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CHAPTER FIFTEEN

DIVIDEND DISCOUNT MODELS

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CAPITALIZATION OF INCOME METHOD

• THE INTRINSIC VALUE OF A STOCK– represented by present value of the income

stream

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CAPITALIZATION OF INCOME METHOD

• formula

where

Ct = the expected cash flow

t = time

k = the discount rate

1 )1(ttk

CV

t

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CAPITALIZATION OF INCOME METHOD

• APPLICATION TO COMMON STOCK– substituting

determines the “true” value of one share

)1(...

)1()1( 22

11

k

D

k

D

k

DV

1 )1(tt

t

k

D

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CAPITALIZATION OF INCOME METHOD

• A COMPLICATION– the previous model assumes can forecast

dividends indefinitely– a forecasting formula can be written

Dt = Dt -1 ( 1 + g t )

where g t = the dividend growth rate

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THE ZERO GROWTH MODEL

• ASSUMPTIONS– the future dividends remain constant such that

D1 = D2 = D3 = D4 = . . . = DN

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THE ZERO GROWTH MODEL

• Applying to V

k

DV 1

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THE ZERO GROWTH MODEL

• Example– If Zinc Co. is expected to pay cash dividends of

$8 per share and the firm has a 10% required rate of return, what is the intrinsic value of the stock?

10.

8V

80 $

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THE ZERO GROWTH MODEL

• Example(continued)If the current market price is $65, the stock is

underpriced.

Recommendation:

BUY

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THE CONSTANT-GROWTH MODEL

• ASSUMPTIONS:

• growth rate in dividends is constant

• earnings per share is constant

• payout ratio is constant

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CONSTANT GROWTH MODEL

• In General

Dt = D0 (1 + g)t

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CONSTANT GROWTH MODEL

• Using the infinite property series,if k > g, then

gk

g

k

g

tt

t

1

)1(

)1(

1

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CONSTANT GROWTH MODEL

• since D1= D0 (1 + g)

gk

DV

1

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Constant Perpetual Growth Model Example

Suppose D(0) = $2; k = 12%; g = 6%.

D(1) = ($2.00 x 1.06) = $2.12

V(0) = $2.12 / (.12 - .06) = $35.33

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Constant Perpetual Growth• Advantage

– easy to compute

• Disadvantages– not usable for firms paying no dividends– not usable when g > k– sensitive to choice of g and k– k and g may be very difficult to estimate– constant perpetual growth is often unrealistic

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THE MULTIPLE-GROWTH MODEL

• ASSUMPTION:– future dividend growth is not constant

• Model Methodology– to find present value of forecast stream of

dividends– divide stream into parts (lifecycle stage)– each representing a different value for g

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THE MULTIPLE-GROWTH MODEL

• Finding PV of all forecast dividends paid after time t– next period dividend Dt+1 and all thereafter are

expected to grow at rate g

gkDV TT

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Two-Stage (any number) Dividend Growth Model

If you have two different growth rates, one for an early period and one for a later period, you would use the two-stage model

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Two-Stage Growth Model Example

Suppose D(0) = $2; k = 12%; g1 = 11%; g2 = 6%; and g1 continues for 4 years .

V(0) = $41.90

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Two-Stage Growth

• Advantage– allows for two different growth rates– g can be greater than k during period 1

• Disadvantages– not usable for firms paying no dividends– sensitive to choice of g and k– k and g may be difficult to estimate

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Estimating the Discount RateStart with the CAPM (covered later):

Discount rate =

Risk-free rate + (Stock beta x Market risk premium)

where:

Risk-free rate = U.S. T-bill rate, which is the wait component or time value of money.

Stock beta measures the individual stock’s risk relative to the market.

Market risk premium measures the difference in return between investing in the market and investing in T-bills.

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Discount Rate ExampleAssume T-bills yield 4.5%; KO’s beta is 1.15; and the

market risk premium = 8%

Discount rate = 4.5% + (1.15 x 8%) = 13.70%

Using the CPGM with D(0) = $2 and g = 6%:

V(0) = $2(1.06)/(.1370 - .06) = $27.53

What if the MRP were 9%?

DR = 4.5% + (1.15 x 9%) = 14.85%

V(0) = $2(1.06)/(.1485 - .06) = $23.95

What if g = 7%?

V(0) = $2(1.07)/(.1370 - .07) = $31.94

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MODELS BASED ON P/E RATIO

• PRICE-EARNINGS RATIO MODEL– Many investors prefer the earnings multiplier

approach since they feel they are ultimately entitled to receive a firm’s earnings

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MODELS BASED ON P/E RATIO

• PRICE-EARNINGS RATIO MODEL– EARNINGS MULTIPLIER:

= PRICE - EARNINGS RATIO

= Current Market Pricefollowing 12 month earnings

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PRICE-EARNINGS RATIO MODEL

• The P/E Ratio is a function of – the expected payout ratio ( D1 / E1 )

– the required return (k)– the expected growth rate of dividends (g)

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High vs. Low P/Es

• A high P/E ratio:– indicates positive expectations for the future of the

company

– means the stock is more expensive relative to earnings

– typically represents a successful and fast-growing company

• A low P/E ratio:– indicates negative expectations for the future of the

company

– may suggest that the stock is a better value or buy

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PRICE-EARNINGS RATIO MODEL

• The Model is derived from the Dividend Discount model:

gk

DP

1

0

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PRICE-EARNINGS RATIO MODEL

• Dividing by the coming year’s earnings

gk

ED

E

P

1

1

1

0

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SOURCES OF EARNINGS GROWTH

• What causes growth?• assume no new capital added

• retained earnings used to pay firm’s new investment

• If pt = the payout ratio in year t

• 1-pt = the retention ratio

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SOURCES OF EARNINGS GROWTH

• Growth rate depends on

– the retention ratio

– average return on equity

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Sustainable Growth RateUsing the sustainable growth rate to estimate g:

Sustainable growth rate = ROE x retention ratio

ROE = return on equity

ROE = net income / book equity

Payout ratio = Dividends per share / EPS

Retention ratio = 1 - payout ratio

Sustainable growth rate = ROE x (1 - Payout ratio)

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Sustainable Growth Rate Example

Assume ROE = 11%; EPS = $3.25; and D(0) = $2.00

SGR = .11 x (1 - 2.00/3.25) = 4.23%

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Price Ratio Analysis

• Price/Cash flow ratio– cash flow = net income + depreciation = cash flow

from operations or operating cash flow

• Price/Sales– current stock price divided by annual sales per

share