Purpose - The purpose of this paper is to present an arbitrarily accurate approximation for the value of European options written on a Black-Scholes stock paying a discrete dividend. Design/methodology/approach - The proposed method is a computational method for the analytical solution of the problem. FindingsIt was found that the proposed method is computationally faster than any other exact computational available method, including Monte-Carlo simulations. Research limitations/implications - The method is applied for a single dividend payment, but can be extended for several payments. The exact amount of the dividend must be known ex-ante, as well as the precise date of payment. Practical implications - The paper provides the most efficient way to compute with absolute precision the value of European options on dividend-paying assets, under the Black-Scholes assumption. Originality/value - The computing time in the approach is several orders of magnitude faster than with traditional Monte Carlo methods, for the same desired accuracy.