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Gordon

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Verband tussen Gordon model en Globalisatie.

Koers/winst verhouding uitgekeerde winst / netto winst (pay out ratio)

The Gordon model [pic]

Gewenst rendement lange termijn groeivoet per aandeel

(risico vrij rend + risico premie) (inhoudingspercentage x REV)

capital asset pricing model

(verwachte inflatie + reële rente voet) (1-pay out ratio) x (winstmarge x omloopsnelheid x hefboomfactor)

Monetair beleid economische groei dividend politiek concurrentie efficiency financial risk

globalization

Risicoanalyse aan de hand van het Gordonmodel.

Voor het bespreken van de marktrisico’s die een onderneming loopt maken we gebruik van het Gordon model. Dit is een model waarmee de theoretische koers van een aandeel berekend kan worden. Dat is niet alleen interessant voor beleggers, maar ook voor ondernemers, omdat het model inzichtelijk maakt welke factoren van invloed zijn op de (aandeelhouders)waarde van een onderneming.

[pic][pic]

(voor de wiskundige afleiding van deze formule, zie appendix)

Po= prijs van het aandeel d=dividendpercentage Eı=verwachte winst g= gemiddelde groeivoet van de winst op lange termijn. (hier komen we later op terug bij de groeianalyse). r=rendementseis van beleggers.
Deze rendementseis bestaat uit: kapitaalmarktrente + risicopremie. Het risico op aandelen is groter dan het risico op staatsobligaties, hoeveel groter hangt samen met de aard en activiteiten van de onderneming. We bespreken hier de volgende risico’s: bedrijfsrisico (business risk), financieel risico (financial risk), wisselkoersrisico (exchange rate risk) en het landenrisico (political risk). De beta is een statistische maat voor het marktrisico (deze bevat ook nog het managementrisico en het externe liquiditeitsrisico).

De vergelijking maakt direct duidelijk dat beleggers minder voor een aandeel willen betalen, naarmate het verwachte dividend kleiner is. Daarbij is uiteraard ook de vraag van belang of het om een eenmalige of om een blijvende dividendverlaging gaat. De oorzaak van een verwachte dividendverlaging is daarom zeker zo belangrijk als het feit op zich.

Verder laat de vergelijking zien dat een hogere rendementseis ook tot een lagere koers van het aandeel kan leiden. De rendementseis kan stijgen omdat de markt aantrekkelijker beleggingsalternatieven biedt doordat de rentevoet is gestegen. Maar het is ook denkbaar dat de risicopremies stijgen omdat de risico perceptie of de risico aversie van beleggers toeneemt. Risico’s die we later zullen bespreken: het managementrisico, het bedrijfsrisico, het financieel risico, het wisselkoersrisico, het landenrisico en het externe liquiditeitsrisico.

De genoemde factoren staan niet altijd los van elkaar. Een voorbeeld. Als de monetaire autoriteiten het monetaire beleid verkrappen, loopt de rentevoet op. Deze rentestijging biedt niet alleen aantrekkelijker beleggingsalternatieven, maar kan ook de winsten van ondernemingen onder druk zetten. Aan de ene kant doordat de financieringskosten van ondernemingen stijgen, anderzijds doordat de effectieve vraag door de rentestijging zal worden afgeremd. De rentestijging kan daarom ook de dividendverwachtingen temperen. Omdat bij een conjunctuuromslag sommige bedrijven in problemen kunnen komen, is ook het stijgen van de risicopremies niet onwaarschijnlijk. Deze veranderingen zullen bijna alle bedrijven treffen, maar niet in gelijke mate. Van de bedrijven die volgens de markt kwetsbaarder zijn, zullen de koersen harder dalen. De meer conjunctuurgevoelige bedrijven hebben een hogere beta.

Opgaven:

Geef voor de volgende gebeurtenissen aan welke onderdelen van vergelijking (9) veranderen en wat de invloed is op de koers van het aandeel. Het gaat om een AEX fonds.

1. Een onderneming laat weten dat de winst over het laatste kwartaal 10% is gestegen. Dat is veel, maar wel minder dan analisten hadden verwacht. 2. Een Amerikaanse concurrent doet een grote overname in Europa en kondigt aan hier versneld te willen groeien. 3. De oorlogsdreiging in het Midden Oosten neemt sterk toe. 4. Er wordt een flinke verlaging van de Vennootschapsbelasting aangekondigd. 5. De centrale bank verhoogt haar rentetarieven minder dan verwacht. 6. Door overbesteding dreigt de inflatie flink op te lopen. 7. Het reeds forse tekort op de Amerikaanse handelsbalans valt veel groter uit dan verwacht. 8. Het financieringstekort van de Duitse overheid valt veel lager uit dan verwacht.

APPENDIX: HET GORDON MODEL

Beleggers zijn bereid vandaag meer geld voor een aandeel te betalen naarmate zij verwachten daar morgen meer mee te kunnen verdienen. Deze zeer algemene uitspraak krijgt in het model van Gordon een precieze vertaling, die bovendien rekening houdt met wat de tijdswaarde van het geld wordt genoemd. Dit laatste houdt in, dat een euro vandaag meer waard is dan een euro morgen. Hoeveel meer? Wel, dat hangt af van de tijdsvoorkeur, de inflatieverwachting en de risicoperceptie van de beleggers. De eerste twee factoren komen ook tot uitdrukking in de rente op staatsobligaties.

Volgens het Gordon model is de marktwaarde van een aandeel de contante waarde van de cash flow die het naar verwachting zal genereren. Als we er van uit gaan dat een aandeel niet wordt verkocht, dan bestaat die cash flow uitsluitend uit dividendbetalingen. Als we echter van een tijdelijke beleggingsperiode of horizon uitgaan, en dus aannemen dat het aandeel na een bepaalde periode wordt verkocht, dan omvat de cash flow naast verwachte dividendbetalingen ook de verwachte verkoopprijs van het aandeel. Het feit nu, dat het bij de waardering van aandelen uitdrukkelijk om verwachtingen gaat, is van doorslaggevende betekenis voor het begrijpen van de prijsvorming van aandelen. Terwijl juist in onzekere situaties rationeel gedrag gewenst is, biedt deze zelfde onzekerheid veel ruimte voor heftige emoties zoals angst en hebzucht. Onze logische benadering van de prijsvorming van aandelen mag ons niet het zicht ontnemen op de psychologische kant.

We kunnen het cash flow model als volgt formaliseren. Bij een oneindige beleggingsperiode is de contante waarde van het aandeel:

(1) [pic]

Hierin is P0 de prijs van het aandeel. Aan de andere kant van de vergelijking staat de contante waarde van de verwachte dividendbetalingen. D1 is het dividend van het eerste jaar, D2 van het tweede jaar, D3 van het derde jaar, enzovoort. Het disconteren gebeurt op basis van de rendementseis r die op dat moment door de markt wordt gehanteerd. Deze bestaat uit de rente op staatsobligaties plus een risicopremie. De rente laat zich ook interpreteren als maat voor de aantrekkelijkheid van alternatieve beleggingsmogelijkheden zoals staatsobligaties in vergelijking tot aandelen. Dat beleggers voor aandelen hogere rendement eisen dan voor staatsobligaties ligt voor de hand. De risico’s zijn immers hoger.

Laten we een andere beleggingsperiode kiezen. Als een belegging na een jaar wordt verkocht, wordt de cash flow:

(2) [pic]

De verwachte cash flow bestaat nu uit een verwacht dividend en een verwachte koers P1 aan het einde van de beleggingsperiode. Het probleem is het bepalen van de te verwachte koers. De eerste vergelijking biedt ons de oplossing. Volgens deze vergelijking moet gelden:

(3) [pic]

Als we deze vergelijking in vergelijking (2) substitueren, krijgen we gewoon vergelijking (1) weer terug:

(4) [pic]

We kunnen dus concluderen dat ongeacht de beleggingsperiode, de waarde van het aandeel kan worden gezien als de contante waarde van de dividenduitkeringen.

Over de ontwikkeling van het dividend kunnen we verschillende veronderstellingen maken. We nemen aan dat het dividend groeit. De gemiddelde lange termijn groeivoet van het dividend geven we aan met de letter g. Het begrip groei wordt ruim geïnterpreteerd. De groeivoet kan negatief, nul of positief zijn. De groeivoet g zal echter wel kleiner moeten zijn dan de rendementseis van beleggers. Als dat niet zo zou zijn, dan zou, zoals straks uit de wiskundige uitwerking van deze ideeën kan worden afgelezen, de prijs van het aandeel oneindig groot worden. Iets dat we in de praktijk niet zien. Waarom niet, dat laat zich economisch goed verklaren. Uiteraard kan de groeivoet van het dividend wel tijdelijk groter zijn dan de rendementseis van beleggers. In dat geval zal het bedrijf echter geprikkeld worden haar investeringen verder en verder op te voeren. Dat leidt via afnemende meeropbrengsten, stijgende prijzen van complementaire productiefactoren en dalende prijzen voor de eigen producten, tot een zodanige daling van het rendement op het geïnvesteerd vermogen, dat de groei van de winst en het dividend dat daaruit betaald wordt weer onder de rendementseis van de beleggers uitkomt. Het precieze verband tussen rendement en groei wordt later besproken.

Als het dividend een groeivoet g heeft, geldt:

[pic], [pic] , enzovoort.

Als we deze uitdrukkingen in vergelijking (1) substitueren, krijgen we:

(5) [pic]

Het rechter lid vormt een meetkundige reeks getallen die we kunnen sommeren mits de positieve reden van de reeks kleiner is dan 1. De reden kan worden gevonden door een willekeurige term door zijn voorganger te delen. We vinden dan: (1+g)/(1+r). Dit getal is kleiner dan 1 als g…...

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Gordon Ramsay Sea Bass with Pepper Sauce

...Gordon Ramsay’s Sea Bass with Pepper Sauce * Filet of Sea Bass * Bell Pepper – 1 large red and 1 large yellow, or several of both * Shallots – 3 * Star Anise – 3 * White Wine Vinegar – 1 1/2 Tbs * Vermouth – 2 Tbs * Olive Oil * Fresh Thyme Sprig leaves * Salt * Fresh Basil – 1 very large sprig, or two smaller ones * Water Directions for the Sauce: Julienne the bell pepper, do the same with the shallots. Heat olive oil in a hot pan, then add the peppers and shallots, add star anise and a pinch of salt. Stir well and cook for several minutes until the peppers are beginning to soften up. Add the basil whole, and pour in the white wine vinegar and vermouth. Reduce for several minutes over moderate heat until liquid is mostly absorbed. Add enough water to the pan to cover the peppers half way. Bring to a boil and simmer until liquid is about half gone. Carefully add all of the ingredients to a blender and liquify. Be sure to hold the lid on the blender. Many of my readers discovered when making another Chef Ramsay dish which required a blender that it’s helpful to hold the lid on with a dry towel (no burns, no messes). Directions for the Fish: Lay the fish on a cutting board skin side up. Score the fish every half inch along the length of the filet. Add salt and thyme leaves to the inside of each score, then drizzle with olive oil. You can now lovingly hold and caress the filet in your hands if you’re as crazy as Chef Ramsay about......

Words: 461 - Pages: 2