FINANCE 5. Stock valuation - DDM

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FINANCE 5. Stock valuation - DDM. Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2006. Stock Valuation. Objectives for this session : Introduce the dividend discount model (DDM) Understand the sources of dividend growth Analyse growth opportunities

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### FINANCE5. Stock valuation - DDM

Professor André Farber

Université Libre de Bruxelles

Fall 2006

Stock Valuation
• 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

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 P0 = (50+2)/1.05 = 49.52

MBA 2006 DDM

Expected price

r = expected return on shareholders'equity

= Risk-free interest rate + risk premium

Dividend Discount Model (DDM): 1-year horizon
• 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

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 P2, use 1-year valuation formula again:
• Current price can be expressed as:
• General formula:

MBA 2006 DDM

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

MBA 2006 DDM

DDM with constant growth : example

Data

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

P0= 6/(.10-.04)

MBA 2006 DDM

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

MBA 2006 DDM

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 DDM

Example
• Data:
• Expected earnings per share year 1: EPS1 = €10
• Payout ratio : 60%
• Required rate of return r : 10%
• Return on Retained Earnings RORE: 15%
• Valuation:
• Expected dividend per share next year: div1 = 10 × 60% = €6
• Retention Ratio = 1 – 60% = 40%
• Growth rate of dividend g = (40%) × (15%) = 6%
• Current stock price:
• P0 = €6 / (0.10 – 0.06) = €150

MBA 2006 DDM

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-TC)]×L

MBA 2006 DDM

Valuing the company
• Assume discount rate r = 15%
• Step 1: calculate terminal value
• As Earnings = Dividend from year 4 on
• V3 = 503.71/15% = 3,358
• Step 2: discount expected dividends and terminal value

MBA 2006 DDM

Valuing Growth Opportunities
• Consider the data:
• Expected earnings per share next year EPS1 = €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

MBA 2006 DDM

NPVGO
• Cy C is a “cash cow” company
• Earnings = Dividend (Payout = 1)
• No net investment
• Cy B does not create value
• Dividend < Earnings, Payout <1, Net investment >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 = P0 – EPS1/r = 150 – 100 = 50

MBA 2006 DDM

Source of NPVG0 ?
• 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

NPVGO: details

MBA 2006 DDM

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

MBA 2006 DDM

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 DDM