1. Théorie Financière 2004-2005 4. Evaluation d’actions et d’entreprises Professeur André Farber

2. August 23, 2004 Tfin 2004 04 Stock valuation |2 Stock Valuation Objectives for this session : 1.Introduce 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)

3. August 23, 2004 Tfin 2004 04 Stock valuation |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 following characteristics: 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

4. August 23, 2004 Tfin 2004 04 Stock valuation |4 Dividend Discount Model (DDM): 1-year horizon 1-year valuation formula Back to example. Assume r = 10% 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%

5. August 23, 2004 Tfin 2004 04 Stock valuation |5 DDM: where does the expected stock price come from? Expected price at forecasting horizon depends on expected dividends and expected prices beyond forecasting horizon To find P 2, use 1-year valuation formula again: Current price can be expressed as: General formula:

6. August 23, 2004 Tfin 2004 04 Stock valuation |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 used formula is the Gordon Growth Model base on the assumption that dividends grow at a constant rate. DDM with constant growth g Note: g < r

7. August 23, 2004 Tfin 2004 04 Stock valuation |7 DDM with constant growth : example YearDividendDiscFacPrice 0100.00 16.000.9091104.00 26.240.8264108.16 36.490.7513112.49 46.750.6830116.99 57.020.6209121.67 67.300.5645126.53 77.590.5132131.59 87.900.4665136.86 98.210.4241142.33 108.540.3855148.02 Data Next dividend: 6.00 Div.growth rate: 4% Discount rate: 10% P 0 = 6/(.10-.04)

8. August 23, 2004 Tfin 2004 04 Stock valuation |8 Differential growth Suppose that r = 10% You have the following data: P 3 = 3.02 / (0.10 – 0.05) = 60.48 Year1234 to ∞ Dividend22.402.883.02 Growth rate20% 5%

9. August 23, 2004 Tfin 2004 04 Stock valuation |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)

10. August 23, 2004 Tfin 2004 04 Stock valuation |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: div 1 = 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

11. August 23, 2004 Tfin 2004 04 Stock valuation |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

12. August 23, 2004 Tfin 2004 04 Stock valuation |12 Growth model: example

13. August 23, 2004 Tfin 2004 04 Stock valuation |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

14. August 23, 2004 Tfin 2004 04 Stock valuation |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 ACy BCy C Payout ratio60% 100% Return on Retained Earnings15%10%- Next year’s dividend€6 €10 g6%4%0% Price per share P 0 €150€100

15. August 23, 2004 Tfin 2004 04 Stock valuation |15 NPVGO Cy C is a “cash cow” company Earnings = Dividend (Payout = 1) No net investment Cy B does not create value Dividend 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

16. August 23, 2004 Tfin 2004 04 Stock valuation |16 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 present value (calculated at time t) of a future investment at time t In previous example: Year 1: EPS 1 = 10 div 1 = 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

17. August 23, 2004 Tfin 2004 04 Stock valuation |17 NPVGO: details

18. August 23, 2004 Tfin 2004 04 Stock valuation |18 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 shareholders’equity –Risky companies should have low P/E Growth opportunities

19. August 23, 2004 Tfin 2004 04 Stock valuation |19 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

20. August 23, 2004 Tfin 2004 04 Stock valuation |20 FCFM: example Current situation # shares: 100m Project Euro m Market value of company (r = 10%) V 0 = 100/0.10 = €1,000m Price per share P 0 = €1,000m / 100m = €10

21. August 23, 2004 Tfin 2004 04 Stock valuation |21 Free Cash Flow Calculation

22. August 23, 2004 Tfin 2004 04 Stock valuation |22 Self financing – DIV = FCF, no stock issue 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 project NPV = 1,694 – 1,000 = 694

23. August 23, 2004 Tfin 2004 04 Stock valuation |23 Outside financing : Dividend = Net Income, SI = Div. – FCF Market value of equity with project: (Discount free cash flow, not total dividends) Same value as before!

24. August 23, 2004 Tfin 2004 04 Stock valuation |24 Why not discount total dividends? 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)

25. August 23, 2004 Tfin 2004 04 Stock valuation |25 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 = 100 P1 = 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 = 5.67 Similar calculations for year 2 lead to: Number of old shares = 105.67 Price per share P2 = 1,900 / 105.67 = 17.98 Number of new share issued = 100 / 17.98 = 5.56

26. August 23, 2004 Tfin 2004 04 Stock valuation |26 From DDM to FCFM: formulas Consider an all equity firm Value of one share: P 0 = (div 1 + P 1 )/(1+r) Market value of company = value of all shares V 0 = n 0 P 0 = (n 0 div 1 + n 0 P 1 )/(1+r) n 0 div 1 = total dividend DIV 1 paid by the company in year 1 n 0 P 1 = Value of “old shares” New shares might be issued (or bought back) in year 1 V 1 = n 1 P 1 = n 0 P 1 + (n 1 -n 0 )P 1 Statement of cash flow (no debt, cash constant): FCF 1 = DIV 1 – (n 1 -n 0 )P 1 → DIV 1 + n 0 P 1 = FCF 1 + V 1 Conclusion: V 0 = (FCF 1 + V 1 ) /(1+r)