5 desg 05-2 stocks ddm

8/13/2019 5 Desg 05-2 Stocks Ddm

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FINANCE5. Stock valuation - DDM

Professor Andr Farber

Solvay Business SchoolUniversit Libre de BruxellesFall 2006


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MBA 2006 DDM | 2

Stock Valuation

Objectives for this session :1. Introduce the dividend discount model (DDM)2. Understand the sources of dividend growth3. Analyse growth opportunities

4. Examine why Price-Earnings ratios vary across firms5. Introduce free cash flow model (FCFM)


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MBA 2006 DDM | 3

DDM: one-year holding period

Review: valuing a 1-year 4% coupon bond Face value: 50 Coupon: 2 Interest rate 5%

How much would you be ready to pay for a stock with the followingcharacteristics:

Expected dividend next year: 2 Expected price next year: 50

Looks like the previous problem. But one crucial difference: Next year dividend and next year price are expectations, the realized

price might be very different. Buying the stock involves some risk.The discount rate should be higher.

Bond price P 0 = (50+2)/1.05 = 49.52


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MBA 2006 DDM | 4

Dividend Discount Model (DDM): 1-yearhorizon

1-year valuation formula

Back to example. Assume r = 10%

r P div

P 1

110

27.4710.01502

0 P

Expected price

r = expected return on shareholders'equity= Risk-free interest rate + risk premium

Dividend yield = 2/47.27 = 4.23%

Rate of capital gain = (50 47.27)/47.27 = 5.77%


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MBA 2006 DDM | 5

DDM: where does the expected stock pricecome from?

Expected price at forecasting horizon depends on expected dividends andexpected prices beyond forecasting horizon

To find P 2, use 1-year valuation formula again:

Current price can be expressed as:

General formula:

r P div

P 1

221

22

221

0 )1()1(1 r P

r div

r div

P

T T

T T

r P

r div

r div

r div

P )1()1(

...)1(1 2

210


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MBA 2006 DDM | 6

DDM - general formula

With infinite forecasting horizon:

Forecasting dividends up to infinity is not an easy task. So, in practice,simplified versions of this general formula are used. One widely usedformula is the Gordon Growth Model base on the assumption thatdividends grow at a constant rate.

DDM with constant growth g

Note: g < r

...)1(

...)1()1()1( 3

32

210

t

t

r

div

r

div

r

div

r

div P

g r

div

P 1

0


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MBA 2006 DDM | 7

DDM with constant growth : example

Year Dividend DiscFac Price

0 100.00

1 6.00 0.9091 104.00

2 6.24 0.8264 108.16

3 6.49 0.7513 112.49

4 6.75 0.6830 116.99

5 7.02 0.6209 121.67

6 7.30 0.5645 126.53

7 7.59 0.5132 131.59

8 7.90 0.4665 136.869 8.21 0.4241 142.33

10 8.54 0.3855 148.02

Data Next dividend: 6.00Div.growth rate: 4%Discount rate: 10%

P 0= 6/(.10-.04)


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MBA 2006 DDM | 8

Differential growth

Suppose that r = 10% You have the following data:

P 3 = 3.02 / (0.10 0.05) = 60.48

Year 1 2 3 4 to

Dividend 2 2.40 2.88 3.02

Growth rate 20% 20% 5%

40.51)10.1(

48.60)10.1(

88.2)10.1(

40.210.12

3320 P


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MBA 2006 DDM | 9

A formula for g

Dividend are paid out of earnings: Dividend = Earnings Payout ratio

Payout ratios of dividend paying companies tend to be stable. Growth rate of dividend g = Growth rate of earnings

Earnings increase because companies invest. Net investment = Retained earnings Growth rate of earnings is a function of:

Retention ratio = 1 Payout ratio Return on Retained Earnings

g = (Return on Retained Earnings) (Retention Ratio)


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MBA 2006 DDM | 10

Example

Data: Expected earnings per share year 1: EPS 1 = 10 Payout ratio : 60% Required rate of return r : 10%

Return on Retained Earnings RORE : 15% Valuation: Expected dividend per share next year: div1 = 10 60% = 6 Retention Ratio = 1 60% = 40% Growth rate of dividend g = (40%) (15%) = 6%

Current stock price: P 0 = 6 / (0.10 0.06) = 150


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MBA 2006 DDM | 11

Return on Retained Earnings and Debt

Net investment = Total Asset For a levered firm:

Total Asset = Stockholders equity + Debt RORE is a function of:

Return on net investment (RONI) Leverage ( L = D/ SE)

RORE = RONI + [RONI i (1-T C )] L


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MBA 2006 DDM | 12

Growth model: example

Dep/TotAsset 10%TaxRate 40%

Year 0 1 2 3 4 to infinityPayout 60% 60% 60% 100%RORE 25% 20% 15% 15%

Depreciation 100.00 116.00 133.60 152.61 Net Income 400.00 440.00 475.20 503.71Dividend 240.00 264.00 285.12 503.71

Cfop 500.00 556.00 608.80 656.32Cfinv -260.00 -292.00 -323.68 -152.61

Cffin -240.00 -264.00 -285.12 -503.71Change in cash 0.00 0.00 0.00 0.00

Total Assets 1,000.00 1,160.00 1,336.00 1,526.08 1,526.08Book Equity 1,000.00 1,160.00 1,336.00 1,526.08 1,526.08


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MBA 2006 DDM | 13

Valuing the company

Assume discount rate r = 15% Step 1: calculate terminal value

As Earnings = Dividend from year 4 on V 3 = 503.71/15% = 3,358

Step 2: discount expected dividends and terminal value

78.803,2)15.1(08.358,3

)15.1(12.285

)15.1(264

15.1240

3320 V


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MBA 2006 DDM | 14

Valuing Growth Opportunities

Consider the data: Expected earnings per share next year EPS 1 = 10 Required rate of return r = 10%

Why is A more valuable than B or C? Why do B and C have same value in spite of different investment policies

Cy A Cy B Cy C

Payout ratio 60% 60% 100%Return on Retained Earnings 15% 10% -

Next years dividend 6 6 10

g 6% 4% 0%

Price per share P 0 150 100 100


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MBA 2006 DDM | 15

NPVGO

Cy C is a cash cow company Earnings = Dividend (Payout = 1) No net investment

Cy B does not create value Dividend < Earnings, Payout 0 But: Return on Retained Earnings = Cost of capital NPV of net investment = 0

Cy A is a growth stock Return on Retained Earnings > Cost of capital

Net investment creates value (NPV>0) Net Present Value of Growth Opportunities (NPVGO) NPVGO = P 0 EPS 1/r = 150 100 = 50


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Source of NPVG0 ?

Additional value if the firm retains earnings in order to fund new projects

where PV(NPV t ) represent the present value at time 0 of the net presentvalue (calculated at time t) of a future investment at time t

In previous example:Year 1: EPS 1 = 10 div1 = 6 Net investment = 4

EPS = 4 * 15% = 0.60 (a permanent increase)

NPV 1 = -4 + 0.60/0.10 = +2 (in year 1)PV(NPV 1) = 2/1.10 = 1.82

.. .)()()( 3210 NPV PV NPV PV NPV PV r EPS

P


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MBA 2006 DDM | 17

NPVGO: details

P0 150.00 Y1 to Y25 30.19PV g = 0 100.00 Y26 to 50 11.96

NPVGO 50.00 Y51 to 75 4.74Y76 to 100 1.88

Year EPS1 EPS t Net Inv. EPS NPV PV(NPV)1 10.00 10.00 4.00 0.60 2.00 1.822 10.00 10.60 4.24 0.64 2.12 1.753 10.00 11.24 4.49 0.67 2.25 1.69

4 10.00 11.91 4.76 0.71 2.38 1.635 10.00 12.62 5.05 0.76 2.52 1.576 10.00 13.38 5.35 0.80 2.68 1.517 10.00 14.19 5.67 0.85 2.84 1.468 10.00 15.04 6.01 0.90 3.01 1.409 10.00 15.94 6.38 0.96 3.19 1.35

10 10.00 16.89 6.76 1.01 3.38 1.3011 10.00 17.91 7.16 1.07 3.58 1.2612 10.00 18.98 7.59 1.14 3.80 1.2113 10.00 20.12 8.05 1.21 4.02 1.1714 10.00 21.33 8.53 1.28 4.27 1.1215 10.00 22.61 9.04 1.36 4.52 1.0816 10.00 23.97 9.59 1.44 4.79 1.0417 10.00 25.40 10.16 1.52 5.08 1.0118 10.00 26.93 10.77 1.62 5.39 0.9719 10.00 28.54 11.42 1.71 5.71 0.9320 10.00 30.26 12.10 1.82 6.05 0.90


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What Do Price-Earnings Ratios mean?

Definition: P/E = Stock price / Earnings per share Why do P/E vary across firms? As: P 0 = EPS/r + NPVGO

Three factors explain P/E ratios: Accounting methods:

Accounting conventions vary across countries The expected return on shareholdersequity

Risky companies should have low P/E

Growth opportunities

EPS NPVGO

r E P

1/


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Beyond DDM: The Free Cash Flow Model

Consider an all equity firm. If the company:

Does not use external financing (not stock issue, # shares constant) Does not accumulate cash (no change in cash)

Then, from the cash flow statement: Free cash flow = Dividend CF from operation Investment = Dividend

Company financially constrained by CF from operation If external financing is a possibility:

Free cash flow = Dividend Stock Issue

Market value of company = PV(Free Cash Flows)

5 desg 05-2 stocks ddm

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