A Central Limit Theorem for Present Values of Discounted Cash Flows

A renewal process is defined to represent the present value of a stream of money payments occurring at random times.The objective is to partially close a gap in the state of knowledge regarding the properties (asymptotic behavior) of certain cashflow models, scheduling models, and inventory models, all of which can be embedded in the context of replacement-reliability theory in general. The contribution of this paper is a characterization of the asymptotic distribution of a general capitalized random variable as the time-invariant rate of discount approaches zero. The main result is a central limit theorem demonstrating that the standardized distribution of the discounted random variable converges to the unit normal as the discount rate approaches zero.