I want to track expenditures by adding the value of purchase orders minus the initial budget.

[Roberto Cioni]

 I have a list for each contract I manage, and I am adding cards for every Purchase Order related to the list. 

 I want to track the contract expenditure by summing the PO value and automatically calculating the remaining budget for each contract (Initial budget-POs totals).

[Luciana Munhoz]

Hi Roberto, welcome to Trello community!

According to what you said, I'm afraid Trello natively is not able to do that kind of calculation. 
In paid Workspaces, you can use Custom Fields to add some information to cards, but not to perform mathematical operations like that.

A suggestion is to take a look at some of the 3rd party Power-ups here: https://trello.com/power-ups/search?q=calculate

And explore the option to see if there's some that would better match your needs.

Hope that helps!