Been on both sides of that coin. The question is not how much something costs but whether the value generated is worth the cost, that would make it in the best interest of the business and not your pocket.
There is a life cycle to a business and one of the surest ways to creating a short one is...
Such a simple question but a way more complex concept as can be seen by all the responses and the number of business management courses in the universe.
I would start by defining what 'Productivity' is in your specific environment, you need to know the face of you're enemy before you attack...