You have most of the material in your post. This is what I would do:
To:
Subject: Justification for Purchase, department scanner
XYZ department is [list what your department does]. Crucial to the success of this department, and the success of the company, is having the ability to prepare customer [or whatever the documents are] documents into digital formats for archieving and retrieval. Approximately 10 documents are scanned per week for the seven employees in the department, with roughly 500 documents scanned annually.
Currently, we are unable to meet this part of our mission because the department scanner is physically broken. It is vital that we be able to return to scanning documents as soon as possible. Request approval for the purchasing of a new scanner for this department.
A replacement scanner for the department needs to be able to handle our annual workload. We have researched various models, and have determined that the following scanner meets our requirements:
Company Scanner Model Name, Model number, price
We have compared this model from three different vendors (list), and have determined that [vendor's name] has the best price and has the model in stock.
If there are any questions concerning this request, please contact [name, extention, email].
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You can change things to meet your local situation. Hope this helps!