In this paper two expressions are derived for the expected gain in information provided by a hybrid censored experiment using Shannon-Lindley's measure. The first expression is used to provide information about the scale parameter of the exponential model or any one-to-one transformation of it whereas the second one is appropriate when the objective is to gain knowledge about a future observation. Attention is restricted to the case where sampling is with replacement. Properties of the derived expressions are studied and some applications are considered particularly in assessing the loss of information through the use of hybrid censoring in comparison to type I and type II censoring. Numerical results are provided for illustration.