1. Common Stock Valuation
Chapter 6
Common Stock Valuation

2. The Stock Market
“If a business is worth a dollar and I can buy it for 40 cents, something good may happen to me.”
–Warren Buffett
“Prediction is difficult, especially about the future.”
–Niels Bohr (among others)

3. having a good understanding of these security valuation methods:
Learning Objectives
having a good understanding of these security valuation methods:
1. The basic dividend discount model.
2. The two-stage dividend growth model.
3. The residual income model and free cash flow model.
4. Price ratio analysis.

4. Security Analysis: Be Careful Out There
Fundamental analysis is a term for studying a company’s accounting statements & other financial and economic information to estimate the economic value of a company’s stock.
The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell.
In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.

5. The Dividend Discount Model
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

6. Example: The Dividend Discount Model
Suppose that a stock will pay three annual dividends of $200 per year; the appropriate risk-adjusted discount rate, k, is 8%.
In this case, what is the value of the stock today?

7. DDM: the Constant Growth Rate Model
Assume that the dividends will grow at a constant growth rate g. The dividend in the next period, (t + 1), is:
For constant dividend growth for “T” years, the DDM formula is:

8. Example: The Constant Growth Rate Model
Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%.
What is the value of the stock, based on the constant growth rate model?

9. DDM: the Constant Perpetual Growth Model
Assuming that the dividends will grow forever at a constant growth rate g.
For constant perpetual dividend growth, the DDM formula becomes:

10. Example: Constant Perpetual Growth Model
Think about the electric utility industry. In 2012, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2.35.
Using D0 =$2.35, k = 4.75%, and g = 2%, calculate an estimated value for DTE.
Note: the actual mid-2012 stock price of DTE was $56.34.
What are the possible explanations for the difference?
Note: the 4.75% 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 2.75%.

11. DDM: 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.
Using an industry median or average growth rate.
Using the sustainable growth rate.

12. The Historical Average Growth Rate
Suppose the Broadway Joe Company paid the following dividends:
2008: $ : $1.80
2009: $ : $2.00
2010: $ : $2.20
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic & geometric averages.

13. 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 (i.e., NOT paid out as dividends)

14. Ex: Using the Sustainable Growth Rate
In 2012, DTE Energy (DTE) had an ROE of 10%, projected earnings per share of $4.05, and had a dividend level of $ What was DTE’s:
Retention rate?
Payout ratio = $2.35/ $4.05 = or about 58%
So, retention ratio = 1 – .58 = .42 or 42%
2. Sustainable growth rate?
sustainable growth rate = .10  .42 = .042, or 4.2%

15. Ex: Using the Sustainable Growth Rate, Cont.
What is the value of DTE stock using the perpetual growth model and a discount rate of 4.75%?
The actual mid-2012 stock price of DTE was $56.34.
In this case, using the sustainable growth rate to value the stock gives an extremely poor estimate.
What can we say about the values of g and k in this example?

16. Analyzing ROE
To estimate a sustainable growth rate, you need the (relatively stable) dividend payout ratio & ROE.
Changes in sustainable growth rate likely from changes in ROE
The DuPont formula separates ROE into three parts:
ROE= Profit Margin X Asset Turnover X Equity Multiplier
Managers can increase the sustainable growth rate by:
Decreasing the dividend payout ratio
Increasing profitability (Net Income / Sales)
Increasing asset efficiency (Sales / Assets)
Increasing debt (Assets / Equity)

17. The Two-Stage Dividend Growth Model
The two-stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years,
and thereafter, it will grow at a rate g2 < k during a perpetual second stage of growth.
The Two-Stage Dividend Growth Model formula is:

18. Using the Two-Stage: Dividend Growth Model,
Although the formula looks complicated, think of it as two parts:
The present value of the first T dividends (it is the same formula we used for the constant growth model).
the present value of all subsequent dividends.
So, suppose MissMolly 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?

19. Using the Two-Stage: Dividend Growth Model, II.
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.

20. Ex: 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.?

21. Ex: DDM & “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

22. Ex: DDM & “Supernormal” Growth, III
To determine the present value of the firm today, we need the present value of $ & 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.

23. The H-Model
For Chain Reaction, we assumed a supernormal growth rate of 30% per year for 3 years, and then growth at a perpetual 10%
The growth rate is more likely to start at a high level & then fall over time until reaching its perpetual level.
Many possible ways to assume how the growth rate declines
A popular way is the H-model: which assumes a linear growth rate decline

24. The H-Model, II. If we assume a linear decline:
Let’s revisit Chain Reaction, Inc.
Suppose the growth rate begins at 30% & reaches 10% in Year 4
Using the H-model, we would assume that the growth rate would decline by 20% from the end of year 1 to the beginning of year 4.
If we assume a linear decline:
the growth rate falls by 6.67% per year (20%/3 years).
G estimates would be: 30%, 23.33%, 16.66%, and 10%
Using these growth estimates, you will find that the firm value is $75.93 million, or $3.80 per share.
The value is lower than before because of the lower growth rates in years 2 and 3.

25. 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.
Can estimate the discount rate for a stock with this formula:
Discount rate = time value of money + risk premium = US 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 avg stock

26. Constant Perpetual Growth Model:
Observations on DDM
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.

27. Two-Stage Dividend Growth Model:
Observations on DDM, 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.

28. 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?
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.

29. Residual Income Model (RIM), II.
Inputs needed:
EPS0 =Earnings per share at time 0
B0 =Book value per share at time 0
G = Earnings growth rate
K = Discount rate
There are two equivalent formulas for the RIM:
BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

30. EX: Using the Residual Income Model
Duckwall- (DUCK). It is July 1, 2010—shares are selling in the market for $ 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?

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

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

33. Depreciation & Capital Spending matter in FCF.
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 = EBIT (1 – Tax rate) + Depreciation – Capital Spending – Change in net working capital
We can see that it is possible for: Net Income < 0 & FCF > 0
Depreciation & Capital Spending matter in FCF.

34. DDMs Versus FCF
The DDMs calculate a value of the equity only. DDMs use
Dividends, a cash flow only to equity holders
The CAPM to estimate required return
An equity beta to account for risk
Using the FCF, we calculate a value for the firm.
FCF can be paid to debt holders & 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
Need a beta for assets, not the equity, to account for risk

35. 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 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.

36. 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.

37. Valuing Landon Air: A New Airline
An estimate of FCF:
EBIT: $45 million
Capital Expenditures: $3 million
Depreciation: $10 million
Growth rate of FCF: 3%
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%

38. Price Ratio Analysis, I.
Price-earnings ratio (P/E ratio): Current stock price per share divided by annual earnings per share (EPS)
Earnings yield: Inverse of the P/E ratio, i.e., earnings per share (EPS) divided by price per share (E/P)
High-P/E stocks are often referred to as growth stocks,
while low-P/E stocks are often referred to as value stocks.

39. 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.

40. 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) also called M/B (Market/book) Market value of a company’s common stock divided by its book (accounting) value of equity
Current stock price divided by book value per share
A ratio bigger than 1.0 indicates that the firm is creating value for its stockholders.

41. Price/Earnings Analysis, Intel Corp
Intel Corp (INTC) - Earnings (P/E) Analysis
5-year average P/E ratio 17.10
Current EPS $2.31
EPS growth rate %
Expected stock price = historical P/E ratio  projected EPS
$42.50 =  ($2.31  1.076)
Mid-2012 stock price = $26.98

42. Price/Cash Flow Analysis, Intel Corp.
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
5-year average P/CF ratio
Current CFPS $3.65
CFPS growth rate %
Expected stock price = historical P/CF ratio  projected CFPS
$31.24 = 8.00  ($3.65  1.07)
Mid-2012 stock price = $26.98

43. Price/Sales Analysis, Intel Corp.
Intel Corp (INTC) - Sales (P/S) Analysis
5-year average P/S ratio
Current SPS $9.99
SPS growth rate %
Expected stock price = historical P/S ratio  projected SPS
$31.32 =  ($6.76  1.07)
Mid-2012 stock price = $19.40

44. Price-Earnings Ratios
Differences in P/E ratios can be explained based on differences in g
An analyst must justify whether he is more or less optimistic about the future growth of the stock compared to the market.

45. Price-Earnings Ratios
The P/E ratio of any company that’s fairly priced will equal its growth rate. I’m talking here about growth rate of earnings…if the the P/E ratio of Coca-Cola is 15, you’d expect the company to be growing at about 15% per year, etc. But if
the P/E ratio is less than the growth rate,
you may have found yourself a bargain.
Do a real-life example
Growth was very clear during the Internet bubble. Crazy valuations
eBay in 1998 had NI of $2.4 M vs Sotheby’s $45 M. eBay’s MV was 10 times that of Sotheby’s. The market turned right here, in 2010 eBay’s NI was $1.8 B 11 times greater than Sotheby’s
If Value is mostly driven by PVGO then it is very sensitive to any small changes in it. Again Internet Bubble
Yahoo dropped form $119 in January 2000 to $8 in September 2001

46. Pitfalls in P/E Analysis
Earnings Management
Practice of using flexibility in accounting rules to improve apparent profitability of firm
Large amount of discretion in managing earnings

47. Enterprise Value Ratios, Overview
The PE ratio is an equity ratio: numerator is price per share of stock & denominator is earnings per share of stock.
Practitioners often use ratios involving both debt & equity
Perhaps the most common one is the enterprise value (EV) to EBITDA ratio.
Enterprise value = the market value of the firm’s equity + the market value of the firm’s debt - cash
EBITDA stands for earnings before interest, taxes, depreciation, and amortization.

48. Enterprise Value Ratios, Example
Kourtney’s Kayaks has equity worth $800 million, debt worth $300 million, and cash of $100 million.
The enterprise value is $1 billion (= ).
Suppose Kourtney’s Kayaks’ income statement is:
The EV to EBITDA ratio is 5 (= $1 billion / $200 million).
Any income statement item below EBITDA is not included in the EV to EBITDA ratio.

49. Using Enterprise Value Ratio to Estimate Stock Price
Analysts often assume that similar firms have similar EV/EBITDA ratios (and similar PE ratio, too).
Suppose the average EB/EBITDA ratio in an industry is 6.
Qwerty Co, a firm in the industry, has EBITDA of $50 million
If Qwerty Co is judged to be similar to the rest of the industry, its EV is estimated at $300 million (= 6 × $50)
If Qwerty Co has $75 M of debt and $25 M of cash, the EV estimate, $250 million (= $300 - $75 + $25).
Consult the textbook: There are four important questions
concerning enterprise value ratios.

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

51. Useful Internet Sites
(The New York Society of Security Analysts)
(The American Association of Individual Investors)
(the web site of the CFA Institute)
(the home of the Value Line Investment Survey)
jmdinvestments.blogspot.com (reference for recent financial news)
Websites for some companies analyzed in this chapter: