Random Variables, the Time Value of Money and Capital Expenditures

This paper treats the following problem. How much money should be invested at time t₀ at an interest rate of I for a time T such that the probability of the funds required “K(T)” exceeding those available “X(T)” equals at most p. That is P{K(T) > X(T)} ≤ p, where X(T) = X(t₀) exp{ I(T − t₀)}. The parameters I, T, X(T) and K(T) are taken to be random variables. The theory to solve the stated problem is presented and solutions to certain specific cases are given.