15.401 Finance Theory I, Equities - MIT OpenCourseWare

15.40115.401 Finance TheoryMIT Sloan MBA ProgramAndrew W. LoHarris & Harris Group Professor, MIT Sloan SchoolLecture 7: Equities 2007–2008 by Andrew W. Lo

Critical Concepts 15.401Industry OverviewThe Dividend Discount ModelDDM with Multiple-Stage GrowthEPS and P/EGrowth Opportunities and Growth StocksReading Brealey, Myers and Allen, Chapter 4Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 2

Industry Overview15.401What Is Common Stock? Equity, an ownership position, in a corporation Payouts to common stock are dividends, in two forms:– Cash dividends– Stock dividends Unlike bonds, payouts are uncertain in both magnitude and timing Equity can be sold (private vs. public equity)Key Characteristics of Common Stock: Residual claimant to corporate assets (after bondholders) Limited liability Voting rights Access to public markets and ease of shortsalesLecture 7: Equities 2007–2008 by Andrew W. LoSlide 3

Industry Overview15.401The Primary Market (Underwriting) Venture capital: A company issues shares to special investmentpartnerships, investment institutions, and wealthy individuals Initial public offering (IPO): A company issues shares to the generalpublic for the first time (i.e., going public) Secondary or seasoned equity offerings (SEO): A public companyissues additional shares Stock issuance to the general public is usually organized by aninvestment bank who acts as an underwriter: it buys part or all of theissue and resells it to the publicSecondary Market (Resale Market) Organized exchanges: NYSE, AMEX, NASDAQ, etc. Specialists, broker/dealers, and electronic market-making (ECNs) OTC: NASDAQLecture 7: Equities 2007–2008 by Andrew W. LoSlide 4

Industry Overview15.4013500902890 285930001868 1960 18512000150013178561000500 3120'90106397950414530716 7225876460 Billions Billions250076752535 258124'92'93'94'95'96'97 '98'99'00'01'02'033736261650'0430481615'912843'90 '91Industry Underwrites Nearly 3 Trillion in UnitedStates for Second-Straight Year'92 '93'94 '95'96 '97'98 '99'00'01 '02'03 '04Initial Public Offerings* Rebound In 2004Source: Thomson Financial*Excludes Closed-End FundsSource: Thomson 19007316136003000176815631500 58 528440383451167'93'94Source: Thomson Financial'95'96'97'98'99'00'01'02'03'04U.S. M&A Cycle Turns UpImages by MIT OpenCourseWare.Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 5

Industry Overview15.401NYSE Daily Share Volume vs.NYSE Composite Index7,2508,0001400120010008002,426 2,5406004002,6531,908200 15702,739'90179 202'91'92265 2915,00014576,876 ,3846746,0005,0004,0003,0005273467,0004122,000NYSE CompositeAverage Daily Volume in Millionsof Shares16001,000'93'94'95'96'97'98'99NYSE Volume'00'01'02'03'040NYSE CompositeNASDAQ Daily Share Volume vs.NASDAQ Composite 22,19310008006002004,0003,50014004004,500374 586132 163677 777 752268 22,175 2,5002,0001,3361,5006481,000NASDAQ CompositeAverage Daily Volume in Millionsof Shares200050000'91'93'94'95'96NASDAQ Volume'97'98'99'00'01'02'03'04NASDAQ CompositeImages by MIT OpenCourseWare.Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 6

The Dividend Discount Model15.401Most Basic Valuation Model for Common Stock Applies PV formulas to common-stock payouts Two inputs: expected future dividends, discount rate Notation:– Pt:Price of stock at t (ex-dividend)– Dt:Cash dividend at t– Et [ ]: Expectation operator (forecast) at t– rt:Risk-adjusted discount rate for cashflow at tLecture 7: Equities 2007–2008 by Andrew W. LoSlide 7

The Dividend Discount Model15.401Most Basic Valuation Model for Common Stock Two additional simplifying assumptions: In this case, we have the first version of the dividend discount modelor the discounted cashflow (DCF) model Suppose dividends grow at rate g over time (Gordon growth model):Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 8

The Dividend Discount Model15.401Most Basic Valuation Model for Common Stock This provides a convenient expression for the discount rate:Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 9

The Dividend Discount Model15.401Example:Dividends are expected to grow at 6% per year and the current dividendis 1 per share. The expected rate of return is 20%. What should thecurrent stock price be? Note: DDM with constant growth gives a relation between currentstock price, current dividend, dividend growth rate and the expectedreturn. Knowing three of the variables determines the fourth.Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 10

The Dividend Discount Model15.401Example:Determine the cost of capital of Duke Power. In 09/92, the dividend yieldfor Duke Power was D0/P0 0.052. Estimates of long-run growth: The cost of capital is given byThus,Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 11

DDM with Multiple-Stage Growth15.401Firms May Have Multiple Stages of Growth Growth Stage: rapidly expanding sales, high profit margins, andabnormally high growth in earnings per share, many new investmentopportunities, low dividend payout ratio Transition Stage: growth rate and profit margin reduced bycompetition, fewer new investment opportunities, high payout ratio Mature Stage: earnings growth, payout ratio and average return onequity stabilizes for the remaining life of the firmExample:A company with D0 1 and r 20% grows at 6% for the first 7 yearsand then drops to zero thereafter. What should its current price be?Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 12

EPS and P/E15.401Dividend Forecasts Involve Many Practical Challenges Terminology:– Earnings: total profit net of depreciation and taxes– Payout Ratio p: dividend/earnings DPS/EPS– Retained Earnings: (earnings - dividends)– Plowback Ratio b: retained earnings/total earnings– Book Value BV: cumulative retained earnings– Return on Book Equity ROE: earnings/BV Using these concepts, different valuation formulas may be derived Note: these are mostly based on accounting data, not market valuesLecture 7: Equities 2007–2008 by Andrew W. LoSlide 13

EPS and P/E15.401Example:(Myers) Texas Western (TW) is expected to earn 1.00 next year. Bookvalue per share is 10.00 now. TW plans an investment programwhich will increase net book assets by 8% per year. Earnings areexpected to grow proportionally. The investment is financed byretained earnings. The discount rate is 10%, which is assumed to bethe same as the rate of return on new investments. Price TW's shareprice if– TW expands at 8% forever– TW's expansion slows down to 4% after year 5 Observe that– Plowback Ratio b (10)(0.08)/(1) 0.8– Payout Ratio p (1-0.8)/(1) 0.2– ROE 10%Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 14

EPS and P/E15.401Example (cont): Continuing Expansion Case:Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 15

EPS and P/E15.401Example (cont): 2-Stage Expansion Case. Forecast EPS, D, BVPS by year:Question: Why are the values the same under both scenarios?Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 16

Growth Opportunities and Growth Stocks15.401What Are Growth Stocks? Stocks of companies that have access to growth opportunities areconsidered growth stocks Growth opportunities are investment opportunities that earnexpected returns higher than the required rate of return on capital Example: IBM in the 60's and 70's. Note: The following may not be growth stocks– A stock with growing EPS– A stock with growing dividends– A stock with growing assets Note: The following may be growth stocks– A stock with EPS growing slower than required rate of return– A stock with DPS growing slower than required rate of returnLecture 7: Equities 2007–2008 by Andrew W. LoSlide 17

Growth Opportunities and Growth Stocks15.401Example:ABC Software has: Expected EPS next year of 8.33; Payout ratio of0.6; ROE of 25%; and, cost of capital of r 15% Following a no-growth strategy (g 0,p 1), its value is Following a growth strategy, its price is Difference of 100 - 55.56 44.44 comes from growthopportunities, which offers a return of 25%, higher than the requiredrate of return 15%Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 18

Growth Opportunities and Growth Stocks15.401Example (cont): At t 1: ABC can invest (0.4)(8.33) 3.33 at a permanent 25% rate ofreturn. This investment generates a cash flow of (0.25)(3.33) 0.83per year starting at the t 2. Its NPV at t 1 is At t 2: Everything is the same except that ABC will invest 3.67,10% more than at t 1 (the growth is 10%). The investment is madewith NPV being The total present value of growth opportunities (PVGO) is This makes up the difference in value between growth and no-growthLecture 7: Equities 2007–2008 by Andrew W. LoSlide 19

Growth Opportunities and Growth Stocks15.401Stock Price Can Be Decomposed Into Two Components1. Present value of earnings under a no-growth policy2. Present value of growth opportunities Terminology*:– Earnings yield: E/P EPS1/P0– P/E ratio: P/E P0/EPS1*Note: In newspapers, P/E ratios are often computed with the most recent earnings, but investorsare more concerned with price relative to future earnings.Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 20

Growth Opportunities and Growth Stocks15.401 If PVGO 0, P/E ratio equals inverse of cost of capital If PVGO 0, P/E ratio becomes higher: PVGO is positive only if the firm earns more than its cost of capitalLecture 7: Equities 2007–2008 by Andrew W. LoSlide 21

Key Points 15.401The Dividend Discount ModelThe Gordon Growth ModelDiscount rate, cost of capital, required rate of returnEstimating discount rates with D/P and gEPS, P/E, and PVGODefinitions of growth stocks and growth opportunitiesLecture 7: Equities 2007–2008 by Andrew W. LoSlide 22

Additional References15.401 Harris, L., 2002, Trading and Exchanges: Market Microstructure for Practitioners. New York: OxfordUniversity Press. Lefevre, E., 2006, Reminiscences of a Stock Operator. New York: John Wiley & Sons. Malkiel, B., 1996, A Random Walk Down Wall Street: Including a Life-Cycle Guide to PersonalInvesting. New York: W.W. Norton.Lecture 7: Equities 2007–2008 by Andrew W. LoSlide 23

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– Payout Ratio p: dividend/earnings DPS/EPS – Retained Earnings: (earnings - dividends) – Plowback Ratio b: retained earnings/total earnings – Book Value BV: cumulative retained earnings – Return on Book Equity ROE: earnings/BV Using these concepts, different valuation formulas may be derived