In this paper exponential distribution is implemented as a demand distribution in newsvendor model with two different and conflicting goals. The first goal is the standard objective of maximization of the expected profit. The second one is to maximize the probability of exceeding the expected profit, called survival probability. Using exponential distribution as the demand distribution allows us to obtain the exact solutions. Also for this distribution we can study the monotonicity of survival probability with respect to various model parameters analytically. Additional results are obtained when various sets of the parameters are considered. Finally, the bicriteria index which combines these conflicting objectives is optimized which gives the compromise solution. Moreover, in order to illustrate theoretical results, we present numerical examples and graphs of auxiliary functions.