copyright © 2010 pearson prentice hall. all rights reserved. chapter 7 stocks and stock valuation

Copyright © 2010 Pearson Prentice Hall. All rights reserved.

Chapter 7

Stocks and Stock Valuation

Copyright © 2010 Pearson Prentice Hall. All rights reserved.7-2

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 and variable

periodic income.


7.1 (A) 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.


7.1 (B) Claim on Assets and Cash Flow (Residual Claim)

• In case of liquidation…– Shareholders have a claim on the residual assets and

cash flow of the company.– Known as “residual” rights.


7.1 (C) 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.


7.1 (D) No Maturity Date

• Considered to be permanent financing• Infinite life, i.e., no maturity date• No promised date when investment is

returned.


7.1 (E) Dividends and Their Tax Effect

• Companies pay cash dividends periodically (usually every quarter) to their shareholders out of net income.

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

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

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


7.1 (F) 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 has already 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).


• 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 later repurchased by the

issuing firm in the market.

7.1 (G) Treasury Stock


7.1 (H) Preemptive Right

• A privilege that allows 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.


7.2 Stock Markets

Stocks are traded in two types of markets:

1. the primary or “first sale” market

2. secondary or “after-sale” market,


7.2 (A) Primary Markets

First-issue market where issuing firm is involved.• Initial public offering (IPO): first public equity issue of a

firm.• Prospectus: document providing information about the

issuing form and its securities.• Due diligence: all relevant information must be

disclosed prior to the sale.• Firm commitment: Investment banker buys the entire

issue from the firm and then tries to sell at a higher price.

• Best efforts: Investment banker pledges to do his or her best in selling the shares in exchange for small commission.


7.2 (B) Secondary Markets

• Forum where common stock can be traded among investors themselves.

• Provides liquidity and variety.• In the United States, three well-known secondary

stock markets:• NYSE• AMEX• NASDAQ

SpecialistAsk priceBid priceBid-ask spread


7.2 (C) Bull Markets and Bear Markets

• A Bull market is a prolonged rising stock market, coined on the analogy that a bull attacks with his horns from the bottom up.

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


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, i.e., 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.


Table 7.1 Differences between Bonds and Stocks


7.3 Stock Valuation (continued)

Example 1: Stock Price with Known Dividends and Sale Price

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



Price = $40.00 x 0.635518 + $4.00 x 3.03734Price = $25.42 + $12.149 = $37.57

Solution

Method 1. Using an equation



Method 2. Using a financial calculator

Mode: P/Y=1; C/Y = 1

Input: N I/Y PV PMT FVKey: 4 12 ? 4 40Output -37.57



Four 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 an infinite horizon4. The constant growth dividend model with a finite horizon

These models make different assumptions about1. The dividend stream--is it constant or growing?2. The maturity of the stock--is it held forever or up to a point

at which it is needed?


7.3 (A) The Constant Dividend Model with an Infinite Horizon

Assumes that the firm is paying the same dividend amount in perpetuity:

DivDiv11 = Div = Div22 = Div = Div33 = Div = Div44 = Div = Div55 = Div = Div∞∞ For perpetuities,

PV PV = = PMTPMT//rrwhere r is the required rate of return and PMT is the cash

flow.

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

Price = Dividend/Required rate ofPrice = Dividend/Required rate of returnreturn


7.3 (A) The Constant Dividend Model with an Infinite Horizon (continued)

Example 2. Quarterly Dividends Forever Problem

Let’s say that the Peak Growth 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?

SolutionQuarterly dividend = $0.50Quarterly rate of return = Annual rate/4= 12%/4 = 3%PV = Quarterly dividend/Quarterly rate of returnPrice = 0.50/.03 = $16.67


7.3 (B) 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.

• Assumes that constant dividends are received over the investment horizon.

• Price is estimated as the sum of the present value of an annuity stream (constant dividend) and that of a single sum (the selling price).


7.3 (B) The Constant Dividend Model with a Finite Horizon (continued)

Example 3. Constant Dividends with a Finite Holding Period

Problem Let’s say that the Peak Growth 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.How much should he offer for the stock?


7.3 (B) The Constant Dividend Model with a Finite Horizon (continued)SolutionAnnual dividend = $2.00 = PMTSelling Price = $20 = FVAnnual rate of return = 12%PV = PV of dividend stream over 5 years + PV of Year 5

price

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

Key: 5 12 ? 2 20Output -18.56


7.3 (C) 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.

Price0 Div0 1 g 1

1 r 1

Div0 1 g 2

1 r 2

Div0 1 g 3

1 r 3L

Div0 1 g

1 r


7.3 (C) The Constant Growth Dividend Model with an Infinite Horizon (cont’d)

• With some algebra, this can be simplified to….

• And since Div0 x (1+g) = Div1

Price0

Div

01g

r g

Price0

Div

1r g



Example 4: Constant Growth Rate, Infinite Horizon (with growth rate given).Problem

Let’s say that Gekko Company just paid its shareholders an annual dividend of $2.00 and has announced that the dividends will 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 will they offer for the stock?



Example 4 (Answer)SolutionDiv0 = $2.00; g=8%; r=12%Div1=Div0*(1+g) Div1=$2.00*(1.08)Div1=$2.16 P0 = Div1/(r-g)$2.16/(.12 - .08)$54 Price0 = $54

Note: r and g must be in decimals.



EXAMPLE 5: Constant Growth Rate, Infinite Horizon (with growth rate estimated from past history)Problem

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.



QuickFix Enterprises’ Annual Dividends

SolutionRequired rate of return = 14%Compound growth rate “g” = (FV/PV)1/n -1Where FV = $1.25; PV = 0.50; n = 9g = (1.25/0.50)1/9 – 1 10.72%Div1 = Div0(1+g)$1.25*(1.1072)$1.384

P0 = Div1/(r-g) $1.384/(.14-.1072)$42.19

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 (D) The Constant Growth Dividend Model with a Finite Horizon

In this model, the investor expects to hold a stock for a limited number of years, Company’s dividends are growing at a constant rate.The following adjusted formula can be 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.


7.3 (D) The Constant Growth Dividend Model with a Finite Horizon (continued)

Example 6: Constant Growth, Finite Horizon

Problem The QuickFix Company just paid a dividend of $1.25,

and analysts expect the dividend to grow at its compound average growth rate of 10.72% 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.



We can solve this in 2 ways.Solution 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


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

Price in year 7 = Div8/(r-g)

Div0 = $1.25; g =10.72%; r=14%; Div8 = D0(1+g)8

Div81.25*(1.1072)8 = 2.82305

P7=2.82305/(.14-.1072)$86.07

= $42.195 *0.184829 + 34.40 = $42.19



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

P0 = $1.25*(1.1072)/(.14-.1072)

P0 = $42.19


7.3 (E) Nonconstant 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.


7.3 (E) Nonconstant Growth Dividends (continued)

Example 7: Nonconstant Dividend PatternProblem 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?

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



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

D1=$1.00; D2=$1.00*(1.25)=$1.25;

D3=$1.25*(1.25) = $1.56; D4=$1.56*(1.18) = $1.84.

Step 2. Calculate the price at the start of the constant growth phase using the Gordon model.

P4 = D4*(1+g)/(r-g) = $1.84*(1.10)/(.16-.10)

= $2.02/.06 = $33.73



Step 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. Then 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+$.999+$1.016+$18.63 = $22.44


7.4 Dividend Model Shortcomings

• Need 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 rather than on historical dividend patterns.


7.5 Preferred Stock

• Pays constant dividend as long as the stock is outstanding.

• Typically, has infinite maturity, but some are convertible into common stock at some predetermined ratio.

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

•• Dividends can be cumulative or noncumulative

• 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.


7.5 Preferred Stock (continued)

Example 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


7.6 Efficient Markets

An efficient market is one in which security prices are current and fair to all traders, and transaction costs are minimal. There are two forms of efficiency:

1. Operational efficiency2. Informational efficiency


7.6 (A) 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.

• Definitely, very operationally efficient markets.


7.6 (B) Informational Efficiency

• Speed and accuracy with which information is reflected in the available prices for trading.

• In this kind of market, securities would always trade at their fair or equilibrium value.

– But information is diverse, so 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).


7.6 (B) Informational Efficiency (continued)

• 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.

• Jury is still out; evidence is not conclusive!


ADDITIONAL PROBLEMS WITH ANSWERSProblem 1

Pricing Constant Growth stock, with Finite Horizon The Crescent Corporation just paid a dividend of $2.00 per share and is expected to continue paying the same amount each year for the next 4 years.

If you have a required rate of return of 13%, plan to hold the stock for 4 years, and are confident that it will sell for $30 at the end of 4 years, how much should you offer to buy it today?


ADDITIONAL PROBLEMS WITH ANSWERSProblem 1 (ANSWER)

In this case, we have an annuity of $2 for 4 periods, followed by a lump sum of $30, to be discounted at 13% for the respective number of years.

Using a financial calculator Mode:P/Y=1; C/Y = 1

Input: N I/Y PV PMT FVKey: 4 13 ? 2 30Output -24.35



Constant Growth Rate, with Infinite Horizon (with growth rate estimated from past history)Using the historical dividend information provided below to calculate the constant growth rate, and a required rate of return of 18%, estimate the price of Nigel Enterprises’ common stock.

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 $0.35 $0.45 $0.51 $0.65 $0.75 $0.88 $0.99 $1.10 $1.13 $1.30



First, estimate the historical average growth rate of dividends by using the following equation:

g = [(FV/PV)1/n – 1] Where FV = Div2008 = $1.30

PV = Div1999 = $0.35 n = number of years in between = 9

g = [(1.30/0.35)1/9 – 1]

15.7%


ADDITIONAL PROBLEMS WITH ANSWERSProblem 2 (ANSWER continued)

Next, use the constant growth dividend model with infinite horizon to calculate price:i.e. Price0 = Div0(1+g)/(r-g)

Div0 = Div2008= $1.30;

Div1= Div0*(1+g) =$1.30*(1.157)$1.504;

r = 18%; g = 15.7% (as calculated above) Price0 = $1.504/(.18-.157)

Price0 = $65.40



Pricing common Stock with Multiple Dividend Patterns The Wonder Products Company is expanding fast and therefore will not pay any dividends for the next 3 years.

After that, starting at the end of Year 4, it will pay a dividend of $0.75 per share to its common shareholders and increase it by 12% each year until it pays $1.50 at the end of Year 10. After that, it will pay $1.50 per year forever. If an investor wants to earn 15% per year on this investment, how much should he pay for the stock?



First, lay out the dividends on a time line. Expected Dividend Stream of The Wonder Products Co. T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 … T ∞

--- $0.00 $0.00 $0.00 $0.75 $0.84 $0.94 $1.05 $1.18 $1.32 $1.50 …$1.50

Note: There are 3 distinct dividend payment

patterns: Years 1-3, no dividends; Years 4-10, dividends grow at 12%; Year 11 onwards, zero-growth in dividends.


ADDITIONAL PROBLEMS WITH ANSWERSProblem 3 (ANSWER continued)

Next, Calculate the price at the end of Year 10, i.e. when the dividend growth rate is zero.

Price10 = Div11/r = 1.50/.15 = $10; Discount each dividend and the Year 10 price back to time 0 at 15%:

0.75(1.15)4+0.84(1.15)5+0.94(1.15)6+1.05(1.15)7+1.18(1.15)8+1.32(1.15)9+1.50(1.15)10+10(1.15)10

Price=$5.25



Pricing Nonconstant Growth Common Stock The WedLink Corporation just paid a dividend of $1.25 to its common shareholders. It announced that it expects the dividends to grow by 25% per year for the next 3 years. Then dividends will drop to a growth rate of 16% for an additional 2 years. Finally, the dividends will converge to the industry median growth rate of 8% per year. If investors are expecting 12% per year on WedLink’s stock, calculate the current stock price.



Determine the dividend per share in Years 1-5 using the stated annual growth rates:

D1=$1.25*(1.25)=$1.56; D2=$1.56*(1.25)=$1.95; D3=1.95*(1.25)=$2.44D4=$2.44*(1.16)=$2.83; D5=$2.83*(1.16)=3.28

Next, calculate the price at the end of Year 5; using the Gordon Model.


ADDITIONAL PROBLEMS WITH ANSWERSProblem 4 (ANSWER–continued)

Using r = 12% and g = 8% (constant growth phase), we have

P5 = D5(1+g)/(r – g) P5 = $3.28*(1.08)/(.12-.08) 3.54/.04=$88.56 Finally calculate the present value of all the dividends in Years 1-5 and the price in Year 5, by discounting them at 12% for the respective number of years:1.56/(1.12)+1.95/(1.12)2+2.44/(1.12)3+2.83/(1.12)4+3.28/(1.12)5+88.56(1.12)5=$58.60


ADDITIONAL PROBLEMS WITH ANSWERSProblem 5 (A)

Pricing Common Stock with Constant Growth and Finite Life versus Infinite Life

The ANZAC Corporation plans to be in business for

30 years. It announces that it will pay a dividend of $3.00 per share at the end of one year, and continue increasing the annual dividend by 4% per year until it liquidates the company at the end of 30 years. If you want to earn a rate of return of 12% by investing in ANZAC’s stock, how much should you pay for the stock?


ADDITIONAL PROBLEMS WITH ANSWERSProblem 5 (A) (ANSWER)

Div1 = $3.00; r = 12%; g = 4%; n = 30

Using the formula for a growing annuity we can solve for the current price.

Price0 = $37.5*0.89174 = $33.44

Price0

Div

1r g 1 1g

1r

30

Price0 $3.00

.12 .04 11.041.12

30


ADDITIONAL PROBLEMS WITH ANSWERSProblem 5 (B)

If the company was to announce that it would continue increasing the dividend at 4% per year forever, how much more would you be willing to pay for its stock, assuming your required rate of return is still 12%?


ADDITIONAL PROBLEMS WITH ANSWERSProblem 5 (B) (ANSWER)

If the growth rate is 4% forever, the price of the stock can be figured out by using the Gordon Model; D1=$3.00; r=12%

$3.00/(.12 - .04) $37.50

Price

0

Div1

r g


Table 7.2 Coca-Cola Annual Dividends


Table 7.3 Annual Dividend Growth for Coca-Cola


Table 7.4 Recent Dividend History of Five Firms


Table 7.5 Ranking of Stock Risk Levels Based on Expected Returns


Table 7.6 Recent Annual Dividends of Five Other Firms

copyright © 2010 pearson prentice hall. all rights reserved. chapter 7 stocks and stock valuation

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