User wants to know the company's financial performance on a monthly or weekly frequency, based on time entries made (not invoices generated). Also wants to see the expenses on a monthly basis, including costs, income, expense and profit.
The Income Vs. Expenses dashboard widget in Core is an option, but it measures income by invoice.
You may want to check the Gross Margin Real-time report as it is agnostic to whether you have billed time or expenses, but it is by project. You can schedule this report to be delivered to key stake holders within your company at a desired frequency.
You can look at the Project Time and Expense report. With correct options and filters, it can work for you especially if you are trying to compare revenue vs. cost.
Then you may find Hours, Staff Utilization and Time Performance widgets useful. Hours widget allows you to look at hours spent by your employees, by quarter, month, week, etc. Also the Utilization widget is real handy to gauge the performance of your employees based on the billable hours spent vs. total time. You can use filters to narrow down the data to the period you are analyzing. The Time Performance chart gives you a company-wide breakdown of PTO, Overhead, and Non-Billable Hours.
Lastly, you can opt for a customized report that will have columns for billable, non-billable and additional expenses. You can memorize this report or schedule it to be delivered to the required employees at a set frequency.