Data-enabled predictive control (DeePC) is a recently proposed approach that combines system identification, estimation and control in a single optimization problem, for which only recorded input/output data of the examined system is required. In this work we present a simple method to identify a multi-step prediction model from the same data required for DeePC. We prove that model predictive control based on this model is equivalent to DeePC in the deterministic case and that its solution has the same structure in the stochastic case. We investigate the advantages and shortcomings of DeePC as opposed to the sequential system identification and control approach for linear models with and without measurement noise. We find that DeePC adds significant complexity to the optimization problem and can also lead to deterioration in control performance for the non-deterministic case, as we illustrate with a simulation example.