Chapter 7 Valuing

高立翰 Topics Covered

and the  Calculate the Value of Stock  Apply Models to a Business  Major Theories of Stocks and the Stock Market (1/3)

– Market for the sale of new securities by corporations  Initial (IPO) – First offering of stock to the general public  Primary Offering – The corporation sells shares in the firm  – Ownership shares in a publicly held corporation  – Market in which previously issued securities are traded among – Periodic cash distribution from the firm to the shareholders  P/E Ratio – Ratio of stock price to Stocks and the Stock Market (2/3)

 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

 e.g. (p.200) – If an 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 ? Payment P/E Ratio 1.00 160.39 100 × 159.99 = $15,999 .65 % 42.25 160.39 3.80 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 power 2. Intangible assets 3. 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) Div 𝑃 𝑉 1𝑟

V0 = The intrinsic value of the share

Div1 = The expected dividend per share at the end of the year

P1 = The predicted stock price in year 1 r = 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 are $3/share and the expected price in 1 year is $81/share? Assume a discount rate of 12%.

Div 𝑃 381 𝑉 $75 1𝑟 1.12 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) Div  P  P Expected return  r  1 1 0 P0  e.g. (p.205) (Continued) – Using the prior example, what is the expected return assuming the stock price started the year at $75? 3  81 75 Expected return  r   .12 75 Expected return = 12% Valuing Common Stocks (4/6)

 The formula can be broken into two parts: – Dividend yield + Capital appreciation Div P  P Expected return  r  1  1 0 P0 P0  e.g. (p.205) (Continued) – Using the prior example, what is the expected dividend yield and capital gain? 3 81 75 Expected return  r    .04 .08  .12 75 75 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

Div 1 Div 2 Div t  Pt P0  1  2  ...  t (1  r) (1  r) (1  r) t - Time horizon for your investment

 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? 3.00 3.24 3.50 94.48 PV , PV  $75.00 (1 .12)12 (1 .12) (1  .12) 3 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)

Div EPS Perpetuity  P  1 or 1 0 r r 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) Div P  1 Given any combination of variables in the 0 r  g equation, you can solve for the unknown variable  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. Div $0.74 P  1   $26.43 0 r  g .078.05 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) – 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 is 7.8%. What is the stock price? EPS $9.86 .125 $1.233 Growth rate .40 .125 .05 or 5.0% 0.74 𝑃 $26.43 Div $1.233.60$0.74 .078 .05 – 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 $1.233 1.233 𝑃 $15.81 .0780 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?

No Growth With Growth 5 g ..20 40 . 08 P $41.67 0 .12 3 P   $75.00 0 ..12 08 – 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). Valuing Non-Constant Growth

 Non-Constant Growth (非固定股利成長模式) Div Div Div P PV  1  2  ...  H  H (1 r)1 (1 r)2 (1 r)H (1 r)H  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?

2.85 3.14 3.45 3.79 4.17 PV       13.50 15 (1 085)1 (1 .085)2 (1 .085)3 (1 .085)4 (1 .085)5

4.17 1.05 4.38 125.14 PV 125.14 𝑃 13.50 $96.72 .085 .05 .085 .05 1.085 Valuing by

 Free Cash Flow FCF FCF FCF PV PV12 ... HH (1rr )12 (1 ) (1  r )H (1  r ) H

– 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 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 term Random Walk Theory (2/5)

 Coin Toss Game Heads $106.09 Heads $103.00 $100.43 Tails $100.00

Heads $100.43 $97.50 Tails $95.06 Tails Random Walk Theory (3/5)

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

200

160 Level

120

80 Month 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 Announcement Date 39 34 29 24 19 14 9 4 ‐1 ‐6

Cumulative Abnormal Return (%) ‐11 ‐16 Days Relative to 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 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)

Attitude

Belief

Sentiment