All answers provides very good insights, but I noticed most of them are attached to the idea that investing means buy... so, two things that could be clarified:
when you mean invest, you'd like to suggest to the owners of this new small company you're working on to buy new productivity softwares or you mean investing man-hours developing new softwares?
Have you searched for free similar softwares?
My point is: there's a slightly possibility of having your bosses hearing your suggestion not as more expenses, but as something that could add value into your daily work.
I see you're a person that's called a 'prophet', a people who thinks beyond the ordinary things. However, there are barriers to cross from a prophet to become a builder... and the first one is to prove that what you're thinking really applies to the scenario you have in place.
I'd go for something like this:
- Brainstorming the idea with some teammates (or maybe part of the idea, in case you're afraid any of them could 'steal' your ideas) and pick some that buy it in;
- Once you have some people, startup a pilot, probably applying a free version of the softwares you want to suggest to your bosses;
- After a while, you'll have the first experiences and outcomes of your suggestion... and will have something to be based on when getting back to your bosses beyond 'I have an Idea'. At this stage, you'll have an idea and some proofs that your idea really works.
And, only after you're comfortable your ideas really worth, I'd go for the meeting with the bosses.
Hope it helps!