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# CHAPTER 18 - PowerPoint PPT Presentation

CHAPTER 18. Equity Valuation. 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)

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CHAPTER 18

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## CHAPTER 18

Equity Valuation

### 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)

• IV > MP: underpriced, buy

• IV < MP: overpriced, sell

• IV = MP: fairly priced, hold

### 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:

### 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) = (52+4-48)/48 = 16.7%

• Step 2: calculate required return from CAPM

• required E(R) = 6 + 1.2(5) = 12

• Step 3: calculate alpha

• alpha = 16.7 – 12 = 4.7 > 0

• stock is undervalued

### 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 sellshort (overvalued)

• In market equilibrium, V0 = P0 (fairly priced)

• k is required return

### Determine underpriced/overpriced stocks (calculate intrinsic value)

• Previous example

• Vo = 50 > Po = 48, the current market price is undervalued compared with the intrinsic value

### Estimate intrinsic value

• Dividend discount model (DDM)

• P/E ratios approach

### One Period Example

• Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a \$2 dividend in one year and you believe that you can sell the stock for \$14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?

• Compute the PV of the expected cash flows

• Price = (14 + 2) / (1.2) = \$13.33

### Two Period Example

• Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of \$2.10 in two years and a stock price of \$14.70 at the end of year 2. Now how much would you be willing to pay?

• PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33

### Three Period Example

• Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of \$2.205 at the end of year 3 and the stock price is expected to be \$15.435. Now how much would you be willing to pay?

• PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33

### Developing The Model

• You could continue to push back when you would sell the stock

• You would find that the price of the stock is really just the present value of all expected future dividends

• So, how can we estimate all future dividend payments?

### 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

### Estimating Dividends: Special Cases

• Constant dividend

• The firm will pay a constant dividend forever

• This is like preferred stock

• The price is computed using the perpetuity formula

• Constant dividend growth

• The firm will increase the dividend by a constant percent every period

• Supernormal growth

• Dividend growth is not consistent initially, but settles down to constant growth eventually

### 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

### Dividend discount model (DDM): constant growth rate

• Constant growth model: dividend grows at a constant rate g

### 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

### Implications of constant growth DDM

• If expected dividend D1increases, then V0increases.

• If kdecreases, then V0increases.

• If gincreases, then V0increases.

• Price grows at the same rate as dividend

### 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

### 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)

### 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

### 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 = (109-100)/100 = 9%

### Plowback Ratio and Growth

Where:

ROE = Return on Equityb = Plowback Ratio

(or Earning Retention Ratio)

Example: g = 15% (0.6) = 9%

### 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)/(0.15-0.125) = 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 = 40 + 17.14

### Partitioning Value: Growth and No Growth Components

E

1

+

V

PVGO

=

o

k

+

D

(

1

g

)

E

1

o

=

-

PVGO

-

(

k

g

)

k

• PVGO = Present Value of Growth Opportunities

• E1 = Earnings Per Share for period 1

### 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?

### Partitioning Value: Example

• ROE = 20% d = 60% b = 40%

• E1 = \$5.00 D1 = \$3.00 k = 15%

• g = .20 x .40 = .08 or 8%

Partitioning Value: Example

3

=

=

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

### 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?

### 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)

### Shifting growth rate model (multistage growth model)

Changing growth rates:

temporary high

(or low) growth

permanent

constant growth

### 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?

### 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) / (.15 - .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

### 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

### P/E Ratio with Constant Growth

-

D

E

(

1

b

)

1

1

=

=

P

0

-

-

´

k

g

k

(

b

ROE

)

-

P

1

b

0

=

-

´

E

k

(

b

ROE

)

1

• b = retention ration

• ROE = Return on Equity

### 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

### P/E ratio and Risk

Holding everything equal:

High risk (k), Low P/E.

### 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.

### 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

### 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

### Free Cash Flow Approach

Discount the free cash flow for the firm

Discount rate is the firm’s cost of capital

Components of free cash flow

After tax EBIT

Depreciation

Capital expenditures

Increase in net working capital

### Comparing the Valuation Models

• In practice

• Values from these models may differ

• Analysts are always forced to make simplifying assumptions

### 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