unless you have reason to adjust so use this amount unless you have reason to adjust otherwise. Be consistent in choosing risk-free rates and risk premia. The risk-free rate of interest. The risk-premium on the market index, usually, S&P 500 index. The beta measures systematic risk. It measures co-movements between the market and the stock. e > 1, riskier than the market portfolio. e < 1, less risky than the market portfolio. e = 1, as risky as the market portfolio. e = 0, risk-free asset. 11 12 Estimating beta from monthly returns Beta adjustment formula
adjusted = (1/3) + (2/3) * raw Beta estimates can be obtained from Yahoo, Stock Val or Bloomberg. These sources use 24 to 60 months of data to estimate betas. The beta-estimation regression is: Rit = a + raw Rmt + et Rit is a stock’s monthly stock return, Rmt is the monthly return on S&P 500 index and monthly return on S&P 500 index, and et is the the idiosyncratic zero-mean regression error. Problems in estimating beta using this equation: Time period Frequency Market Index This adjustment takes into account meanreversion in individual stock betas and the noise in estimating them. Raw beta is the historical beta. Adjusted beta is the predicted future beta. Equation is the the predicted future beta. Equation is the forecasting equation estimated from past data. Make sure to do the adjustment when using individual stock betas. An alternative is to average the betas of similar firms in the industry. If you have more than 10 stocks, no need for the adjustment since stocks, no need for the adjustment since portfolio betas are less noisy. 13 14 A checklist for using Beta from online data sources SBUX Cost of Equity Is the Beta computed from monthly returns? Use betas computed from daily returns only as a last resort. If it is based on monthly returns, how many months of data were used? At least 24 months of data is preferable. Finally, has the Beta been adjusted? If not has the Beta been adjusted? If not perform the adjustment. The Betas on yahoo are not adjusted. Unadjusted: Adjusted: re = 3.77%+ 0.88*(5.77%) = 8.85% re = 3.77%+ 0.92*(5.77%) = 9.08% 10-year T-Bond in Feb. 2008 Avg. equity premium, 1968 1968-2007 15 16 Valuation Date Adjustments Valuation Date Adjustments All forecasts using pro-formas are inherently treated as of the date of the previous fiscal year treated as of the date of the previous fiscal year end. Hence, adjustments need to be made to bring value current to today’s date. 1. Estimate days outstanding from the valuation date and the last fiscal year end. 2. Adjust your final value to reflect the passage of time since the prior fiscal year end.
Current value = Estimated value*(1+re)(months since last fiscal year end / 12) or Current value = Estimated value*(1+re)(days since last fiscal year end / 365) General Technique: Technique: For example, if you are 9 months into the year example if you are months into the year (i.e., September 30 for a calendar year company), have a 10% cost of capital, and derived a value of $30 as of the last fiscal year end, your value today would be: ld $30*(1.10)9/12 = $32.22
17 18 Cost of Equity (cont.) it Additional guidance for forecasting expenses on the income statement You can also adjust betas for mean reversion - as follows: adj = 1/3 + 2/3*historical What is the logic behind this adjustment? e.g. TBL Cost of Equity Capital:
Unadjusted: re = 5.45%+ 1.30*(5.4) = 12.47% Adjusted: re = 5.45%+ 1.20*(5.4) = 11.93% Cost of Goods Sold The ratio of cost of goods sold (COGS) to sales describes (COGS) how much of every sales dollar is spent directly on providing the product or delivering the service. When forecasting this item, think about the firm’s strategy – does the firm follow a product differentiation strategy can they charge a price premium over their competitors? Is this premium sustainable in the long run? In addition, you may find some guidance for this forecast by reading the firm's MD&A. Note that the discussion in th MD&A the MD&A may be pitched in terms of the gross profit th margin, defined as Gross Profit Margin = 1 - COGS/Sales It is possible that a firm's COGS/Sales ratio will exhibit economies of scale if you are forecasting significant sales growth, but this depends on the firm mix of fixed and growth, but this depends on the firm's mix of fixed and variable costs. If the COGS is due primarily to deprecia-tion (and you are sure that depreciation expense is being included as part of COGS), then as sales increase, the depreciation will not increase proportionally, so this ratio could enjoy some economies of scale You should ratio could enjoy some economies of scale. You should still ask yourself how much longer you expect this trend to con-tinue. Even if the primary component of COGS is depreciation, at some point in-creasing sales will probably require increasing the asset base, which will engender yet more depreciation.
20 30-year T-Bond in Jan. 2001 Avg. equity premium, 1963-1999
19 Selling, General, and Administrative Expenses Selling, general, and administrative (SG&A) expenses (SG&A) have some components that move directly with sales, such as commissions paid to the sales force, and other components that are only weakly related to sales, such as clerical staff salaries. The fixed components will give this ratio some economies of scale, so it may decline as a percentage of sales if sales grow. There is evidence that SG&A costs are "sticky" in the sense that they increase when times are good, but they fail to decrease when times are bad. ti Examine how this ratio has changed in the past in response to changes in the sales growth rate for evidence of economies of scale. As an example, Figure 8.6 plots the SG&A/Sales and COGS/Sales ratios for Amazon.com SG&A/Sales and COGS/Sales ratios for Amazon.com over the five years between 2000 and 2004 when sales grew about 150 percent. Note the severe economies of scale for the SG&A ratio, which drops from 25.5 percent to 13.2 percent over the five-year pe-riod, whereas the COGS ratio hardly changes at all COGS ratio hardly changes at all. Interest Expense The ratio of interest expense to average debt is the firm's average interest rate on all their debt combined. The past rate at which the firm has borrowed is a good in-dicator of their future borrowing rate, unless you forecast a large change in either the firm's default risk or macro-level interest rates. You also may want to read the debt footnote and see what rate the firm has borrowed at most recently. 21 22 The Different “Brand Names” of Residual Income Valuation Model Residual Income Valuation Model The residual income valuation model is identical to the dividend discount model and other brand name valuation dividend discount model and other “brand name” valuation models. Because it directly discounts the forecasted earnings, it is often easier to implement.
Capital Cost of Capital Earnings Examples in the literature I. Value to both debtholders and shareholders: Total assets (or Net assets WACC EBI or NOPLAT+/Stern Stewart: EVA™ +/- adjustments for specific items) specific adjustments (depending on how capital is defined) Book value + Accum Dep + Inflation Adj to Gross Plant + Op. leases + Off B/S Assets - Nondebt Liabs Liabs Zero WACC EBI +/- accounting WACC NI + Dep + Int + Model McKinsey & Co's Economic Profit ModelTM HOLT Value Touche: CFROITM (BCG uses a very similar metric) similar metric) Rappaport: ALCAR™ Rental Exp + Holding Associates, Deloitte & gains (losses) - FIFO profits accruals +/- net capital Model McKinsey's & exp. Co. Discounted Cashflow Model (ROIC) Shareholder's equity (reported book value) under a particular country's GAAP II. Value to shareholders directly: Cost of equity NI to shareholders Frankel & Lee (1998), under the same GAAP Penman et. al. (1997): EBO or Discounted Residual Income Model Zero Cost of equity NI, where NI is paid out 100% Dividend Discount model (DDM)
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This note was uploaded on 04/09/2010 for the course NBA 5090 taught by Professor Yehuda,nir during the Fall '10 term at Cornell University (Engineering School).
- Fall '10