Download - 15.401 Finance Theory I, Equities
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15.401 Finance Theory15.401 Finance TheoryMIT Sloan MBA Program
Andrew W. LoAndrew W. LoHarris & Harris Group Professor, MIT Sloan SchoolHarris & Harris Group Professor, MIT Sloan School
Lecture 7: EquitiesLecture 7: Equities
© 2007–2008 by Andrew W. Lo
© 2007–2008 by Andrew W. LoLecture 7: Equities
15.401
Slide 2
Critical ConceptsCritical Concepts
Industry OverviewThe Dividend Discount ModelDDM with Multiple-Stage GrowthEPS and P/EGrowth Opportunities and Growth Stocks
ReadingBrealey, Myers and Allen, Chapter 4
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Slide 3
Industry OverviewIndustry Overview
What Is Common Stock?Equity, an ownership position, in a corporationPayouts to common stock are dividends, in two forms:– Cash dividends– Stock dividends
Unlike bonds, payouts are uncertain in both magnitude and timingEquity can be sold (private vs. public equity)
Key Characteristics of Common Stock:Residual claimant to corporate assets (after bondholders)Limited liabilityVoting rightsAccess to public markets and ease of shortsales
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Industry OverviewIndustry OverviewThe Primary Market (Underwriting)
Venture capital: A company issues shares to special investment partnerships, investment institutions, and wealthy individualsInitial public offering (IPO): A company issues shares to the general public for the first time (i.e., going public)Secondary or seasoned equity offerings (SEO): A public company issues additional sharesStock issuance to the general public is usually organized by an investment bank who acts as an underwriter: it buys part or all of the issue and resells it to the public
Secondary Market (Resale Market)Organized exchanges: NYSE, AMEX, NASDAQ, etc.Specialists, broker/dealers, and electronic market-making (ECNs)OTC: NASDAQ
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Industry OverviewIndustry Overview
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Images by MIT OpenCourseWare.
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Industry OverviewIndustry Overview
Images by MIT OpenCourseWare.
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© 2007–2008 by Andrew W. LoLecture 7: Equities
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Slide 7
The Dividend Discount ModelThe Dividend Discount ModelMost Basic Valuation Model for Common Stock
Applies PV formulas to common-stock payoutsTwo inputs: expected future dividends, discount rateNotation:– 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 t
© 2007–2008 by Andrew W. LoLecture 7: Equities
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The Dividend Discount ModelThe Dividend Discount ModelMost Basic Valuation Model for Common Stock
Two additional simplifying assumptions:
In this case, we have the first version of the dividend discount model or the discounted cashflow (DCF) model
Suppose dividends grow at rate g over time (Gordon growth model):
© 2007–2008 by Andrew W. LoLecture 7: Equities
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The Dividend Discount ModelThe Dividend Discount ModelMost Basic Valuation Model for Common Stock
This provides a convenient expression for the discount rate:
© 2007–2008 by Andrew W. LoLecture 7: Equities
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The Dividend Discount ModelThe Dividend Discount ModelExample:
Dividends are expected to grow at 6% per year and the current dividend is $1 per share. The expected rate of return is 20%. What should the current stock price be?
Note: DDM with constant growth gives a relation between current stock price, current dividend, dividend growth rate and the expected return. Knowing three of the variables determines the fourth.
© 2007–2008 by Andrew W. LoLecture 7: Equities
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The Dividend Discount ModelThe Dividend Discount ModelExample:
Determine the cost of capital of Duke Power. In 09/92, the dividend yield for Duke Power was D0/P0 = 0.052. Estimates of long-run growth:
The cost of capital is given by
Thus,
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Slide 12
DDM with MultipleDDM with Multiple--Stage GrowthStage GrowthFirms May Have Multiple Stages of Growth
Growth Stage: rapidly expanding sales, high profit margins, and abnormally high growth in earnings per share, many new investment opportunities, low dividend payout ratioTransition Stage: growth rate and profit margin reduced by competition, fewer new investment opportunities, high payout ratioMature Stage: earnings growth, payout ratio and average return on equity stabilizes for the remaining life of the firm
Example:A company with D0 = $1 and r = 20% grows at 6% for the first 7 years
and then drops to zero thereafter. What should its current price be?
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Slide 13
EPS and P/EEPS and P/EDividend 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 derivedNote: these are mostly based on accounting data, not market values
© 2007–2008 by Andrew W. LoLecture 7: Equities
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EPS and P/EEPS and P/EExample:(Myers) Texas Western (TW) is expected to earn $1.00 next year. Book
value per share is $10.00 now. TW plans an investment program which will increase net book assets by 8% per year. Earnings areexpected to grow proportionally. The investment is financed by retained earnings. The discount rate is 10%, which is assumed to be the same as the rate of return on new investments. Price TW's share price 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%
© 2007–2008 by Andrew W. LoLecture 7: Equities
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EPS and P/EEPS and P/EExample (cont):
Continuing Expansion Case:
© 2007–2008 by Andrew W. LoLecture 7: Equities
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EPS and P/EEPS and P/EExample (cont):
2-Stage Expansion Case. Forecast EPS, D, BVPS by year:
Question: Why are the values the same under both scenarios?
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Growth Opportunities and Growth StocksGrowth Opportunities and Growth StocksWhat Are Growth Stocks?
Stocks of companies that have access to growth opportunities areconsidered growth stocksGrowth opportunities are investment opportunities that earn expected returns higher than the required rate of return on capitalExample: 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 return
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Growth Opportunities and Growth StocksGrowth Opportunities and Growth StocksExample:ABC Software has: Expected EPS next year of $8.33; Payout ratio of
0.6; 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 growth opportunities, which offers a return of 25%, higher than the required rate of return 15%
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Growth Opportunities and Growth StocksGrowth Opportunities and Growth StocksExample (cont):
At t = 1: ABC can invest (0.4)(8.33)=$3.33 at a permanent 25% rate of return. This investment generates a cash flow of (0.25)(3.33) = $0.83 per 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 made with NPV being
The total present value of growth opportunities (PVGO) is
This makes up the difference in value between growth and no-growth
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Growth Opportunities and Growth StocksGrowth Opportunities and Growth StocksStock 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 investors are more concerned with price relative to future earnings.
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Growth Opportunities and Growth StocksGrowth Opportunities and Growth Stocks
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 capital
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Key PointsKey PointsThe 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 opportunities
© 2007–2008 by Andrew W. LoLecture 7: Equities
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Additional ReferencesAdditional ReferencesHarris, L., 2002, Trading and Exchanges: Market Microstructure for Practitioners. New York: Oxford University 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 Personal Investing. New York: W.W. Norton.
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15.401 Finance Theory I Fall 2008
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