1. Chapter 6
Stock Valuation

2. Key Concepts and Skills
Comprehend that stock prices depend on future dividends and dividend growth
Compute stock prices using the dividend growth model
Understand how growth opportunities affect stock values
Appreciate the PE ratio
Know how stock markets work

3. The PV of Common Stocks
The value of any asset is the present value of its expected future cash flows.
Stock ownership produces cash flows from:
Dividends
Capital Gains
Valuation of Different Types of Stocks
Zero Growth
Constant Growth
Differential Growth

4. Case 1: Zero Growth
Assume that dividends will remain at the same level forever
Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:

5. Zero Growth Example
Suppose Big Red Corporation will pay an annual dividend of $2.00 per common share that will never increase or decrease.
The market rate of return is 8.5%.
What is the maximum amount you should be willing pay for a common share of Big Red Corporation?
Formula for Zero Growth Model: P = Div / R
Solution: P = $2.00 / .085
P = $23.53

6. Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g, forever, i.e., . . .
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:

7. Constant Growth Example
Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?
P0 = .50(1+.02) / ( ) = $3.92

8. A Word About Dividends in the Constant Growth Model
It is critical to understand that in the constant growth model calculations are based on the next dividend
If a situation only provides information on the last dividend it must be increased by the growth rate to arrive at the next dividend
If a situation provides the value of the next dividend, then the data necessary for the calculation is known and need not be derived.
An analyst must discriminate whether they have information about the next or last dividend and proceed with calculation accordingly

9. Case 3: Differential Growth
Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.
To value a Differential Growth Stock, we need to:
Estimate future dividends in the foreseeable future.
Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2).
Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.

10. Case 3: Differential Growth
Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter. . . . . . .

11. Case 3: Differential Growth
We can value this as the sum of:
a T-year annuity growing at rate g1
plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1

12. Case 3: Differential Growth
Consolidating gives:
Or, we can “cash flow” it out!

13. A Differential Growth Example
A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%.

14. With the Formula

15. With Cash Flows …
The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.

16. Estimates of Parameters
The value of a firm depends upon its growth rate, g, and its discount rate, R.
Where does g come from?
g = Retention ratio × Return on retained earnings
Example: Suppose a company has a retention ratio of 70% and earns an ROE of 12%. What is the Growth Rate, g?
g = .70 X g = .084 = 8.4%

17. Where Does R Come From?
The discount rate can be broken into two parts.
The dividend yield
The growth rate (in dividends)
AKA: Capital Gains Yield
In practice, there is a great deal of estimation error involved in selecting R.
Cases calling for special skepticism:
Stocks not paying dividends
Stocks with g expected to equal or exceed R

18. Growth Opportunities
Growth opportunities are opportunities to invest in positive NPV projects.
The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities.
A firm that pays out 100% of its earnings is essentially a zero growth firm since the retention rate is zero. This, however, does not imply the firm is not profitable.
Two conditions must exist if a company is to grow:
It must not pay out all of its earnings as dividends; and,
It must invest in projects with a positive NPV

19. The NPVGO Model We have two ways to value a stock:
The dividend discount model
The sum of its price as a “cash cow” plus the per share value of its growth opportunities

20. What About Stocks That Pay No Dividends?

21. What About Stocks That Pay No Dividends?
If investors value dividends, how much is a stock that pays no dividends worth – $0?
Such firms believe their earnings are better used to pursue growth opportunities
Investors pay a stock price that conforms to their own calculus of the NPVGO of the no-payout firm
The dividend growth model does not work in valuing this firm
A company that has not paid dividends to date can be worth a lot, if the company has good investment projects or it has assets that can be liquidated.

22. Valuation of a Firm: What Is a Firm Worth?
Multiples or Relative Valuation Models
TRADING MULTIPLES – Use comparable publicly traded companies
TRANSACTION MULTPLES -- Use comparable recent transactions
Discounted Cash Flows
Conceptually, a firm should be worth the present value of the firm’s cash flows.
The tricky part is determining the size, timing and risk of those cash flows.

23. MULTIPLES VALUATION CHOOSE A RATIO, OR MULTIPLE, OF FIRM VALUE
EBITDA, NET INCOME, SALES REVENUE, BOOK VALUE
INTERNET PORTAL REGISTERED USERS, ETC…
Relative to
ENTERPRISE VALUE (Market value of equity plus debt)
MARKET VALUE OF EQUITY
PRICE PAID IN ACQUISITION, ETC…
SELECT COMPARABLE FIRM OR FIRMS
A. FIRMS IN THE SAME INDUSTRY
B. RECENT ACQUISITIONS IN THE SAME INDUSTRY
MULTIPLY THE MULTIPLE BY FIRM’S RATIO

24. Price-Earnings Ratio
Many analysts frequently relate earnings per share to price.
The price-earnings ratio is calculated as the current stock price divided by annual EPS.
The Wall Street Journal uses last 4 quarter’s earnings
Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example.
Firms whose shares are out of favor sell at low multiples. Value stocks for example.

25. Multiples Example
Software Firms are currently trading at average P/E ratios of 15.
Anderson Software has 1 million shares outstanding and has no debt. Anderson expects Earnings Per Share of $2. What is the firm worth?
15 * $2 per share * 1 million shares = $30 million

26. MULTIPLES VALUATION ASSUMPTIONS
Comparable firms are similar in terms of risk and future expected cash flows
The item used is proportional to value
WEAKNESSES
Can provide wide dispersion of estimates
Different accounting methods used by firms
Different capital structures, risk characteristics, and growth opportunities

27. Valuing a firm using DCF and Free Cash Flows (FCF)
PV (free cash flows)
PV (Horizon value)
Horizon value == Terminal Value

28. Estimating Free Cash Flows for DCF Analysis
FCF = OCF – ∆FA –∆NWC -- Also referred to occasionally as “Cash Flow from Assets”
OCF – Operating Cash Flow
∆FA - Capital Expenditures, Capital spending or Change in Fixed Assets
∆NWC - Changes in Net Working Capital
FCF is the amount of the cash flow freely available to investors – providers of debt and equity capital.
Cash flows -- should be unbiased estimates, generally for 5 to 10 years
Requires a competitive analysis of the firm and its industry.
Make sure to include changes in Capital Expenditures and Working Capital (replace worn out equipment or to support future growth)
Terminal Value or Horizon value
The terminal value captures the present value of the cash flows beyond the forecast period, as of the final year of the forecast period
can use constant growth model or multiples, assumes that you have reached a long-run competitive equilibrium

29. COMMON STOCK: VALUATION EXAMPLE STOCKS THAT PAY NO DIVIDENDS
Assume that Google generated $8 billion of Operating Cash Flow in They spent $3 billion on Fixed Assets and increased Working Capital by $1 billion, giving them $4 billion in Free Cash Flow. For this example, assume Google has no debt.
You expect Free Cash Flow to grow by 50% in the next 3 years and then 5% from then on. You require a 15% return.
Google has a market value of $161 billion (8/10).
Do you think that Google is worth that much?

30. COMMON STOCK: VALUATION EXAMPLE STOCKS THAT PAY NO DIVIDENDS
FCF1 = $4 Billion * 1.5 = $6 B
Estimate of Enterprise value

31. COMMON STOCK: VALUATION EXAMPLE STOCKS THAT PAY NO DIVIDENDS What perpetual growth rate would justify the valuation?

32. The Stock Markets Dealers vs. Brokers New York Stock Exchange (NYSE)
Largest stock market in the world
License Holders (formerly “Members”)
Entitled to buy or sell on the exchange floor
Commission brokers
Specialists
Floor brokers
Floor traders
Operations
Floor activity

33. NASDAQ Not a physical exchange – computer-based quotation system
Multiple market makers
Electronic Communications Networks
Three levels of information
Level 1 – median quotes, registered representatives
Level 2 – view quotes, brokers & dealers
Level 3 – view and update quotes, dealers only
Large portion of technology stocks

34. Stock Market Reporting
Gap has been as high as $25.72 in the last year.
Gap has been as low as $18.12 in the last year.
Given the current price, the dividend yield is .8%.
Gap pays a dividend of 18 cents/share.
Gap ended trading at $21.35, which is unchanged from yesterday.
Given the current price, the PE ratio is 18 times earnings.
3,996,100 shares traded hands in the last day’s trading.