IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1611.03740.html
   My bibliography  Save this paper

Properties of the financial break-even point in a simple investment project as a function of the discount rate

Author

Listed:
  • Domingo A. Tarzia

Abstract

We consider a simple investment project with the following parameters: I>0: Initial investment 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; r: 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) 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 r and we prove that: (i) For r negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null) ; (ii) When r 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 r; (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.

Suggested Citation

  • Domingo A. Tarzia, 2016. "Properties of the financial break-even point in a simple investment project as a function of the discount rate," Papers 1611.03740, arXiv.org.
    • Handle: RePEc:arx:papers:1611.03740
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1611.03740
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Reichelstein, S, 2000. "Providing managerial incentives: Cash flows versus accrual accounting," Journal of Accounting Research, Wiley Blackwell, vol. 38(2), pages 243-269.
    2. Mario Vanhoucke & Erik Demeulemeester & Willy Herroelen, 2001. "On Maximizing the Net Present Value of a Project Under Renewable Resource Constraints," Management Science, INFORMS, vol. 47(8), pages 1113-1121, August.
    3. Grinyer, John R & Walker, Martin, 1990. "Deprival Value-Based Accounting Rates of Return under Uncertainty: A Note," Economic Journal, Royal Economic Society, vol. 100(402), pages 918-922, September.
    4. Robert E. Stanford, 1989. "Optimizing Profits from a System of Accounts Receivable," Management Science, INFORMS, vol. 35(10), pages 1227-1235, October.
    5. Brick, Ivan E & Weaver, Daniel G, 1997. "Calculating the Cost of Capital of an Unlevered Firm for Use in Project Evaluation," Review of Quantitative Finance and Accounting, Springer, vol. 9(2), pages 111-129, September.
    6. Christoph Schwindt & Jürgen Zimmermann, 2001. "A steepest ascent approach to maximizing the net present value of projects," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 435-450, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Domingo Alberto Tarzia, 2016. "Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate," Journal of Economic and Financial Studies (JEFS), LAR Center Press, vol. 4(2), pages 31-45, April.
    2. M. Vanhoucke, 2006. "A scatter search procedure for maximizing the net present value of a project under renewable resource constraints," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/417, Ghent University, Faculty of Economics and Business Administration.
    3. Thomas Pfeiffer, 2004. "Net Present Value‐Consistent Investment Criteria Based on Accruals: A Generalisation of the Residual Income‐Identity," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(7‐8), pages 905-926, September.
    4. Wenhui Zhao & Nicholas G. Hall & Zhixin Liu, 2020. "Project Evaluation and Selection with Task Failures," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 428-446, February.
    5. M. Vanhoucke, 2006. "An efficient hybrid search algorithm for various optimization problems," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/365, Ghent University, Faculty of Economics and Business Administration.
    6. Leyman, Pieter & Vanhoucke, Mario, 2017. "Capital- and resource-constrained project scheduling with net present value optimization," European Journal of Operational Research, Elsevier, vol. 256(3), pages 757-776.
    7. Mika, Marek & Waligora, Grzegorz & Weglarz, Jan, 2005. "Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models," European Journal of Operational Research, Elsevier, vol. 164(3), pages 639-668, August.
    8. He, Zhengwen & Wang, Nengmin & Jia, Tao & Xu, Yu, 2009. "Simulated annealing and tabu search for multi-mode project payment scheduling," European Journal of Operational Research, Elsevier, vol. 198(3), pages 688-696, November.
    9. Chen, Jiaqiong & Askin, Ronald G., 2009. "Project selection, scheduling and resource allocation with time dependent returns," European Journal of Operational Research, Elsevier, vol. 193(1), pages 23-34, February.
    10. Magni, Carlo Alberto, 2009. "Splitting up value: A critical review of residual income theories," European Journal of Operational Research, Elsevier, vol. 198(1), pages 1-22, October.
    11. Ivan E. Brick & Hong-Yi Chen & Chia-Hsun Hsieh & Cheng-Few Lee, 2016. "A comparison of alternative models for estimating firm’s growth rate," Review of Quantitative Finance and Accounting, Springer, vol. 47(2), pages 369-393, August.
    12. Pfaff, & Troßmann,, 2016. "Die Kosten- und Leistungsrechnung – Ein Blick auf mehr als 70 Jahre Vergangenheit und eine spannende Zukunft," Die Unternehmung - Swiss Journal of Business Research and Practice, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 70(4), pages 365-386.
    13. Alfred Wagenhofer, 2014. "Trading off Costs and Benefits of Frequent Financial Reporting," Journal of Accounting Research, Wiley Blackwell, vol. 52(2), pages 389-401, May.
    14. Meißner, Fabian & Schneider, Georg & Sureth, Caren, 2013. "The impact of corporate taxes and flexibility on entrepreneurial decisions with moral hazard and simultaneous firm and personal level taxation," arqus Discussion Papers in Quantitative Tax Research 141, arqus - Arbeitskreis Quantitative Steuerlehre.
    15. Gunther Friedl & Björn Anton, 2010. "Anforderungen an ein wertorientiertes Management Accounting in Banken," Schmalenbach Journal of Business Research, Springer, vol. 62(61), pages 83-107, January.
    16. Tubetov, Dulat & Maart, Syster Christin & Musshoff, Oliver, 2012. "Comparison of the investment behavior of Kazakhstani and German farmers: An experimental approach," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 124650, Agricultural and Applied Economics Association.
    17. Cheung, Grace & Davies, Peter J. & Trück, Stefan, 2016. "Financing alternative energy projects: An examination of challenges and opportunities for local government," Energy Policy, Elsevier, vol. 97(C), pages 354-364.
    18. Eisdorfer, Assaf & Giaccotto, Carmelo & White, Reilly, 2015. "Do corporate managers skimp on shareholders' dividends to protect their own retirement funds?," Journal of Corporate Finance, Elsevier, vol. 30(C), pages 257-277.
    19. Andreas Haake, 2012. "Die Grundregeln von Herbert Hax zur Performance-Messung und die Bilanzierung von Kreditrisiken," Schmalenbach Journal of Business Research, Springer, vol. 64(1), pages 71-110, February.
    20. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1611.03740. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.