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FINANCE 5. Stock valuation - DDM

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FINANCE5. Stock valuation - DDM

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

Fall 2006

- Objectives for this session :
- Introduce the dividend discount model (DDM)
- Understand the sources of dividend growth
- Analyse growth opportunities
- Examine why Price-Earnings ratios vary across firms
- Introduce free cash flow model (FCFM)

MBA 2006 DDM

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

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

- 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 P0 = (50+2)/1.05 = 49.52

MBA 2006 DDM

Expected price

r = expected return on shareholders'equity

= Risk-free interest rate + risk premium

- 1-year valuation formula
- Back to example. Assume r = 10%

Dividend yield = 2/47.27 = 4.23%

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

MBA 2006 DDM

- Expected price at forecasting horizon depends on expected dividends and expected prices beyond forecasting horizon
- To find P2, use 1-year valuation formula again:
- Current price can be expressed as:
- General formula:

MBA 2006 DDM

- 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

MBA 2006 DDM

Data

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

P0= 6/(.10-.04)

MBA 2006 DDM

- Suppose that r = 10%
- You have the following data:
- P3 = 3.02 / (0.10 – 0.05) = 60.48

MBA 2006 DDM

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

- Growth rate of dividend g = Growth rate of earnings

- Net investment = Retained earnings

- Retention ratio = 1 – Payout ratio
- Return on Retained Earnings

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

MBA 2006 DDM

- Data:
- Expected earnings per share year 1: EPS1 = €10
- Payout ratio : 60%
- Required rate of return r : 10%
- Return on Retained Earnings RORE: 15%

- Expected dividend per share next year: div1 = 10 × 60% = €6
- Retention Ratio = 1 – 60% = 40%
- Growth rate of dividend g = (40%) × (15%) = 6%

- P0 = €6 / (0.10 – 0.06) = €150

MBA 2006 DDM

- Net investment = Total Asset
- For a levered firm:
- Total Asset = Stockholders’ equity + Debt

- Return on net investment (RONI)
- Leverage (L = D/ SE)
RORE = RONI + [RONI – i (1-TC)]×L

MBA 2006 DDM

MBA 2006 DDM

- Assume discount rate r = 15%
- Step 1: calculate terminal value
- As Earnings = Dividend from year 4 on
- V3 = 503.71/15% = 3,358

MBA 2006 DDM

- Consider the data:
- Expected earnings per share next year EPS1 = €10
- Required rate of return r = 10%

MBA 2006 DDM

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

- Dividend < Earnings, Payout <1, Net investment >0
- But: Return on Retained Earnings = Cost of capital
- NPV of net investment = 0

- Return on Retained Earnings > Cost of capital
- Net investment creates value (NPV>0)
- Net Present Value of Growth Opportunities (NPVGO)
- NPVGO = P0 – EPS1/r = 150 – 100 = 50

MBA 2006 DDM

- 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: EPS1 = 10 div1 = 6 Net investment = 4

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

NPV1 = -4 + 0.60/0.10 = +2 (in year 1)

PV(NPV1) = 2/1.10 = 1.82

MBA 2006 DDM

MBA 2006 DDM

- 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

- Accounting methods:

MBA 2006 DDM

- 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

- Then, from the cash flow statement:

- Company financially constrained by CF from operation

- Free cash flow = Dividend – Stock Issue

MBA 2006 DDM