Present values and internal rates of return

This paper resolves the question of finding the complete set of conditions under which the present value of a return stream decreases as interest rates rise. Previous work has shown that if a return stream can be costlessly abandoned, or truncated, at any date prior to its natural termination, then its value is monotone. We show that truncation is the same as monotonicity. First, monotonicity is equivalent to the value function being identical to the truncation set value function. Second, monotonicity is equivalent to the truncation set being contained within the convex hull, augmented by free (value) disposal.