The "trick" is to show clearly and in writing the payoff from an improvement. In my business, if a guy comes to me with an idea, I make him put a case for it together. I'm fortunate in that I am still an engineer at heart, and I can usually tell if it's a good idea or not. But, you should pity the poor bean counter, who has no idea what you are talking about most of the time. You have to convert your ideas, and the reasons for implementing them, into a language he understands - namely, costs and savings.
You don't need to know ROI (Return On Invsetment) or present worth or double entry accounting to do that. You do need to analyze the problem, and state it clearly in writing. This includes the costs in lost production or wasted energy or whatever applies. You need to know the solution, and the cost of the solution, including material, manpower, and energy. You need to know the savings the solution will create, in dollars, or manpower, or energy, or increased production, or reduced scrap, or whatever. You need to state these savings in writing. Then, you divide the cost by the net savings per year, and you get the time required for the investment to payback by virtue of the savings. Then, the bean counters can decide if that is the best use of the money available at the time.
Remember, there are lots of competing uses for the cash your company has available. Some of these, like taxes and payroll and electric bills, are not optional. Others, like investments to improve productivity, are either optional or at least can be postponed if cash is short. It is the accountant's job to decide which of the many uses for cash are the best at any given time. If your idea has a payback of three years, and another has a payback of one year, which one should the company spend its money on? If management has a choice between an idea with a calculated payback of one and a half years, and another that just has you saying "This is a good idea and can save tons of money", which one should the company spend its money on?
After all, it is probably a good idea for you to have a little car to use for grocery shopping, a larger car for vacations and long trips, a big truck for hauling things around, a sports car for nights on the town, and a full sized used car for the kids to drive. Do you have all of these? Why not? Why should management treat their money or the stockholders money differently than you treat your own?