This paper studies the discrete-time cheap control problem for sampled data systems using the theory of singular perturbations. It is shown, by using the two time-scale property of singularly perturbed systems, that the problem can be solved in terms of two reduced-order subproblems for which computations can be done in parallel, thus increasing the computational speed. Similarly to the continuous-time case, the singular perturbation approach enables the decomposition of the algebraic Riccati equation into two reduced-order pure-slow and pure-fast continuous-time algebraic equations.