You have a quote. You have a manager who said "run it by finance." The draft you send is the quote and "can we get this approved?" Finance now has to invent the decision you did not write.
They see a lot of these. The ones that get a same-day answer look like a decision request, not a vendor PDF.
Open with the choice, not the vendor
"I need a decision on the log vendor for the next year: keep the current one, switch to the one in the linked quote, or do nothing until next quarter. I recommend the switch. If I have not heard by Thursday 16:00 UTC I will stay on the current one."
That is a note someone can answer from a phone. Respect their time. The quote can be a link. A briefing cannot hold the file, and it should not try. Put the numbers that decide the yes in sentences: term, seats or volume, what is already budgeted, what is not.
Do not write a price theatre of adjectives. Write the facts you have and mark the rest as estimates.
Show the alternatives you already killed
Finance will generate them anyway. "The cheaper tool does not retain enough history for the audit we already promised." "Building it ourselves is a quarter we do not have." One line each.
Include doing nothing as a real option, with its cost in risk rather than in money if that is the honest unit. An ask that treats "no" as hostility is an ask that will be delayed.
State the assumption the purchase sits on. "I am assuming we will still be on this stack in twelve months." If that is wrong, the rest of the note is cheap to redo. Buried in a paragraph, it will be approved by accident.
Say who owns it after the yes
Approvals fail after they succeed. Nobody named the owner, the renewal date, or the person who will notice if the seats go unused. Two sentences. Owner, review date.
If someone else already said yes in a hallway, write that as a claim with a name and a date, not as "this is already approved." Finance is allowed to disagree with a hallway.
Send a briefing they can file
You approve the words. If the finance partner has an account, you need an accepted contact. If they do not, they get email and a page. You do not need to share their planning tool.
A nickname you use for the vendor stays off the package unless it is a name they already use. Use the legal name on the quote.
If you already compared the options in a session, connect your assistant and have it list the rejected ones while you still remember why they lost.