1. Chapter 13 Equity Valuation
Describes the financial instruments traded in primary and secondary markets.
Discusses Market indexes. Discusses options and futures. 1

2. 13.1 Valuation by Comparables
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3. Fundamental Stock Analysis: Models of Equity Valuation
Basic Types of Models
Balance Sheet Models
Dividend Discount Models
Price/Earnings Ratios
Free Cash Flow Models
All are covered in the PPT
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4. Models of Equity Valuation
Valuation models using comparables
Look at the relationship between price and various determinants of value for similar firms
The internet provides a convenient way to access firm data. Some examples are:
EDGAR
Finance.yahoo.com
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5. Table 13.1 Microsoft Corporation Financial Highlights 2009
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6. Valuation Methods Book value
Value of common equity on the balance sheet
Based on historical values of assets and liabilities, which may not reflect current values
Some assets such as brand name or specialized skills are not on a balance sheet
Is book value a floor value for market value of equity?
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7. Valuation Methods Market value
Current market value of assets minus current market value of liabilities
Market value of assets may be difficult to ascertain
Market value based on stock price
Better measure than book value of the worth of the stock to the investor.
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8. Valuation Methods (Other Measures)
Liquidation value
Net amount realized from sale of assets and paying off all debt
Firm becomes a takeover target if market value stock falls below this amount, so liquidation value may serve as floor to value
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9. Valuation Methods (Other Measures)
Replacement cost
Replacement cost of the assets less the liabilities
May put a ceiling on market value in the long run because values above replacement cost will attract new entrants into the market.
Tobin’s Q = Market Value / Replacement Cost; should tend toward 1 over time.
Tobin’s Q varies between 1 and 1.5
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10. 13.2 Intrinsic Value Versus Market Price
These are methods of estimating cash flows rather than balance sheet quantities.
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11. Expected Holding Period Return
The return on a stock investment comprises cash dividends and capital gains or losses
Assuming a one-year holding period
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12. Required Return CAPM gave us required return, call it k:
k = market capitalization rate
If the stock is priced correctly
Required return should equal expected return =
A lot of corporate work uses k for return on equity
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13. Intrinsic Value Intrinsic Value
The present value of a firm’s expected future net cash flows discounted by a risk adjusted required rate of return.
The cash flows on a stock are?
Dividends (Dt)
Sale price (Pt)
Intrinsic Value today (time 0) is denoted V0 and for a one year holding period may be found as:
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14. Intrinsic Value and Market Price
Consensus value of all traders
In equilibrium the current market price will equal intrinsic value
Trading Signals
If V0 > P0
If V0 < P0
If V0 = P0
Buy
Sell or Short Sell
Hold as it is Fairly Priced
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15. 13.3 Dividend Discount Models
For now assume price = intrinsic value
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16. Basic Dividend Discount Model
Intrinsic value of a stock can be found from the following:
What happened to the expected sale price in this formula?
Why is this an infinite sum?
Is stock price independent of the investor’s holding period?
V0 = Intrinsic Value of Stock
Dt = Dividend in time t
k = required return
What happened to the expected sale price in this formula?
The expected sale price is simply the present value at that point in time of all future dividends.
Why is this an infinite sum? Because stocks are infinitely lived.
Is stock price independent of the investor’s holding period?
Yes, and this is a crucial point. Many uninitiated believe that because of the growth of day traders, and rapid stock trading that stock prices are determined based on short term prospects of the firm. If this model is correct, then this conclusion is untrue. We have had large scale failures in corporate governance and reward systems that promoted short term thinking by managers.
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17. Basic Dividend Discount Model
Intrinsic value of a stock can be found from the following:
This equation is not useable because it is an infinite sum of variable cash flows.
Therefore we have to make assumptions about the dividends to make the model tractable.
V0 = Intrinsic Value of Stock
Dt = Dividend in time t
k = required return
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18. No Growth Model
Use: Stocks that have earnings and dividends that are expected to remain constant over time (zero growth)
Preferred Stock
A preferred stock pays a $2.00 per share dividend and the stock has a required return of 10%. What is the most you should be willing to pay for the stock?
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19. Constant Growth Model
Use: Stocks that have earnings and dividends that are expected to grow at a constant rate forever
A common stock share just paid a $2.00 per share dividend and the stock has a required return of 10%. Dividends are expected to grow at 6% per year forever. What is the most you should be willing to pay for the stock?
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20. Comparing Value and Returns
Why do you have to pay more for the constant growth stock?
Must pay for expected growth
What is the one year rate of return for each stock?
No Growth Stock
V0 = $20.00
D = $2.00
V1 =
Constant Growth Stock
V0 = $53.00; D0 = $2.00
Point is that both stocks give an investor a 10% (pre-tax) return.
Note that V1 can be found more easily as V0 x (1+g) = $53 x 1.06 = $56.18, also k = D1/P0 + g, as long as there is only one constant growth rate
$2.00 / 0.10 = $20.00
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21. Comparing Value and Returns
Both stocks given an investor a pre-tax return of 10%.
Is one stock a better buy than the other?
Not if both are actually priced at their intrinsic value (ignoring taxes).
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22. Stock Prices and Investment Opportunities
g = growth rate in dividends is a function of two variables:
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)
g increases if a firm increases its retention ratio and/or its ROE
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23. Value of Growth Opportunities
Value with 100% dividend payout
Cash Cow, Inc. (CC)
E1 = $5
D1 = $5
b = ; therefore g =
k = 12.5% ; Find VCC
ROE = 12.5%
Growth Prospects (GP)
E1 = $5
D1 = $5
b = 0; therefore g = 0
k = 12.5%, Find VGP
ROE = 15%
You can relate these two to the prior chapter. The cash cow is a mature firm without high ROI investments. The growth firm may be in the growth phase of the industry life cycle.
Should either or both firms retain some earnings?
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24. Value of Growth Opportunities
Value with 40% dividend payout
Cash Cow, Inc. (CC)
E1 = $5
b = 60%; therefore g
D1 = 0.40 x $5 = $2.00
k = 12.5%; Find VCC
ROE = 12.5%
CC value is the same, why?
Growth Prospects (GP) E1 = $5 b = 60%; therefore g = 9% D1 = 0.40 x $5 = $2.00 k = 12.5%; Find VGP ROE = 15% GP Value has increased, why?
7.5%
g = ROE x b, For CC g = 12.5 x 0.60 = 7.5%; For GP g = 15% x 0.60 = 9%
CC value stays the same because the retained earnings is invested at the same rate as ROE, there is no economic value added. GP grows in value by retaining earnings because the funds are invested at a 15% return. CC should pay out all earnings as dividends and let investors choose where to put their money (in the absence of taxes) and GP should retain a sufficient amount of their earnings to fund all projects where the ROE > k.
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25. Value of Growth Opportunities
Value of assets in place for GP = $40.00 (value with all dividends paid out, with ROE = 12.5%) Value of growth opportunities with ROE = 15% may be inferred from the difference between the new VGP = $57.14 and the no growth value of $40.00 Thus the present value of growth opportunities (PVGO) = $ $40.00 = $17.14
Note that the PVGO equation is the intrinsic value at the current dividend policy of 40% payout, less the value of the firm under the old dividend policy of 100% payout. Note that in the latter case E1 = D1 so we can replace the D with the E.
In general:
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26. Figure 13.1 Dividend Growth for Two Earnings Reinvestment Policies
(for a given ROE)
High reinvestment increases stock price only if ROE > k
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27. Multistage Growth Models
As firms progress through their industry life cycle, earnings and dividend growth rates (ROE) are likely to change.
A two stage growth model:
g1 = first growth rate
g2 = second growth rate
T = number of periods of growth at g1
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28. Multistage Growth Rate Model: Example
D0 = $ g1 = 20% g2 = 5%
k = 15% T = 3
D1 = D2 = D3 = D4 = 3.63
V0 = = $30.40
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29. Table 13.2 Financial Ratios
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30. Figure 13.2 Honda Motor
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31. Two Stage DDM for Honda
Year
Dividend
2009
0.90
2010
0.98
2011
1.06
2012
1.15
From Value Line
Dividends: Assume the dividend growth rate will be steady beyond Value Line forecasts b = 70% and ROE of 11.0%. What should be the long term growth rate?
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32. Two Stage DDM for Honda
The required rate of return: Honda = 1.05 Rf in 2008 = 3.5% Market risk premium = historical average of 8%
From Value Line
The market risk premium is assumed to equal the historical average.
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33. Two Stage DDM for Honda
Year
Dividend
2009
0.90
2010
0.98
2011
1.06
2012
1.15
k = 11.90% g = 7.70% Find the intrinsic value Value Line reported the actual price = $21.37, so Honda was undervalued by $0.51 or about 2.4%.
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34. Two Stage DDM for Honda
Should we trust the valuation result? What if the beta is slightly incorrect, suppose it is 1.10 (< 5% error) rather than 1.05? Now k = 12.3% and the intrinsic value estimate V0= $19.98, reversing our conclusion that Honda is undervalued
Year
Dividend
2009
0.90
2010
0.98
2011
1.06
2012
1.15
Actual price = $21.37
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35. 13.4 Price-Earnings (P/E) Ratios
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36. P/E Ratio and Growth Opportunities
P/E Ratios are a function of two factors
Required Rates of Return (k) (inverse relationship)
Expected Growth in Dividends (direct relationship)
Uses
Estimate intrinsic value of stocks
Conceptually equivalent to the constant growth DDM
Extensively used by analysts and investors
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37. P/E, ROE and Growth
With positive growth: With zero growth: If g = 0 then b should = 0 and the ratio simplifies to:
Are the elements of the P/E ratio similar to the constant growth DDM?
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38. Numerical Example: No Growth
E1 = $ g = 0 k = 12.5%; Find P/E and V0
P/E = 1/k = 1/.125 = 8
V0 = P/E x E1 = 8 x $2.50 = $20.00
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39. Numerical Example with Growth
b = 60% ROE = 15%; k = 12.5% (1-b) = 40%, E0 = $2.50
Find the P/E and V0:
g = ROE x b = 15% x 60% = 9%
E1 = $2.50 (1.09) = $2.725
P/E = ( ) / ( ) = 11.4
V0 = P/E x E1 = 11.4 x $2.73 = $31.14
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40. ROE and b and growth and P/E
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41. P/E Ratios and Stock Risk
Riskier firms will have higher required rates of return (higher values of k)
Riskier stocks will have lower P/E multiples
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42. Pitfalls in Using P/E Ratios
Earnings management is a serious problem,
P/E should be calculated using pro forma earnings,
A high P/E implies high expected growth, but not necessarily high stock returns,
Simplistic, assumes the future P/E will not be lower than the current P/E. If expected growth in earnings fails to materialize the P/E will fall and investors may incur large losses.
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43. Figure 13.3 P/E Ratios and Inflation
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44. Figure 13.4 Earnings Growth for Two Companies
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45. Figure 13.5 Price-Earnings Ratios
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46. Figure 13.6 P/E Ratios 
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47. Other Comparative Valuation Ratios
Price-to-book
High ratio indicates a large premium over book value, and a ‘floor’ value that is often far below market price
Price-to-cash flow
P/Cash Flow instead of P/E; less subject to accounting manipulation
Price-to-sales
Useful for firms with low or negative earnings in early growth stage
Be creative
Be creative: Need to know the key variable(s) in an industry. For example, hits on a web page for some Internet firms, then can compare price/hits ratio.
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48. Figure 13.7 Valuation Ratios for the S&P 500
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49. 13.5 Free Cash Flow Valuation Approaches
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50. Free Cash Flow
Capitalize or discount the free cash flow for the firm (FCFF) at the weighted-average cost of capital and then subtract the existing (market) value of debt
Useful for firms that don’t pay dividends,
Helpful to understand sources and uses of cash
where:
EBIT = earnings before interest and taxes
Tc = the corporate tax rate
NWC = net working capital
If your students used the Ross, Westerfield and Jordan Fundamentals or Essentials of Corporate Finance texts for their introductory corporate course, you can remind them that the FCFF measure is Cash Flow From Assets (CFA) in that text.
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51. FCFF, Firm Value & Equity Value
The free cash flow methods discount year to year cash flows plus some estimate of the terminal value PT where WACC = Weighted average cost of capital g = estimate of long run growth in free cash flow T = time period when the firm approaches constant growth Equity value =
Firm Value
Firm Value – Market Value of Debt
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52. Free Cash Flow (cont.)
Another approach calculates the free cash flow to the equity holders (FCFE) and discounts the cash flows directly at the cost of equity, kE.
Equity value can then be estimated as:
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53. FCF Valuation Example
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54. Comparing the Valuation Models
In theory free cash flow approaches should provide the same estimate of intrinsic value as the dividend growth model
In practice the various approaches often differ substantially
Simplifying assumptions are used in all models
The models establish ranges of likely intrinsic value
Using multiple models forces rigorous thinking about the inputs
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55. 13.6 The Aggregate Stock Market
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56. Earnings Multiplier Approach
Forecast corporate profits for the coming period for an index such as the S&P 500.
Derive an estimate for the aggregate P/E ratio using long-term interest rates
Based on the relationship between the ‘earnings yield’ or E/P ratio for the S&P 500 and the yield on 10 year Treasuries
Product of the two forecasts is the estimate of the end-of-period level of the market
The text states that this is the most popular approach to aggregate market forecasting
Aggregate corporate profit forecasts are available from Standard & Poor’s, among others
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57. Figure 13.8 Earnings Yield of the S&P 500 Versus 10-year Treasury Bond Yield
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58. Earnings Multiplier Approach
2009 Data: Starting S&P500 level = 900 Treasury yield = 3.2% Implied Earnings Yield = 2.5% + 3.2% = 5.7% If E/P = 5.7% then P/E = 1 / = If forecast EPS = $55 what is the expected forecast for the S&P500 one year later and the % gain or loss?
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59. Table 13.4 S&P 500 Index Forecasts
An analyst should not rely on a point estimate. Table 13.4 includes a simple scenario analysis.
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