I am looking for advice/guidance (on specific points) on generating/creating a document for convincing my boss to invest in some hardware to make my job easier and more-productive.
Background
The background of why I'll put simply, I work in automation developing scripts and when I run them it occupies one of my screens and sometimes two screens which ends up limiting my ability to get any work done somedays. A solution proposed by my boss was to get another machine installed at my desk and use it as a 'remote' machine where I install all the software I need and that IS a viable solution however it will cost a bomb, like €1500 for it. (Most of the cost is from hiring to 3rd party contractors to install an extra LAN port for the new machine, I'll break it down in the comments if someone wants)
After talking with other people in the industry some have recommended a USB to VGA cable which for all purposes I can see, is exactly what I need.
Question
I'm stuck on how to formulate a document to give to my boss that demonstrates this is a much better investment of money and to present it to him. If you were a manager what details would you look for on a document that would make you say "Yes you are right D, this would be a better option for us in many ways." In my company I am not familiar with any formal way of submitting a document that is present here, I don't think there is one and I want to submit something that won't be scorned at or passed off without proper consideration.
Addendum.
So far on my document I have a short 2 line intro, a price comparison between the adapter I found and the new machine install, a chart showing my screen occupation time by my scripts and how much it impacts my work capability (per week) and another chart beside it showing how much more I could accomplish with something that is cheaper (in a man day count over 6 months). I also have where we can buy it and how soon we can install it. I feel like something is missing that when looked at from a managerial position is incredibly obvious but that I am lacking in knowledge of knowing while writing one with no formal guidelines here to follow.
EDIT: Thanks for the duplicate marking, I didn't see that other question. Found my answer there that helped me in identifying details I need for my document. Details in how to outline "business case" better specifically for me in GuyM's answer.