1. Equity Valuation b Basic Types of Models Balance sheet modelsBalance sheet models Dividend discount modelsDividend discount models EPS (cashflow) discount modelsEPS (cashflow) discount models b Modeling Framework DeterministicdynamicsDeterministicdynamics Stochastic dynamicsStochastic dynamics

2. Fair Value vs Market Price b Fair Value Self assigned ValueSelf assigned Value Variety of models are used for estimationVariety of models are used for estimation b Market Price Consensus value assessment by all market participantsConsensus value assessment by all market participants b Trading Signal FV > MP: BuyFV > MP: Buy FV < MP: Sell or Short SellFV < MP: Sell or Short Sell FV = MP: Hold or Fairly PricedFV = MP: Hold or Fairly Priced

3. Dividend Discount Models b V 0 = Value of Stock D t = Dividend k = required return

4. No Growth Model b Where the stock has earnings and dividends that are expected to remain constant foreever. Example: Preferred Stock

5. No Growth Model: Example b E 1 = D 1 = $5.00 k =.15 Then, V 0 = $5.00 /.15 = $33.33

6. Constant Growth Model b g = constant perpetual growth rate

7. Constant Growth Model: Example b E 1 = $5.00b = 40% (1-b) = 60% k = 15%D 1 = $3.00 g = 8% (b: EPS retention ratio) V 0 = 3.00 / (.15 -.08) = $42.86

8. Estimating Dividend Growth Rates b b g = growth rate in dividends b ROE = Return on Equity for the firm b b = EPS retention rate (1- dividend payout ratio)

9. Partitioning Value: Growth and No Growth Components b b PVGO = Present Value of Growth Opportunities b E 1 = Earnings Per Share for period 1

10. Partitioning Value: Example ROE = 20% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%

11. Partitioning Value: Example b V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

12. Multi-Period Dividend-Discount Model b P N = expected sales price of stock at time N N = number of years the stock is to be held

13. Practical Difficulties with DDM b Some firms do not pay dividends b Can you forecast future dividends? b Can you predict the terminal liquidation value P n ? b What about the discount rate k? (perhaps, the CAPM? The APT?)

14. Multi-Period Earnings-Discount Model b P N = expected sales price of stock at time N N = number of years the stock is to be held

15. Practical Concerns with EDM b EPS forecasts are available from I/B/E/S, First Call, Zacks, …. b Dividend payout ratio (1-b) can be estimated, either based on cash dividend or dividend- in-kind b But, what about Pn and k?

16. P/E Ratios d: dividend payout ratio k: cost-of-capital (or, risk-adjusted discount rate) g: EPS growth rate

17. P/E Example k = 12.5% g = 9%d = 40% k = 12.5% g = 9%d = 40% Thus, P/E = (1 -.60) / (.125 -.09) = 11.4 If E = $2.73, we have P = 11.4 X 2.73 =$31.14

18. Problems with P/E Ratios b What is E ? E = trailing 12-month EPS?E = trailing 12-month EPS? E = 12-month-forward EPS?E = 12-month-forward EPS? b What is g ? g = average historical EPS growth?g = average historical EPS growth? g = expected next-yr EPS growth?g = expected next-yr EPS growth? g = long-run EPS growth?g = long-run EPS growth?