1. Lecture Seven - Stock and Stock Valuation
Corporate Finance
Lecture Seven - Stock and Stock Valuation

2. Learning Objectives Explain the basic characteristics of common stock.
Define the primary market and the secondary market.
Calculate the value of a stock given a history of dividend payments.
Explain the shortcomings of the dividend pricing models.
Calculate the price of preferred stock.
Understand the concept of efficient markets.

3. 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.

4. 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.

5. 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.

6. 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. 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.

8. 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, however, dividends are considered to be taxable income.
More material on dividends and dividend policy is covered in Chapter 17.

9. 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).

10. 7.1 (G) 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.

11. 7.1 (H) 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.

12. 7.2 Stock Markets Stocks are traded in two types of markets;
the primary or “first sale” market, and the
secondary or “after-sale” market,

13. 7.2 (A) Primary Markets First issue market where issuing
firm is involved.
Initial public offering (IPO):
Prospectus:
Due diligence:
Firm commitment:
Best efforts:

14. 7.2 (B) Secondary Markets: How Stocks Trade
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
Specialist
Ask price
Bid price
Bid-ask spread

15. 7.2 (C) 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.

16. 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.

17. 7.3 Stock Valuation (continued)
Table 7.1 Differences between Bonds and Stocks

18. 7.3 Stock Valuation (continued)
Example 1: Stock price with known dividends and sale price.
Agnes wants to purchase common stock of New Frontier Inc. and hold it for 3 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?

19. 7.3 Stock Valuation (continued) Example 1 Answer
Price = $40.00 x $4.00 x
Price = $ $ = $37.57

20. 7.3 Stock Valuation (continued)
Example 1 Answer (continued)
Method 2. Using a financial calculator
Mode: P/Y=1; C/Y = 1
Input: N I/Y PV PMT FV
Key: ?
Output

21. 7.3 Stock Valuation (continued)
4 variations of a dividend pricing model have been used to value common stock
The constant dividend model with an infinite horizon
The constant dividend model with a finite horizon
The constant growth dividend model with a finite horizon
The constant growth dividend model with an infinite horizon

22. 7.3 (A) The Constant Dividend Model with an Infinite Horizon
Assumes that the firm is paying the same dividend
amount in perpetuity.
i.e. Div1 = Div2 = Div3 = Div4 = Div5 = Div∞
For perpetuities,
PV = 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,
  Price = Dividend/Required rate of return

23. 7.3 (A) The Constant Dividend Model with an Infinite Horizon (continued)
Example 2. Quarterly dividends forever 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? Answer Quarterly dividend = $0.50 Quarterly rate of return = Annual rate/4= 12%/4 = 3% PV = Quarterly dividend/Quarterly rate of return Price = 0.50/.03 = $16.67

24. 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.
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 single sum (the selling price).
Similar to a typical non-zero coupon, corporate bond.
Have to estimate the future selling price, since that is not a given value, unlike the par value of a bond

25. 7.3 (B) The Constant Dividend Model with a Finite Horizon (continued)
Example 3. Constant dividends with finite holding period. 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 to buy the stock at?

26. 7.3 (B) The Constant Dividend Model with a Finite Horizon (continued)
Example 3 Answer
Annual dividend = $2.00 = PMT
Selling Price = $20 = FV
Annual 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: ?
Output

27. 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

28. With some algebra, this can be simplified to….
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
Or more generally Pn = Divn+1/(r-g)

29. 7.3 (C) The Constant Growth Dividend Model with an Infinite Horizon (cont’d)
Example 4: Constant growth rate, infinite horizon (with growth rate given). Let’s say that the Peak Growth Company just paid its shareholders an annual dividend of $2.00 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?

30. Note: r and g must be in decimals.
7.3 (C) The Constant Growth Dividend Model with an Infinite Horizon (cont’d)
Example 4 Answer
Div0 = $2.00; g=8%; r=12%
Div1=Div0*(1+g)
Div1=$2.00*(1.08)Div1=$2.16
 P0 = Div1/(r-g)$2.16/( )$54
Price0 = $54
Note: r and g must be in decimals.

31. 7.3 (C) The Constant Growth Dividend Model with an Infinite Horizon (cont’d)
EXAMPLE 5: 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.

32. 7.3 (C) The Constant Growth Dividend Model with an Infinite Horizon (cont’d)
QuickFix Enterprises’ Annual Dividends Required rate of return = 14% Compound growth rate “g” = (FV/PV)1/n -1 Where FV = $1.25; PV = 0.50; n = 9 g = (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/( )$42.19

33. 7.3 (D) 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.

34. 7.3 (D) The Constant Growth Dividend Model with a Finite Horizon (continued)
Example 6: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 10.72% 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.

35. 7.3 (D) The Constant Growth Dividend Model with a Finite Horizon (continued)
Example 6 Answer 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

36. 7.3 (D) The Constant Growth Dividend Model with a Finite Horizon (continued)
Example 6 Answer (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
Div81.25*(1.1072)8 =
P7= /( )$86.07
 = $ * = $42.19

37. 7.3 (D) The Constant Growth Dividend Model with a Finite Horizon (continued)
Example 6 Answer (continued) Method 2: Use the Gordon Model P0 = D0(1+g)/(r-g) P0 = $1.25*(1.1072)/( ) P0 = $42.19

38. 7.3 (E) 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 of most firms 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.

39. 7.3 (E) Non-constant Growth Dividends (continued)
Example 7: 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? D1=$1.00; g1=25%; n1=2; g2=18%; n2=1; gc=10%; r=16%

40. 7.3 (E) Non-constant Growth Dividends (continued)
Example 7 Answer 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)/( ) = $2.02/.06 = $33.73

41. 7.3 (E) Non-constant Growth Dividends (continued)
Example 7 Answer (continued)
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, and add them up to solve for the current price. 
P0 = $1.00/(1.16) /(1.16)2+$1.56/(1.16)3+$1.84/(1.16)4+$33.73/(1.16)4
P0 = $$ $.999+$1.016+$18.63 = $22.44 
Note: This uneven cash flow stream can also be discounted by using the NPV function of the financial calculator…. 
CF0=0;CF1=1.00;CF2=1.25;CF3=1.56;CF4= ;I=16%;
NPV=$22.44

42. 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 and not on their historical dividend patterns.

43. 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 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.

44. 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? Answer Annual dividend = .08*$60 = $4.80 Price = $4.80/0.10 = $48

45. 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:
Operational efficiency and
Informational efficiency.

46. 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.
Therefore definitely very operationally efficient markets.

47. 7.6 (B) 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).

48. 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!

49. Additional Problems with Answers Problem 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 at today?

50. Additional Problems with Answers Problem 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 FV
Key: ?
Output

51. Additional Problems with Answers Problem 2
Constant growth rate, 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.

52. Additional Problems with Answers Problem 2 (Answer)
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%

53. Additional Problems with Answers Problem 2 (Answer) (continued)
Next, use the constant growth, infinite horizon model 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/( )
Price0 = $65.40

54. Additional Problems with Answers Problem 3
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?

55. Additional Problems with Answers Problem 3 (Answer)
First lay out the dividends on a time line.
Expected Dividend Stream of The Wonder Products Co.
T T T T T T T T T T T … 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%; Years 11 onwards, zero-growth in dividends.

56. Additional Problems with Answers Problem 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; Using the NPV function and the annual cash flows calculate the price; NPV(15,0,{0.00,0.00,0.00,0.75,0.84,0.94,1.05,1.18,1.32, } $5.25 Price = $5.25

57. Additional Problems with Answers Problem 4
Pricing non-constant 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 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.

58. Additional Problems with Answers Problem 4 (Answer)
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)=$2.44;
D4=$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.

59. Additional Problems with Answers Problem 4 (Answer) (continued)
Using r = 12% and g = 8% (constant growth phase) i.e. P5 = D5(1+g)/(r – g) P5 = $3.28*(1.08)/( ) 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 using the NPV function….(TI-83 keystrokes shown here) NPV(12,0,{1.56, 1.95, 2.44, 2.83, } = $58.60

60. Additional Problems with Answers Problem 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.
They announce that they 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 they liquidate the company at the end of 30 years.
If you want to earn a rate of return of 12% by investing in their stock, how much should you pay for the stock?

61. Additional Problems with Answers Problem 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* = $33.44

62. Additional Problems with Answers Problem 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%?

63. Additional Problems with Answers Problem 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/( ) $37.50

64. Table 7.2 Coca-Cola Annual Dividends

65. Table 7.3 Annual Dividend Growth for Coca- Cola

66. Table 7.4 Recent Dividend History of Five Firms

67. Table 7.5 Ranking of Stock Risk Levels Based on Expected Returns

68. Table 7.6 Recent Annual Dividends of Five Other Firms