Chapter 7Valuing Stock

高立翰

Topics Covered

Stocks and the Stock Market Calculate the Value of Stock Apply Valuation Models to a Business Major Theories of Stock Valuation

Stocks and the Stock Market (1/3) Primary Market

– Market for the sale of new securities by corporations Initial Public Offering (IPO)

– First offering of stock to the general public Primary Offering

– The corporation sells shares in the firm Common Stock

– Ownership shares in a publicly held corporation Secondary Market

– Market in which previously issued securities are traded among investors Dividend

– Periodic cash distribution from the firm to the shareholders P/E Ratio

– Ratio of stock price to earnings per share

Stocks and the Stock Market (2/3)

e.g. (p.200) – If an investor wishes to purchase 100 shares of FedEx with a bid price of $159.78 and an

ask price of $159.99, how much could the investor expect to pay for the shares? What is the P/E Ratio and Dividend Yield?

Bid Price The prices at which investors are

willing to buy shares Ask Price

The prices at which current shareholders are willing to sell their shares

Payment

100 × 159.99 = $15,999

P/E Ratio160.39

3.80 42.25

Dividend Yield1.00

160.39 .65 %

Stocks and the Stock Market (3/3)

Share price history for FedEx

Market, Book, and Liquidation Values The difference between a firm’s actual market value and its’

liquidation or book value is attributable to its “going-concern value”– Factors of “Going Concern Value”

1. Extra earning power2. Intangible assets3. Value of future investments

Book Value– Net worth of the firm according to the balance sheet

Liquidation Value– Net proceeds that could be realized by selling the firm’s assets and

paying off its creditors Market Value Balance Sheet

– Financial statement that uses market value of all assets and liabilities

Valuing Common Stocks (1/6)

Stock Valuation Methods– Valuation by comparables (類比方式)

Ratios Multiples

– Intrinsic Value (真實價值) Present value of future cash payoffs from a stock or other security

– Dividend Discount Model (股利折現模式)

𝑉Div 𝑃

1 𝑟V0 = The intrinsic value of the shareDiv1 = The expected dividend per share at the end of the yearP1 = The predicted stock price in year 1r = The discount rate for the stock’s expected cash flows

Valuing Common Stocks (2/6)

e.g. – What is the intrinsic value of a share of stock if expected dividends are

$3/share and the expected price in 1 year is $81/share? Assume a discount rate of 12%.

𝑉Div 𝑃

1 𝑟3 81

1.12 $75

Valuing Common Stocks (3/6)

Expected Return– The percentage yield that an investor forecasts from a specific

investment over a set period of time. Sometimes called the holding period return (HPR)

e.g. (p.205) (Continued)– Using the prior example, what is the expected return assuming the stock

price started the year at $75?

0

011Divreturn ExpectedP

PPr

12.75

75813return Expected

r

Expected return = 12%

Valuing Common Stocks (4/6)

The formula can be broken into two parts:– Dividend yield + Capital appreciation

e.g. (p.205) (Continued)– Using the prior example, what is the expected dividend yield and capital

gain?

0

01

0

1Divreturn ExpectedP

PPP

r

12.08.04.75

7581753return Expected

r

Expected dividend yield = 4%Expected capital gain = 8%

Valuing Common Stocks (5/6)

Dividend Discount Model– Discounted cash-flow model which states that today’s stock price

equals the present value of all expected future dividends

e.g. (p.207)– Current forecasts are for Dritter Company to pay dividends of $3, $3.24,

and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

ttt

rP

rrP

)1(Div...

)1(Div

)1(Div

22

11

0

t - Time horizon for your investment

1 2 3

3.00 3.24 3.50 94.48PV , PV $75.00(1 .12) (1 .12) (1 .12)

Valuing Common Stocks (6/6)

Dividend Discount Model (1/6)

If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. (股利固定模式)

rEPSor

rPPerpetuity 11

0Div

Assumes all earnings are paid to shareholders

Dividend Discount Model (2/6)

Constant-Growth DDM (股利固定成長模式)– A version of the dividend growth model in which dividends grow at a

constant rate (Gordon Growth Model)

e.g. (p.210)– What is the value of a stock that expects to pay a $0.74 dividend next year,

and then increase the dividend at a rate of 5% per year, indefinitely? Assume a 7.8% expected return.

Given any combination of variables in the equation, you can solve for the unknown variable

10

DivPr g

43.26$05.078.

74.0$Div10

grP

Dividend Discount Model (3/6)

If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher– Payout Ratio (股利支付率)

Fraction of earnings paid out as dividends

– Plowback Ratio (再投資比率) Fraction of earnings retained by the firm

– Sustainable Growth Rate (持續成長率) The firm’s growth rate if it plows back a constant fraction of earnings, maintains

a constant return on equity, and keeps its debt ratio constant

Dividend Discount Model (4/6)

Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations

Present Value of Growth Opportunities (PVGO)– Net present value of a firm’s future investments (成長機會淨現值)

Dividend Discount Model (5/6)

e.g. (pp. 213)– Aqua America has an ROE of 12.5% and a book value per share of $9.86.

It intends to plowback 40% of its earnings and the opportunity cost of capital is 7.8%. What is the stock price?

– If Aqua America decides not to reinvest any earnings, what is the value of the stock and what is the PVGO of the firm that is lost?

EPS $9.86 .125 $1.233Growth rate .40 .125 .05 or 5.0%

Div $1.233 .60 $0.74 𝑃0.74

.078 .05 $26.43

EPS $9.86 .125 $1.233

𝑃1.233

.078 0 $15.81

PVGO 26.43 15.81 $10.62

Dividend Discount Model (6/6)

Another e.g. – Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its

earnings. This will provide investors with a 12% expected return. Instead, we decide to plowback 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

– If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.

– The difference between these two numbers (75.00 - 41.67 = 33.33) is called the Present Value of Growth Opportunities (PVGO).

P0512

67 .

$41.

No Growth With Growthg

P

. . .

. .$75.

20 40 083

12 08000

Valuing Non-Constant Growth

Non-Constant Growth (非固定股利成長模式)

e.g. (p.215)– Given the following earnings and dividends, an 8.5% discount rate and a

perpetual growth rate of 5%,which begins in year 6, what is the value of the stock?

HH

HH

rP

rrr )1()1(Div...

)1(Div

)1(DivPV 2

21

1

50.13)085.1(

17.4)085.1(

79.3)085.1(

45.3)085.1(

14.3)0851(

85.2PV 5432151

PV4.17 1.05.085 .05

4.38.085 .05 125.14 𝑃 13.50

125.141.085 $96.72

Valuing by Discounted Cash Flow

Free Cash Flow

– The present value of Free Cash Flow plus the present value of firm’s horizon value

– For firms without dividend payout – The valuation of firms to have merge and acquisition

1 21 2

FCF FCF FCFPV ...(1 ) (1 ) (1 ) (1 )

H HH H

PVr r r r

No Free Lunches

Technical Analysts (技術分析)– Investors who attempt to identify undervalued stocks by searching for

patterns in past stock prices– Forecast stock prices based on watching the fluctuations in historical

prices (thus “wiggle watchers”)Average Annual Return on Mutual Funds and the Market Index

Random Walk Theory (1/5)

Security prices change randomly, with no predictable trends or patterns (隨機漫步理論)

Statistically speaking, the movement of stock prices is random – Skewed positive over the long term

Random Walk Theory (2/5)

Coin Toss Game

$103.00

$100.00

$106.09

$100.43

$97.50

$100.43

$95.06

Heads

Heads

Heads

Tails

Tails

Tails

Random Walk Theory (3/5)

80

120

160

200

Lev

el

Month

S&P 500 Five Year Trend orFive Years of the Coin Toss Game?

Random Walk Theory (4/5)

Scatter plot of NYSE Composite Index over two successive weeks. Where’s the pattern?

Random Walk Theory (5/5)

Cycles disappear 

once identified

Another Tool

Fundamental Analysts– Investors who attempt to find mispriced securities by analyzing

fundamental information, such as accounting data and business prospects

– Research the value of stocks using NPV and other measurements of cash flow

Efficient Market Theory (1/3)

Efficient Market (效率市場理論)– Market in which prices reflect all available information

Weak Form Efficiency (弱式市場)– Market prices reflect all historical information

Semi-Strong Form Efficiency (半強式市場)– Market prices reflect all publicly available information

Strong Form Efficiency (強式市場)– Market prices reflect all information, both public and private

Efficient Market Theory (2/3)

Impact of leaked information

‐16

‐11

‐6

‐1

4

9

14

19

24

29

34

39

Cumulative Ab

norm

al Return (%

)

Days Relative to Announcement Date

Announcement Date

Efficient Market Theory (3/3)

The average return 1972–2001 on stocks of firms over the six months following an announcement of quarterly earnings. The 10% of stocks with the best earnings news (portfolio 10) outperformed those with the worst news (portfolio1) by about 1% per month.

Market Anomalies

Existing Anomalies– The Momentum Factor– The New-Issue Puzzle

Old Anomalies– The Small Firm Effect (小型公司效應：小公司投報率較高)– The January Effect (元月效應：每年元月份的投資報酬率較高)– The PE Effect (本益比效應：低本益比公司投報率較高)– The Neglected Firm Effect (遺珠效應：被忽略公司投報率較高)– The Value Line Effect (機構誤差效應)

Behavioral Finance

Attitudes towards risk (風險傾向) Beliefs about probabilities (機率看法) Sentiment (情感分析)

Sentiment

Belief

Attitude