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

Journal of Economics and Financial Studies, Vol. 4 No. 2 (2016), pp 31-45

18 Pages Posted: 29 Jun 2016

See all articles by Domingo A. Tarzia

## Domingo A. Tarzia

Univ. Austral, FCE, Mathematics Department & CONICET

Date Written: March 16, 2016

### 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.

Keywords: Financial break-even point, investment project, net present value, discount rate, accounting break-even point, break-even analysis, growth rate, asymptotic behavior, sensitivity analysis

JEL Classification: C02, C63, G10, G31

Suggested Citation

Tarzia, Domingo A., Properties of the Financial Break-Even Point in a Simple Investment Project as a Function of the Discount Rate (March 16, 2016). Journal of Economics and Financial Studies, Vol. 4 No. 2 (2016), pp 31-45, Available at SSRN: https://ssrn.com/abstract=2801369