{"id":957,"date":"2021-04-09T04:16:24","date_gmt":"2021-04-09T03:16:24","guid":{"rendered":"https:\/\/agripedia.ch\/terminologie\/?page_id=957"},"modified":"2024-04-29T14:17:20","modified_gmt":"2024-04-29T13:17:20","slug":"anhang-10-dynamische-investitionsrechnung","status":"publish","type":"page","link":"https:\/\/agripedia.ch\/terminologie\/anhaenge\/anhang-10-dynamische-investitionsrechnung\/","title":{"rendered":"Anhang 10: Dynamische Investitionsrechnung"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1144px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><script src=\"https:\/\/polyfill.io\/v3\/polyfill.min.js?features=es6\"><\/script>\n<script id=\"MathJax-script\" async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-mml-chtml.js\"><\/script><div class=\"fusion-title title fusion-title-1 fusion-sep-none fusion-title-text fusion-title-size-two\"><h2 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:40;line-height:1.5;\">Dynamische Investitionsrechnung<\/h2><\/div><div class=\"fusion-text fusion-text-1\"><p lang=\"de-DE\" align=\"justify\">Alle drei Methoden beruhen auf folgendem finanzmathematischem Ansatz.<\/p>\n<p lang=\"de-DE\" align=\"justify\">\\(C = \\frac + \\frac + \u2026 + \\frac + \u2026 + \\frac \\)<\/p>\n<p lang=\"de-DE\" align=\"justify\">oder<\/p>\n<p lang=\"de-DE\" align=\"justify\">\\(C = \\sum\\limits_^n \\frac \\)<\/p>\n<p align=\"justify\">wobei:<\/p>\n<p align=\"justify\">\\(C\\) = Barwert aller \u00dcbersch\u00fcsse aus der Differenz von Einnahmen und Ausgaben (discounted Cashflow); wird auch als Kapitalwert bezeichnet<br \/>\n\\(E\\) = Einnahmen<br \/>\n\\(A\\) = Ausgaben<br \/>\n\\(j\\) = \\(j\\)-te Periode<br \/>\n\\(n\\) = Anzahl Perioden<br \/>\n\\(p\\) = kalkulatorischer Zinsfuss<br \/>\n\\(r\\) = Auszinsungsfaktor = \\( (1 + \\frac)\\)<\/p>\n<p align=\"justify\">Gemeinsames Merkmal aller drei Methoden ist es auch, dass die Periodenzahl und die darin anfallenden Ausgaben und Einnahmen als bekannt bzw. absch\u00e4tzbar vorausgesetzt werden.<\/p>\n<p align=\"justify\">Bei der <b>Kapitalwertmethode<\/b> wird zus\u00e4tzlich ein Zinsfuss (= Kalkulationszinsfuss) \u2013 meist in Anlehnung an einen Marktzinsfuss \u2013 in die Beziehung eingesetzt. Aus dem finanzmathematischen Ansatz resultiert dann der Barwert aller \u00dcbersch\u00fcsse oder mit anderen Worten der Kapitalwert als direktes Ergebnis. Eine sich lohnende Investition weist einen positiven Kapitalwert auf.<\/p>\n<p align=\"justify\">Bei der <b>Methode des internen Zinsfusses<\/b> wird der Barwert aller \u00dcbersch\u00fcsse Null gesetzt. Gesucht ist dann derjenige Zinsfuss, der zur Erf\u00fcllung der Beziehung f\u00fchrt. Man bezeichnet diesen Zinsfuss auch als interne Rendite. Ist die interne Rendite h\u00f6her als ein Vergleichszinsfuss, so lohnt sich die Investition. Der Rechnungsgang ist mathematisch anspruchsvoll. Der interne Zinsfuss kann in der Regel nur mit Hilfe eines N\u00e4herungsverfahrens ermittelt werden.<\/p>\n<p align=\"justify\">Bei der <b>Annuit\u00e4tenmethode<\/b> ist das durchschnittliche Jahresergebnis, oder allgemeiner formuliert, das durchschnittliche Periodenergebnis von Interesse. Mathematisch gesehen, l\u00e4sst sich die Annuit\u00e4tenmethode als eine Erweiterung der Kapitalwertmethode interpretieren. Um durchschnittliche j\u00e4hrliche \u00dcbersch\u00fcsse zu erhalten, wird der Kapitalwert mit dem Annuit\u00e4tenfaktor multipliziert.<\/p>\n<p align=\"justify\">Der Annuit\u00e4tsfaktor lautet: \\( \\frac\\)<\/p>\n<p align=\"justify\">Zusammen mit dem oben erw\u00e4hnten Ansatz ergeben sich f\u00fcr die Berechnung der Annuit\u00e4t (\\(a\\)) folgende Formeln:<\/p>\n<p align=\"justify\">\\( a = C \\cdot \\biggl[ \\frac \\biggr] = \\biggl[ \\sum\\limits_^n \\frac \\biggr] \\cdot\u00a0 \\biggl[ \\frac \\biggr]\u00a0 \\)<\/p>\n<p align=\"justify\">Eine sich lohnende Investition weist eine positive Annuit\u00e4t aus.<\/p>\n<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-1 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><a class=\"fusion-modal-text-link agri-feedback-link\" data-toggle=\"modal\" data-target=\".fusion-modal.feedback_form_de\" href=\"#\">Haben Sie einen Fehler gefunden? 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