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Chapter 13

Equity Valuation

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Fundamental Stock Analysis: Models of Equity Valuation

Basic Types of ModelsBalance Sheet ModelsDividend Discount ModelsPrice/Earning Ratios

Estimating Growth Rates and Opportunities

3 3

Intrinsic Value and Market PriceIntrinsic Value

Self assigned ValueVariety of models are used for estimation

Market PriceConsensus value of all potential traders

Trading SignalIV > MP BuyIV < MP Sell or Short SellIV = MP Hold or Fairly Priced

444

Dividend Discount Models:General Model

VDk

ot

tt

=+=

¥

å( )11

V0 = Value of StockDt = Dividendk = required return

555

No Growth Model

VDk

o=

Stocks that have earnings and dividends that are expected to remain constant

Preferred Stock

666

No Growth Model: Example

E1 = D1 = $5.00

k = .15V0 = $5.00 / .15 = $33.33

VDk

o=

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Exercise in class

Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

888

Constant Growth Model

VoD gk g

o

=+-

( )1

g = constant perpetual growth rate

999

Constant Growth Model: Example

VoD gk g

o

=+-

( )1

E1 = $5.00 b = 40% k = 15%

g = 8%V0 = 3/(.15-.08) = 42.86.

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Exercise in class

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, how much should the stock be selling for?

111111

Estimating Dividend Growth Rates

g ROE b= ´

g = growth rate in dividendsROE = Return on Equity for the firmb = plowback or retention percentage rate

(1- dividend payout percentage rate)

121212

Shifting Growth Rate Model

V Dgk

D gk g k

o o

t

tt

TT

T=++

++

- +=å ( )

( )( )

( )( )11

11

1

1

2

2

g1 = first growth rate

g2 = second growth rate

T = number of periods of growth at g1

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Shifting Growth Rate Model: ExampleD0 = $2.00 g1 = 20% for 3years g2 = 5%

forever k = 15% T = 3 D1 = 2.40

D2 = 2.88 D3 = 3.46 D4 = 3.63

V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +

D4 / (.15 - .05) ( (1.15)3

V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

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Exercise in class

Suppose a firm is expected to increase dividends by 20% in one year and by 15% in the next two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

151515

Specified Holding Period Model

01

12

2

1 1 1V Dk

Dk

D Pk

N NN

= + ++

+ + +( ) ( ) ( )...

PN = the expected sales price for the stock at time N

N = the specified number of years the stock is expected to be held

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Exercise in class1. Gagliardi Way Corporation has an expected ROE of 15%. Its dividend growth rate will be

__________ if it follows a policy of paying 30% of earning in the form of dividends. A) 4.5% B) 10.5% C) 15.0% D) 30.0%

2. Rose Hill Trading Company is expected to have EPS in the upcoming year of $8.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its dividend in the upcoming year should be __________. A) $1.12 B) $1.44 C) $2.40 D) $5.60

3. Rose Hill Trading Company is expected to have EPS in the upcoming year of $6.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its intrinsic value should be __________. A) $20.93 B) $69.77 C) $128.57 D) $150.00

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Exercise in class4. Cache Creek Manufacturing Company is expected to pay a dividend of $3.36 in the upcoming year.

Dividends are expected to grow at 8% per year. The riskfree rate of return is 4% and the expected return on the market portfolio is 14%. Investors use the CAPM to compute the market capitalization rate, and the constant growth DDM to determine the value of the stock. The stock's current price is $84.00. Using the constant growth DDM, the market capitalization rate is __________. A) 9% B) 12% C) 14% D) 18%

5. Caribou Gold Mining Corporation is expected to pay a dividend of $6 in the upcoming year. Dividends are expected to decline at the rate of 3% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 13%. The stock of Caribou Gold Mining Corporation has a beta of -0.50. Using the constant growth DDM, the intrinsic value of the stock is __________. A) $50.00 B) $150.00 C) $200.00 D) $400.00

6. Lifecycle Motorcycle Company is expected to pay a dividend in year 1 of $2.00, a dividend in year 2 of $3.00, and a dividend in year 3 of $4.00. After year 3, dividends are expected to grow at the rate of 7% per year. An appropriate required return for the stock is 12%. Using the multistage DDM, the stock should be worth __________ today. A) $63.80 B) $65.13 C) $67.98 D) $85.60

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Partitioning Value: Growth and No Growth Components

VEk

PVGO

PVGOD g

k gEk

o

o

= +

=+

--

1

11( )( )

PVGO = Present Value of Growth OpportunitiesE1 = Earnings Per Share for period 1

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Partitioning Value: Example

ROE = 20% dy = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%

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V

NGV

PVGO

o

o

=-

=

= =

= - =

315 08

86

515

33

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

Partitioning Value: Example

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities

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Price Earnings RatiosP/E Ratios are a function of two factors

Required Rates of Return (k)Expected growth in Dividends

UsesRelative valuationExtensive Use in industry

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P/E Ratio: No expected growth

PEk

PE k

01

0

1

1

=

=

E1 - expected earnings for next yearE1 is equal to D1 under no growth

k - required rate of return

232323

P/E Ratio with Constant Growth

PD

k gE b

k b ROEPE

bk b ROE

01 1

0

1

1

1

=-

=-

- ´

=-

- ´

( )( )

( )

b = retention ration ROE = Return on Equity

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Numerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8

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Numerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%PE=?

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Example 223The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12%

and its expected EPS is $5.00. If the firm's plow-back ratio is 40%, its P/E ratio will be __________. A) 8.33 B) 11.54 C) 19.23 D) 50.00

Gagliardi Way Corporation has an expected ROE of 15%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A) 4.5% B) 10.5% C) 15.0% D) 30.0%

Brevik Builders has an expected ROE of 25%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A) 5.0% B) 15.0% C) 17.5% D) 45.0%

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Example 2223ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will

maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.

At what price would you expect ART to sell? A) $25.00 B) $34.29 C) $42.86 D) none of the above

At what P/E ratio would you expect ART to sell? A) 8.33 B) 11.43 C) 14.29 D) none of the above

What is the present value of growth opportunities for ART? A) $8.57 B) $9.29 C) $14.29 D) none of the above

What price do you expect ART shares to sell for in 4 years? ? A) $53.96 B) $44.95 C) $41.68 D) none of the above

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Pitfalls in Using PE Ratios

Flexibility in reporting makes choice of earnings difficult

Pro forma earnings may give a better measure of operating earnings

Problem of too much flexibility

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Other Valuation Ratios & Approaches

Price-to-bookPrice-to-cash flowPrice-to-salesPresent Value of Free Cash FlowResidual Income Model