We consider a discrete-time dividend payout problem with risk sensitive shareholders. It is assumed that they are equipped with a risk aversion coefficient and construct their discounted payoff with the help of the exponential premium principle. This leads to a non-expected recursive utility of the dividends. Within such a framework not only the expected value of the dividends is taken into account but also their variability. Our approach is motivated by a remark in Gerber and Shiu (2004). We deal with the finite and infinite time horizon problems and prove that, even in general setting, the optimal dividend policy is a band policy. We also show that the policy improvement algorithm can be used to obtain the optimal policy and the corresponding value function. Next, an explicit example is provided, in which the optimal policy of a barrier type is shown to exist. Finally, we present some numerical studies and discuss the influence of the risk sensitive parameter on the optimal dividend policy.