Mid-Year and End-of-Year Conventions in Achieving Convergence Among Discounted Cash Flow Models

Abstract

In my paper, I have managed to achieve full convergence of the results of valuation executed by four methods (CCF, APV, DCF and CFE), provided that cash flow is generated throughout the year (Mid-Year Convention). I have shown that convergence among all methods can be achieved whether we use the End-of-Year Convention or Mid-Year Convention. I have demonstrated an analytical solution to the circularity problem in practice using the End-of-Year Convention proposed by Velez-Pareja and Mejia (2010). Based upon their solution to the circularity problem I propose a new, universal solution to achieving convergence among all methods on the condition that the Mid-Year Convention holds true. All four methods coincide with the APV and CCF methods, which are the best methods to calculate value without circularity. These two methods require neither target leverage nor iterations.One of the most significant findings of this paper is how the generally accepted Mid-Year Convention (the 0.5 time-factor) differs from the accurately calculated, proper Time-Factor for the FCF and CFE methods which has to be applied in order to achieve convergence among all four methods. I have proved scientifically that the generally accepted Mid-Year Convention (the 0.5 time factor or approximately 0.5) produces significant bias in the DCF and CFE methods which can materially distort the resulting values. Now I can soundly argue with many authors and some practitioners who state that annual cash flow with the generally accepted mid-year factor (0.5 or approximately 0.5) does not produce a material bias in the cash flows on a daily, weekly or monthly basis.