Appropriated fund time limits fall into two categories: expiration and cancellation. Each has unique restrictions, so a good understanding of both is integral to proper and efficient management of financial assistance awards.
This information applies to:
Discretionary financial assistance programs
Each year Congress passes an appropriations bill which authorizes the federal government to expend public funds in specified ways. This is a constitutional requirement, often referred to as the ‘power of the purse’, which means the federal government cannot spend federal funds without express congressional approval.
Included in the annual appropriations bill is the time limit Congress establishes for expenditure of the specified funds. This is referred to as the ‘period of availability’ or 'period of obligational availability'.
Unless otherwise stated in the bill, appropriations are available for one federal fiscal year. This means those funds must be properly expended by the relevant governmental entity by the end of the current federal fiscal year. Some appropriations have longer or shorter periods of availability, specifically determined in the bill. For example, Resource Management funds appropriated to FWS are authorized for two-year periods of availability.
Excerpt from the FY2017 Appropriations Bill:
For necessary expenses of the United States Fish and Wildlife Service, as authorized by law, and for scientific and economic studies, general administration, and for the performance of other authorized functions related to such resources, $1,255,004,000 (reduced by $1,000,000) (increased by $1,000,000), to remain available until September 30, 2018. 
Time Limit Categories
The Service's program offices that award financial assistance awards need to be aware of both the expiration and cancellation time limits related to federal appropriations.
Appropriated funds expire following their period of availability as established in the Appropriations Bill.
An appropriation account expires “[a]t midnight on the last day of an appropriation’s period of availability” and is “no longer available for incurring new obligations.” 
Those funds which remain unobligated following their period of availability are considered expired. Deobligated funds after their period of availability are also considered expired. In each case, those expired funds are no longer available for use by the program office. The only expired funds that are "protected" are those which have been obligated to FA awards within their period of availability. These funds remain available to the recipient for drawdown ("liquidation") for eligible expenses for the period of performance of the award, or the appropriation's cancellation deadline (see below), whichever is earlier.
In practical terms, this means that FY2017 appropriated Resource Management funds are available for obligation on financial assistance awards until September 30, 2018. Any funds not obligated, or any portion of those obligated funds that are deobligated after midnight on September 30, 2018 expire. In both cases, expired unobligated Resource Management funds are lost to the program. 
Following their expiration, obligated appropriations remain available for five federal fiscal years for liquidation. Any remaining obligations left unliquidated after the fifth year are cancelled and returned to the U.S. Treasury.
The expired appropriation remains available for 5 years for the purpose of paying obligations incurred prior to the account’s expiration and adjusting obligations that were previously unrecorded or under recorded. 31 U.S.C. § 1553(a). After 5 years, the expired account is closed and the balances remaining are canceled. 31 U.S.C. § 1552(a). 
Looking back to our example above, the FY2017 Resource Management funds obligated to FA awards have a five-year period following the appropriation's expiration before being cancelled. This means that these funds are available to the recipient to liquidate project costs until September 30, 2023. After this date, however, those funds are canceled, even though obligated, and the program office must then take steps to backfill the cancelled funds on the FA award; typically with newer appropriations. This, as you can see, is not good. It means the program office is essentially paying a portion of the project twice.
Federal Awarding Agency compliance with appropriation time limits
Federal awarding agencies are directed by congressional law to expend appropriated funds properly and within the legally set time-frame.
Federal agencies spend appropriated funds properly via application of what is know as "the bona fide need rule", which establishes that an appropriation is available for obligation only to fulfill a genuine, or bona fide, need of the period of availability for which it was made. 
Frequently Asked Questions
How is the bona fide need rule met with financial asisstance awards (grant and cooperative agreements)?
With FA awards, the bona fide need rule is met at the time of the award's obligation.
An agency's compliance with the bona fide need rule is measured at the time the agency incurs an obligation. In the grant context, the obligation occurs at the time of award. 
With FA awards, expenditures against the obligation, even though after the appropriation expiration itself, are valid for the award’s entire period of performance (which could be more than one year), or the cancellation of the appropriation, whichever is earlier. Unless, of course, a specific legislation states otherwise.
Briefly stated, the "obligational event" for a grant generally occurs at the time of grant award. Therefore, this is when the grantor agency must record an obligation under 31 U.S.C. § 1501(a)(5), not when the grantee draws down the funds or when the grantee incurs its own obligations. See B-300480, Apr. 9, 2003, affd, B-300480.2, June 6, 2003.
An appropriation account expires “[a]t midnight on the last day of an appropriation’s period of availability” and is “no longer available for incurring new obligations.” However, an expired appropriation “remains available for 5 years for the purpose of paying obligations incurred prior to the account’s expiration and adjusting obligations that were previously unrecorded or under recorded.” Following the five-year period, the account is closed, and “[a]ny remaining balance (whether obligated or unobligated) in the account shall be cancelled and shall thereafter not be available for obligation or expenditure for any purpose.” This means that the funds are “returned to the general fund of the Treasury.” “Collections authorized or required to be credited to ... [the] appropriation account, but not received before closing of the account ... shall be deposited in the Treasury as miscellaneous receipts.” In the event that obligations or adjustments to obligations that should have been charged to an account are discovered after the account is closed, they “may be charged to any current appropriation account of the agency available for the same purpose” as the closed account as long as they are “not chargeable to any current appropriation account of the agency.” Congress may exempt appropriations from these rules through specific legislation. 
How does this apply to Inter-/Intra-Agency Agreements (IAAs) and the Economy Act?
The Economy Act (31 U.S.C. § 1535-1536) gives broad authority to Federal government-wide engagement in inter- and intra-agency reimbursable agreements, which result in a more economical or convenient transaction for the customer agency over the use of commercial services. Under these agreements, the bona fide need rule, as explained above, still exists. In other words, the appropriation year time limits on the funds is still in place within these agreements, and the bona fide need is met at the time the requesting agency obligates those funds in a financial assistance award
For example, if NOAA issues appropriated funds to a FWS program via an IAA, and the FWS program issues an FA award with those funds, the FWS program must obligate the funds prior to the expiration date of the appropriation for NOAA funds obligated from the IAA.
 Principles of Federal Appropriations Law, Vol. II, p.10-39 (Feb. 2006).
 Ibid., Vol. I, p.1-37 (Jan. 2004).
 H.R.5538 - Department of the Interior, Environment, and Related Agencies Appropriations Act, 2017. (n.d.). Retrieved from https://www.congress.gov/bill/114th-congress/house-bill/5538/text.
 Congressional Research Service. (2010). Interagency Contracting: An Overview of Federal Procurement and Appropriations Law, 5-6. (Publication No. R40810). Retrieved from https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA529123.xhtml.
 In special situations, the Service may request from DOI's Division of Financial Management (DFM) a special exception to use expired funds.
Ibid., Vol I, p.1-37.
 "The BFN Rule "which establishes that an appropriation is available for obligation only to fulfill a genuine or bona fide need of the period of availability for which it was made. Office of the Assistant General Counsel for Finance and Litigation (2004). Financial Assistance and The Bona fide Need Rule: Severability No Longer An Issue, 1 (Federal Assistance Law Division: It's the Law, Vol. 16). Retrieved from http://2010-2014.commerce.gov/sites/default/files/documents/2012/march/financial_assistance_and_the_bona_fide_need_rule_severability_no_longer_an_issue.pdf.
 Ibid., p. 2.
 Principles, Vol. II, p.10-107.
 CRS "Interagency Contracting", pp.5-6.