Introduction to Stock Valuation. Background


 Joseph Ellis
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1 Intoduction to Stock Valuation (Text efeence: Chapte 5 (Sections )) Topics backgound dividend discount models paamete estimation gowth oppotunities piceeanings atios some final points AFM Intoduction to Stock Valuation Slide 1 Backgound ecall that a copoation is owned by its shaeholdes and that the shaeholdes equity is the potion of total assets that belong to the shaeholdes the value of shaeholdes equity as ecoded on the balance sheet is the book value of equity; dividing the book value of equity by the numbe of outstanding shaes gives the book value pe shae the maket value of each shae is the pice equied to puchase a shae in the fim fom a tade on a stock exchange; multiplying the shae pice by the numbe of outstanding shaes gives the maket value of equity these two equity values (book vs. maket) ae seldom equal fo most healthy fims, maket value exceeds book value AFM Intoduction to Stock Valuation Slide 2
2 why does maket value book value? shae pice is based on the etuns o cash flows that the investo expects to eceive fom owning the shae (depends on the ability of the company to ean a pofit) book value depends on the histoical costs of the fim s assets (this may tell us the eplacement value of the fim s assets, but it does not necessaily eflect the ability of the fim to tun the assets into pofits) moe pecisely, maket value is detemined by the ability of the fim to ean a etun on its investments above the oppotunity cost of capital compaed to bonds, stocks ae moe difficult to value because: cash flows ae not pespecified no matuity date can t easily detemine o obseve equied maket etun AFM Intoduction to Stock Valuation Slide 3 Dividend Discount Models as with any asset, the (maket) value of a shae of common stock is detemined by the PV of its expected futue cash flows shaeholdes eceive cash in the fom of dividends (assume annually fo simplicity) o capital gains/losses, o both notation: P 0 maket pice of a shae today P t Div t maket pice of a shae afte the end of yea t dividend pe shae paid at the end of yea t discount ate suppose an investo buys the stock and holds it fo one yea: AFM Intoduction to Stock Valuation Slide 4
3 what about P 1? extend until time T : basic dividend discount (a.k.a. Godon) model: AFM Intoduction to Stock Valuation Slide 5 Cont d the dividend discount model simply says that today s stock pice is the PV of all expected futue dividends takes into account both dividends and capital gains longtem model holds even when investos have shot hoizons special cases: 1. Zeo gowth: dividends emain at the same level foeve 2. Constant gowth: dividends gow at the same ate g foeve 3. Diffeential gowth: dividends gow at diffeent ates ove time (see examples below) AFM Intoduction to Stock Valuation Slide 6
4 the basic idea fo diffeential gowth is something like this: T T + 1 T Div 1 Div 1 (1 + g 1 ) Div 1 (1 + g 1 ) 2 Div T Div T (1 + g 2 ) Div T (1 + g 2 ) 2 in this case, we have high gowth (at the ate g 1 ) fo T peiods and then low gowth (at the ate g 2 ) foeve afte P 0 = = T t=1 Div t (1 + ) t + P T (1 + ) T T Div 1 (1 + g 1 ) t 1 t=1 (1 + ) t + Div T+1 (1 + ) T g 2 AFM Intoduction to Stock Valuation Slide 7 Cont d example: a fim s dividends ae expected to gow at 25% pe yea fo thee yeas afte which gowth will slow to 8% pe yea foeve. The fim just paid a dividend of $0.60 pe shae and = 15%. What is P 0? AFM Intoduction to Stock Valuation Slide 8
5 example: fou yeas ago a fim paid a dividend of $0.32 pe shae. Today it paid a dividend of $0.62 pe shae. Dividends will continue to gow at this same ate fo the next fou yeas, afte which the gowth ate will be 5% pe yea foeve. Suppose the oppotunity cost of capital is 10%. If someone offes to sell you this stock fo $22, should you buy it? AFM Intoduction to Stock Valuation Slide 9 Paamete Estimation gowth ate g: net investment is total investment less depeciation if net investment equals zeo, the fim is maintaining its poductive capacity but not expanding net investment is positive only if some eanings ae etained since eanings next yea = eanings this yea + etained eanings this yea etun on etained eanings, we have g = etention atio etun on etained eanings = etention atio ROE AFM Intoduction to Stock Valuation Slide 10
6 discount ate : we will conside only one simple way hee (see Chaptes fo moe sophisticated altenatives) in the case of the constant gowth model: P 0 = Div 1 g = Div 1 + g P 0 the estimated value of will be vey sensitive to the estimated value fo g (and thus to assumptions made when estimating g) some analysts ague that the eos ae so lage when calculating fo a single fim that one should do it fo each fim in an industy and use the aveage estimate of AFM Intoduction to Stock Valuation Slide 11 Gowth Oppotunities the models above use pojected futue dividends to detemine common stock value while in geneal the payment of dividends eflects that a fim is pofitable, thee is often little elationship between pofitability and size of dividend dividends often do not povide sufficient infomation egading futue pofitability the key to fim valuation is the ate of etun that the fim eans elative to the cost of capital if a fim pays out all eanings as dividends, it will have no gowth: P 0 = Div 1 = EPS 1 AFM Intoduction to Stock Valuation Slide 12
7 howeve, fims typically do have gowth oppotunities. If so, the stock will have additional value equal to the net pesent value (pe shae) of gowth oppotunities (NPVGO): P 0 = EPS + NPVGO note that the stock pice will be lowe than the zeo gowth case if NPVGO < 0, even if eanings and dividends ae gowing (see text example pp ) AFM Intoduction to Stock Valuation Slide 13 Cont d example: a fim has EPS 1 = $4.50 and a etention atio of 30%. Its etun on etained eanings is 25%. If = 15%, what is P 0? What potion of this is due to NPVGO? AFM Intoduction to Stock Valuation Slide 14
8 PiceEanings Ratios the decomposition of P 0 = EPS PE atio depends on: discount ate NPVGO + NPVGO implies that P 0 EPS = 1 + NPVGO EPS choice of accounting method tailing o fowad EPS a ecently popula vaiation: PEG (PE divided by gowth ate) (see text discussion pp ) AFM Intoduction to Stock Valuation Slide 15 Some Final Points stock value can be estimated fom eithe a discounted dividend appoach o a gowth oppotunities appoach why not discount eanings? investos eceive dividends, not eanings the discounted value of eanings would be too high how do we value a fim which neve pays any dividends? many fims (especially high gowth fims) do not pay a dividend had to apply dividend discount models must assume something about cash flows ultimately eceived by investos (e.g. futue dividends o shae pice) AFM Intoduction to Stock Valuation Slide 16
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