To make sure this is understood, take a very simple example. Let v(k) = 2-k for all k. This is a constant interest rate per period of 100 %. In other words, money doubles itself every period. This is of course not very realistic for a period of a year, but it could hold for a sufficiently long interval. Suppose we are to receive 12 units at time 2, but will be required to pay out 8 units at time 3. Find the present value, and verify that it makes sense.