Some engineers assume reimbursement is automatically set by the legal pro rata permitted by a federal fund type and expect invoices to be paid at that rate.  That’s true for most projects, but inaccurate for underfunded projects.  (Just in case you were unfamiliar with the term, underfunded projects are essentially projects where local agencies are contributing more local/other funds than are required to match for their federal funds.)  The LAPM provides a good example to help explain how the reimbursement ratio is calculated for underfunded projects:

The calculated federal reimbursement ratio is computed by dividing the amount of federal funds authorized by the total participating costs as shown on the E-76. If the local agency has obtained a better estimate of the project costs, it is the responsibility of the agency to contact the DLAE to request a revision of the E-76 to reflect the proper reimbursement ratio.

For example, project CML – XXXX (XXX) has:

• Federal participating ratio of 100%

• Normal pro-rata share of 88.53%.

• Total estimated costs of the project are $100,000.00

• Total federal funds are $60,000.00

• The Federal Appropriation Code is Q240

• The reimbursement ratio would be: $60,000.00 / $100,000.00 = 60%

If the federal funding ($60,000) divided by the federally participating costs ($100,000) is less than the full pro-rata share (88.53%), the project is considered under funded. In this case, the progress payments must be reimbursed at the lower reimbursement ratio, which is 60%. On the final invoice, the reimbursement ratio may float up to 88.53% to allow all of the federal funds to be used as long as the total payments for the project do not exceed the total federal funds authorized.

Using the example above, project CML-XXXX (XXX) has incurred actual costs of $100,000.00. The federal reimbursement would cap at $60,000 since that was the amount requested/allocated for this project. If the project was fully funded, the federal reimbursement would have been capped at $88,530 ($100,000 x 88.53%).

via Local Assistance Procedures Manual, Chapter 5, Page 5-8