1. Stock Valuation: Free Cash Flow
Chapter 10
Stock Valuation: Free Cash Flow

2. Chapter Outline 1 The Discounted Free Cash Flow Model
Valuation Based on Comparable Firms
Valuation and Finance Crisis
4 Information, Competition, and Stock Prices
5 Individual Biases and Trading

3. Limitations of the Dividend-Discount Model
Again, the dividend-discount model has some limitations.
Uncertain Dividend Forecasts
The dividend-discount model values a stock based on a forecast of the future dividends, but a firm’s future dividends carry a tremendous amount of uncertainty
Non-Dividend-Paying Stocks
Many companies do not pay dividends, thus the dividend-discount model must be modified.
Often of limited use of internal management purpose.
For example, GE have many affiliates and subsidiaries but only few of them pay dividends as separate entities.
Therefore, we suggest the alternative model – The discounted free cash flow model.
Not only we can value the firm with no dividend payments, but we can also value the firm or operating units within the firm

4. Discounted free cash flow model

5. Free Cash Flow (FCF) What is it?
The cash from operations that is actually available for distribution to investors (including stockholders, bondholders, and preferred stockholders), after the company has made all the investments in fixed assets and working capital necessary to sustain ongoing operations.

6. 10.1 The Discounted Free Cash Flow Model
Begins by determining the total value of the firm to all investors—both equity holders and debt holders.
Estimate the firm’s enterprise value, defined as the net cost of acquiring the firm’s equity, paying of all debt, and taking its cash; in essence, it is equivalent to owning the unlevered business.
Valuing the Enterprise
To estimate a firm’s enterprise value, we compute the present value of the firm’s free cash flow available to pay all investors.
𝑴𝑽𝑬𝒒𝒖𝒊𝒕𝒚=𝑬𝑽+𝑪𝒂𝒔𝒉 −𝑫𝒆𝒃𝒕
(Eq. 10.1)

7. 10.1 The Discounted Free Cash Flow Model
Estimating process
Step 1: Project future FCFs.
Step 2: Find the enterprise value by taking the present value of all future FCFs.
V0 =PV(Future Free Cash Flow of Firm) (Eq. 10.3)
Step 3: Given the enterprise value, use Eq to solve for the value of equity and divide by the total number of shares outstanding.
(Eq 10.2)
(Eq. 10.4)

8. 10.1 The Discounted Free Cash Flow Model
Implementing the Model
Since we are discounting the cash flows to all investors, we use the weighted average cost of capital (WACC), denoted by rwacc
Forecast free cash flow up to some horizon, together with a terminal value of the enterprise:
Estimate the terminal value by assuming a constant long-run growth rate gFCF for free cash flows beyond year N.
The long-run growth rate gFCF is typically based on expected long-run growth rate of revenues

9. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Problem:
Recall our example of Nike, Inc., from Chapter 7. Nike had sales of $19.2 billion in Suppose you expect its sales to grow at a rate of 10% in 2010, but then slow by 1% per year to the long-run growth rate that is characteristic of the apparel industry—5%—by Based on Nike’s past profitability an investment needs, you expect EBIT to be 10% of sales, increases in net working capital requirements to be 10% of any increase in sales, and capital expenditures to equal depreciation expenses. If Nike has $2.3 billion in cash, $32 million in debt, 486 million shares outstanding, a tax rate of 24%, and a weighted average cost of capital of 10%, what is your estimate of the value of Nike’s stock in early 2010? 9

10. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Solution:
We can estimate Nike’s future free cash flow by constructing a pro forma statement as we did for HomeNet in Chapter 9. The only difference is that the pro forma statement is for the whole company, rather than just one project. Further, we need to calculate a terminal (or continuation) value for Nike at the end of our explicit projections.
Because we expect Nike’s free cash flow to grow at a constant rate after 2015, we can use Eq to compute a terminal enterprise value. The present value of the free cash flows during the years 2010–2015 and the terminal value will be the total enterprise value for Nike. Using that value, we can subtract the debt, add the cash, and divide by the number of shares outstanding to compute the price per share (Eq. 10.4). 10

11. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Execute:
The spreadsheet below presents a simplified pro forma for Nike based on the information we have: 11

12. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Execute (cont’d):
Because capital expenditures are expected to equal depreciation, lines 7 and 8 in the spreadsheet cancel out. We can set them both to zero rather than explicitly forecast them.
Given our assumption of constant 5% growth in free cash flows after 2015 and a weighted average cost of capital of 10%, we can use Eq to compute a terminal enterprise value: 12

13. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Execute (cont’d):
From Eq. 10.5, Nike’s current enterprise value is the present value of its free cash flows plus the firm’s terminal value:
We can now estimate the value of a share of Nike’s stock using Eq. 10.4: 13

14. Example 10.1 Valuing Nike, Inc., Stock Using Free Cash Flow
Evaluate:
The total value of all of the claims, both debt and equity, on the firm must equal the total present value of all cash flows generated by the firm, in addition to any cash it currently has. The total present value of all cash flows to be generated by Nike is 32,542 million and it has 2,300 million in cash. Subtracting off the value of the debt claims (32 million), leaves us with the total value of the equity claims and dividing by the number of shares produces the value per share. 14

15. Example 10.1b Valuing Navarro Stock Using Free Cash Flows
Problem:
Navarro had sales of $630 million in Suppose you expect its sales to grow at an 8% rate in 2010, but that this growth rate will slow by 2% per year to a long-run growth rate for the industry of 2% by Based on Navarro’s past profitability and investment needs, you expect EBIT to be 10% of sales, increases in net working capital requirements to be 8% of any increase in sales, and capital expenditures to equal depreciation expenses. If Navarro has $125 million in cash, $5 million in debt, 25 million shares outstanding, a tax rate of 35%, and a weighted average cost of capital of 12.5%, what is your estimate of the value of Navarro’s stock in early 2010? 15

16. Example 10.1b Valuing Navarro Stock Using Free Cash Flows
Solution:
The spreadsheet below presents a simplified pro forma for Navarro based on the information we have:
We can estimate Navarro’s future free cash flow by constructing a pro forma statement as we did in Chapter 9. The only difference is that the pro forma statement is for the whole company, rather than just one project. Further, we need to calculate a terminal (or continuation) value for Navarro at the end of our explicit projections. Because we expect Navarro’s free cash flow to grow at a constant rate after 2013, we can use Eq to compute a terminal enterprise value.
The present value of the free cash flows during the years 2010 – 2013 and the terminal value will be the total enterprise value for Navarro. Using that value, we can subtract the debt, add the cash, and divide by the number of shares outstanding to compute the price per share. 16

17. Example 10.1b Valuing Navarro Stock Using Free Cash Flows
Execute (cont’d):
The Value Principle tells us that the present value of all future cash flows generated by Navarro plus the value of the cash held by the firm today must equal the total value today of all the claims, both debt and equity, on those cash flows and cash. Using that principle, we can calculate the total value of all of Navarro’s claims and then subtract the debt portion to value the equity (stock). 17

18. 10.1 The Discounted Free Cash Flow Model
We must forecast all the inputs to free cash flow.
This process gives us flexibility to incorporate many details
However, some uncertainty surrounds each assumption
Given this fact, sensitivity analysis is important
Translates the uncertainty into a range of values for the stock.

19. Example 10.2 Sensitivity Analysis for Stock Valuation
Problem:
In Example 10.1, Nike’s EBIT was assumed to be 10% of sales. If Nike can reduce its operating expenses and raise its EBIT to 11% of sales, how would the estimate of the stock’s value change? 19

20. Example 10.2 Sensitivity Analysis for Stock Valuation
Solution:
In this scenario, EBIT will increase by 1% of sales compared to Example From there, we can use the tax rate (24%) to compute the effect on the free cash flow for each year. Once we have the new free cash flows, we repeat the approach in Example 10.1 to arrive at a new stock price.
In year 1, EBIT will be 1% X $21,120.0 million = $211.2 million higher. After taxes, this increase will raise the firm’s free cash flow in year 1 by (1-0.24) X $211.2 million = $160.5 million, to $1,573.6 million. Doing the same calculation for each year, we get the following revised FCF estimates:
Year
2010
2011
2012
2013
2014
2015
FCF
1,573.6
1,734.5
1,894.3
2,050.0
2,197.8
2,334.3 20

21. Example 10.2 Sensitivity Analysis for Stock Valuation
Continued:
We can now re-estimate the stock price as in Example The terminal value is V2015=[1.05/( ) X 2,334.3=$49,020.3 million, so
The new estimate for the value of the stock is P0=(36, ,300-32)/486=$78.82 per share, a difference of about 10% compared to the result found in Example 10.1
Nike’s stock price is fairly sensitive to changes in the assumptions about its profitability. A 1% permanent change in its margins affects the firm’s stock price by 10%. 21

22. Example 10.2b Sensitivity Analysis for Stock Valuation
Problem:
In Example 10.1b, Navarro’s EBIT was assumed to be 10% of sales. If Navarro can reduce its operating expenses and raise its EBIT to 12% of sales, how would the estimate of the stock’s value change? 22

23. Example 10.2b Sensitivity Analysis for Stock Valuation
Solution:
In this scenario, EBIT will increase by 2% of sales compared to Example 10.1b. From there, we can use the tax rate (35%) to compute the effect on the free cash flow for each year. Once we have the new free cash flows, we repeat the approach in Example 10.1b to arrive at a new stock price.
In year 1, EBIT will be 2% × $680.4 million = $13.6 million higher. After taxes, this increase will raise the firm’s free cash flow in year 1 by ( ) × $13.6 million = $8.8 million, to $49.0 million. Doing the same calculation for each year, we get the following revised FCF estimates:
This is a difference of about 16.3% compared to the result found in Example 10.1b.
Navarro’s stock price is fairly sensitive to changes in the assumptions about its profitability. A 2% permanent change in its margins affects the firm’s stock price by 16.3%. 23

24. Figure 10.1 A Comparison of Discounted Cash Flow Models of Stock Valuation

25. Valuation based on comparable firms (Skipped)

26. Valuation and financial crisis 2007 ~ 2009 (Skipped)

27. Errors in Valuation
Although the pricing models are useful, market participants frequently encounter problems in using them. Any of these can have a significant impact on price in the Gordon model.
Problems with Estimating Growth
Problems with Estimating Risk
Problems with Forecasting Dividends

28. Case: The 2007–2009 Financial Crisis and the Stock Market
The financial crisis, which started in August 2007, was the start of one of the worst bear markets.
The crisis lowered “g” in the Gordon Growth model—driving down prices.
Also impacts rE—higher uncertainty increases this value, again lowering prices.
The expectations were still optimistic at the start of the crisis. But, as the reality of the severity of the crisis was understood, prices plummeted.

29. Case: The 2007–2009 Financial Crisis
Financial innovation in mortgage markets developed along a few lines:
Less-than-credit worthy borrowers found the ability to purchase homes through subprime lending, a practice almost nonexistent until the 2000s
Financial engineering developed new financial products to further enhance and distribute risk from mortgage lending

30. Case: The 2007–2009 Financial Crisis
Agency problems in mortgage markets also reached new levels:
Mortgage originators did not hold the actual mortgage, but sold the note in the secondary market
Mortgage originators earned fees from the volume of the loans produced, not the quality
In the extreme, unqualified borrowers bought houses they could not afford through either creative mortgage products or outright fraud (such as inflated income)

31. Case: The 2007–2009 Financial Crisis
Finally, the rating agencies didn’t help:
Agencies consulted with firms on structuring products to achieve the highest rating, creating a clear conflict
Further, the rating system was hardly designed to address the complex nature of the structured debt designs
The result was meaningless ratings that investors had relied on to assess the quality of their investments

32. Case: The 2007–2009 Financial Crisis
Initially, the housing boom was lauded by economics and politicians. The housing boom helped stimulate growth in the subprime market as well.
However, underwriting standard fell. People were clearly buying houses they could not afford, except for the ability to sell the house for a higher price.
Lending standards also allowed for near 100% financing, so owners had little to lose by defaulting when the housing bubble burst.
The next slide shows the rise and fall of housing prices in the U.S. The number of defaults continues to plague the U.S. banking system.

33. Housing Prices: 2002–2010
Some argue that low interest rates from 2003 to 2006 fueled the housing bubble.
In early 2009, Mr. Bernanke rebutted this argument. He argued rates were appropriate.
He also pointed to new mortgage products, relaxed lending standards, and capital inflows as more likely causes.

34. Case: The 2007–2009 Financial Crisis
As mortgage defaults rose, banks and other FIs saw the value of their assets fall. This was further complicated by the complexity of mortgages, CDOs, defaults swaps, and other difficult-to-value assets.
Banks began the deleveraging process, selling assets and restricting credit, further depressing the struggling economy

35. Stock Market Indexes, DJIA (b)

36. Case: The 2007–2009 Financial Crisis
Finally, the collapse of several high-profile U.S. investment firms only further deteriorated confidence in the U.S.
March 2008: Bear Sterns fails and is sold to JP Morgan for 5% of its value only 1 year ago
September 2008: Both Freddie and Fannie put into conservatorship after heaving subprime losses.
September 2008: Lehman Brothers files for bankruptcy. Merrill Lynch sold to Bank of America at “fire” sale prices. AIG also experiences a liquidity crisis.

37. Case: The 2007–2009 Financial Crisis
The crisis and impaired credit markets have caused the worst economic contraction since World War II. The fall in real GDP and increase in unemployment to over 10% in 2009 impacted almost everyone.

38. Valuation, Efficient market, and Behavioral biases (skipped)

39. Intrinsic Values and Market Prices
The Company, the Economic
Environment, and the Political Climate
All Relevant Available Information
Selected Information and Its Interpretation
Unbiased Expected Future Cash Flows
Unbiased Risk
“Perceived” Future Cash Flows
“Perceived” Risk
Equal?
Intrinsic Value
Market Price

40. What is required for the market to be in equilibrium?
The market price of a security must equal the security’s intrinsic value (intrinsic value reflects the size, timing, and risk of the future cash flows).
Market price = Intrinsic value 25

41. How is equilibrium established?
If the market price is below the intrinsic, then the security is a “bargain.”
Buy orders will exceed sell orders, bidding up the market price.
“Profitable” trading (i.e., earning a return greater than justified by risk) will continue until the market price is equal to the intrinsic value.
The opposite occurs if the market price is above the intrinsic value. 25

42. Efficient Market Hypothesis (EMH): It’s all about the info.
The EMH asserts that when new information arrives, prices move to the new equilibrium price very, very quickly because:
There are many really smart analysts looking for mispriced securities.
New information is available to most professional traders almost instantly.
When mispricing occurs (due to new info or inefficient markets), analysts have billions of dollars to use in taking advantage of the mispricing– which then quickly eliminates the mispricing. 28

43. Implications of Efficient Market Hypothesis (EMH)
Stocks are normally in equilibrium.
One cannot “beat the market” by consistently earning a return higher than is justified by a stock’s risk. 28

44. Market Efficiency: The Bottom Line
For most stocks, for most of the time, it is generally safe to assume that the market is reasonably efficient.
Many investors have given up trying to beat the market, which helps explain the popularity of index funds.
However, bubbles do occur infrequently. 32

45. 10.3 Information, Competition, and Stock Prices

46. Market Efficiency vs. Behavioral Finance
Market Efficiency Camp
Behavioral Finance Camp
Investors are rational.
Rational investors dominate irrational investors.
Even if some investors are not rational, irrationality does not occur collectively.
Prices are correct; equal to intrinsic value.
If prices are not right, mispricing will be easily eliminated via sharp-eyed arbitrageurs.
The current stock price reflect new information efficiently.
Arbitrageurs can profit in most of time, restoring mispricing to equilibrium.
Investors are emotional or irrational.
From time to time, crowd mentality dictates in the market.
The market sometimes over- (or under-) reacts to new information.
Arbitrageurs cannot often take advantage of mispricing, failing to restore the price to equilibrium.

47. Behavioral Finance, Definition
Behavioral Finance The area of research that attempts to understand and explain how reasoning errors influence investor decisions and market prices.
Much of behavioral finance research stems from the research in the area of cognitive psychology.
Cognitive psychology: the study of how people (including investors) think, reason, and make decisions.
Reasoning errors are often called cognitive errors.
Some people believe that cognitive (reasoning) errors made by investors will cause market inefficiencies.

48. Evidence Against Market Efficiency: Market Bubbles
Prices climb rapidly to heights that would have been considered extremely unlikely before the run-up.
Trading volume is unusually high.
Many new investors (or speculators?) eagerly enter the market.
Prices suddenly fall precipitously.
What does this imply about the EMH?

49. Bubbles are hard to puncture.
If there is a bubble, why don’t traders take positions that make big profits when the bubble bursts?
It is hard to recognize a bubble until after it bursts—then it seems obvious!
Trading strategies expose traders to possible big negative cash flows if the bubble is slow to burst.

50. 10.4 Individual Biases and Trading
Excessive Trading and Overconfidence
Trading is expensive because of commissions and the difference between the bid and ask
Given the difficulty of finding over- and under-valued stocks, you might expect individual investors to trade conservatively.
However, a study of the trading behavior of individual investors at a discount brokerage found individual investors trade very actively.
Average turnover almost 50% above overall rates during the time of the study.

51. 10.4 Individual Biases and Trading
Overconfidence hypothesis
Tendency of individual investors to trade too much based on the mistaken belief that they can pick winners and losers better than investment professionals.
Implication is that investors who trade more will not earn higher returns.
Performance will actually be worse because of trading costs.
Researchers have found that the average household earned an annual return of 16.4 percent.
Researchers have found that households that traded the most earned an annual return of only 11.4 percent.
The moral is clear: Excessive trading is hazardous to your wealth.

52. Overconfidence and Trading Frequency Is Overtrading “a Guy Thing?”
Psychologists have found that men are more overconfident than women in the area of finance. So,
Do men trade more than women?
Do portfolios of men under-perform the portfolios of women?
Researchers show that the answer to both questions is yes.
Men trade about 50 percent more than women.
Researchers show that both men and women reduce their portfolio returns when they trade excessively.
The portfolio return for men is 94 basis points lower than portfolio returns for women.
The portfolio return for single men is 144 basis points lower than the portfolio return for single women.
Accounting for the effects of marital status, age, and income, researchers also show that men invest in riskier positions.

53. Figure 10.7 Individual Investor Returns Versus Portfolio Turnover

54. 10.4 Individual Biases and Trading
Hanging On to Losers and the Disposition Effect
Investors tend to hold on to stocks that have lost value and sell stocks that have risen in value
We call this tendency the disposition effect.
Researchers Hersch Shefrin and Meir Statman suggest that this effect arises due to investors’ increased willingness to take on risk in the face of possible losses.
May also reflect a reluctance to admit a mistake by taking the loss.
From a tax perspective, this behavioral tendency is costly.
Capital gains are taxed only when an asset is sold, so delaying the tax payment reduces its present value.
Capital losses are tax deductible (to a certain extent), so investors should capture tax losses early.

55. The Fact on Loss Aversion
Research shows that
Individual investors are typically about 1.5 times more likely to sell a stock that has gone up in price then they are to sell a stock that has fallen in price.
With mutual funds, when investors choose to sell, they are more than 2.5 times as likely to sell a winning fund than a losing fund.
What does this all mean?
Investors tend to sell a winning stock too early, while they sell a losing stock too late!

56. Loss Aversion
Scenario One. Suppose we give you $1, Then, you have the following choice to make:
A. You can receive another $500 for sure.
B. You can flip a fair coin. If the coin-flip comes up “heads,” you get another $1,000, but if it comes up “tails,” you get nothing.
Scenario Two. Suppose we give you $2, Then, you have the following choice to make:
A. You can lose $500 for sure.
B. You can flip a fair coin. If the coin-flip comes up “heads,” you lose another $1,000, but if it comes up “tails,” you lose nothing.

57. 10.4 Individual Biases and Trading
Investor Attention, Mood, and Experience
Individual investors are not generally full-time traders
They have limited time and attention
More likely to buy stocks that have been in the news, advertised more, had very high trading volume, or recently had extreme (high or low) returns.
Investor mood affects investment behavior
Annualized market returns at the location of the stock exchange is higher on sunny days than on cloudy days.
Investors appear to put too much weight on their own experience rather than considering historical evidence
People who grow up and live during a time of high stock returns are more likely to invest in stocks.

58. Evidence Against Market Efficiency: The Day-of-the-Week Effect
The day-of-the-week effect refers to the tendency for Monday to have a negative average return—which is economically significant.
Interestingly, the effect is much stronger in the time period than in the time period.
The day-of-the-week effect exists in other markets (i.e., bonds) and it exists in stock markets outside the U.S.
It has defied explanation since it was discovered in the early 1980s.

59. Evidence Against Market Efficiency: The Amazing January Effect
Critics of market efficiency point to enormous gains to be had from simply investing in January and ask:
How can an efficient market have such unusual behavior?
Why don’t investor take advantage of this opportunity and thereby drive it out of existence?

60. Chapter Quiz
What is the relation between capital budgeting and the discounted free cash flow model?
What implicit assumptions do we make when valuing a firm using multiples based on comparable firms?
What are the implications of the efficient markets hypothesis for investors?
What are the implications of the efficient markets hypothesis for corporate managers?
What are several systematic behavioral biases that individual investors fall prey to?
Why would excessive trading lead to lower realized returns?