CHAPTER FIFTEENCAPITALIZATION OF INCOME METHODSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8THE ZERO GROWTH MODELSlide 10Slide 11Slide 12Slide 13Slide 14CONSTANT GROWTH MODELSlide 16Slide 17Slide 18Slide 19Slide 20THE MULTIPLE-GROWTH MODELSlide 22Slide 23Slide 24Slide 25MODELS BASED ON P/E RATIOSlide 27PRICE-EARNINGS RATIO MODELSlide 29Slide 30THE ZERO-GROWTH MODELSlide 32THE CONSTANT-GROWTH MODELSlide 34SOURCES OF EARNINGS GROWTHSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 431CHAPTER FIFTEENDIVIDEND DISCOUNT MODELS2CAPITALIZATION OF INCOME METHOD•THE INTRINSIC VALUE OF A STOCK–represented by present value of the income stream3CAPITALIZATION OF INCOME METHOD•formulawhere Ct = the expected cash flow t = time k = the discount rate1)1(ttkCVt4CAPITALIZATION OF INCOME METHOD•NET PRESENT VALUE–FORMULANPV = V - P5CAPITALIZATION OF INCOME METHOD•NET PRESENT VALUE–Under or Overpriced?•If NPV > 0 •If NPV < 0underpricedoverpriced6CAPITALIZATION OF INCOME METHOD•INTERNAL RATE OF RETURN (IRR)–set NPV = 0, solve for IRR, or–the IRR is the discount rate that makes the NPV = 07CAPITALIZATION OF INCOME METHOD•APPLICATION TO COMMON STOCK–substitutingdetermines the “true” value of one share)1(...)1()1(2211kDkDkDV1)1(tttkD8CAPITALIZATION OF INCOME METHOD•A COMPLICATION–the previous model assumes dividends can be forecast indefinitely–a forecasting formula can be writtenDt = Dt -1 ( 1 + g t )where g t = the dividend growth rate9THE ZERO GROWTH MODEL•ASSUMPTIONS–the future dividends remain constant such thatD1 = D2 = D3 = D4 = . . . = DN10THE ZERO GROWTH MODEL•THE ZERO-GROWTH MODEL–derivation 10)1(ttkDV100)1(ttkDD11THE ZERO GROWTH MODEL•Using the infinite series property, the model reduces to•if g = 0kktt1)1(1112THE ZERO GROWTH MODEL•Applying to VkDV113THE ZERO GROWTH MODEL•Example–If Zinc Co. is expected to pay cash dividends of $8 per share and the firm has a 10% required rate of return, what is the intrinsic value of the stock?10.8V80$14THE ZERO GROWTH MODEL•Example(continued)If the current market price is $65, the stock is underpriced.Recommendation: BUY15CONSTANT GROWTH MODEL•ASSUMPTIONS:–Dividends are expected to grow at a fixed rate, g such thatD0 (1 + g) = D1andD1 (1 + g) = D2or D2 = D0 (1 + g)216CONSTANT GROWTH MODEL•In GeneralDt = D0 (1 + g)t17CONSTANT GROWTH MODEL•THE MODEL:D0 = a fixed amount10)1()1(tttkgDV10)1()1(tttkgDV18CONSTANT GROWTH MODEL•Using the infinite property series,if k > g, thengkgkgttt1)1()1(119CONSTANT GROWTH MODEL•SubstitutinggkgDV1020CONSTANT GROWTH MODEL•since D1= D0 (1 + g)gkDV121THE MULTIPLE-GROWTH MODEL•ASSUMPTION:–future dividend growth is not constant•Model Methodology–to find present value of forecast stream of dividends–divide stream into parts–each representing a different value for g22THE MULTIPLE-GROWTH MODEL–find PV of all forecast dividends paid up to and including time T denoted VT-TttTkDV10)1(23THE MULTIPLE-GROWTH MODEL•Finding PV of all forecast dividends paid after time t–next period dividend Dt+1 and all thereafter are expected to grow at rate ggkDVTT1124THE MULTIPLE-GROWTH MODELTTTkVV)1(1TTkgkD)1)((125THE MULTIPLE-GROWTH MODEL•Summing VT- and VT+V = VT- + VT+TTTttTkgkDkD)1)(()1(1126MODELS BASED ON P/E RATIO•PRICE-EARNINGS RATIO MODEL–Many investors prefer the earnings multiplier approach since they feel they are ultimately entitled to receive a firm’s earnings–P/E ratio is also known as:•“Earnings multiplier”•“Capitalization factor”27MODELS BASED ON P/E RATIO•PRICE-EARNINGS RATIO MODEL–EARNINGS MULTIPLIER:= PRICE - EARNINGS RATIO= Current Market Pricefollowing 12 month earnings28PRICE-EARNINGS RATIO MODEL•The Model is derived from the Dividend Discount model:gkDP1029PRICE-EARNINGS RATIO MODEL•Dividing by the coming year’s earningsgkEDEP111030PRICE-EARNINGS RATIO MODEL•The P/E Ratio is a function of –the expected payout ratio ( D1 / E1 )–the required return (k)–the expected growth rate of dividends (g)31THE ZERO-GROWTH MODEL•ASSUMPTIONS:•dividends remain fixed•100% payout ratio to assure zero-growth32THE ZERO-GROWTH MODEL•Model:kEV1033THE CONSTANT-GROWTH MODEL•ASSUMPTIONS:•growth rate in dividends is constant•earnings per share is constant•payout ratio is constant34THE CONSTANT-GROWTH MODEL•The Model:where ge = the growth rate in earningseegkgPEV1035SOURCES OF EARNINGS GROWTH•What causes growth?•assume no new capital added•retained earnings used to pay firm’s new investment•If pt = the payout ratio in year t•1-pt = the retention ratio36SOURCES OF EARNINGS GROWTH•New Investments:tttEpI )1( 37SOURCES OF EARNINGS GROWTH•What about the return on equity?Let rt = return on equity in time t rt I t is added to earnings per share in year t+1 and thereafter38SOURCES OF EARNINGS GROWTH•Assume constant rate of returnttttIrEE 1 )1(1tttprE 39SOURCES OF EARNINGS GROWTH•IF•then)1(1 etttgEE )1(11 etttgEE40SOURCES OF EARNINGS GROWTH•and)1(1 ttetprg 41SOURCES OF EARNINGS GROWTH•If the growth rate in earnings per share get+1 is constant, then rt and pt are constant42SOURCES OF EARNINGS GROWTH•Growth rate depends on–the retention ratio–average return on equity43SOURCES OF EARNINGS GROWTH•such