Stocks and Stock Markets
Common Stock - Ownership shares in a publicly held corporation.
Primary Market - Market for the sale of new securities by corporations. (vs. secondary market)
Initial Public Offering (IPO) - First offering of stock to the general public.
Seasoned Issue - Sale of new shares by a firm that has already been through an IPO 1 Common Stock Valuation
2 Professor: Burcu Esmer Primary vs. Secondary Markets: Example
Shannon sells 100 shares of Google stock from her portfolio to Mike for $500 per share to help pay for her son Domenic’s college education.
How much does Google receive from the sale of its shares?
Does this transaction occur on the primary or secondary market? 3 Bid Price/Ask Price 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.
Example: If an investor wishes to purchase 100 shares of Apple with a bid price of $253.40 and an ask price of $253.48, how much could the investor expect to pay for the shares? What is the bid-ask spread?
Answer: $253.48 4 Stocks & Stock Market
Dividend - Periodic cash distribution from the firm to the shareholders.
P/E Ratio - Price per share divided by earnings per share. www.finance.yahoo.com
5 Basic Terminology: Example
You are considering investing in a firm whose shares are currently selling for $50 per share with 1,000,000 shares outstanding. Expected dividends are $2/share and earnings are $6/share. What is the firm’s Market Cap? P/E Ratio? Dividend Yield?
Market Capitalization $50 1,000,000 $50,000,000 $50 P/E Ratio 8.33 $6 $2 Dividend Yield .04 4% 6 $50 Stocks & Stock Market
• Book Value - Net worth of the firm according to the balance sheet.
• Does the stock price equal to book value? No!!!
http://finapps.forbes.com/finapps/jsp/finance/compinfo/FinancialIndustri al.jsp?tkr=FDX
• Liquidation Value - Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.
• Does the stock price equal to liquidation value? No!!!
• Market Value -The value of the firm as determined by investors who 7 would be willing to purchase the company. Stocks & Stock Market
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” • Extra earning power • Intangible assets (R&D) • Value of future investments (growth companies)
• What determines firms’ future profits? The earnings that can be generated by the firm’s current tangible and intangible
assets and the future growth opportunities. 8 Valuing Common Stocks
• Stock Valuation Methods • Valuation by comparables • Ratios and multiples • Price and Intrinsic Value • Dividend Discount Model
9 Valuing Common Stocks Valuation Using Multiples
10 For industry financials: Source: MSN money http://biz.yahoo.com/p/s_peeu.html Price-to-earnings ratio: Method: using your company's EPS and a comparable company's P/E ratio (or the industry or market average):
Market-to-book ratio: Method: using your company's book value of equity, the number of shares outstanding and a comparable company's market-to-book ratio (or the industry or market average):
High PE and high MB generally mean investors are expecting high growth.
EBITDA (cash flow) Multiples: Investment bankers’ shortcut to valuation Method: using your company's income statement and value of equity, the number of shares outstanding and a comparable company's Capital/EBITDA ratio (or the industry or market average)
Note.. Undervalued stocks generaly have low PE ratios 11 Valuing Common Stocks Price and Intrinsic Value • Remember: Price of any security = PV of future cash flows
If you hold a stock forever, cash flows = all future dividends
• If you sell the stock eventually, what are the cash flows? • = dividends received + future sale price of the stock
value of all dividends thereafter
Price = the PV of all future dividends! 12 Valuing Common Stocks
Suppose you buy a stock and sell it next year, then;
Div P Intrinsic Value V 1 1 1 r
You can think of intrinstic value as the ‘fair’ price of the stock.
13
Div: Dividend Payment Example
• Suppose that an investor buys a share of Besmer Corp. Today and plans to sell it in 1 year. Suppose investors expect a cash dividend of $3 over the next year and expect the stock to sell for $81 a year. If the discount rate is 12%, then instrintic value is : Div P Intrinsic Value V 1 1 1 r
381 Intrinsic Value V $75 1.12
14 Valuing Common Stocks
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). Suppose you buy a stock and sell it next year, then;
Div P P Expected Return r 1 1 0 P0
15
Div: Dividend Payment Valuing Common Stocks
The formula can be broken into two parts.
Dividend Yield + Capital Appreciation
Div P P Expected Return r 1 1 0 P0 P0
If investors buy the stock at intrinsic value then their expected return will 16 equal the discount rate. Example (Cont.)
• Calculate the expected return if the price of the stock is $75 and you expect the stock to sell for $81 next yext year. You will get $3 dividend payment next year. Div P P Expected Return r 1 1 0 P0 P0 3 81 75 Expected Return 12% 75 75
Dividend yield Capital appreciation 3 81 75 Expected Return 12% 17 75 What happens if price is above $75? What happens if price is below $75? Valuing Common Stocks Dividend Dicount Model Computation of today’s stock price which states that share value equals the present value of all expected future dividends.
Div Div Div P P 1 2 ... t t 0 (1 r)1 (1 r)2 (1 r)t
18 Valuing Common Stocks
Example Current forecasts are for Besmer 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 (1.12)1 (1.12)2 (1.12)3 PV $75.00 19 Value of Besmer Corp for different horizons • Do investors with different horizons will come to different conclusions about the value of the stock?
Year 1 Year 2 Year 3 Basak Div=3 P=81 Zeynep Div=3 Div=3.24 P=87.48 Aslihan Div=3 Div=3.24 Div=3.5 P=94.48
• Estimate the price of the Besmer Stock for each of the investor. 20 Value of Besmer Corp for different horizons
80
70
60
50
40 PV (Terminal Price)
30 PV (Dividends)
20 Value per share, per share, dollars Value
10
0 1 2 3 10 20 30 50 100 Investment Horizon, Years 21 Dividend Discount Model Special Cases
• Zero Dividend Growth
• Constant Growth
• Non-Constant Growth
22 1. Zero Dividend Growth
• If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. (D1 = D2 = D3 = … = D∞ (a perpetuity)) Div EPS Perpetuity P 1 or 1 0 r r
Assumes all earnings are paid to shareholders. Remember there is no growth!
23 Example
• Stock XYZ has an expected growth rate of 0%. Each share of stock just received an annual $3.24 dividend per share. If the required return on the stock is 12% what is the value of the common stock?
3.24 Perpetuity P $27 0 0.12
24 2. Constant Growth
• A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). • The constant growth model assumes that dividends will grow forever at the rate g.
Div P 1 0 r g Given any combination of variables in the equation, you can solve for the unknown variable.
Note: This formula only works when g is less 25 than r! 2. Constant Growth
D0 = current (most recently paid) dividend
D1 = D0(1+g) 2 D2 = D1(1+g) = D0(1+g)(1+g) = D0(1+g) … … n Dn = D0(1+g)
26 Example
What is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return. Div $3.00 P 1 $75.00 0 r g .12 .08
• What is the value of a stock which just paid a dividend of $3.00, the expected growth rate is 8% per year. Assume a 12% expected return?
• Calculate next year’s dividend first! Div1 = Div0 x (1+g)= 3x1.08 = $3.24 Div $3.24 P 1 $81.00 27 0 r g .12 .08 Required Rates of Return (using constant growth)
Estimating Expected Required Rates of Return:
Expected rate of return offered by other, equally risky stocks
Example: What rate of return should an investor expect on a share of stock with a $2 expected dividend and 8% growth rate that sells today for $60?
28 3. Nonconstant Growth
Div Div Div P PV 1 2 ... H H (1 r)1 (1 r)2 (1 r)H (1 r)H
• Set the investment horizon (year H) at the future year by which you expect the company’s growth to settle down.
29 Changing Growth (steps)
1) Calculate dividends at end of each period of non-constant growth. 2) Calculate price at end of non-constant growth window. 3) Compute PVs of steps (1) and (2). This is your stock price.
30 Example
Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock just received an annual $3.24 dividend per share. If the required return on the stock is 15% what is the value of the common stock under this scenario?
31 Stock GP has two phases of growth. The first, 16%, starts at time t=0 for 3 years and is followed by 8% thereafter starting at time t=3. We should view the time line as two separate time lines in the valuation.
0 1 2 3 4 5 6
D1 D2 D3 D4 D5 D6
Growth of 16% for 3 years Growth of 8% to infinity!
32 Example (cont.)
Determine the annual dividends.
D0 = $3.24 (this has been paid already) 1 1 D1 = D0(1+g1) = $3.24(1.16) =$3.76 2 2 D2 = D0(1+g1) = $3.24(1.16) =$4.36 3 3 D3 = D0(1+g1) = $3.24(1.16) =$5.06 1 1 D4 = D3(1+g2) = $5.06(1.08) =$5.46
33 We determine the PV of cash flows.
PV(D1) = D1(PVIF15%, 1) = $3.76 (.870) = $3.27
PV(D2) = D2(PVIF15%, 2) = $4.36 (.756) = $3.30
PV(D3) = D3(PVIF15%, 3) = $5.06 (.658) = $3.33
P3 = $5.46 / (.15 - .08) = $78 [CG Model]
PV(P3) = P3(PVIF15%, 3) = $78 (.658) = $51.32
34 Finally, we calculate the intrinsic value by summing all the cash flow present values.
V = $3.27 + $3.30 + $3.33 + $51.32 = $61.22
• Preferred Stock = debt/equity “hybrid” security
• debt-like features: • often lack voting rights • dividend payments usually fixed and paid before common stock dividends • sometimes convertible to common stock • similarity to common stock: • preferred dividends have lower priority than debt interest payments • preferred dividends usu. not tax-deductible to corp. • Preferred Stock Valuation: • use perpetuity PV formula when appropriate 36 Preferred Stock Example
• Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock?
DivP = $100 ( 8% ) = $8.00.
P0 = Div1 / r = $8.00 / 10% = $80
37 Valuing common stocks Where does growth come from? Firm invests in projects
… which is paid out as divs, or reinvested in the firm.
…which produces cash flow
38 Valuing Common Stocks
What determines the growth rate (g)?
Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.
g = return on equity X plowback ratio (sustainable growth rate)
Payout Ratio - Fraction of earnings paid out as dividends Plowback Ratio - Fraction of earnings retained by the firm Sustainable Growth Rate - Steady rate at which firm can 39 grow; return on equity x plowback ratio Valuing Common Stocks
• If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.
40 What determines the growth rate (g)? • Suppose that BlueSkies starts the year with book equity (book value of equity) of $25 a share and earns return on equity of 20% per year. (remember roe: net income/book value of equity). • EPS= book value of equity per share x ROE = 25 x .2= $5 • İf BlueSkies pays $3 dividend next year then • Payout ratio = 3/ 5 = .60 and Plowback ratio=2/5= .40 • After reinvesting 40% of earnings, BlueSkies will start the next year with additional equity per share of • Earnings per share in the first year x plowback ratio= = book equity per share x ROE year x plowback ratio = 25 x .2 x .4 = $2 • The growth rate of BlueSkies’s equity = $2 / $25 = 8% 41 • g = return on equity X plowback ratio = .2 x .4 = 8% Valuing Common Stocks
Example BlueSkies 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?
42 Valuing Common Stocks
Example BlueSkies 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 P $41.67 g .20.40 .08 0 .12 3 The value of earnings from P0 $75.00 assets that are already in .12.08 43 place. Valuing Common Stocks
Example - continued 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).
• Present Value of Growth Opportunities (PVGO). • Net present value of a firm’s future investments. 44 Valuing Common Stocks
Value of assets in place $41.67 + Present Value of growth $33.33 opportunities (PVGO) Total Value of the stock $75
Note that if return on equity was 12% (=discount rate) – keeping the plowback ratio as 40%, then the price of the stock would still be $41.67. Plowing earnings back does increase stock price if investors believe that the reinvested earnings will earn a higher rate of return than the rate investors require (the discount rate). 45 Valuing Common Stocks
Note with growth opportunities, P/E is 15 (=75/5). without growth opportunities, P/E is 8.33 (=41.67/5). Example Suppose that instead of plowing money back into lucrative ventures, BlueSkies’s management is investing at an expected return on equity of 10%, which is below the return of 12% that investors could expect to get from comparable securities. A. Find the sustainable growth rate of dividends and earnings. Assume a 60% payout ratio. B. Find the new value of its investment opportunities. Explain why this value is negative despite the positive growth rate of earnings and dividends. C. İf you were a corporate raider, would BlueSkies be a good 46 candidate for an attempted takeover? Example cont.
• A. Sustainable growth rate= g = roe x plowback ratio = .1 x .4 = 4% • B. No growth case: P= 5/.12 = $41.67 with 4% growth: P= 3 / .12-0.04 = $ 37.50 The difference (41.67 – 37.50 = $4.17) is the money BlueSkies is wasting by investing in bad projects. • C. Sure! Buy the company for 37.50 (less than the pv of assets in place)
47 Valuing Common Stocks
• If return on equity= r then NPV of funds plowed back into firm is zero. (does not matter if invest EPS or pay as dividend).
• If return on equity > r then NPV>0 and shareholder value is increased.
• If return on equity < r then NPV<0 and shareholder value declines. • Note: By retaining earnings and then investing at return on equity, with r > return on equity the stock price will grow each year, but by less than shareholders could have earned investing the $ themselves!
48 Valuing Growth Stocks
Present Value of Growth Opportunities (PVGO) –
where: EPS = Earnings per share 49 PVGO = Present Value of Growth Opportunities Valuing Growth Stocks: Example
Suppose a stock is selling today for $55/share and there are 10,000,000 shares outstanding. If earnings are projected to be $20,000,000, how much value are investors assigning to growth per share? Assume a discount rate of 10%.
50 Growing Annuity Growing annuities are written one of two ways. Either in terms of the first cash flow (CF1) or in terms of a growth rate on a previous cash flow (CF0(1+g)).
2 N-1 CF1 CF1(1+g) CF1(1+g) CF1(1+g)
0 1 2 3 r N
2 3 N CF0(1+g) CF0(1+g) CF0(1+g) CF0(1+g)
0 1 2 3 N r where
CF0=CF1/(1+g)
We could discount each cash flow individually and then sum them, or we could rewrite the above as the difference between two growing 51 perpetuities. Growing perpetuity
2 N N+1 CF0(1+g) CF0(1+g) CF0(1+g) CF0(1+g) 1) 1 2 N N+1 0 r
Growing perpetuity that starts in N+1 years
N+1 0 0 0 0 CF0(1+g) 2) 1 2 3 N N+1 0 r
2 N CF0(1+g) CF0(1+g) CF0(1+g) 1) - 2) = 0 1 2 N 51
Subtracting the 2) from 1) leaves the first N Cash Flows Find the PV of timeline 1) and 2)
CF (1 g) CF (1 g)N1 1 0 PV(2) 0 PV(1) N r g r g (1 r)
Discounts (PVIFr,N) to time N
PV0 PV(1) PV(2) CF (1 g) CF (1 g)N1 1 0 0 N r g r g (1 r) CF (1 g) (1 g)N 0 1 N r g (1 r) 52 2 N-1 CF1 CF1(1+g) CF1(1+g) CF1(1+g)
0 1 2 3 r N
2 3 N CF0(1+g) CF0(1+g) CF0(1+g) CF0(1+g)
0 1 2 3 r N
Notice that if CF1 = CF0(1+g) the above two timelines are identical
N N CF0 (1 g) (1 g) CF1 (1 g) PV0 1 N 1 N r g (1 r) r g (1 r) A very common mistake is to put (N-1) into the formula when you see the top timeline. To avoid this mistake remember N in the formula is the number of cash flows and NOT NECESSARILY the 54 exponent on the last cash flow. Growing Annuity Example:
You are asked to value an existing security that makes a series of cash flows that grow by 5% each year. There are 8 cash flows left. The previous cash flow was just paid and was $3. What is the value of the security if the discount rate is 10%?
3(1.05) 3(1.05)2 3(1.05)3 3(1.05)8
0 1 2 3 r 8
CF (1 g) (1 g) N 3(1.05) (1.05)8 PV 0 1 1 $19.58 0 N 8 r g (1 r) .10 .05 (1.10) 55 Growing Annuity Example (Cont’d):
Identical problem asked another way:You are asked to value an existing security that pays a series of cash flows that grow by 5% each year. There are 8 cash flows left. The NEXT cash flow will be $3.15. What is the value of the security if the discount rate is 10%?
3.15 3.15(1.05) 3.15(1.05)2 3.15(1.05)7
0 1 2 3 r 8 N is # of CFs not the exponent on last CF! N 8 CF1 (1 g) 3.15 (1.05) PV0 1 N 1 8 $19.58 r g (1 r) .10.05 (1.10) 56 TVM Formula Summary CF Single Cash Flow CF N 0 (1 r) N CF Perpetuity PV 0 r
(CF CF1 CF2 ...) 1 1 1 Annuity PV0 CF N r r (1 r) (1 r) N 1 (CF CF1 CF2 ... CFN ) FV0 CF r CF (1 g) CF Growing Perpetuity PV 0 1 0 r g r g 2 (CF1 CF0 (1 g),CF2 CF0 (1 g) ,...) N CF 1 (1 g) Growing Annuity PV0 1 N r g (1 r) 57 N (CF1 CF0 (1 g),...,CFN CF0 (1 g) ) Finding mispriced stocks
58 Mutual Fund Performance
40 30 20 10 0 -10 Return (%) Return Funds -20 Market -30 -40
1962 1977 1992
Carhart (1997) study of 1,493 US mutual funds and 59 the market index Source: Brealey, Myers, & Allen Mutual Fund Performance Relative to the Market from 1970 to 2001
35 34 30 28 29 25 21 20 17 15 13 11 10 5 3 1 1 0 -4% -3% -2% -1% 0 to - 0 to 1% 2% 3% 4% or or 1% +1% more less Note: These are only surviving mutual funds, so it is probably biased upwards. Many of the poorest performing 60 funds likely shut down during this time period. Source: Malkiel, A Random Walk Down Wall Street Finding mispriced stocks (cont.)
Method I: Technical Analysis Investors who attempt to identify undervalued stocks by searching for patterns in past stock prices. Forecast stock prices based on the watching the fluctuations in historical prices (thus “wiggle watchers”)
61 Any predictability here?
62 Random Walk Theory
• Security prices change randomly, with no predictable trends or patterns. • Statistically speaking, the movement of stock prices is random • They are equally likely to offer a high or low return on any particular day, regardless of what has occurred on previous days.
63 Random Walk Theory
Market Index 1,300 Cycles Actual price as disappear soon as upswing is recognized once identified 1,200
1,100
Last This Next 64 Month Month Month S&P 500 and random draw… which is which?
1.8
1.6
1.4
1.2
1
0.8
Value of Investment $1 0.6
0.4
0.2
65 0 Months Finding mispriced stocks
Method II: 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
Fundamental analysts are paid to uncover stocks for which price does not equal intrinsic value.
What happens in a market with many talented and competitive fundamental analysts?
67 Efficient Market Theory
Efficient Market - Market in which prices reflect all available information.
• Weak Form Efficiency • Market prices reflect all historical information • Semi-Strong Form Efficiency • Market prices reflect all publicly available information • Strong Form Efficiency • Market prices reflect all information, both public and 68 private Degree of Market Efficiency Strong
Semi-strong
Weak
69 Efficient Market Theory
Announcement Date 39 34 29 24 19 14
(%) 9 4 -1 -6
Cumulative Abnormal Return Abnormal Return Cumulative -11 -16 Days Relative to annoncement date 70 Weak form efficiency • Prices contain all information from past prices • Stock prices are not predictable returns follow a random walk Highly recommend: A Random Walk Down Wall Street by Burton G. Malkiel
Random Error
Pt rt 1 Expected Re turn t Pt1
71 Weak form market efficiency
• Weak form market efficiency states that the current stock price reflects all past price information • Implications • Patterns in prices don’t exist • Prices follow a random walk • “Technical” trading strategies that just try to find patterns in stock prices don’t earn excess returns
72 Semi-strong form efficiency:
• Prices contain all publicly available information (past and current) • Accounting statements • News • Everything publicly available: “No stone left unturned” • Implications • Prices adjust immediately to new public information • “News” • “Fundamental” trading strategies that pick stocks based on financial characteristics don’t earn excess returns 73 Strong form efficiency
• Price reflects all information • All public information • All private information, including inside information • Implications • Prices would immediately adjust to reflect any new event that occurs in the firm, industry, and economy • It would be impossible for any investor (even the firm CEO) to consistently gain excess returns
74 Market Anomalies There are a number of market anomalies that seem to puzzle efficient market theorists, including:
The Earnings Announcement Puzzle
The New-Issue Puzzle
Bubbles
75 Behavioral Finance
Some believe that deviations in prices from intrinsic value can be explained by behavioral psychology, in two broad areas:
Attitudes toward risk--People generally dislike incurring losses, yet they are more apt to take bigger risks if they are experiencing a period of substantial gains. e.g. In the dot-com boom, it is theorized that investors experienced such great consistent gains that they stopped worrying about the risk of loss; thus driving prices artificially higher than their fundamental values.
Beliefs about probabilities--Individuals commonly look back to what has happened in recent periods and assume this is representative of future outcomes. e.g. Most investors believe they are better-than-average investors, but not every speculator can consistently profit at the other’s expense. «Overconfidence» 76