Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate
- Autores
- Tarzia, Domingo Alberto
- Año de publicación
- 2016
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We consider a simple investment project with the following parameters: I>0: Initial outlay which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0; Price of the product with P>Cv; Cf>0: Annual fixed costs; te: Tax of earnings; : Annual discount rate. We also assume inflation is negligible. We derive a closed expression of the financial break-even point Qf (i.e. the value of Q for which the net present value (NPV) of the investment project is zero) as a function of the parameters I, n, Cv, Cf, te, r, p. We study the behavior of Qf as a function of the discount rate and we prove that: (i) For negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null); (ii) When is large the graph of the function Qf = Qf(r) has an asymptotic straight line with positive slope. Moreover, Qf (r) is an strictly increasing and convex function of the variable ; (iii) From a sensitivity analysis we conclude that, while the influence of p and Cv on Qf is strong, the influence of Cf on Qf is weak; (iv) Moreover, if we assume that the output grows at the annual rate g the previous results still hold, and, of course, the graph of the function Qf = Qf (r,g) vs r has, for all g>0 the same asymptotic straight line when r trends to infinite as in the particular case with g=0. From our point of view, a result of this type is the first time which is obtained by a simple investment project being the cornerstone of our proof the explicit expression of the net present value and the corresponding financial break-even point value. A policy implication of our findings is that the results can be taken into account for investment projects, especially in countries with very small or very large discount rates.
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina - Materia
-
Financial break-even point
Net present value
Discount rate
Investment project - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60904
Ver los metadatos del registro completo
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Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount RateTarzia, Domingo AlbertoFinancial break-even pointNet present valueDiscount rateInvestment projecthttps://purl.org/becyt/ford/5.2https://purl.org/becyt/ford/5We consider a simple investment project with the following parameters: I>0: Initial outlay which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0; Price of the product with P>Cv; Cf>0: Annual fixed costs; te: Tax of earnings; : Annual discount rate. We also assume inflation is negligible. We derive a closed expression of the financial break-even point Qf (i.e. the value of Q for which the net present value (NPV) of the investment project is zero) as a function of the parameters I, n, Cv, Cf, te, r, p. We study the behavior of Qf as a function of the discount rate and we prove that: (i) For negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null); (ii) When is large the graph of the function Qf = Qf(r) has an asymptotic straight line with positive slope. Moreover, Qf (r) is an strictly increasing and convex function of the variable ; (iii) From a sensitivity analysis we conclude that, while the influence of p and Cv on Qf is strong, the influence of Cf on Qf is weak; (iv) Moreover, if we assume that the output grows at the annual rate g the previous results still hold, and, of course, the graph of the function Qf = Qf (r,g) vs r has, for all g>0 the same asymptotic straight line when r trends to infinite as in the particular case with g=0. From our point of view, a result of this type is the first time which is obtained by a simple investment project being the cornerstone of our proof the explicit expression of the net present value and the corresponding financial break-even point value. A policy implication of our findings is that the results can be taken into account for investment projects, especially in countries with very small or very large discount rates.Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaLAR Center Press2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60904Tarzia, Domingo Alberto; Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate; LAR Center Press; Journal of Economic & Financial Studies; 4; 2; 5-2016; 31-452379-9471CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.journalofeconomics.org/index.php/site/article/view/226info:eu-repo/semantics/altIdentifier/doi/10.18533/jefs.v4i02.226info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:05:35Zoai:ri.conicet.gov.ar:11336/60904instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:05:35.718CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| title |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| spellingShingle |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate Tarzia, Domingo Alberto Financial break-even point Net present value Discount rate Investment project |
| title_short |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| title_full |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| title_fullStr |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| title_full_unstemmed |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| title_sort |
Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate |
| dc.creator.none.fl_str_mv |
Tarzia, Domingo Alberto |
| author |
Tarzia, Domingo Alberto |
| author_facet |
Tarzia, Domingo Alberto |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Financial break-even point Net present value Discount rate Investment project |
| topic |
Financial break-even point Net present value Discount rate Investment project |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/5.2 https://purl.org/becyt/ford/5 |
| dc.description.none.fl_txt_mv |
We consider a simple investment project with the following parameters: I>0: Initial outlay which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0; Price of the product with P>Cv; Cf>0: Annual fixed costs; te: Tax of earnings; : Annual discount rate. We also assume inflation is negligible. We derive a closed expression of the financial break-even point Qf (i.e. the value of Q for which the net present value (NPV) of the investment project is zero) as a function of the parameters I, n, Cv, Cf, te, r, p. We study the behavior of Qf as a function of the discount rate and we prove that: (i) For negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null); (ii) When is large the graph of the function Qf = Qf(r) has an asymptotic straight line with positive slope. Moreover, Qf (r) is an strictly increasing and convex function of the variable ; (iii) From a sensitivity analysis we conclude that, while the influence of p and Cv on Qf is strong, the influence of Cf on Qf is weak; (iv) Moreover, if we assume that the output grows at the annual rate g the previous results still hold, and, of course, the graph of the function Qf = Qf (r,g) vs r has, for all g>0 the same asymptotic straight line when r trends to infinite as in the particular case with g=0. From our point of view, a result of this type is the first time which is obtained by a simple investment project being the cornerstone of our proof the explicit expression of the net present value and the corresponding financial break-even point value. A policy implication of our findings is that the results can be taken into account for investment projects, especially in countries with very small or very large discount rates. Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina |
| description |
We consider a simple investment project with the following parameters: I>0: Initial outlay which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0; Price of the product with P>Cv; Cf>0: Annual fixed costs; te: Tax of earnings; : Annual discount rate. We also assume inflation is negligible. We derive a closed expression of the financial break-even point Qf (i.e. the value of Q for which the net present value (NPV) of the investment project is zero) as a function of the parameters I, n, Cv, Cf, te, r, p. We study the behavior of Qf as a function of the discount rate and we prove that: (i) For negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null); (ii) When is large the graph of the function Qf = Qf(r) has an asymptotic straight line with positive slope. Moreover, Qf (r) is an strictly increasing and convex function of the variable ; (iii) From a sensitivity analysis we conclude that, while the influence of p and Cv on Qf is strong, the influence of Cf on Qf is weak; (iv) Moreover, if we assume that the output grows at the annual rate g the previous results still hold, and, of course, the graph of the function Qf = Qf (r,g) vs r has, for all g>0 the same asymptotic straight line when r trends to infinite as in the particular case with g=0. From our point of view, a result of this type is the first time which is obtained by a simple investment project being the cornerstone of our proof the explicit expression of the net present value and the corresponding financial break-even point value. A policy implication of our findings is that the results can be taken into account for investment projects, especially in countries with very small or very large discount rates. |
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2016 |
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2016-05 |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/60904 Tarzia, Domingo Alberto; Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate; LAR Center Press; Journal of Economic & Financial Studies; 4; 2; 5-2016; 31-45 2379-9471 CONICET Digital CONICET |
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http://hdl.handle.net/11336/60904 |
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Tarzia, Domingo Alberto; Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate; LAR Center Press; Journal of Economic & Financial Studies; 4; 2; 5-2016; 31-45 2379-9471 CONICET Digital CONICET |
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eng |
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info:eu-repo/semantics/altIdentifier/url/https://www.journalofeconomics.org/index.php/site/article/view/226 info:eu-repo/semantics/altIdentifier/doi/10.18533/jefs.v4i02.226 |
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LAR Center Press |
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