Here's the scenario: Your budget is tight tight tight. You could use a new car, but there's no way it will fit into your budget. Somebody comes along and says, "I will cover the first 36 months of a 48 month car loan, but you have to pay the final 12 months". You don't know what your budget will look like after three years. You assume it will be better, but there's just no way to know. Taking the deal may put you in financial distress three years from now. Not taking it seems foolish because, well, who turns down that kind of a gift? What do you do?
Now you're the City of Lincoln. The Feds want to pay for four police officers for three years, as long as Lincoln covers year four. (We also have to fund them beyond year four if we want to keep them, but at that point it's up to us.) Do we take the cash (and the cops)?