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Asset Valuation P.V. Viswanath Class Notes for Corporate Finance and Mergers and Acquisitions Discounted Cashflow Valuation t = n CF Value = t t t =1 (1 + r) where, n = life of the asset CFt = cashflow in period t r = discount rate reflecting the riskiness of the estimated cashflows P.V. Viswanath 2 Two Measures of Discount Rates Cost of Equity: This is the rate of return required by equity investors on an investment. It will incorporate a premium for equity risk -the greater the risk, the greater the premium. This is used to value equity. Cost of capital: This is a composite cost of all of the capital invested in an asset or business. It will be a weighted average of the cost of equity and the after-tax cost of borrowing. This is used to value the entire firm. P.V. Viswanath 3 Equity Valuation Figure 5.5: Equity Valuation Assets Liabilities Assets in Place Debt Cash flows considered are cashflows from assets, after debt payments and after making reinvestments needed for future growth Discount rate reflects only the cost of raising equity financing Growth Assets Equity Present value is value of just the equity claims on the firm Free Cash Flow to Equity = Net Income – Net Reinvestment (capex as well as change in working capital) – Net Debt Paid (or + Net Debt Issued) P.V. Viswanath 4 Firm Valuation Figure 5.6: Firm Valuation Assets Liabilities Assets in Place Debt Cash flows considered are cashflows from assets, Discount rate reflects the cost prior to any debt payments of raising both debt and equity but after firm has financing, in proportion to their reinvested to create growth assets use Growth Assets Equity Present value is value of the entire firm, and reflects the value of all claims on the firm. Free Cash Flow to the Firm = Earnings before Interest and Taxes (1-tax rate) – Net Reinvestment Net Reinvestment is defined as actual expenditures on short-term and long-term assets less depreciation. The tax benefits of debt are not included in FCFF because they are taken into account in the firm’s cost of capital. P.V. Viswanath 5 Valuation with Infinite Life DISCOUNTED CASHFLOW VALUATION Expe cte d Growth Cash flows Firm: Growth in Firm: Pre-debt cash Operating Earnings flow Equity: Growth in Equity: After debt Net Income/EPS Firm is in stable growth: cash flows Grows at con stant rate forever Terminal Value CF1 CF2 CF3 CF4 CF5 CFn Value ......... Firm: Value of Firm Fore ver Equity: Value of Equity Le ngth of Pe riod of High Growth Disc ount Rate Firm:Cost of Capital Equity: Cost of Equity P.V. Viswanath 6 Valuing the Home Depot’s Equity Assume that we expect the free cash flows to equity at Home Depot to grow for the next 10 years at rates much higher than the growth rate for the economy. To estimate the free cash flows to equity for the next 10 years, we make the following assumptions: The net income of $1,614 million will grow 15% a year each year for the next 10 years. The firm will reinvest 75% of the net income back into new investments each year, and its net debt issued each year will be 10% of the reinvestment. To estimate the terminal price, we assume that net income will grow 6% a year forever after year 10. Since lower growth will require less reinvestment, we will assume that the reinvestment rate after year 10 will be 40% of net income; net debt issued will remain 10% of reinvestment. P.V. Viswanath 7 Estimating cash flows to equity: The Home Depot Year Net Income Reinvestment Needs Net Debt Paid FCFE PV of FCFE 1 $ 1,856 $ 1,392 $ (139) $ 603 $ 549 2 $ 2,135 $ 1,601 $ (160) $ 694 $ 576 3 $ 2,455 $ 1,841 $ (184) $ 798 $ 603 4 $ 2,823 $ 2,117 $ (212) $ 917 $ 632 5 $ 3,246 $ 2,435 $ (243) $ 1,055 $ 662 6 $ 3,733 $ 2,800 $ (280) $ 1,213 $ 693 7 $ 4,293 $ 3,220 $ (322) $ 1,395 $ 726 8 $ 4,937 $ 3,703 $ (370) $ 1,605 $ 761 9 $ 5,678 $ 4,258 $ (426) $ 1,845 $ 797 10 $ 6,530 $ 4,897 $ (490) $ 2,122 $ 835 Sum of PV of FCFE = $6,833 P.V. Viswanath 8 Terminal Value and Value of Equity today FCFE11 = Net Income11 – Reinvestment11 – Net Debt Paid (Issued)11 = $6,530 (1.06) – $6,530 (1.06) (0.40) – (-277) = $ 4,430 million Terminal Price10 = FCFE11/(ke – g) = $ 4,430 / (.0978 - .06) = $117,186 million The value per share today can be computed as the sum of the present values of the free cash flows to equity during the next 10 years and the present value of the terminal value at the end of the 10th year. Value of the Stock today = $ 6,833 million + $ 117,186/(1.0978)10 = $52,927 million P.V. Viswanath 9 Valuing Boeing as a firm Assume that you are valuing Boeing as a firm, and that Boeing has cash flows before debt payments but after reinvestment needs and taxes of $ 850 million in the current year. Assume that these cash flows will grow at 15% a year for the next 5 years and at 5% thereafter. Boeing has a cost of capital of 9.17%. P.V. Viswanath 10 Expected Cash Flows and Firm Value Terminal Value = $ 1710 (1.05)/(.0917-.05) = $ 43,049 million Year Cash Flow Terminal Present Value Value 1 $978 $895 2 $1,124 $943 3 $1,293 $994 4 $1,487 $1,047 5 $1,710 $43,049 $28,864 Value of Boeing as a firm = $32,743 P.V. Viswanath 11 What discount rate to use? Since financial resources are finite, there is a hurdle that projects have to cross before being deemed acceptable. This hurdle will be higher for riskier projects than for safer projects. A simple representation of the hurdle rate is as follows: Hurdle rate = Return for postponing consumption + Return for bearing risk Hurdle rate = Riskless Rate + Risk Premium The two basic questions that every risk and return model in finance tries to answer are: How do you measure risk? How do you translate this risk measure into a risk premium? P.V. Viswanath 12 The Capital Asset Pricing Model Uses variance as a measure of risk Specifies that a portion of variance can be diversified away, and that is only the non-diversifiable portion that is rewarded. Measures the non-diversifiable risk with beta, which is standardized around one. Relates beta to hurdle rate or the required rate of return: Reqd. ROR = Riskfree rate + b (Risk Premium) Works as well as the next best alternative in most cases. P.V. Viswanath 13 Inputs required to use the CAPM According to the CAPM, the required rate of return on an asset will be: Required ROR = Rf + b (E(Rm) - Rf) The inputs required to estimate the required ROR are: (a) the current risk-free rate (b) the expected market risk premium (the premium expected for investing in risky assets over the riskless asset) (c) the beta of the asset being analyzed. P.V. Viswanath 14 The Riskfree Rate For an investment to be riskfree, i.e., to have an actual return be equal to the expected return, there must be: No default risk; this usually means a government-issued security; but, not all governments are default free. No uncertainty about reinvestment rates. In practice, the riskfree rate is the rate on a zero coupon government bond matching the time horizon of the cash flow being analyzed. Using a long term government rate (even on a coupon bond) as the riskfree rate on all of the cash flows in a long term analysis will yield a close approximation of the true value. P.V. Viswanath 15 Measurement of the risk premium The risk premium is the premium that investors demand for investing in an average risk investment, relative to the riskfree rate. As a general proposition, this premium should be greater than zero increase with the risk aversion of the investors in that market increase with the riskiness of the “average” risk investment P.V. Viswanath 16 The Historical Premium Approach This is the default approach used by most to arrive at the premium to use in the model In most cases, this approach does the following it defines a time period for the estimation (1926-Present, 1962- Present....) it calculates average returns on a stock index during the period it calculates average returns on a riskless security over the period it calculates the difference between the two and uses it as a premium looking forward The limitations of this approach are: it assumes that the risk aversion of investors has not changed in a systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages) it assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time. P.V. Viswanath 17 Historical Average Premiums for the United States Historical period Stocks - T.Bills Stocks - T.Bonds Arith Geom Arith Geom 1926-1999 9.41% 8.14% 7.64% 6.60% 1962-1999 7.07% 6.46% 5.96% 5.74% 1981-1999 13.24% 11.62% 16.08% 14.17% Considering that market rates of return since 1999 have been lower, it is probably more appropriate to use a market risk premium, which is somewhat lower, such as 5.5% P.V. Viswanath 18 Estimating Beta The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm where a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. P.V. Viswanath 19 Setting up for the Estimation Decide on an estimation period Services use periods ranging from 2 to 5 years for the regression Longer estimation period provides more data, but firms change. Shorter periods can be affected more easily by significant firm-specific event that occurred during the period Decide on a return interval - daily, weekly, monthly Shorter intervals yield more observations, but suffer from more noise. Noise is created by stocks not trading and biases all betas towards one. Estimate returns (including dividends) on stock Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning Included dividends only in ex-dividend month Choose a market index, and estimate returns (inclusive of dividends) on the index for each interval for the period. P.V. Viswanath 20 Choosing the Parameters: Boeing Period used: 5 years Return Interval = Monthly Market Index: S&P 500 Index. For instance, to calculate returns on Boeing in May 1995, Price for Boeing at end of April= $ 27.50 Price for Boeing at end of May = $ 29.44 Dividends during month = $0.125 (It was an ex-dividend month) Return =($29.44 - $ 27.50 + $ 0.125)/$27.50= 7.50% To estimate returns on the index in the same month Index level (including dividends) at end of April = 514.7 Index level (including dividends) at end of May = 533.4 Dividends on the Index in May = 1.84 Return =(533.4-514.7+1.84)/ 514.7 = 3.99% P.V. Viswanath 21 Boeing’s Historical Beta Boeing versus S&P 500: 10/93-9/98 10.00% Regression 5.00% line Returns on Boeing 0.00% -25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% -5.00% Beta is slope of this line -10.00% -15.00% Each point represents a month of data. -20.00% Returns on S&P 500 P.V. Viswanath 22 The Regression Output ReturnsBoeing = -0.09% + 0.96 ReturnsS & P 500 R squared=29.57% Intercept = -0.09% Slope = 0.96 P.V. Viswanath 23 Estimating Expected Returns: December 31, 1998 Boeing’s Beta = 0.96 Riskfree Rate = 5.00% (Long term Government Bond rate) Risk Premium = 5.50% (Approximate historical premium) Expected Return = 5.00% + 0.96 (5.50%) = 10.31% P.V. Viswanath 24 Fundamental Determinants of Betas Type of Business: Firms in more cyclical businesses or that sell products that are more discretionary to their customers will have higher betas than firms that are in non-cyclical businesses or sell products that are necessities or staples. Operating Leverage: Firms with greater fixed costs (as a proportion of total costs) will have higher betas than firms will lower fixed costs (as a proportion of total costs) Financial Leverage: Firms that borrow more (higher debt, relative to equity) will have higher equity betas than firms that borrow less. P.V. Viswanath 25 Determinant 1: Product Type Industry Effects: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market. Cyclical companies have higher betas than non-cyclical firms Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products P.V. Viswanath 26 Determinant 2: Operating Leverage Effects Operating leverage refers to the proportion of the total costs of the firm that are fixed. Other things remaining equal, higher operating leverage results in greater earnings variability which in turn results in higher betas. P.V. Viswanath 27 Determinant 3: Financial Leverage As firms borrow, they create fixed costs (interest payments) that make their earnings to equity investors more volatile. This increased earnings volatility which increases the equity beta P.V. Viswanath 28 Equity Betas and Leverage The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio bL = bu (1+ ((1-t)D/E) where bL = Levered or Equity Beta bu = Unlevered Beta t = Corporate marginal tax rate D = Market Value of Debt E = Market Value of Equity The unlevered beta measures the riskiness of the business that a firm is in and is often called an asset beta. P.V. Viswanath 29 Effects of leverage on betas: Boeing The regression beta for Boeing is 0.96. This beta is a levered beta (because it is based on stock prices, which reflect leverage) and the leverage implicit in the beta estimate is the average market debt equity ratio during the period of the regression (1993 to 1998) The average debt equity ratio during this period was 17.88%. The unlevered beta for Boeing can then be estimated:(using a marginal tax rate of 35%) = Current Beta / (1 + (1 - tax rate) (Average Debt/Equity)) = 0.96 / ( 1 + (1 - 0.35) (0.1788)) = 0.86 P.V. Viswanath 30 Betas are weighted Averages The beta of a portfolio is always the market-value weighted average of the betas of the individual investments in that portfolio. Thus, the beta of a mutual fund is the weighted average of the betas of the stocks and other investment in that portfolio the beta of a firm after a merger is the market-value weighted average of the betas of the companies involved in the merger. P.V. Viswanath 31 The Boeing/McDonnell Douglas Merger Company Beta Debt Equity Firm Value Boeing 0.95 $ 3,980 $ 32,438 $ 36,418 McDonnell Douglas 0.90 $ 2,143 $ 12,555 $ 14,698 P.V. Viswanath 32 Beta Estimation: Step 1 Calculate the unlevered betas for both firms Boeing = 0.95/(1+0.65*(3980/32438)) = 0.88 McDonnell Douglas = 0.90/(1+0.65*(2143/12555)) = 0.81 Calculate the unlevered beta for the combined firm Unlevered Beta for combined firm = 0.88 (36,418/51,116) + 0.81 (14,698/51,116) = 0.86 P.V. Viswanath 33 Beta Estimation: Step 2 Boeing’s acquisition of McDonnell Douglas was accomplished by issuing new stock in Boeing to cover the value of McDonnell Douglas’s equity of $12,555 million. Debt = McDonnell Douglas Old Debt + Boeing’s Old Debt = $3,980 + $2,143 = $6,123 million Equity = Boeing’s Old Equity + New Equity used for Acquisition = $ 32,438 + $ 12,555 = $44,993 million D/E Ratio = $ 6,123/44,993 = 13.61% New Beta = 0.86 (1 + 0.65 (.1361)) = 0.94 P.V. Viswanath 34 The Home Depot’s Comparable Firms Co mpan y Name Be ta Marke t Ca p $ (Mi l) De bt Du e 1 -Yr Out Lo ng-Te rm Deb t Bu il di ng Materi al s 1.05 $1 36 $1 $1 13 Ca tal i na Li gh ti ng 1 $1 6 $7 $1 9 Co nt'l Materi al s Corp 0.55 $3 2 $2 $7 Ea gle Hardware 0.95 $6 12 $6 $1 46 Emco Li mited 0.65 $1 87 $3 9 $1 19 Fa stena l Co . 1.25 $1 ,1 57 $1 6 $ - Ho me Base Inc. 1.1 $2 27 $1 16 Hu ghes Supp ly 1 $6 10 $1 $3 35 Lo we's Co s. 1.2 $1 2,554 $1 11 $1 ,0 46 Waxman Indu stri es 1.25 $1 8 $6 $1 21 Westb urne Inc. 0.65 $6 07 $9 $3 4 Wol oh an Lumb er 0.55 $7 6 $2 $2 0 Su m $1 6,232 $2 00 $2 ,0 76 Average 0.93 P.V. Viswanath 35 Estimating The Home Depot’s Bottom-up Beta Average Beta of comparable firms = 0.93 D/E ratio of comparable firms = (200+2076)/16,232 = 14.01% Unlevered Beta for comparable firms = 0.93/(1+(1-.35)(.1401)) = 0.86 If the Home Depot’s D/E ratio is 20%, our bottom- up estimate of Home Depot’s beta is 0.86[1+(1-.35)(.2)] = 0.9718 P.V. Viswanath 36 From Cost of Equity to Cost of Capital The cost of capital is a composite cost to the firm of raising financing to fund its projects. In addition to equity, firms can raise capital from debt P.V. Viswanath 37 Estimating the Cost of Debt If the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate. If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt. If the firm is not rated, and it has recently borrowed long term from a bank, use the interest rate on the borrowing or estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation. P.V. Viswanath 38 Estimating Synthetic Ratings The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest Expenses Consider InfoSoft, a firm with EBIT of $2000 million and interest expenses of $ 315 million Interest Coverage Ratio = 2,000/315= 6.15 Based upon the relationship between interest coverage ratios and ratings, we would estimate a rating of A for the firm. P.V. Viswanath 39 Interest Coverage Ratios, Ratings and Default Spreads Interest Coverage Ratio Rating Default Spread > 12.5 AAA 0.20% 9.50 - 12.50 AA 0.50% 7.50 – 9.50 A+ 0.80% 6.00 – 7.50 A 1.00% 4.50 – 6.00 A- 1.25% 3.50 – 4.50 BBB 1.50% 3.00 – 3.50 BB 2.00% 2.50 – 3.00 B+ 2.50% 2.00 - 2.50 B 3.25% 1.50 – 2.00 B- 4.25% 1.25 – 1.50 CCC 5.00% 0.80 – 1.25 CC 6.00% 0.50 – 0.80 C 7.50% < 0.65 D 10.00% P.V. Viswanath 40 Estimating Market Value Weights Market Value of Equity should include the following Market Value of Shares outstanding Market Value of Warrants outstanding Market Value of Conversion Option in Convertible Bonds Market Value of Debt is more difficult to estimate because few firms have only publicly traded debt. There are two solutions: Assume book value of debt is equal to market value Estimate the market value of debt from the book value; for Boeing, the book value of debt is $6,972 million, the interest expense on the debt is $ 453 million, the average maturity of the debt is 13.76 years and the pre-tax cost of debt is 5.50%. 1 (1 13.76 (1.055) 6, 972 Estimated MV of Boeing Debt = 453 $7, 631 .055 (1.055 )13.76 P.V. Viswanath 41 Estimating Cost of Capital: Boeing Equity Cost of Equity = 5% + 1.01 (5.5%) = 10.58% Market Value of Equity = $32.60 Billion Equity/(Debt+Equity ) = 82% Debt After-tax Cost of debt = 5.50% (1-.35) = 3.58% Market Value of Debt = $ 8.2 Billion Debt/(Debt +Equity) = 18% Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17% P.V. Viswanath 42 Estimating the Expected Growth Rate Expected Growth Net Income Operating Income Rete ntion Ra tio= Retu rn on Equity Reinvestment Retu rn on Capital = 1 - Dividends/Net X Net Income/Book Value of Rate = (Net Ca p X EBIT(1-t)/Book Value of Income Equity Ex + Chg in Capital WC/EBIT(1-t) P.V. Viswanath 43 Expected Growth in EPS gEPS = (Retained Earningst-1/ NIt-1) * ROE = Retention Ratio * ROE = b * ROE • ROE = (Net Income)/ (BV: Common Equity) • This is the right growth rate for FCFE • Proposition: The expected growth rate in earnings for a company cannot exceed its return on equity in the long term. P.V. Viswanath 44 Expected Growth in EBIT And Fundamentals Reinvestment Rate and Return on Capital gEBIT = (Net Capex + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC Return on Capital = (EBIT(1-tax rate)) / (BV: Debt + BV: Equity) This is the right growth rate for FCFF Proposition: No firm can expect its operating income to grow over time without reinvesting some of the operating income in net capital expenditures and/or working capital. P.V. Viswanath 45 Getting Closure in Valuation A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash t = CFt flows forever. Value = t = 1 (1+ r) t Since we cannot estimate cash flows forever, we estimate cash flows for a “growth period” and then estimate a terminal value, to capture the value at the end of the period: Value = t =N CFt t Terminal Value t = 1 (1 + r) (1 + r)N P.V. Viswanath 46 Stable Growth and Terminal Value When a firm’s cash flows grow at a “constant” rate forever, the present value of those cash flows can be written as: Value = (Expected Cash Flow Next Period) / (r - g) where, r = Discount rate (Cost of Equity or Cost of Capital) g = Expected growth rate This “constant” growth rate is called a stable growth rate and cannot be higher than the growth rate of the economy in which the firm operates. While companies can maintain high growth rates for extended periods, they will all approach “stable growth” at some point in time. When they do approach stable growth, the valuation formula above can be used to estimate the “terminal value” of all cash flows beyond. P.V. Viswanath 47 Estimating Stable Growth Inputs Start with the fundamentals: Profitability measures such as return on equity and capital, in stable growth, can be estimated by looking at industry averages for these measure, in which case we assume that this firm in stable growth will look like the average firm in the industry cost of equity and capital, in which case we assume that the firm will stop earning excess returns on its projects as a result of competition. Leverage is a tougher call. While industry averages can be used here as well, it depends upon how entrenched current management is and whether they are stubborn about their policy on leverage (If they are, use current leverage; if they are not; use industry averages) Use the relationship between growth and fundamentals to estimate payout and net capital expenditures. P.V. Viswanath 48 Estimating Stable Period Net Cap Ex gEBIT = (Net Capex + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC Therefore, Reinvestment Rate = gEBIT / Return on Capital For instance, assume that Disney in stable growth will grow 5% and that its return on capital in stable growth will be 16%. The reinvestment rate will then be: Reinvestment Rate for Disney in Stable Growth = 5/16 = 31.25% In other words, the net capital expenditures and working capital investment each year during the stable growth period will be 31.25% of after-tax operating income. P.V. Viswanath 49 Relative Valuation In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues. Examples include -- • Price/Earnings (P/E) ratios and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples) • Price/Book (P/BV) ratios and variants (Tobin's Q) • Price/Sales ratios P.V. Viswanath 50 Multiples and DCF Valuation Gordon Growth Model: P rDPS g 0 1 n Dividing both sides by the earnings, P0 Payout Ratio* (1 g n ) PE = EPS0 r-gn Dividing both sides by the book value of equity, P0 ROE * Payout Ratio* (1 g n ) PBV = BV 0 r-g n If the return on equity is written in terms of the retention ratio and the expected growth rate P0 ROE - gn PBV = BV 0 r-gn Dividing by the Sales per share, P0 Profit Margin* Payout Ratio* (1 g n ) PS = Sales 0 r-g n P.V. Viswanath 51