Before revision:  We prove the existence of a solution to the sender's utility maximization problem and characterize its properties . In solving this problem, we develop a novel approach for solving Bayesian persuasion problems, which can be applied to a wide range of settings. We characterize the sender's willingness to pay for an additional signal as a function of the prior belief, which we interpret as the value of precise communication.
After revision:  We prove the existence of a solution to the sender's problem is proven and its properties are characterized. This generalizes the standard Bayesian Persuasion framework, in which existence results rely on the assumption of rich signal spaces. We analyze the sender's willingness to pay for an additional signal as a function of the prior belief, which we interpret as the value of precise communication.