15.401 finance theory i, equities

15.401

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


15.401

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


15.401

Slide 4

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


15.401

Slide 5


$ B

illio

ns

90

75

60

45

30

155

1624

41

28 30

5043

37

64

76

36

26

16

48

0'90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04

Initial Public Offerings* Rebound In 2004

Source: Thomson Financial*Excludes Closed-End Funds

312587

8561063

716 722979

1317

1868 1960 1851

2535 25812890 2859

3500

3000

2500

2000

1500

1000

500

0'90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04

$ B

illio

ns

Industry Underwrites Nearly $3 Trillion in United States for Second-Straight Year

Source: Thomson Financial

1800

1500

1200

900

600

300

0'92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04

$ B

illio

ns

Source: Thomson Financial

162112

167269

383

592718

1314 1314

1768

1160

558451

749

279376

613731

1031

1735

1563

1741

771

440528

834

U.S. M&A Cycle Turns Up

Announced

Completed

Images by MIT OpenCourseWare.


15.401

Slide 6


Images by MIT OpenCourseWare.

157 179 202265 291

346412

527

674

809

1042

6,236

5,000

1,9082,426 2,540

2,7392,653

3,384

4,148

5,405

6,3006,9466,876 6,440

1457

7,250

1398

1240

1441

'90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04

1600

1400

1200

1000

800

600

400

200

0

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

Aver

age

Dai

ly V

olum

e in

Mill

ions

of S

hare

sN

YSE C

omposite

NYSE Volume NYSE Composite

NYSE Daily Share Volume vs. NYSE Composite Index

132 163 191 268 295401

544648

802

1082

17571900

1753 18011686

374 586 677 777 7521,052

1,2911,570

2,193

4,069

2,471

1,950

1,336

2,1752,003

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

2000

1800

1600

1400

1200

1000

800

600

400

200

0'90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04

Ave

rage

Dai

ly V

olum

e in

Mill

ions

of

Sha

res

NA

SDA

Q C

omposite

NASDAQ Daily Share Volume vs. NASDAQ Composite Index

NASDAQ Volume NASDAQ Composite


15.401

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


15.401

Slide 8


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):


15.401

Slide 9


This provides a convenient expression for the discount rate:


15.401

Slide 10

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.


15.401

Slide 11

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,


15.401

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?


15.401

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


15.401

Slide 14

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%


15.401

Slide 15

EPS and P/EEPS and P/EExample (cont):

Continuing Expansion Case:


15.401

Slide 16

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?


15.401

Slide 17

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


15.401

Slide 18

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%


15.401

Slide 19

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


15.401

Slide 20

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.


15.401

Slide 21

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


15.401

Slide 22

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


15.401

Slide 23

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.

MIT OpenCourseWarehttp://ocw.mit.edu

15.401 Finance Theory I Fall 2008

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

http://ocw.mit.edu/terms

http://ocw.mit.edu

15.401 finance theory i, equities

Documents