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# Dividend Discount Model author: Dr. Jean Snavely - PowerPoint PPT Presentation

CHAPTER FIFTEEN. DIVIDEND DISCOUNT MODELS. CAPITALIZATION OF INCOME METHOD. THE INTRINSIC VALUE OF A STOCK represented by present value of the income stream. CAPITALIZATION OF INCOME METHOD. formula where C t = the expected cash flow t = time

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### CHAPTER FIFTEEN

DIVIDEND DISCOUNT MODELS

1

• THE INTRINSIC VALUE OF A STOCK

• represented by present value of the income stream

2

• formula

where

Ct = the expected cash flow

t = time

k = the discount rate

3

• APPLICATION TO COMMON STOCK

• substituting

determines the “true” value of one share

7

• 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

8

• ASSUMPTIONS

• the future dividends remain constant such that

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

9

• Applying to V

12

• 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?

13

• Example(continued)

If the current market price is \$65, the stock is underpriced.

Recommendation:

14

• ASSUMPTIONS:

• growth rate in dividends is constant

• earnings per share is constant

• payout ratio is constant

*

• In General

Dt = D0 (1 + g)t

16

• Using the infinite property series,

if k > g, then

18

• since D1= D0 (1 + g)

20

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

*

• easy to compute

• 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

*

• 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

21

• 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

23

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

*

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

V(0) = \$41.90

*

• allows for two different growth rates

• g can be greater than k during period 1

• not usable for firms paying no dividends

• sensitive to choice of g and k

• k and g may be difficult to estimate

*

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.

*

Assume 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

*

• PRICE-EARNINGS RATIO MODEL

• Many investors prefer the earnings multiplier approach since they feel they are ultimately entitled to receive a firm’s earnings

26

• PRICE-EARNINGS RATIO MODEL

• EARNINGS MULTIPLIER:

= PRICE - EARNINGS RATIO

= Current Market Price

following 12 month earnings

27

• 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)

30

• 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

*

• The Model is derived from the Dividend Discount model:

28

• Dividing by the coming year’s earnings

29

• What causes growth?

• assume no new capital added

• retained earnings used to pay firm’s new investment

• Ifpt = the payout ratio in year t

• 1-pt = the retention ratio

35

• Growth rate depends on

• the retention ratio

• average return on equity

42

Using 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)

*

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

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

*

• 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

*