Value-of-time is a critical willingness-to-pay indicator in many transportation applications. In this paper, we discuss the computation of this measure in the case of discrete choice models allowing for random taste heterogeneity. We first present the theoretical assumptions associated with models using randomly distributed travel-time coefficients, and highlight several important issues that must not be neglected when such an approach is adopted in practice. We then look in detail at the issue of models producing a non-zero probability of positive travel-time coefficients, and discuss the consistency of such estimates with theories of rational economic behaviour. We note that by using an unbounded statistical distribution, positive travel-time coefficients are postulated empha priori by the researcher, rather than being emphrevealed by the data. We then illustrate how to compute the value-of-time from randomly distributed travel-time coefficients, using various experiments. Finally, we present a simple application to illustrate some concrete difficulties associated with estimating such models. Our results show that the model providing the best estimation results (in terms of recovering the true distribution of the value-of-time) is not necessarily the model giving the best fit to the data. Furthermore, our results show that the use of distributions whose behaviour in the tails is inconsistent with the intuitive understanding of the associated coefficients may sometimes lead to better estimates of the moments of the emphtrue distribution of the value-of-time savings.