Stocks and Stock Valuation

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1. Explain the basic characteristics of common stock.

2. Define the primary market and the secondary market.

3. Calculate the value of a stock given a history of dividend payments.

4. Explain the shortcomings of the dividend pricing models.

5. Calculate the price of preferred stock.

6. Understand the concept of efficient markets.

LEARNING OBJECTIVES

7.1 Characteristics of Common Stock

• Major financing vehicle for corporations

• Provides holders with an opportunity to share in the future cash flows of the issuer.

• Holders have ownership in the company.

• Unlike bonds, no maturity date (considered permanent financing) and variable periodic income.

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7.1 Ownership• Share in the residual profits of the company.• Claim to all its assets and cash flow once the

creditors, employees, suppliers, and taxes are paid off.

• Voting rights – participate in the management of the company– Elect the board of directors which selects the

management team that runs the company’s day-to-day operations.

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7.1 Claim on Assets and Cash Flow (Residual Claim)

In case of liquidation…Shareholders have a claim on the residual

assets andcash flow of the company.Known as “residual” rights.

Back to the balance sheetAssets reflect the “value of the company.”Liabilities reflect the non owner claims to the

assets.Owners get the remaining value of the assets.

Owner’s Equity = Assets - Liabilities 7-5

7.1 Vote (Voice in Management)

• Standard voting rights: Typically, one vote per share provided to shareholders to vote in board elections and other key changes to the charter and bylaws.

• Can be altered by issuing several classes of stock.

– Non-voting stock, which is usually for a temporary period of time,

– Super voting rights, which provide the holders with multiple votes per share, increasing their influence and control over the company.

Proxies transfer voting rights to another party7-6

7.1 No Maturity DateNo promised date when investment is returned.

Purchasing of shares means you hold ownership rights until you sell the shares or the firm goes bankrupt

There is no return of your original purchase price (principal) of the stock by the company

Infinite life, i.e. no maturity datePrincipal (par value plus paid in excess) is

permanently retained by the company Exception, repurchase of stock by company

(Treasury Stock)Therefore, considered to be permanent financing

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7.1 Dividends and Their Tax EffectCompanies pay cash dividends periodically

(usually every quarter) to their shareholders out of income generated by the operations.

Unlike coupon interest paid on bonds, dividends cannot be treated as a tax-deductible expense by the company.

For the recipient, however, dividends are considered to be taxable income.

More material on dividends and dividend policy is covered in Chapter 17.

 

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7.1 Authorized, Issued, and Outstanding Shares

• Authorized shares: maximum number of shares that the company may sell,

as per charter.  • Issued shares: the number of shares that have been

sold by the company and are either currently available for public

trading (outstanding shares) or held by the company for future uses such as rewarding employees (treasury stock).

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Non-dividend paying, non-voting shares being held by the issuing firm right from the time they were first issued

OR Shares that have been repurchased by the

issuing firm in the market. Why no voting rights for Treasury Stock?Why no dividend payments to Treasury

Stock?

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7.1 Treasury Stock

7.1 Preemptive Rights Privileges that allow current shareholders to buy

a fixed percentage of all future issues before they are offered to the general public.

Enables current common stockholders to maintain their proportional ownership in the company.

ExampleCurrent shareholder owns 10% of the outstanding

shares of the company…Company issues new shares…Current owner faces dilution if unable to purchase

10% of the new issue, so must be offered 10% of issue before open to the public

Not required to purchase more shares

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7.2 Stock Markets

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Stocks are traded in two types of markets; 1.the primary or “first sale” market

• Think of a new car sale, the manufacturer sells the car and collects the money from the buyer

• Title goes from originator to “first” owner

2.Or secondary or “after-sale” market, • Think of used car market• Title goes from “first” owner to

new owner and money from buyer to seller

7.2 Primary Markets

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Market where issuing firm is involved.

•Initial public offering (IPO) •Prospectus•Due diligence•Firm commitment•Best efforts

•More in Chapter 15 on Raising Capital

7.2 Secondary Markets

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• Forum where common stock can be traded among investors themselves.• Provides liquidity and variety.• In the United States, 3 well-known secondary stock markets:

• NYSE• AMEX• NASDAQ

• Some Special TermsSpecialist Ask price Bid price Bid-ask

spread

7.2 Bull Markets and Bear Markets A Bull market: prolonged rising stock

market, coined on the analogy that a bull attacks with his horns from the bottom up.

A Bear market: prolonged declining market, based on the analogy that a bear swipes with his paws from the top down.

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7.3 Stock Valuation• Value of a share of stock, the present value of

its expected future cash flow …– Cash dividends paid (if any). – Future selling price of the stock.– The discount rate is the risk-appropriate rate of

return to be earned on the investment.

• No guaranteed cash flow information.• No maturity date.• Valuation is more of an “art” than a science.

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7.3 Stock Valuation

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7.3 Stock Valuation

Example: Stock price with known dividends and sale price.

  Agnes wants to purchase common stock of New Frontier Inc. and hold it for 4 years. The directors of the company just announced that they expect to pay an annual cash dividend of $4.00 per share for the next 5 years. Agnes believes that she will be able to sell the stock for $40 at the end of three years. In order to earn 12% on this investment, how much should Agnes pay for this stock?

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7.3 Stock Valuation – Known Cash Flow

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Price =

r

nr1

11

Stream Dividendnr1

1Price Future

Price =

0.12

40.121

11

$4.0040.121

1$40.00

Price = $40.00 x 0.635518 + $4.00 x 3.03734 Price = $25.42 + $12.15 = $37.57$37.57

7.3 Stock Valuation - Known Cash Flow

Method 2. Using a financial calculator 

Mode: P/Y=1; C/Y = 1 

Key: N I/Y PV PMT FVInput: 4 12 ? 4 40Compute: --37.5737.57

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7.3 Stock Valuation – Estimating Cash Flow

4 variations of a dividend pricing model have been used to value common stock

 1. The constant dividend model with an infinite

horizon2. The constant dividend model with a finite horizon3. The constant growth dividend model with a finite horizon4. The constant growth dividend model with an

infinite horizon 

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7.3 The Constant Dividend Model with an Infinite HorizonAssumes that the firm is paying the same dividend amount in perpetuity.

DivDiv11 = Div = Div22 = Div = Div33 = Div = Div44 = Div = Div55 ……= Div= Div∞∞

Recall a perpetuityPV = PMT/rPV = PMT/r

where r the required rate and PMT is the cash flow.

 Thus, for a stock that is expected to pay the same

dividend forever we have its price as:Price = Dividend/Required rate ofPrice = Dividend/Required rate of returnreturn

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7.3 The Constant Dividend Model with an Infinite HorizonExample: Quarterly dividends forever 

Let’s say that the Peak Construction Company is paying a quarterly dividend of $0.50 and has decided to pay the same amount forever. If Joe wants to earn an annual rate of return of 12% on this investment, how much should he offer to buy the stock at? Quarterly dividend = $0.50Quarterly rate of return = Annual rate/4= 12%/4 = 3%PV = Quarterly dividend/Quarterly rate of returnPrice = 0.50/.03 = $16.67$16.67

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7.3 The Constant Dividend Model with a Finite Horizon• Assumes that the stock is held for a finite period

of time and then sold to another investor. • Constant dividends received over the investment

horizon.• Price estimated as the sum of the present value of

an annuity (constant dividend) and that of a lump sum (the selling price).

• Similar to a typical corporate bond. • Have to estimate the future selling price, since

that is not a given value like the par value of a bond.

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7.3 The Constant Dividend Model with a Finite Horizon

Example: Constant dividends with finite holding period.

  Let’s say that the Peak Construction Company is paying an annual dividend of $2.00 and has decided to pay the same amount forever. Joe wants to earn an annual rate of return of 12% on this investment, and plans to hold the stock for 5 years, with the expectation of selling it for $20 at the end of 5 years.What is his offer price for the stock?

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7.3 The Constant Dividend Model with a Finite HorizonAnnual dividend = $2.00 = PMTSelling Price = $20 = FVAnnual rate of return = 12% = I/YHorizon or Holding Period = 5 = NOffer Price (PV) = PV of dividend stream over 5

years + PV of Year 5 price

Mode: P/Y=1; C/Y = 1  Key: N I/Y PV PMT FV

Input: 5 12.0 ? 2.00 20.00Compute: --18.5618.56

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7.3 The Constant Growth Dividend Model with an Infinite Horizon

Known as the Gordon model (after its developer, Myron Gordon).

Estimate is based on the discounted value of an infinite stream of future dividends that grow at a constant rate, g.

where r is the required rate of return and new owner gets the next dividend payment (Div1 or Div0 x (1 + g)1)

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r1

g10Div

3r1

3g10Div

2r1

2g10Div

1r1

1g10Div

0Price

7.3 The Constant Growth Dividend Model with an Infinite HorizonWith some algebra, this can be simplified

And since Div0 x (1+g)1 = Div1

Or more generally Pn = Divn+1/(r-g)7-28

gr

g10

Div

0Price

gr1

Div

0Price

7.3 The Constant Growth Dividend Model with an Infinite Horizon Example: Constant growth rate, infinite

horizon (with growth rate given).  Let’s say that the Peak Construction

Company just paid its shareholders an annual dividend of $2.00 (DIV0) and has announced that the dividends would grow at an annual rate of 8% forever. If investors expect to earn an annual rate of return of 12% on this investment how much would they offer to buy the stock for?

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7.3 The Constant Growth Dividend Model with an Infinite HorizonExample (Answer)Div0 = $2.00; g=8%; r=12% with infinite horizon

Div1= Div0 x (1+g)

Div1=$2.00 x (1.08) or Div1=$2.16

 P0 = Div1 / (r-g) = $2.16 / (0.12 - 0.08) = $54.00 $54.00

Price0 = $54.00$54.00

Note: r and g are in decimal format

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7.3 The Constant Growth Dividend Model with an Infinite HorizonEXAMPLE: Constant growth rate, infinite horizon (with growth rate estimated from past history).

  Let’s say that you are considering an investment in the common stock of QuickFix Enterprises and are convinced that its last paid dividend of $1.25 will grow at its historical average growth rate from here on. Using the past 10 years of dividend history and a required rate of return of 14%, calculate the price of QuickFix’s common stock. 

We must estimate g from the dividend history of the firm…

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7.3 The Constant Growth Dividend Model with an Infinite HorizonQuickFix Enterprises’ Annual Dividends

Required rate of return = 14%Compound growth rate “g” = (FV/PV)1/n -1Where FV = $1.25; PV = 0.50; n = 9 (number of

dividend changes) g = (1.25/0.50)1/9 – 1 = 10.7173% (or on calculator, g =

I/Y)Div1 = Div0(1+g)= $1.25 x (1.107173)= $1.383966

P0 = Div1/(r-g) = $1.383966 / (0.14 - 0.107173) = $42.16$42.16

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1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 $0.50 $0.55 $0.61 $0.67 $0.73 $0.81 $0.89 $0.98 $1.08 $1.25

7.3 The Constant Growth Dividend Model with a Finite Horizon

Investor expects to hold a stock for a limited number of years,Company’s dividends are growing at a constant rate.Following formula is used to value the stock…

Note: This formula would lead to the same price estimate as the Gordon model, if it is assumed that the growth rate of dividends and the required rate of return of the next owner, (after n years) remain the same.

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n

r1g11gr

g10

Div

0Price +

nr1nPrice

7.3 The Constant Growth Dividend Model with a Finite HorizonExample: Constant growth, finite horizon.  The QuickFix Company just paid a dividend of

$1.25 and analysts expect the dividend to grow at its compound average growth rate of 10.7173% forever. If you plan on holding the stock for just 7 years, and you have an expected rate of return of 14%, how much would you pay for the stock? Assume that the next owner also expects to earn 14% on his or her investment.

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7.3 The Constant Growth Dividend Model with a Finite Horizon

We can solve this in 2 ways.  Method 1: Use the constant growth, finite

horizon formula

Method 2: Use the Gordon Model since g is constant forever, and both investors have the same required rates of return

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7.3 The Constant Growth Dividend Model with a Finite Horizon Method 1 Use the following equation:

Price at end of year 7 or P7 = Div8/(r-g)

Div0 = $1.25; g =10.7173%; Div8 = D0(1+g)8 = $1.25 x (1.107173)8 = $2.8225

P7=2.8225 /(0.14 - 0.107173)= $85.98$85.98

Price0 = $42.16 x 0.1849684 + 34.36 = $42.16$42.167-36

n

r1g11

gr

g10

Div

0Price +

nr1nPrice

7

0 14.1

107173.11

107173.14.

107173.125.1Price +

714.1

98.85

7.3 The Constant Growth Dividend Model with a Finite Horizon

Method 2: Use the Gordon ModelP0 = D0(1+g)/(r-g)

P0 = $1.25 x (1.107173)/(0.14 - 0.107173)

P0 = $42.16$42.16

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7.3 Non-constant Growth Dividends• The above 4 models work if a firm is either

expected to pay a constant dividend amount indefinitely, or is expected to have its dividends grow at a constant rate for long periods of time.

• For most firms, the dividend growth patterns tend to be variable, making the valuation process complicated.

• However, if we can assume that at some point in the future, the dividend growth rate will become constant, we can use a combination of the Gordon Model and present value equations to calculate the price of the stock.

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7.3 Non-constant Growth DividendsExample: Non-constant dividend pattern  The Rapid Growth Company is expected to pay a

dividend of $1.00 at the end of this year. Thereafter, the dividends are expected to grow at the rate of 25% per year for 2 years, and then drop to 18% for 1 year, before settling at the industry average growth rate of 10% indefinitely. If you require a return of 16% to invest in a stock of this risk level, how much would you be justified in paying for this stock?

DD11=$1.00; g=$1.00; g11=25%; n=25%; n11=2; g=2; g22=18%; n=18%; n22=1; g=1; gcc=10%; =10%; r=16% r=16%

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7.3 Non-constant Growth Dividends

Step 1. Calculate the annual dividends expected in Years 1-4, using the appropriate growth rates.

 D1 = $1.00$1.00; D2 = $1.00 x (1.25) = $1.25$1.25; D3= $1.25 x (1.25) = $1.56$1.56; D4 = $1.56 x (1.18) =

$1.84$1.84; Step 2. Calculate the price at the start of the

constant growth phase using the Gordon model. P4 = D4 x (1+g)/(r-g) = $1.84 x (1.10)/(0.16 - 0.10)

= $2.02/.06 = $33.73$33.73

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7.3 Non-constant Growth DividendsStep 3. Discount the annual dividends in Years 1-4

and the Price at the end of Year 4, back to Year 0 using the required rate of return as the discount rate, and add them up to solve for the current price. 

P0 = $1.00/(1.16) + $1.25/(1.16)2 + $1.56/(1.16)3 + $1.84/(1.16)4 + $33.73/(1.16)4

P0 = $0.862 + $0.928 + $0.999 + $1.016 + $18.629

P0 = $22.43 $22.43 7-41

7.4 Dividend Model ShortcomingsNeed future cash flow estimates and a required rate of return,

therefore difficult to apply universally. Erratic dividend patterns, Long periods of no dividends, Declining dividend trends

Need a pricing model that is more inclusive than the dividend model, one that can estimate expected returns for stocks without the need for a stable dividend history.

The capital asset pricing model (CAPM), or the security market line (SML), which will be covered in Chapter 8, is one option.

SML can be used to estimate expected returns for companies based on their risk, the premium for taking on risk, and the reward for waiting and not on their historical dividend patterns.

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7.5 Preferred StockPays constant dividend as long as the stock is outstanding.

Typically has infinite maturity, but some are convertible into common stock at some pre-determined ratio.

Have “preferred status” over common stockholders in the case of dividend payments and liquidation payouts.

Dividends can be cumulative or non-cumulative

To calculate the price of preferred stock, we use the PV of a perpetuity equation, i.e. Price0 = PMT/r

PMT = Annual dividend (dividend rate * par value); and

r = investor’s required rate of return.7-43

7.5 Preferred StockExample 8: Pricing preferred stock. 

The Mid-American Utility Company’s preferred stock pays an annual dividend of 8% per year on its par value of $60. If you want to earn 10% on your investment how much should you offer for this preferred stock?

 Annual dividend = .08*$60 = $4.80

 Price = $4.80/0.10 = $48.00$48.00

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7.6 Efficient Markets

Market in which security prices are current and fair to all traders.Transactions costs are minimal. There are two forms of efficiency:

1. Operational efficiency and 2. Informational efficiency.

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7.6 Operational Efficiency• Speed and accuracy with which trades are

processed. • Ease with which the investing public can

access the best available prices. – The NYSE’s SuperDOT computer system, – NASDAQ’s SOES

• Match buyers and sellers very efficiently and at the best available price.

• Therefore definitely very operationally efficient markets.

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7.6 Informational Efficiency• Speed and accuracy with which information is

reflected in the available prices for trading. • Securities would always trade at their fair or

equilibrium value. – Diverse information --financial economists have

come up with three versions of efficient markets from an information perspective:

– weak form, – semi-strong form– strong form.

• These three forms make up what is known as the efficient market hypothesis (EMH).

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7.6 Informational Efficiency• Weak-form efficient markets :

– Current prices reflect past prices and trading volume. – Technical analysis –not useful

•  Semi-strong-form efficient markets:– Current prices reflect price and volume information and all

available relevant public information as well. – Publicly available news or financial statement information

not very useful.•  Strong-form efficient markets:

– Current prices reflect price and volume history of the stock, all publicly available information, and even all private information.

– All information is already embedded in the price--no advantage to using insider information to routinely outperform the market.

• Most academic research supports semi-strong form of efficient markets. Public information is fully reflected in markets within minutes.

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