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Equity Valuation
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15.1 VALUATION BY COMPARABLES
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Basic Types of Models ◦ Balance Sheet Models ◦ Dividend Discount Models ◦ Price/Earnings Ratios
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Valuation models use comparables ◦ Look at the relationship between price and various determinants of value for similar firms
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Financial Highlights for Microsoft Corporation, 2007
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Book value ◦ Based on historical values ◦ Not the floor Can book value represent a floor value? Better approaches ◦ Liquidation value If below, attractive ◦ Replacement cost Tobin ’ s q (ratio of market price to replacement cost)
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14.2 INTRINSIC VALUE VERSUS MARKET PRICE
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Example (1-year horizon), whether the price today is attractively priced given your forecast of next year’s price and dividend Rf=6%, beta=1.2 Rm=11%
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compare expected HPR and required return expected HPR ◦ The return on a stock investment comprises cash dividends and capital gains or losses Assuming a one-year holding period
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required return CAPM gave us required return: If the stock is priced correctly ◦ Required return should equal expected return
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Intrinsic value ◦ The present value of all cash payments to the investor, including dividends and proceeds from the ultimate sale of the stock, discounted at the appropriate risk-adjusted interest rate, k Example: 50>48, undervalued
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Market Price ◦ Consensus value of all potential traders ◦ Current market price will reflect intrinsic value estimates ◦ This consensus value of the required rate of return, k, is the market capitalization rate Trading Signal ◦ IV > MP Buy ◦ IV < MP Sell or Short Sell ◦ IV = MP Hold or Fairly Priced
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14.3 DIVIDEND DISCOUNT MODELS
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DDM ◦ Stock price should equal the present value of all expected future dividends into perpetuity V D k o t t t ()1 1
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V D k o t t t ()1 1 V 0 = Value of Stock D t = Dividend k = required return
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Constant Growth Model ◦ Assuming dividends are trending upward at a stable growth rate g g = constant perpetual growth rate VoVo Dg kg o ()1
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Constant growth DDM A Stock ’ s price will be greater ◦ Larger its expected dividend per share ◦ Lower k ◦ Higher g
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Stock price is expected to grow at the same rate as dividends If market price equals its intrinsic value, expected HPR will be equal to required return
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Vo Dg kg o ()1 E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / (.15 -.08) = $42.86
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V D k o g=0 Stocks that have earnings and dividends that are expected to remain constant ◦ Preferred Stock Vo Dg kg o ()1
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E 1 = D 1 = $5.00 k = 12.5% V 0 = $5.00 /.125 = $40 V D k o
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Consider two companies ◦ Cash Cow, Inc ◦ Growth Prospects k=12.5% IF pay out all as dividends (payout ratio =100%), perpetual dividend=5 Both valued at 5/12.5%=40, neither firm will grow in value GP, project ’ s ROE=15%, what should be GP’s dividend policy ? investment=$100 million, 3 million shares outstanding, expected earnings in coming year (EPS)=$100*15%/3= $5
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Suppose, Growth Prospects lower payout ratio (40%) Earnings retention ratio b=1-40%=60% Total earning=$100*15%=$15 million Reinvestment=$15*60%=$9 million (capital increase 9/100=9%) 9% more capital, 9% more income, 9% higher dividend Low-reinvestment-rate plan, pay higher initial dividends, but result in a lower dividend growth rate High-reinvestment-rate, lower initial dividends, but result in higher dividend growth
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gROEb g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate = (1- dividend payout percentage rate)
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g=15%*60%=9% The project ’ s ROE >required rate (the project has positive NPV), reduce dividend payout ratio and reinvest in the positive NPV project. The firm ’ s value rises by the NPV of the project PVGO: net present value of growth opportunities
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Value of the firm rises by the NPV of the investment opportunities Price = No-growth value per share (NGV) +present value of growth opportunities (PVGO) PVGO=57.14-40=17.14 Where: E 1 = Earnings Per Share for period 1 and
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Growth enhance company value only if it is achieved by investment in projects with attractive profit opportunities (ROE>k) If the project ’ s ROE=12.5%=k, lower the dividend payout ratio (40%) Then stock price=?
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g= ROE*b=12.5%*60%=7.5% No different from no-growth strategy To justify reinvestment, the firm must engage in projects with better prospective returns than those shareholders can find elsewhere If ROE=k, no advantage to reinvestment
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ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%
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P NGV PVGO o o 3 1508 86 5 15 33 863352 (..) $42.. $33. $42.$33.$9. Partitioning Value: Example P o = price with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities
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Constant-growth DDM ◦ Assume dividend growth rate be constant In fact, different dividend profiles in different phases ◦ In early years, high return, high reinvestment, high growth ◦ In later years, low return, low reinvestment, low growth, as mature companies Multistage version of DDM
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Financial Ratios in Two Industries
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PD g k Dg kgk oo t t t T T T () () () ()() 1 1 1 1 1 1 2 2 g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1
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D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 =2*1.2= 2.40 D 2 = 2.4*1.2=2.88 D 3 =2.88*1.2= 3.46 D 4 =3.46*1.05= 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / (.15 -.05) ( (1.15) 3 V 0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
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14.4 PRICE-EARNINGS RATIOS
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Used to assess the valuation of one firm versus another based on a fundamental indicator such as earnings. Price-to-earnings multiple Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio
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P/E Ratios are a function of two factors ◦ Required Rates of Return (k) ◦ Expected growth in Dividends Uses ◦ Relative valuation ◦ Extensive use in industry
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Useful indicator of expectations of growth opportunities Ratio of PVGO/(E/k), component of firm value due to growth opportunities to the component of value due to assets already in place High P/E ratio indicates ample growth opportunities ◦ GROWTH PROSPECT, 57.14/5=11.4 ◦ CASH COW, 40/5=8
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Investor may well pay a higher price per dollar of current earnings if he or she expects that earnings stream to grow more rapidly P/E ratio a reflection of the market’s optimism concerning a firm’s growth prospects, but whether they are more of less optimistic than the market ?
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P E k P Ek 0 1 0 1 1 E 1 - expected earnings for next year ◦ E 1 is equal to D 1 under no growth k - required rate of return
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P D kg Eb kbROE P E b kb 0 11 0 1 1 1 () () ( ) b = retention ration ROE = Return on Equity Higher ROE, higher P/E Higher b, higher P/E, only if ROE>k
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Effect of ROE and Plowback on Growth and the P/E Ratio
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E 0 = $2.50 k = 12.5%, ROE=15%, No growth: g=0 P/E=? With growth: payout ratio=40%, P/E=?
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E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 P/E = 1/k = 1/.125 = 8
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b = 60% ROE = 15% (1-b) = 40% g = (.6)(.15)= 9% E 1 = $2.50 (1 +9%) = $2.73 D 1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P 0 = 1.09/(.125-.09) = $31.14 P/E = 31.14/2.73 = 11.4 P/E = (1 -.60) / (.125 -.09) = 11.4
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P/E Ratios and Stock Risk Holding all else equal ◦ Riskier stocks will have lower P/E multiples ◦ Higher values of k; therefore, the P/E multiple will be lower
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Pitfalls in P/E Analysis Use of accounting earnings ◦ Influenced by somewhat arbitrary accounting rules, use of historical cost in depreciation and inventory valuation (earnings management) Inflation ◦ P/E ratio have tended to be lower when inflation has been higher ◦ Market ’ s assessment that earnings in these periods are of lower quality Reported earnings fluctuate around the business cycle No way to say P/E is overly high or low without referring to the company’s long-run growth and current EPS relative to the long-run trend line
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P/E Ratios of the S&P 500 Index and Inflation
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Earnings Growth for Two Companies
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Price-Earnings Ratios
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P/E Ratios for Different Industries, 2007
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Other Comparative Value Approaches Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio Creative: price-to-hits ratio for retail internet firms
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Market Valuation Statistics
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14.5 FREE CASH FLOW VALUATION APPROACHES
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Free Cash Flow Approach Discount the free cash flow for the firm Discount rate is the firm ’ s cost of capital Components of free cash flow ◦ After tax EBIT ◦ Depreciation ◦ Capital expenditures ◦ Increase in net working capital
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discount FCFF at the weighted-average cost of capital, Subtract existing value of debt FCFF = EBIT (1- t c ) + Depreciation – Capital expenditures – Increase in NWC where: EBIT = earnings before interest and taxes t c = the corporate tax rate NWC = net working capital
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Another approach focuses on the free cash flow to the equity holders (FCFE) and discounts the cash flows directly at the cost of equity FCFE = FCFF – Interest expense (1- t c ) + Increases in net debt
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Free cash flow approach should provide same estimate of IV as the dividend growth model In practice the two approaches may differ substantially ◦ Simplifying assumptions are used
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