Corporate Finance Stock Valuation Prof Andr Farber SOLVAY

Corporate Finance Stock Valuation Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES A. Farber Vietnam 2004

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) A. Farber Vietnam 2004 2

DDM: one-year holding period • Review: valuing a 1 -year 4% coupon bond ü ü ü • € 50 Coupon: € 2 Interest rate 5% Bond price P 0 = (50+2)/1. 05 = 49. 52 How much would you be ready to pay for a stock with the following characteristics: ü ü • Face value: 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. A. Farber Vietnam 2004 3

Dividend Discount Model (DDM): 1 -year horizon • 1 -year valuation formula Expected price r = expected return on shareholders'equity = Risk-free interest rate + risk premium • Back to example. Assume r = 10% Dividend yield = 2/47. 27 = 4. 23% Rate of capital gain = (50 – 47. 27)/47. 27 = 5. 77% A. Farber Vietnam 2004 4

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: A. Farber Vietnam 2004 5

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. ü DDM with constant growth g ü Note: g < r A. Farber Vietnam 2004 6

DDM with constant growth : example Data Next dividend: 6. 00 Div. growth rate: 4% Discount rate: 10% Year Dividend Disc. Fac 0 Price 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. 86 9 8. 21 0. 4241 142. 33 10 8. 54 0. 3855 148. 02 P 0= 6/(. 10 -. 04) A. Farber Vietnam 2004 7

Differential growth • Suppose that r = 10% • You have the following data: Year 1 2 3 4 to ∞ Dividend 2 2. 40 2. 88 3. 02 20% 5% Growth rate • P 3 = 3. 02 / (0. 10 – 0. 05) = 60. 48 A. Farber Vietnam 2004 8

A formula for g • Dividend are paid out of earnings: ü Dividend = Earnings × Payout ratio • Payout ratios of dividend paying companies tend to be stable. ü Growth rate of dividend g = Growth rate of earnings • Earnings increase because companies invest. ü Net investment = Retained earnings • Growth rate of earnings is a function of: ü Retention ratio = 1 – Payout ratio ü Return on Retained Earnings g = (Return on Retained Earnings) × (Retention Ratio) A. Farber Vietnam 2004 9

Example • Data: ü ü 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: ü Expected dividend per share next year: div 1 = 10 × 60% = € 6 ü Retention Ratio = 1 – 60% = 40% ü Growth rate of dividend g = (40%) × (15%) = 6% • Current stock price: ü P 0 = € 6 / (0. 10 – 0. 06) = € 150 A. Farber Vietnam 2004 10

Return on Retained Earnings and Debt • Net investment = Total Asset • For a levered firm: ü Total Asset = Stockholders’ equity + Debt • RORE is a function of: ü Return on net investment (RONI) ü Leverage (L = D/ SE) RORE = RONI + [RONI – i (1 -TC)]×L A. Farber Vietnam 2004 11

Growth model: example A. Farber Vietnam 2004 12

Valuing the company • Assume discount rate r = 15% • Step 1: calculate terminal value ü As Earnings = Dividend from year 4 on ü V 3 = 503. 71/15% = 3, 358 • Step 2: discount expected dividends and terminal value A. Farber Vietnam 2004 13

Valuing Growth Opportunities • Consider the data: ü Expected earnings per share next year EPS 1 = € 10 ü Required rate of return r = 10% Cy A Cy B Cy C Payout ratio 60% 100% Return on Retained Earnings 15% 10% - Next year’s dividend € 6 € 10 g 6% 4% 0% € 150 € 100 Price per share P 0 • Why is A more valuable than B or C? • Why do B and C have same value in spite of different investment policies A. Farber Vietnam 2004 14

NPVGO • Cy C is a “cash cow” company ü Earnings = Dividend (Payout = 1) ü No net investment • Cy B does not create value ü Dividend < Earnings, Payout <1, Net investment >0 ü But: Return on Retained Earnings = Cost of capital ü NPV of net investment = 0 • Cy A is a growth stock ü ü 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 A. Farber Vietnam 2004 15

Source of NPVG 0 ? • Additional value if the firm retains earnings in order to fund new projects • where PV(NPVt) 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 A. Farber Vietnam 2004 16

NPVGO: details A. Farber Vietnam 2004 17

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: ü Accounting methods: – Accounting conventions vary across countries ü The expected return on shareholders’equity – Risky companies should have low P/E ü Growth opportunities A. Farber Vietnam 2004 18

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) ü 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 ü Market value of company = PV(Free Cash Flows) A. Farber Vietnam 2004 19

FCFM: example Current situation Euro m # shares: 100 m Market value of company (r = 10%) V 0 = 100/0. 10 = € 1, 000 m Price per share P 0 = € 1, 000 m / 100 m = € 10 Project A. Farber Vietnam 2004 20

Free Cash Flow Calculation A. Farber Vietnam 2004 21

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 A. Farber Vietnam 2004 22

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! A. Farber Vietnam 2004 23

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) A. Farber Vietnam 2004 24

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 P 1 = 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 P 2 = 1, 900 / 105. 67 = 17. 98 Number of new share issued = 100 / 17. 98 = 5. 56 A. Farber Vietnam 2004 25

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 ü 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” ü New shares might be issued (or bought back) in year 1 ü V 1 = n 1 P 1 = n 0 P 1 + (n 1 -n 0)P 1 • Statement of cash flow (no debt, cash constant): ü FCF 1 = DIV 1 – (n 1 -n 0)P 1 → DIV 1 + n 0 P 1 = FCF 1 + V 1 • Conclusion: ü V 0 = (FCF 1 + V 1) /(1+r) A. Farber Vietnam 2004 26