Equity Valuation

15.1 VALUATION BY COMPARABLES

 Basic Types of Models ◦ Balance Sheet Models ◦ Dividend Discount Models ◦ Price/Earnings Ratios

 Valuation models use comparables ◦ Look at the relationship between price and various determinants of value for similar firms

Financial Highlights for Microsoft Corporation, 2007

 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)

14.2 INTRINSIC VALUE VERSUS MARKET PRICE

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%

 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

 required return  CAPM gave us required return:  If the stock is priced correctly ◦ Required return should equal expected return

 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

 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

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

 V D k o t t t     ()1 1  V 0 = Value of Stock  D t = Dividend  k = required return

 Constant Growth Model ◦ Assuming dividends are trending upward at a stable growth rate g  g = constant perpetual growth rate VoVo Dg kg o    ()1

 Constant growth DDM  A Stock ’ s price will be greater ◦ Larger its expected dividend per share ◦ Lower k ◦ Higher g

 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

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 / ( ) = $42.86

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

E 1 = D 1 = $5.00 k = 12.5% V 0 = $5.00 /.125 = $40 V D k o 

 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

 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

gROEb   g = growth rate in dividends  ROE = Return on Equity for the firm  b = plowback or retention percentage rate = (1- dividend payout percentage rate)

 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

 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= =17.14  Where: E 1 = Earnings Per Share for period 1 and

 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=?

 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

 ROE = 20% d = 60% b = 40%  E 1 = $5.00 D 1 = $3.00 k = 15%  g =.20 x.40 =.08 or 8%

P NGV PVGO o o      (..) $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

 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

Financial Ratios in Two Industries

PD g k Dg kgk oo t t t T T T         () () () ()()  g 1 = first growth rate  g 2 = second growth rate  T = number of periods of growth at g 1

 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 / ( ) ( (1.15) 3 V 0 = = $30.40

14.4 PRICE-EARNINGS RATIOS

 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

 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

 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

 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 ?

P E k P Ek    E 1 - expected earnings for next year ◦ E 1 is equal to D 1 under no growth  k - required rate of return

P D kg Eb kbROE P E b kb         () () ( ) b = retention ration ROE = Return on Equity  Higher ROE, higher P/E  Higher b, higher P/E, only if ROE>k

Effect of ROE and Plowback on Growth and the P/E Ratio

E 0 = $2.50 k = 12.5%, ROE=15%, No growth: g=0 P/E=? With growth: payout ratio=40%, P/E=?

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

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/( ) = $31.14 P/E = 31.14/2.73 = 11.4 P/E = (1 -.60) / ( ) = 11.4

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

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

P/E Ratios of the S&P 500 Index and Inflation

Earnings Growth for Two Companies

Price-Earnings Ratios

P/E Ratios for Different Industries, 2007

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

Market Valuation Statistics

14.5 FREE CASH FLOW VALUATION APPROACHES

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

 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

 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

 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