  We establish a link between the distribution of an exponential functional I
and the undershoots of a subordinator, which is given in terms of the
associated harmonic potential measure. This allows us to give a necessary and
sufficient condition in terms of the L\'evy measure for the exponential
functional to be multiplicative infinitely divisible. We then provide a formula
for the moment generating function of an exponential functional $I$ and the so
called remainder random variable $R$ associated to it. We provide a realization
of the remainder random variable $R$ as an infinite product involving
independent last position random variables of the subordinator. Some properties
of harmonic measures are obtained and some examples are provided.
