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)
MBA 2006 FCFM |3
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
MBA 2006 FCFM |4
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)
MBA 2006 FCFM |5
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/
MBA 2006 FCFM |7
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)
MBA 2006 FCFM |8
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!
MBA 2006 FCFM |12
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
MBA 2006 FCFM |14
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)
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