1. Common Stock Valuation6
Common Stock Valuation

2. Learning Objectives Our goal in this chapter is to
Examine natures of investing on common stocks
Examine the methods commonly used by financial analysts to assess the economic value of common stocks.
The valuation is a big topic in investments. These methods are grouped into three categories:
Dividend discount models
Residual Income models (we will not cover this one)
Price ratio models

3. Common stock valuation: Dividend discount model

4. Security Analysis: Be Careful Out There
Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock.
The basic idea: to identify both “undervalued” or “cheap” stocks to buy and “overvalued” or “rich” stocks to sell.
In practice, however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.
The pure form of these models may return the unrealistic prices in the real world. More “applied” version of these models are recommended.

5. Dividend Discount Model (DDM)
Let’s start with the Divided Discount Model first.
There are many different names for this model but they are all special cases of the Dividend Discount Model.
Constant Perpetual Growth Model
Two-Stage Dividend Growth Model
Non-constant Growth Model
We need to do some math to derive the model formally.
In addition, we need to refresh our memory on time value of money - such concepts as perpetuity and growing perpetuity.

6. Notations P0 Pt g k Dt Price Today Expected price in year t
Dividend growth rate k
Required rate of return: Let’s use ”k” instead of “r” to be consistent with our book notations. Dt
Dividend in year t

7. Starting point,

8. Continued,
Conclusion:
P0 = Present Value of D1 plus Present Value of P1

10. Developing The Model
You could continue to push back when you would sell the stock.
You would find that the price of the stock is really just the present value of all expected future dividends.

11. Stock Value = PV of Dividends
Note: Here we are measuring a theoretical value of a
stock. A theoretical value (or, intrinsic value) often
differs from the actual market value at a given time. 6

12. Intrinsic Value and Market Price
The intrinsic value (IV) is the “true” value, according to a model.
That is, IV is the value of sum of discounted future dividends.
The market value (MV) is the consensus value of all market participants
Trading Signal:
IV > MV Buy
IV < MV Sell or Short Sell
IV = MV Hold or Fairly Priced

13. Review: Perpetuity Definition Perpetuity formula
infinite series of equal payments
Perpetuity formula
PV = C / i
For example, you could invest $100 in a bank account paying 5% interest per year forever.
Suppose you withdraw $5 (=$100*5%) per year and leave $100 intact.
This means that you receive $5 perpetuity.
That is, PV = $100, C = $5, i = 5%.
PV * i = 100 * 5% = $5 = C
PV = C / I = $5 / 5% = $100
This is a good preview to the valuation issues discussed in future chapters. The price of an investment is just the present value of expected future cash flows.
Example statement:
Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will Fellini have to offer if the preferred stock is going to sell.

14. Example: Endowing a Perpetuity
You want to endow an annual MBA graduation party at your name recognition. You budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first payment is in one year from now, how much will you need to donate to endow the party?
PV = 30,000 / 8% = $375,000
375000

15. Review: Growing Perpetuities
Assume you expect the amount of your perpetual payment to increase at a constant rate,

16. Example 2: Endowing a Growing Perpetuity
In the earlier example, you planned to donate $30,000 per year. Given an interest rate of 8% per year, the required donation was the present value of $375,000.
Before accepting the money, however, the MBA student association asked that you increase the donation to account for the effect of inflation on the cost of the party in future years. Although $30,000 is adequate for next year’s party, the students estimate that the party’s cost will rise by 4% per year thereafter. To satisfy their request, how much do you need to donate now?
PV = 30,000 / (8% - 4%) = $750,000
Suppose you want to create a perpetuity growing at 2%, so you invest $100 in a bank account that pays 5% interest.
At the end of year, you will have $105 in the bank. If you withdraw only $3, you will have $102 to reinvest – 2% more than the amount you had initially.
This amount will then grow to $102 * 1.05 = $ in the following year, and you can withdraw $3*1.02 = $3.06.
At the end of first year, $105=PV * (1 + i)
At the end of first year, $102=PV * (1 + g)
At the end of first year, $105 – $102 = $3 = C
Thus, C = PV * (1+ i) – PV * (1+g) = PV (i – g)
Thus, PV = C / (i – g) Yes!

17. The Dividend Discount Model
The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The basic DDM equation is:
In the DDM equation:
P0 = the present value of all future dividends
Dt = the dividend to be paid t years from now
k = the appropriate risk-adjusted discount rate

18. Several Variations of DDM
Be careful because there are several variations for this model, and you need to be able to see through which variation you are dealing with.
However, I will work you through each variation carefully.
Several variations
DDM with a finite series of dividends with constant dividends
DDM with an infinite series of dividends with constantly growing dividends
DDM with an infinite series of dividends with non-constantly growing dividends

19. Example: The Dividend Discount Model
This is an example of DDM with a finite series of dividends with constant dividends.
Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%.
In this case, what is the value of the stock today?

20. The Dividend Discount Model: the Constant Perpetual Growth Model.
Assuming that the dividends will grow forever at a constant growth rate g.
DDM with an infinite series of dividends with constantly growing dividends
For constant perpetual dividend growth, the DDM formula becomes:
Note that this is the Growing Perpetuity formula.

21. Example: Constant Perpetual Growth Model
Think about the electric utility industry.
In 2007, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2.12.
Using D0 =$2.12, k = 6.7%, and g = 2%, calculate an estimated value for DTE.
Note: the actual mid-2007 stock price of DTE was $ So, we may conclude that this stock is possibly slightly overvalued.
Note: the 6.7% comes from a rule of thumb for the electric utility industry of adding 2% to the current 20-year U.S. T-bond yield. At the time of this writing, that yield was about 4.7%.

22. The Dividend Discount Model: Estimating the Growth Rate
The growth rate in dividends (g) can be estimated in a number of ways:
Using the company’s historical average growth rate.
Arithmetic average
Geometric average
Using an industry median or average growth rate.
Using the sustainable growth rate.

23. Growth Rates

24. The Historical Average Growth Rate
Suppose the Broadway Joe Company paid the following dividends:
2002: $ : $1.80
2003: $ : $2.00
2004: $ : $2.20
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

25. The Sustainable Growth Rate
Return on Equity (ROE) = Net Income / Equity
Payout Ratio = Proportion of earnings paid out as dividends
Retention Ratio = Proportion of earnings retained for investment

26. Example: Calculating and Using the Sustainable Growth Rate
In 2007, American Electric Power (AEP) had an ROE of 10.17%, projected earnings per share of $2.25, and a per-share dividend of $ What was AEP’s:
Retention rate?
Sustainable growth rate?
Payout ratio = $1.56 / $2.25 = .693
So, retention ratio = 1 – .693 = .307 or 30.7%
Therefore, AEP’s sustainable growth rate =  .307 = , or 3.122%

27. Example: Calculating and Using the Sustainable Growth Rate, Cont.
What is the value of AEP stock, using the perpetual growth model, and a discount rate of 6.7%?
The actual mid-2007 stock price of AEP was $45.41.
In this case, using the sustainable growth rate to value the stock gives a reasonably accurate estimate.
What can we say about g and k in this example?
In this example, the model gives a positive stock price, which is fine.
If g is higher than k, then we have a problem because the estimated stock price will be negative.
In this case, we can conclude that g is too high because any company cannot grow at a rate greater than the required return. Why not?

28. The Two-Stage Dividend Growth Model
DDM with an infinite series of dividends with non-constantly growing dividends
The two-stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years, and thereafter grow at a rate g2 < k during a perpetual second stage of growth.
The Two-Stage Dividend Growth Model formula is:

29. Using the Two-Stage Dividend Growth Model, I.
Although the formula looks complicated, think of it as two parts:
Part 1 is the present value of the first T dividends (it is the same formula we used for the constant growth model).
Part 2 is the present value of all subsequent dividends.

30. Using the Two-Stage Dividend Growth Model, II.
So, suppose MissMolly.com has a current dividend of D0 = $5, which is expected to shrink at the rate, g1 = 10% for 5 years, but grow at the rate, g2 = 4% forever.
With a discount rate of k = 10%, what is the present value of the stock?

31. Using a formula,
The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present value of all subsequent dividends.

32. “A Conceptually Easier Way to Understand”
I would say this formula is “too” long. Is there any alternative to solve this problem?
First stage, find dividends for year 1 through 6.
D0=5, D1=4.5, D2=4.05, D3=3.645, D4=3.2805, D5=2.9525
D6= (=2.9525*1.04)
Second, find a stock price at the end of last year of first growth stage.
P5 = D6 / (k - g) = / ( )=
Third, find the NPV.
CF0 = 0, CF1 = 4.5, CF2 = 4.05, , CF3=3.645, CF4=3.2805
CF5 = =
I = 10%
NPV = 46.03

33. Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, I.
Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year.
You believe that this rate will last for only three more years.
Then, you think the rate will drop to 10% per year.
Total dividends just paid were $5 million.
The required rate of return is 20%.
What is the total value of Chain Reaction, Inc.?

34. Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, II.
First, calculate the total dividends over the “supernormal” growth period:
Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as:
P3 = [D3 x (1 + g)] / (k – g)
P3 = [$ x 1.10] / (0.20 – 0.10) = $
Year
Total Dividend: (in $millions) 1
$5.00 x 1.30 = $6.50 2
$6.50 x 1.30 = $8.45 3
$8.45 x 1.30 = $10.985

35. Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, III.
Therefore, to determine the present value of the firm today, we need the present value of $ and the present value of the dividends paid in the first 3 years:
If there are 20 million shares outstanding, the price per share is $4.38.

36. Discount Rates for Dividend Discount Models
The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ).
We will discuss the CAPM in a later chapter.
However, we can estimate the discount rate for a stock using this formula:
Discount rate = time value of money + risk premium
= U.S. T-bill Rate + (Stock Beta x Stock Market Risk Premium)
T-bill Rate:
return on 90-day U.S. T-bills
Stock Beta:
risk relative to an average stock
Stock Market Risk Premium:
risk premium for an average stock

37. Observations on Dividend Discount Models, I.
Constant Perpetual Growth Model:
Simple to compute
Not usable for firms that do not pay dividends
Not usable when g > k
Is sensitive to the choice of g and k
k and g may be difficult to estimate accurately.
Constant perpetual growth is often an unrealistic assumption.

38. Observations on Dividend Discount Models, II.
Two-Stage Dividend Growth Model:
More realistic in that it accounts for two stages of growth
Usable when g > k in the first stage
Not usable for firms that do not pay dividends
Is sensitive to the choice of g and k
k and g may be difficult to estimate accurately.

39. Common stock valuation: residual income model

40. Residual Income Model (RIM), I.
We have valued only companies that pay dividends.
But, there are many companies that do not pay dividends.
What about them?
It turns out that there is an elegant way to value these companies, too.
The model is called the Residual Income Model (RIM).
Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends.

41. Residual Income Model (RIM), II.
Inputs needed:
Earnings per share at time 0, EPS0
Book value per share at time 0, B0
Earnings growth rate, g
Discount rate, k
Residual income = Actual earnings – Required earnings = EPSt - Bt-1 x k
There are two equivalent formulas for the Residual Income Model:
BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

42. Using the Residual Income Model
Duckwall—Alco Stores, Inc. (DUCK)
It is July 1, 2010—shares are selling in the market for $10.94.
Using the RIM:
EPS0 = $1.20
DIV = 0
B0 = $5.886
g = 0.09
k = .13
What can we say about the market price of DUCK?

43. The Growth of DUCK
Using the information from the previous slide, what growth rate results in a DUCK price of $10.94?

44. Common stock valuation: free cash flow model

45. Free Cash Flow, I.
We can value companies that do not pay dividends using the residual income model.
Note: We assume positive earnings when we use the residual income model.
But, there are companies that do not pay dividends and have negative earnings.
Do negative earnings imply little value?
We calculate earnings based on accounting rules and tax codes.
It is possible that a company has:
negative earnings
positive cash flows
a positive value.

46. FCF = Net Income + Depreciation – Capital Spending
Free Cash Flow, II.
Depreciation—the key to understand how a company can have negative earnings and positive cash flows
Depreciation reduces earnings because it is counted as an expense (more expenses = lower taxes paid).
Most stock analysts, however, use a relatively simple formula to calculate Free Cash Flow, FCF:  
FCF = Net Income + Depreciation – Capital Spending
We can see that it is possible for: Net Income < 0 and FCF > 0
Depreciation and Capital Spending matter in FCF.

47. DDMs Versus FCF The DDMs calculate a value of the equity only.
DDMs use dividends, a cash flow only to equity holders
DDMs use the CAPM to estimate required return
DDMs use an equity beta to account for risk
Using the FCF model, we calculate a value for the firm.
Free cash flow can be paid to debt holders and to stockholders.
We can still calculate the value of equity using FCF
Calculate the value of the entire firm
Subtract out the value of debt
We need a beta for assets, not the equity, to account for risk.

48. What happens when a firm has no debt?
Asset Betas
Asset betas measure the risk of the company’s industry.
Firms in an industry should have about the same asset betas.
Their equity betas can be quite different.
Investors can increase portfolio risk by borrowing money.
A business can increase risk by using debt.
So, to value the company, we must “convert” reported equity betas into asset betas by adjusting for leverage.
The following conversion formula is widely used:
What happens when a firm has no debt?
tax rate.

49. The FCF Approach, Example
Inputs
An estimate of FCF:
Net Income
Depreciation
Capital Expenditures
The growth rate of FCF
The proper discount rate
Tax rate
Debt/Equity ratio
Equity beta
Calculate value using a “DDM” formula
“DDM” because we are using FCF, not dividends.

50. Valuing Landon Air: A New Airline
An estimate of FCF:
EBIT: $45 million
Depreciation: $10 million
Capital Expenditures: $3 million
Growth rate of FCF: 3%
10 million shares
Tax rate: 35%
Debt/Equity ratio: .40
Equity beta: 1.2
Asset Beta:
1.2 = BAsset x [1+.4 x (1-.35)]
1.2 = BAsset x 1.26
BAsset = 0.95
The proper discount rate:
k = (7.00 × 0.95)
= 10.65%
Assume:
No dividends
Risk-free rate = 4%
Market risk premium = 7%

51. Common stock valuation: price ratio analysis

52. Price Ratio Analysis, I. Price-earnings ratio (P/E ratio)
Current stock price divided by annual earnings per share (EPS)
High-P/E stocks are often referred to as growth stocks, while low-P/E stocks are often referred to as value stocks.
Earnings yield
Inverse of the P/E ratio: earnings divided by price (E/P)
Money managers often compare the earnings yield of a broad market index (such as the S&P 500) to prevailing interest rates, such as the current 10-year Treasury yield.
If the earnings yield is less than the rate of the 10-year Treasury yield, stocks as a whole may be considered overvalued. If the earnings yield is higher, stocks may considered undervalued relative to bonds.
Economic theory suggests that investors in equities should demand an extra risk premium of several percentage points above prevailing risk-free rates (such as T-bills) in their earnings yield to compensate them for the higher risk of owning stocks over bonds and other asset classes.

53. P/E Ratios for Different Industries, 2007

54. Price Ratio Analysis, II.
Price-cash flow ratio (P/CF ratio)
Current stock price divided by current cash flow per share
In this context, cash flow is usually taken to be net income plus depreciation.
Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income.
Earnings and cash flows that are far from each other may be a signal of poor quality earnings.

55. Price Ratio Analysis, III.
Price-sales ratio (P/S ratio)
Current stock price divided by annual sales per share
A high P/S ratio suggests high sales growth, while a low P/S ratio suggests sluggish sales growth.
Price-book ratio (P/B ratio)
Market value of a company’s common stock divided by its book (accounting) value of equity
A ratio bigger than 1.0 indicates that the firm is creating value for its stockholders.

56. Price/Earnings Analysis, Intel Corp.
Intel Corp (INTC) - Earnings (P/E) Analysis
5-year average P/E ratio 27.30
Current EPS $.86
EPS growth rate %
Expected stock price = historical P/E ratio  projected EPS
$25.47 =  ($.86  1.085)
Mid-2007 stock price = $24.27

57. Price/Cash Flow Analysis, Intel Corp.
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
5-year average P/CF ratio 14.04
Current CFPS $1.68
CFPS growth rate %
Expected stock price = historical P/CF ratio  projected CFPS
$ =  ($1.68  1.075)
Mid-2007 stock price = $24.27

58. Price/Sales Analysis, Intel Corp.
Intel Corp (INTC) - Sales (P/S) Analysis
5-year average P/S ratio 4.51
Current SPS $6.14
SPS growth rate %
Expected stock price = historical P/S ratio  projected SPS
$29.63 =  ($6.14  1.07)
Mid-2007 stock price = $24.27

59. An Analysis of the McGraw-Hill Company
The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.

60. The McGraw-Hill Company Analysis, I.

61. The McGraw-Hill Company Analysis, II.

62. The McGraw-Hill Company Analysis, III.
Based on the CAPM, k = 4.5% + (.90  9%) = 12.6%
Retention ratio = 1 – $.82/$3.45 = .762
Sustainable g = Retention ratio x ROE
=.762  38.5% = 29.34%
Because g > k, the constant growth rate model cannot be used. (We would get a value of -$6.34 per share)
P0 = (.82x1.2934) / ( ) =

63. The McGraw-Hill Company Analysis, IV.

64. Summary

65. An Analysis of the Procter and Gamble Company
The next few slides contain a financial analysis of Procter & Gamble, using data from the Value Line Investment Survey.

66. The Procter & Gamble Company Analysis, I.

67. The Procter & Gamble Company Analysis, II.

68. The Procter & Gamble Company Analysis, III.
Based on the CAPM, k = 4.0% + (0.6  7%) = 8.2%
Retention ratio = 1 – $2.15/$4.00 = .46
Sustainable g = .46  17% = 7.82%
Using the constant dividend growth rate model, we get:
Value Line reports a projected ROE of 17%
Stock price observed at the time we made this calculation: $67.21.

69. The Procter & Gamble Company Analysis (Using the Residual Income Model, I.)
Let’s assume that “today” is January 1, 2012, g =11.5%, and k = 8.2%.
Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table.
We use column one and our growth assumption for column three (CSR) of the table.
End of 2012
2013 (VL)
2013 (CSR)
Beginning BV per share NA
$25.80
EPS
$4.00
$4.35
$4.46
DIV
$2.15
$2.33
$1.493
Ending BV per share
$27.65
$28.767

70. Stock price at the time, about $51.82. What can we say?
The Proctor and Company Analysis (Using the Residual Income Model, II.)
Using the CSR assumption:
Using Value Line numbers:
Stock price at the time, about $ What can we say?
We say, we better find another way to value P&G
Note: The growth rate is higher than the discount rate, causing a negative stock value.

71. The Procter & Gamble Company Analysis, IV.
Table 6.3

72. Some Lessons from Peter Lynch
Favorable Attributes of Firms
1. Firm’s product should not be faddish
2. Firm should have some long-run comparative advantage over its rivals
3. Firm’s industry or product has market stability
4. Firm can benefit from cost reductions
5. Firms that buy back shares show there are putting money into the firm

73. Tenets of Warren Buffet
Business Tenets
Is the business simple and understandable?
Does the business have a consistent operating history?
Does the business have favorable long-term prospects?
Management Tenets
Is management rational?
Is management candid with its shareholders?
Does management resist the institutional imperative?
Financial Tenets
Focus on return on equity, not earnings per share
Calculate “owner earnings”
Look for companies with high profit margins
For every dollar retained, make sure the company has created at least one dollar of market value
Market Tenets
What is the value of the business?
Can the business be purchased at a significant discount to its fundamental intrinsic value?

74. Useful Internet Sites
(the New York Society of Security Analysts)
(the American Association of Individual Investors)
(Economic Value Added)
(the home of the Value Line Investment Survey)