•1Chapter 12Equity Valuation2/22/2006 Fin 3710 - Investment - Professor Rui Yao 2Value vs. Price What is value?¾ A numerical quantity determined by careful research and analysis What is price?¾ The cash that can be received if selling a stock in the market Can value and price be different?¾ Absolutely! Heterogeneous valuations Market inefficiency, transaction costs …•22/22/2006 Fin 3710 - Investment - Professor Rui Yao 3Dividend Discount Model (DDM) How does dividend discount model work?¾ DDM is about finding the intrinsic value of a stock by discounting cash flows that a company is expected to generate in the future. Two Critical Inputs:¾ Future cash flows (dividends and terminal value)¾ Market capitalization rate k (cost of equity, required rate of return, or discount rate)  The cap rate depends on another model, e.g. CAPMkVEDEV++=1][][1102/22/2006 Fin 3710 - Investment - Professor Rui Yao 4An Example of DDM Q: ABC is forecasted to pay $4 dividend at the year end, and have 12 month price target of $52. If k = 12%, what is the stock value today?•32/22/2006 Fin 3710 - Investment - Professor Rui Yao 5Dividend Discount Model More General Setup Convention: use ex-dividend value/price()()2222101][1][1][kVEkDEkDEV+++++=()()()333322101][1][1][1][kVEkDEkDEkDEV+++++++=kVEDEVE++=1][][][443kVEDEVE++=1][][][332kVEDEVE++=1][][][221()()()"++++++++=443322101][1][1][1][kDEkDEkDEkDEVkVEkDEkVEDEV+++=++=1][1][1][][11110D1V1V0D2V2D3V3D4V42/22/2006 Fin 3710 - Investment - Professor Rui Yao 6Dividend Discount Model Structured DDM¾ The general setup applies to any situation, but only if one knows the all intermediate dividends, and terminal value Constant Dividend Model¾ Assumption: D1= D2= D2= … = D Constant-Growth DDM (Gordon Model)¾ Assumption: D1= D0×(1+g); D2= D1×(1+g); …Dt+1= Dt×(1+g)kDV =0gkDEgkgDV−=−+×=][)1(100•42/22/2006 Fin 3710 - Investment - Professor Rui Yao 7An Example of Constant Growth DDM Q: if the market cap rate is 12%, what is the value of a stock which just paid a dividend of $3.81, and has an expected dividend growth rate of 5%?14.5705.012.0)05.01(81.3][)1(100=−+×=−=−+×=gkDEgkgDV2/22/2006 Fin 3710 - Investment - Professor Rui Yao 8Return Decomposition Under cg-DDM The return is composed of dividend yield and capital gains¾ Expected capital gain under Gordon model same as dividend growth rategDEDEVVEgkDEgkgDVgkDEgkgDV+==−=−+×=⇒−=−+×=1][][][][)1(][)1(1201211100kgVDEVVVEVDEVVDEVEHPRE =+=−+=−+=01001010011][][][][][][•52/22/2006 Fin 3710 - Investment - Professor Rui Yao 9An Example of Return Decomposition Q: IBM’s year-end dividend is expected to be $2.15, the growth rate will be 11.2% forever, and your required return is 15.2%¾ What is the intrinsic value now?¾ If the market is efficient, what’s the next year’s expected price?¾ If you buy it now and sell it after div. payment, what’s your expected capital gain, div. yield, and holding period return? A: Applying the cg-DDM, we have¾ V0= 2.15/(0.152 – 0.112) = $53.75¾ E[P1] = E[V1] = V0×(1+g) = $59.77¾ Capital gains = 59.77 – 53.75 = 6.02; 6.02/53.75=11.2%¾ div yield = D1/P0 =4%¾ Total return = 15.2% = Div. yield + Capital gain yield = required return (cap rate)2/22/2006 Fin 3710 - Investment - Professor Rui Yao 10Multi-stage Growth DDM Q: When is cg-DDM not applicable? A: Two most obvious situations:¾ When expected dividends do not grow at a constant rate¾ When the growth rate is higher than required return in short term Solution – Multi-stage growth model¾ Forecast the dividend at various stages of the future¾ Using cg-DDM to find value for the last stage¾ Move back to calculate the value using discounted cash flow analysis•62/22/2006 Fin 3710 - Investment - Professor Rui Yao 11An Example of Multistage Growth On the end of year 2000, the forecasts for Motorola are¾ Next four years dividends : 0.17, 0.183, 0.197, & 0.21¾ The dividend growth rate thereafter: 12.74%¾ The required return: 13.8% Q: What is the value of Motorola’s stock (V0)? A: Year 2000 is time 0, and year 2004 is time 4. More Q: ¾ If Motorola’s stock price was $33, was it over-valued?¾ What should be the value if the required return is 13.00%?()()()8.13$111134.22$)1(44433221044=++++++++=⇒=−+×=kVDkDkDkDVgkgDV2/22/2006 Fin 3710 - Investment - Professor Rui Yao 12Source of Dividend Growth Retained earning can generate dividend growth Q: what will the dividend growth rate be if a company’s ROE is 14%, and it retains 91% of its earnings (i.e., 9% dividend payout ratio) A: assume the company’s current equity is 100¾ Earnings by the end of year = $100×0.14 = $14¾ Pays D0= $14×0.09 = $1.26 and retain $14 - $1.26 = $12.74¾ The new equity base is $100 + $12.74 = $112.74¾ Next year’s earning = $112.74×0.14 = $15.78¾ Pays D1= $15.78×0.09 = $1.42, this is 12.74% higher than D0•72/22/2006 Fin 3710 - Investment - Professor Rui Yao 13Source of Dividend Growth Q: What did we learn from the previous example? A: Growth can be internally generated from retained earnings¾ ROE – return on equity¾ b – plowback ratio (earning retention ratio) Assumptions necessary to apply the growth rate from the above formula to cg-DDM¾ Constant ROE applies for all future investment¾ Constant payout ratio Q: Is dividend growth by retaining earnings alwaysgood?bROEg×=2/22/2006 Fin 3710 - Investment - Professor Rui Yao 14Present Value of Growth Opportunity Q: CashCow and Growth Inc. share the following: k = 12.5%, E1= $5/shr. But, CashCow pays all earnings out as div while Growth Inc retains 60%.¾ What is the value and P/E ratio of CashCow if its ROE=10%?¾ CashCow: all earnings as dividend D1= E1= $5, g = 0. ¾ What are the value and P/E ratio of Growth Inc. if its ROE=15%?¾ Growth Inc: retains b = 60%, D1 = $2 (40% of E1)854040$0125.05101010===⇒=−=−=EVEPgkDV4.11514.5714.57$09.0125.02%9ROE%,15ROE101010===⇒=−=−==×==EVEPgkDPbg•82/22/2006 Fin 3710 - Investment - Professor Rui Yao 15Present Value of Growth Opportunity Growth Inc. pays less today in dividend yet priced higher.¾ The premium comes from the growth opportunity¾ PVGO = Value with growth – value without growth Q: Can Cashcow mimic the strategy of Growth Inc. (by reinvesting 60% earnings) to achieve a higher price?14.17$40$14.57$PVGO10=−=−=kEP2/22/2006 Fin 3710 - Investment - Professor Rui