  We establish explicit exponential convergence estimates for the renewal
theorem, in terms of a uniform component of the inter arrival distribution, of
its Laplace transform which is assumed finite on a positive interval, and of
the Laplace transform of some related random variable. Our proof is based on a
coupling construction relying on discrete-time Markovian structures that
underly the renewal processes and on Lyapunov-Doeblin type arguments.
