FINANCE6. Stock valuation - FCFM

Professor André Farber

Solvay Business SchoolUniversité Libre de BruxellesFall 2006

MBA 2006 FCFM |2

Stock Valuation

• Objectives for this session :

1. Review the dividend discount model (DDM)

2. Understand the sources of dividend growth

3. Analyse growth opportunities

4. Examine why Price-Earnings ratios vary across firms

5. Introduce free cash flow model (FCFM)

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Dividend Discount Model

• General formula:

• r is the required return

• Constant growth model

TT

TT

r

P

r

div

r

div

r

divP

)1()1(...

)1(1 221

0

gr

divP

1

0

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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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NPVGO

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

• where PV(NPVt) is the present value at time 0 of the net present value (calculated at time t) of a future investment at time t

...)()()( 3210 NPVPVNPVPVNPVPVr

EPSP

MBA 2006 FCFM |6

What Do Price-Earnings Ratios mean?

• Definition: P/E = Stock price / Earnings per share

• Why do P/E vary across firms?

• As: P0 = EPS/r + NPVGO

• Three factors explain P/E ratios:

• Accounting methods:

– Accounting conventions vary across countries

• The expected return on shareholders’equity

– Risky companies should have low P/E

• Growth opportunities

EPS

NPVGO

rEP

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)

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FCFM: example

Year 1 2 3 - Net Income 100 100 100 Depreciation 50 50 50 Investment 50 50 50 Dividends 100 100 100

Current situation

# shares: 100m

Year 1 2 3 - Investment 100 110 20 Net Income 50 100 Depreciation 10 20

Project

Euro m

Market value of company (r = 10%) V0 = 100/0.10 = €1,000mPrice per share P0 = €1,000m / 100m = €10

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Free Cash Flow Calculation

Year 1 2 3 - Net income Depreciation CF from op

100 50

150

150 60

210

200 70

270 Replacement Expansion CF investment

50 100 -150

60 100 -160

70 0

-70 Free cash flow 0 50 200

MBA 2006 FCFM |10

Self financing – DIV = FCF, no stock issue

Free cash flow 0 50 200 Dividends 0 50 200 Stock issue 0 0 0

Market value of equity with project:(As the number of shares is constant, discounting free cash flows or total dividends leads to the same result)

NPV = increase in the value of equity due to projectNPV = 1,694 – 1,000 = 694

694,110.0

200

)10.1(

1

)10.1(

50

10.1

022

V

MBA 2006 FCFM |11

Outside financing : Dividend = Net Income, SI = Div. – FCF

Free cash flow 0 50 200 Dividends 100 150 200 Stock issue 100 100 0

Market value of equity with project:(Discount free cash flow, not total dividends)

694,110.0

200

)10.1(

1

)10.1(

50

10.1

022

V

Same value as before!

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Why not discount total dividends?

Year 0 1 2 Vt 1,694 1,864 2,000 Old shares 1,694 1,764 1,900 New shares 100 100

Because part of future total dividends will be paid to new shareholders. They should not be taken into account to value the shares of current shareholders.

To see this, let us decompose each year the value of all shares between old shares (those outstanding one year before) and new shares (those just issued)

MBA 2006 FCFM |13

Year 0 1 2 3 Total div. 100 150 200 Nb shares 100 105.67 111.23 Div./share 1 1.42 1.7981 Price per share

16.94 17.64 17.98

The price per share is obtained by dividing the market value of old share by the number of old shares:Year 1:

Number of old shares = 100P1 = 1,764 / 100 = 17.64

The number of shares to issue is obtained by dividing the total stock issue by the number of shares:Year 1:

Number of new shares issued = 100 / 17.74 = 5.67Similar calculations for year 2 lead to:

Number of old shares = 105.67Price per share P2 = 1,900 / 105.67 = 17.98Number of new share issued = 100 / 17.98 = 5.56

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From DDM to FCFM: formulas

• Consider an all equity firm

• Value of one share: P0 = (div1 + P1)/(1+r)

• Market value of company = value of all shares

• V0 = n0P0 = (n0div1 + n0P1)/(1+r)

• n0 div1 = total dividend DIV1 paid by the company in year 1

• n0 P1 = Value of “old shares”

• New shares might be issued (or bought back) in year 1

• V1 = n1P1 = n0P1 + (n1-n0)P1

• Statement of cash flow (no debt, cash constant):

• FCF1 = DIV1 – (n1-n0)P1 → DIV1 + n0P1 = FCF1 + V1

• Conclusion:

• V0 = (FCF1 + V1) /(1+r)