A method has been proposed for the exact evaluation of the Vainshtein-Presnyakov-Sobel'man (VPS) amplitude (1964) as applied to electron-atom excitation processes, without resorting to any peaking approximation as used so far by all previous authors. The present approach is equally applicable to excitation processes under heavy-particle impact. The final scattering amplitude has been reduced to a simple one-dimensional real integral which can be evaluated numerically. Both the post and the prior versions of the VPS theory have been studied through the present approach and the post-prior discrepancy has been examined critically. The present post results are found to be in agreement with the corresponding results of Crothers and McCarroll using the peaking approximation. However, the present prior results, through exact calculations, are found to differ markedly from the prior results of Vainshtein et al. who adopted some ad hoc approximations in their peaking approximation.