1. Equity Valuation
CHAPTER 12

2. Fundamental analysis
Identify stocks that are mispriced relative to true value
Compare the actual market price and the true price estimated from various models using publicly available information
The true price estimated from models is the intrinsic value (IV)
Market price (MP): consensus value of all potential trades (buyers and sellers)
Trading signal
IV > MP: underpriced, buy
IV < MP: overpriced, sell
IV = MP: fairly priced, hold

3. Determine underpriced/overpriced stocks (calculate alpha)
If estimated E(r) > Required Return, the stock is undervalued.
If estimated E(r) < required return, the stock is overvalued
required return is from a pricing model, e.g. CAPM:

4. Determine underpriced/overpriced stocks (calculate alpha)
example: stock ABC, the current price Po = 48, expected price in 1 year E(P1) = 52, expected dividend in 1 year E(D1) = 4
rf = 6, RPm = 5, beta = 1.2
Is this stock overpriced or underpriced?
Step 1: calculate the estimated expected return
estimated E(R) = ( )/48 = 16.7%
Step 2: calculate required return from CAPM
required E(R) = (5) = 12
Step 3: calculate alpha
alpha = 16.7 – 12 = 4.7 > 0
stock is undervalued

5. Determine underpriced/overpriced stocks (calculate intrinsic value)
Intrinsic value --The present value of a firm’s expected future net cash flows discounted by the required rate of return.
V0 (intrinsic value) > P0 (market price) Þ buy (undervalued)
V0 (intrinsic value) < P0 (market price) Þ sell or sell short (overvalued)
In market equilibrium, V0 = P0 (fairly priced)
k is required return

6. Determine underpriced/overpriced stocks (calculate intrinsic value)
Previous example
Vo = 50 > Po = 48, the current market price is undervalued compared with the intrinsic value

7. Estimate intrinsic value
Dividend discount model (DDM)
P/E ratios approach

8. Dividend discount model (DDM)
Dividend discount model (infinite horizon):
the intrinsic value is the present value of all futures dividends discounted by the required return
go on forever

9. Dividend discount model (DDM)
No growth model: The same amount of dividend every year (perpetuity)
Example: a preferred stock, D = 5, required return k = 15%. What is the value of this stock
Vo = 5/.15 = 33.33

10. Dividend discount model (DDM): constant growth rate
Constant growth model: dividend grows at a constant rate g

11. Dividend discount model (DDM): constant growth rate
Example 1: stock ABC, next year dividend = 3, required return k = 15%, constant growth rate = 8%. What is the value of the stock
Example 2: stock ABC, just paid dividend = 0.50, required return k = 15%, constant growth rate = 2%. What is the value of the stock

12. Implications of constant growth DDM
If expected dividend D1 increases, then V0 increases.
If k decreases, then V0 increases.
If g increases, then V0 increases.
Price grows at the same rate as dividend

13. Implications of constant growth DDM
Required return k:
In equilibrium, the intrinsic value = market price i.e. Vo = Po, therefore,
Dividend
Yield
Capital
Gains Yield

14. Estimate growth rate g Company A: 2 scenarios
No investment opportunities: the expected return of all projects in the company < required return k. In this case, the company would choose to pay 100% of the earning as dividends and let the stockholders invest in the market by themselves
Has investment opportunities: if the company has investment opportunity, expected return of projects is higher than required return k, then the company would choose low dividend payout policy, (a smaller fraction of earning goes to dividend) say
40% dividend (dividend payout ratio)
60% retained earning to be used for reinvestment (plow-back ratio or earning retention ratio)

15. Dividend Payout Ratio and Plowback Ratio
Dividend Payout Ratio: Percentage of earnings paid out as dividends
Plowback (or Earning Retention) Ratio:
Fraction of earnings retained and reinvested in the firm

16. Estimate growth rate g
Company A, total asset 100 mil, all equity financed. ROE = 15%.
Total earning = 15% (100) = 15 mil
If 60% of earning is reinvested, new additional capital is 60%(15) = 9 mil
Old capital = 100, new capital = 9, total capital = 109
Growth rate g is the growth rate in value of capital (stock)
g = ( )/100 = 9%

17. Plowback Ratio and Growth
Where:
ROE = Return on Equity b = Plowback Ratio
(or Earning Retention Ratio)
Example: g = 15% (0.6) = 9%

18. Partitioning value
Example, Company A, expected earning E1=5, k = 12.5%
No growth: pay all earnings as dividend, D = 5
With growth: ROE = 15%, b = 0.6 so g = ?
No growth: P*0= E1/k = D/k = 40
with growth: P0 = D1/(k-g) = 5(.4)/( ) = 57.14
Why the price with growth is higher than the price with no growth?
Price (with growth) = P*0 (no growth) + PVGO (present value of growth opportunities)
PVGO is reward to growth opportunities
57.14 =

19. Partitioning Value: Growth and No Growth Components1 V +
PVGO o = k D ( 1 + g ) E o 1 = -
PVGO - ( k g ) k
PVGO = Present Value of Growth Opportunities
E1 = Earnings Per Share for period 1

20. Partitioning Value: Growth and No Growth Components
Example: Takeover Target has a dividend payout ratio of 60% and an ROE of 20%. If it expects earnings to be $ 5 per share, the appropriate capitalization rate is 15%? What is the intrinsic value, what is PVGO, what is NGVo?

21. Partitioning Value: Example
ROE = 20% d = 60% b = 40%
E1 = $5.00 D1 = $3.00 k = 15%
g = .20 x .40 = .08 or 8%

22. Partitioning Value: Example3 V = =
$42 . 86 o (. 15 - . 08 ) 5
NGV = =
$33 . 33 o . 15
PVGO =
$42 . 86 -
$33 . 33 = $9 . 52
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities

23. Growth opportunity: another example
Takeover Target is run by entrenched management that insists on reinvesting 60% of its earnings in projects that provide an ROE of 10% despite the fact that the firm’s required return k = 15%. The firm’s next year dividend = $2 per share, paid out of earnings of $5 per share. At what price should the firm sell? what is the present value of growth opportunities? Can we increase the firm’s value?

24. Shifting growth rate model (multistage growth model)
In constant growth DDM, g is constant over time
In practice, there are some periods g is high (when more investment opportunities), some periods g is low (when less investment opportunities)

25. Shifting growth rate model (multistage growth model)
Changing growth rates:
temporary high
(or low) growth
permanent
constant growth

26. Shifting growth rate model (multistage growth model)
Example: Whitewater Rapids Company is expected to have dividends grow at a rate of 20% for the next three years. In three years, the dividends will settle down to a more sustainable growth rate of 5% which is expected to last “forever.” If Whitewater just paid a dividend of $2.00 and its level of risk requires a discount rate of 15%, what is the intrinsic value of Whitewater stock?

27. Shifting growth rate model (multistage growth model)
Compute the dividends until growth levels off
D1 = 2(1.2) = $2.40
D2 = 2.4(1.2) = $2.88
D3 = 2.88(1.2) = $3.46
Find the expected future price at the year growth leves off
P3 = D3(1+g) / (k – g) = 3.46(1.05) / ( ) = 36.3
Find the intrinsic value which is the present value of the all expected future cash flows
V0 = 2.4 / (1.15) + (2.88) / (1.15)2 + (3.46) / (1.15)3
+ (36.3) / (1.15)3 = 30.40

28. Price-Earning (P/E) Ratios
Ratio of Stock price to its earnings per share
Useful for firm valuation:
in practice
Forecasts of E
Forecasts of P/E

29. Price-Earning (P/E) Ratios and growth

30. P/E Ratio with Constant GrowthD E ( 1 - b ) 1 1 P = = k - g k - ( b
ROE ) P 1 - b = E k - ( b
ROE ) 1
b = retention ration
ROE = Return on Equity

31. Price-Earning (P/E) Ratio
Plowback ratio (b) (k = 12%)
0.25
0.50
0.75
A. Growth rate g
ROE 10
2.5 5
7.5 12 3 6 9 14
3.5 7
10.5
B. P/E ratio
8.33
7.89
7.14
5.56
8.82
10.00
16.67

32. Some comments with P/E Ratios
High plowback ratio (b) High Growth Rate (g) (g = ROE*b)
BUT
High g (if due to high b) High P/E ratio
higher b higher P/E only when ROE > k

33. P/E ratio and Risk
Holding everything equal:
High risk (k), Low P/E.

34. P/E ratios in practice
P/E ratio proxies for expected growth in dividends or earnings.
If the stock is correctly priced, the rule of thumb is
P/E ≈ g or PEG ≈ 1
PEG > 1 then overpriced
PEG < 1 then underpriced
PEG: no theoretical explanation but works very well
Peter Lynch, the famous portfolio manager, said in this book One Up on Wall Street
The P/E ratio of any company that is fairly priced will equal its growth rate. I am talking here about growth rate of earnings.... If the P/E ratio of Coca-Cola is 15, you’d expect the company to be growing at 15% per year, etc. But if the P/E ratio is less than the growth rate, you may have found yourself a bargain.

35. Pitfalls in P/E Analysis
Earnings are based on accounting data
Current price and current earnings
Future expected earnings is more appropriate
In P/E formula, E is an expected trend
In financial pages, E is the actual past period's earnings
Different accounting methods will give different earnings

36. Other Valuation Ratios & Approaches
Price-to-book: price per share/book value per share
How aggressively the market values the firm
Price-to-cash flow: price per share/cash flow per share
Price-to-sales: price per share/sales per share
Some start-up firms do not have earnings so sale is more appropriate.
Be creative: depending on particular situation to design your own ratio

38. Summary Valuation approaches: Balance sheet values (P/E ratio)
-Present value of expected future dividends
DDM states that the price of a share of stock is equal to the present value of all future dividends discounted at the appropriate required rate of return
Constant growth model DDM:
P/E ratio is an indication of the firm's future
growth opportunities