Random Variables, the Time Value of Money and Capital Expenditures

Abstract

This paper treats the following problem. How much money should be invested at time t 0 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 ( t 0 ) exp{ I ( T − t 0 )}. 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.