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Properties of the Financial Break-Even Point in a Simple Investment Project As a Function of the Discount Rate

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  • Domingo Alberto Tarzia

    (Depto. Matemática – CONICET, FCE, Univ. Austral, Paraguay 1950, S2000FZF Rosario, Argentina.)

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:lrc:lareco:v:4:y:2016:i:2:p:31-45
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    References listed on IDEAS

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    More about this item

    Keywords

    Financial break-even point; Investment project; Net present value; Discount rate; Accounting break-even point; Asymptotic behavior; Sensitivity analysis.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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