MGT 326 Ch 7 Stock Valuation (bdh2e) 1 STOCK (EQUITY) Learning Objectives: Understand Fundamental...

MGT 326 Ch 7 Stock Valuation (bdh2e)

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STOCK (EQUITY)

Learning Objectives:

Understand Fundamental Stock Concepts, Terms & CharacteristicsDefine the Stock Investor's Rqd RORCompute Stock Realized & Expected Total YieldCompute the Theoretical Value of a Zero Dividend Growth Stock (Div. Discount Model)Compute the Theoretical Value of a Constant Dividend Growth Stock (DDM)Compute the Theoretical Value of a Non-constant Dividend Growth Stock (DDM)Explain When to Use the Above Pricing Models wrt the Corporate Life CycleExplain How Firms Meet the Cost of StockUnderstand the Relationship Between NI Growth, Divi. Growth & Stock Price Growth

Ver. 1.2 Fall 2013


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Common Stock Basics: Shares of stock are initially sold by a firm; proceeds usually used to buy capital assets (plant, machinery, equipment, etc.)Large quantities of stock are usually only issued once by a firm Small quantities may be issued later (stock options, convertible bonds, warrants, etc.)A share of stock is ownership in a company (see below)The publicly traded stock from a particular company has a unique symbol (the “ticker” symbol) Ex: Apple Inc.: AAPL

Common Stock Financial Considerations:May or may not pay a dividendMay or may not be publicly traded in a market (i.e. NYSE)Usually gains or loses value over time (capital gains/losses). Price (perceived value) based on many company specific factors to include:

Recent and expected earningsRecent or pending litigationProduct/service reliability (ex: auto recall)Financial health/stability (ex: ability to service debt)Quality of managementIntegrity of financial reporting

Legal Rights & Privileges of Common Stock HoldersControl of the firm:

A stock owner has voting rights; the right to vote on key company issues such as electing the board of directorseach share of stock has one votestates regulate (by law) frequency and conduct of votingstockholders who cannot attend voting sessions can vote by proxy

2e created Sum ‘11 v1.1 Spr ‘12


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Legal Rights & Privileges of Common Stock HoldersStockholders are entitled to all of a firm’s Net Income

The Market for Common StockClosely Held or Private Stock: Stock from small privately owned firms

small companies often don’t have much stock outstandingwhat stock there is, is usually held by senior management or private ownersthis stock is often not publicly traded

Publicly Held Stock: Stock from large firmsmost large firms have financed themselves over years (decades) through one or more stock issuesstock from these firms is usually (but not always) publicly traded and has been so for a long timein essence, the “public” owns these firms

Types of Stock Market Transactions:primary vs. secondary markets (Ch 2)Initial Public Offering (IPO) Market:

an IPO occurs when a firm decides to issue stock to the public for the first timemany firms have had non-publicly traded stock (private stock) for years prior to going public (i.e. Microsoft 1986)investment banks “underwrite” the IPOIPOs occur in the primary market and, in effect, are OTC transactions almost always limited to large investor firms; this is why you & I can’t get a piece of the actionthere are initiatives to end this situation


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What makes stocks valuable (why anyone would want to buy them):

A way to rearrange cash flows (hopefully in a positive, profitable way) in the form of an investment:

stock ownership entitles holders to dividends, however…..dividends (on common stock) are not guaranteeda firm’s management may decide to retain all earnings for various reasons & purposes

stock value may appreciate over time; opportunity for capital gain by selling the stock at a price higher than you paid for itthus the expected cash flows from stock consists of two parts: expected dividends & expected capital gains

A chance to own a piece of a firmthis isn’t a big deal for most individual investorsthis is a very big deal for corporations wishing to acquire other firms

Why firms care about the price of their outstanding stock:

Stock prices reflect public perception of and confidence in the firm’s future prospects

They want to avoid hostile take-over

Question: How do we determine the fair market value of a stock? Answer: One way is to find the PV of all dividends expected to be paid in the future and sum them because……The value of any financial asset is determined by discounting all future cash flows to the present (i.e. find the PV @ t = 0) and adding them up!!!!


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Common Stock Valuation (continued)Some Terms & Concepts:

D0: The most recent dividend paid (usually just before t = 0). This is not a future or present cash flow; it has already occurred.Dt: the dividend a stockholder expects to receive at the end of a some future period ( t is an index)P0: The actual price (market value) of the stock today (t = 0)P0: The expected, theoretical, intrinsic value of the stock at t = 0; (Note: the symbol is the statistics way to say “expected”Pt: The expected price of a stock at the end of some future period ( t is an index)g: Expected growth rate of the dividend rs: Required ROR/Yield.

This is the minimal acceptable ROR for an investor; it’s an opportunity cost. For example, if the NYSE has been paying 8% recently then rs for any particular NYSE stock might be 8%rs is also the “cost of stock” from the firm’s perspective (more on this later)

rs: Actual or “realized” ROR or Yield; a historical ROR rs: Expected and/or theoretical ROR/Yield


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Expected/Theoretical Yield (rs) on a Stock (This is rE as discussed in your text book)Can we determine the expected ROR on a stock? Yes.There are two ways to make a profit from stocks:

dividendscapital gains

Expected Dividend Yield = ROR from dividends = D1 / P0

Expected Capital Gains Yield = Potential ROR from Selling the stock at some point in the future (let’s say one year from now) = (P1 - P0)/P0

Expected Total Yield = rs = Expected Dividend Yield + Expected Capital Gains Yield

rs = D1 / P0 + (P1 - P0)/P0

= (D1 + P1 - P0)/P0

rs is the discount rate we will use to find the theoretical value of the stock by discounting all future cash flows to t = 0 and adding them up

→it is the best available expected return offered in the stock market on a stock of comparable risk →it should compensate us for r*, inflation and the associated level of risk for that particular stock→it is the rate at which we expect our investment to grow to achieve a future value→since discounting is the opposite of compounding, we must discount at that exact same rate in order to find the present value→rs (rE)is also called the “Opportunity Cost of Equity” because it is the return the investor forgoes on an alternative investment of equivalent risk and term when the investor takes on the alternative investment


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Expected/Theoretical Yield (rs) on a Stock (continued) Example: A firm’s stock is expected to pay a dividend of $1.25 per share at the end of the year. The stock price was $37.75 at the beginning of the year. The firm’s stock is expected to be at around $38.90 by the end of the year. What is the firm’s expected annual ROR?

1) Find Dividend Yield: D1/P0 = $1.25/$37.75 = 3.3113% 2) Find Cap. Gains Yield: (P1 - P0)/P0 = (38.90 - 37.75)/37.75 = 3.0464%3) Find rs: 3.3113% + 3.0464% = 6.3576%

Finding Realized Return (Yield) (rs) with Dividend Yield and Capital Gains YieldCan we determine the historical ROR on a stock? Yes.There are two ways to make a profit from stocks:

dividendscapital gains

Thus the total realized return has two parts:rs = Total Realized Return/Yield = Realized Dividend Yield + Realized (or Potential) Capital Gains Yieldrs = D0/P-1 + (P0 - P-1)/P-1

= (D0 + P0 – P-1) / P-1

Example: A firm’s last stock dividend of $0.75 per share was paid at the end of the 2008. This was the only dividend paid in 2008. The price of that firm’s stock at that time (P0) was $31.95. The stock price was $33.75 at the beginning of 2008 (P-1). What was the firm’s realized 2008 ROR?1) Find Dividend Yield: D0/P-1 = $0.75/$33.75 = 2.2222% 2) Find Capital Gains Yield: (P0 - P-1)/P-1 = (31.95 - 33.75)/33.75 = -5.3333%3) Find rs (Total Realized Return): 2.22% - 5.33% = -3.1111%

Another Way to Find rs: Compute the average period-to-period ROR over a given length of time (more on this in Ch 10)


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The key principle of statistics is past performance is a predictor of future performance. Therefore:rs is often used for rs; i.e. rs rs

Estimates of future stock values and future dividends are just educated guessesThere’s not much guessing about past dataAnalyst feel more confident using past data than future estimatesThis is the most common method for finding rs

Required ROR (rs)Whenever we invest in something we require compensations for r*, inflation and the associated level of risk of that investment The same holds for stock investmentsThe required ROR for a particular stock is rs

There are at least two ways to come up with a value for rs:

1.Suppose your are considering buying stock in Black & Decker Inc., a power tool manufacturing company. You do some research and find that the average stock total yield of all power tool manufacturing firms was 8% for the last five years. You may choose to call 8% your required ROR (rs).

2.Because an investor requires at least what was earned in the past and you may choose to use rs as rs

Note on How These Terms are Used in Common Practice:

rs, rs and rs are often used interchangeably because rs is often used for rs and rs is often used for rs

Realized ROR (rs) vs. Expected ROR (rs)


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As t in the perpetuity equation continues to infinity, the equation converges to:

P0 = D/ rs [This is the same thing as a perpetuity (Ch 4) but with

different variables]

Example: The stock of Jihad Jim’s Travel Adventures Corp. pays an annual dividend of $2. If the required ROR (rs) is 8%, what is the “theoretical” or “expected” price of this stock?

P0 = D/ rs = $2 / 0.08 = $25

Required ROR on Bonds (rd) vs. Required ROR on Stocks (rs)There is no doubt about rd; it is the current market interest rate for all bonds of the same rating and maturityThere is no definitive answer for the value of rs

Common Stock Valuation: The Dividend Discount ModelFinding the Expected (Theoretical, Fair Market) Value of a Stock (P0)A basic assumption is: any company that issues stock is planning on being around at least for the foreseeable futureTherefore, we don’t know when the last dividend will occurTherefore, we will assume that the firm will exist indefinitely Thus, we can model a stock as a perpetuity

(recall from Ch 4: PVperpetuity = PMT/ r )

“Pricing” a “zero-growth” stock; (i.e. the dividend always remains the same, forever)Expected Value of the Stock (Base Equation) = Vs = P0

1tt

s

t

s2

s

21

s

1

1

D̂

1

D̂

1

D̂

1

D̂

r

rrr


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Common Stock Valuation (continued)

“Pricing” a “constant-growth” stock; (i.e. the dividend grows at a constant rate, forever)

P0 = D0(1 + g) = D1

rs – g rs - gWe don’t know what D1 will be but we can estimate itA firm’s net income usually grows from year to year (see next page). That rate of grow is “g”We assume that dividends grow at that same rateWe know what D0 (the last dividend paid) isTo estimate D1, we simply grow D0 one period at growth rate g; D1= D0(1 + g)1 (i.e. FV = PV(1 + g)n)

Example: The CEO of Jihad Jim’s Travel Adventures Corp. has decided that, since the firm is doing exceedingly well and since future prospects look very promising, all dividends for the foreseeable future will be increased at an annual rate of 2% (g = 2%). The last dividend (D0) was $2. If the required ROR (rs) is 8%, what is the “theoretical” or “expected” price of this stock?

P0 = D0(1 + g) rs - g

= $2(1 + 0.02) / (0.08 - 0.02) = $34.00

Note: rs must be > g or the model makes no sense

t = ? (infinity)0 41 2 3

D0

D1

D2

D3DinfinityNormal Growth (g=2%, t=0 & onward)

Solving the above equation for rs we get: rs = D1/P0 + g


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Common Stock Valuation (continued)Rationale for Constant Dividend Growth:

We expect a firm’s net income to grow at least as fast as inflation or else the firm loses valueWe expect all stock dividends to grow at least as fast as inflation (disregarding any possible capital gains by selling the stock in the future) If this were not the case, why invest in that stock?Thus, it is fair to conclude that an adequate model for basic stock valuation is that for a constant growth stock in which the dividend grows at least as fast as inflationAn average growth rate for all stock dividends is the GDP growth rate plus inflation (i.e. g = GDP + inflation)Firm specific growth estimates are produced by financial services companies and are available from many online sources

“Pricing” Stocks with Non-constant Dividend Growth:For most firms, NI doesn’t grow at a constant rate indefinitelyCorporate life cycle: emergence, growth, maturity & decline

Dividend Growth Rates:Supernormal Growth: “above average” dividend growth typically occurring during the “emergence” phase of a firm’s life cycle

Normal Growth: “average” growth typically occurring during the “growth” phase of a firm’s life cycle

Zero or Low Growth: typically occurs during the “mature” phase of a firm’s life cycle; if the firm’s NI is growing at all, it’s just keeping pace with inflation; dividends may or may not be growing

Negative Growth: typically occurs during the “decline” phase of a firm’s life cycle. This doesn’t necessarily mean the firm is losing money, just that dividends are shrinking


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Common Stock Valuation (continued)“Pricing” Stocks with Non-constant Dividend Growth: (continued)

Usually, only the supernormal growth period and the normal growth period are considered; the other two growth phases are too far into the future to accurately forecast

Example: A firm just recently paid a stock dividend of $1.15 (D0 = $1.15). The firm pays only 1 dividend per year and that occurs at the end of the year. The firm expects its dividends to grow by 30% for the next 3 years (t=1 thru t=3). After that, dividends are expected to grow at 8% per year for the foreseeable future. What is the theoretical value of this firm’s stock (P0)? Assume rs is 13.4%


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7 t = ? (infinity)0 4 5 61 2 3

rs = 13.4%

D0 = $1.15D1

D2

D3D4Supernormal Growth

(gSN=30%, t=0 thru t=3) D5

D6

Dinfinity

D7

Normal Growth (gN=8%, t=3 & onward)

Common Stock Valuation (continued)Pricing Stocks with Non-constant Dividend Growth: (continued)Example: (continued)

Approach: break the problem down into two parts; a supernormal growth part and a normal growth part

Note: the dividends occur at the end of each periodThe solution approach is kind of like the changing interest rate problem we looked at in Ch 4

P0 = PV0(CFs1-3) + PV0(PVt=3, CFs 4-infinity)

1) Find PV0(CFs1-3) : Compute each dividend (gSN=30%) then discount each of the dividends (@ rs = 13.4%) back to t=0.Note: D0 has already been paid and is thus not included in the PV

Dividend Dt = Dt-1 (1 + 0.3) PV(t=0)

0 $1.1500

1 $1.4950 $1.3183

2 $1.9435 $1.5113

3 $2.5266 $1.7326

PV0(CFs1-3) = $4.5622

I/Y=13.4, CF0=0, CF1=1.4950, CF2=1.9435, CF3=2.5266; NPV = $4.5622

N=1, I/Y=13.4, FV=1.4950; PV = $1.3183N=2, I/Y=13.4, FV=1.9435; PV = $1.5113N=3, I/Y=13.4, FV=2.5266; PV = $1.7326

$4.5622

N=1, I/Y=30, PV=1.15; FV = 1.4950N=2, I/Y=30, PV=1.15; FV = 1.9435N=3, I/Y=30, PV=1.15; FV = 2.5266

or


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2) Find PVt=3, CFs 4-infinity :We will find this by viewing this portion of the problem as a stock that has constant growthWe will find the theoretical value of a constant growth stock at t = 3 (This is called the “terminal” or “horizon” value)This is equivalent to the PV @ t=3 of all future cash flowsThus PVt=3, = P3 = Vhorizon = D3(1+gN)/(rs - gN)

PVt=3, CFs 4-infinity = D3(1+gN)/(rs - gN) = 2.5266(1.08)/(0.134 - 0.08) = $50.5320

The cash flow diagram now looks like this:

Common Stock Valuation (continued)Pricing Stocks with Non-constant Dividend Growth: (continued)


7 t = ? (infinity)0 4 5 61 2 3

rs = 13.4%

D4D5

D6

Dinfinity

D7

Normal Growth (gN=8%, t=3 & onward)

PV0,CFs1-3 = $4.5622

7 t = ? (infinity)0 4 5 61 2 3rs = 13.4%

PV0,CFs1-3 = $4.5622PVt=3,CFs4-infinity = $50.5320

PVt=3,CFs4-infinity = Vterminal = Vhorizon = P3 =?


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3) Find PV0(PVt=3, CFs 4-infinity) Discount PVCFs 4-infinity back to t = 0

PV0(PV t=3, CFs 4-infinity) = $50.5320 / (1 + 0.134)3 = $34.6519or

N=3, I/Y=13.4, FV=50.5320; CPT,PV: = $34.6519


4) Find P0: P0 = $4.5622 + $34.6519 = $39.21

What’s the point of all this?Answer:

This is how the price is estimated for an IPO of stockThis is how you can get a more accurate estimate of what any stock should (in theory) cost in order to determine if the current market value of a stock is way over/under valued

7 t = ? (infinity)0 4 5 61 2 3rs = 13.4%

PV0,CFs1-3 = $4.5622PVt=3,CFs4-infinity = $50.5320

Discount 3 periods

7 t = ? (infinity)0 4 5 61 2 3rs = 13.4%

PV0,CFs1-3 = $4.5622

PV0(PVt=3,CFs4-infinity) = $34.6519


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Common Stock Valuation (continued)Example: The stock of Java Jim’s Gourmet Coffee Inc. is currently selling for $65 per share. The firm pays dividends each quarter and they are expected to grow at a rate of 16% per year for the next nine months. After this time, the dividends are expected to grow at a constant rate of 8% per year for the foreseeable future. The firm’s most recent dividend was $0.50. The stock's required rate of return is 12%. What is the theoretical value of this stock?


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Common Stock Valuation (continued)

What do you do if a company doesn’t pay dividends?Answer: Use Free Cash Flows (FCF) per share instead of dividend per shareFor a definition of FCF, refer to pp 299-303Using FCF/share for future cash flows will produce a higher P0 than if you use dividends for future cash flows

Stock Valuation Summary:These models for stock valuation are not precise since:

g is the result of an educated guesswe assume g is stable and constant; even in the case when we have more than one g (non-constant dividend growth), but g can and probably will change and thus not be constantnothing lasts foreverrisk (volatility, uncertainty associated with indefinite life, etc.) has not been addressed

These models are useful for comparative stock analysisyou can compare the theoretical values with market values to determine if stocks are over/under valuedif you use the same model for all the stocks you evaluate, the biases discussed above apply uniformly

Point: Because of the uncertainty of the stock valuation parameters, (g, rs and no specified end date) the best we can do is estimate the theoretical value of stockThis is also why there are several methods (Discounted Free Cash Flow model, Comparable Firm Valuation method, Total Payout Model) to find stock theoretical value


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Estimating a Future Stock Price

Example: Jihad Jim’s Travel Adventures Corp. stock currently sells for $35, its dividends have an annual growth rate of 1.5% and its next dividend is expected to be $1 per share. If the dividends for this stock actually grow 1.5% per year, what is the expected value of the stock one year from now?

P1 = P0(1 + g) = $35(1 + 0.015) = $35.53

orN=1, I/Y=1.5, PV=35; FV = $35.53

Note: g is a periodic rate!

Example (continued): The dividends for the above stock actually grow at 3% per year and the firm pays quarterly dividends. What is the expected value of the stock one year from now?

P1 = P0(1 + g/m)n = $35(1 + 0.03/4)4 = $36.06or

P/Y=4, N=4, I/Y=3, PV=35; CPT,FV = $36.06


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Some Important Theoretical Relationships

Consider the formula for theoretical value of a constant growth stock:

Solving the above equation for rs we get: rs = D1/P0 + g

Shift the from P0 to rs and we get rs = D1/P0 + g (Eqn 1)

Now consider the formula for expected total yield: rs = D1 / P0 + (P1 - P0)/P0

Substitute Eqn 1 for rs in the above equation and we get: D1/P0 + g = D1 / P0 + (P1 - P0)/P0

Thus g = (P1 - P0)/P0 = Capital Gains Yield

What Does All This Mean?In theory, expected dividend growth rate equals the rate at which one should expect stock price to increaseSince we have assumed the g equals the rate at which NI increases then: In theory, the rate at which a stock’s price increases should equal the rate at which that firm’s NI increases

P0 = D1

rs – g

Dividend Yield Capital Gains Yield


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Preferred Stock:

Definition: A security that provides a share in a company and a scheduled payment of a fixed dividend.

They are not usually offered to the general public

Similar to a coupon bond because the dividend is a fixed amount and paid on a fixed schedule

Similar to common stock since the dividend does not have to be paid on schedule (it can be deferred) and there is no expiration date of the stock

Holders of preferred stock have priority over common stock holders in the distribution of a company's funds (dividends and bankruptcy proceeds)

Preferred Stock Dividend: Dp

Preferred Stock Required ROR: rp; this is not the same as rs; Why not?

Vp = Dp / rp

rp = Dp / Vp

The Cost of StockAs previously mentioned rs (required ROR, from investor’s perspective) is also the “cost of stock” from a firm’s perspectiveThe cost of stock is, in essence, a management goal:

→management must run the firm such that its value continues to improve→this means that a firm’s mgt must try to make stock total yield (dividends & cap. gains) match investors’ required ROR→If not, investors buy less of the firm’s outstanding stock the stock falls in price due to decreased demand the firm becomes more vulnerable to take-over


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Failure to Meet the Cost of Debt vs. Failure to Meet the Cost of Stock

Failure to Meet the Cost of Debt is more imminent but recoverable→if you miss an interest payment, you’re (technically) bankrupt→this is a periodic (month to month, quarter to quarter) possibility; thus this possibility is imminent→however, firms can recover from bankruptcy

Failure to Meet the Cost of Stock is not imminent but unrecoverable→if the firm fails to meet investor’s required ROR on stock, current stock holders will sell their stock and potential new stock investors won’t buy it→if this continues, quarter after quarter, year after year, the stock price will continue to fall until it becomes cheap enough for a hostile take-over→firms rarely recover from hostile take-overs

Price/Earnings Ratio (P/E):

Shows the dollar amount investors are willing to pay for $1of reported (current) earningsMust calculate Earning per Share (EPS) first

EPS = NI available to common stockholders / # of common shares outstanding

P/E = Market price per share of common stock / EPS


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Price/Earnings Ratio (P/E) (continued):

Example: A firm has 5,000,000 shares of common stock outstanding. Its most recent quarterly earning report indicated NI of $7m. This firms stock currently sells for $25.60. Find the P/E Ratio for this firm

a) Compute EPS: EPS = $72,000,000 / 5,000,000 shares = $1.40 per share

b) Compute P/E Ratio: P/E = $25.60 / $1.40 = 18.29 “times earnings”

P/E Analysis Interpretation:Smaller is usually (but not necessarily) better. Indicates whether a firm’s stock is undervalued or over valued

If the P/E is higher than average, the stock is overvaluedIf the P/E is lower than average, the stock is undervalued

Example: Consider the following P/E Ratios:Firm A Firm B Industry Ave. 20 40 30

Which firm’s stock is overvalued? Undervalued?

P/E is higher for firms with high growth prospects Why?P/E is lower for firms considered to be risky Why?One must always ask why (the stock is over/under valued)

P/E represents the markets perception of the stock’s valueIs the market seeing something that you aren't?

“Irrational Exuberance” (ref. ‘90’s tech. stock boom)bad press / bad rep (ref. Phillip Morris)


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Cost of Additional Issue of Common Stock:Firm’s rarely issue new stock in large quantitiesViewed as a negative signal with respect to a stock’s true valueNew stock issue devaluates stock currently outstanding

→dilutes ownership value→automatically lowers EPS

A new issue of stock typically lowers the price of that firm’s stock (supply & demand forces a new price equilibrium)Cost of new common stock (equity): re = D1 / [P0(1 - F )]

→F = Flotation Costs: the cost (per share) to issue the new stock, expressed as a percentage of the stock price (P0)

Other Ch 9 Topics (read them if you plan to be a Finance major)-Dividends vs. Investment growth-Share Repurchases and the Total Payout Model-Discounted Free Cash Flow Model-Valuation Based on Comparable Firms-Valuation Multiples , Limitations of Multiples and Comparison With Discounted Cash Flow Methods-Information, Competition and Stock Prices

MGT 326 Ch 7 Stock Valuation (bdh2e) 1 STOCK (EQUITY) Learning Objectives: Understand Fundamental...

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Transcript of MGT 326 Ch 7 Stock Valuation (bdh2e) 1 STOCK (EQUITY) Learning Objectives: Understand Fundamental...