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Revenues
6 Months Ended
Jun. 30, 2021
Revenue from Contract with Customer [Abstract]  
Revenues Revenues
We generate the majority of our revenues by providing consulting services to our clients. Most of our consulting service contracts are based on one of the following types of contract arrangements:
Time and expense arrangements require the client to pay us based on the number of hours worked at contractually agreed-upon rates. We recognize revenues for these contract arrangements based on hours incurred and contracted rates utilizing a right-to-invoice practical expedient because we have a right to consideration for services completed to date. When a time and expense arrangement has a not-to-exceed or "cap" amount and we expect to perform work in excess of the cap, we recognize revenues up to the cap amount specified by the client, based on the efforts or hours incurred as a percentage of total efforts or hours expected to be incurred (i.e., proportional performance method).
Fixed-fee arrangements require the client to pay a fixed fee in exchange for a predetermined set of professional services. We recognize revenues earned to date by applying the proportional performance method. Generally, these arrangements have one performance obligation.
Performance-based or contingent arrangements represent forms of variable consideration. In these arrangements, our fees are based on the attainment of contractually defined objectives with our client, such as completing a business transaction or assisting the client in achieving a specific business objective. We recognize revenues earned to date in an amount that is probable not to reverse and by applying the proportional performance method when the criteria for over time revenue recognition are met.
Certain fees in our time and materials arrangements may be subject to approval by a third-party, such as a bankruptcy court and other regulatory agency. In such cases, we record revenues based on the amount we estimate we will be entitled to in exchange for our services and only to the extent a significant reversal of revenue is not likely to occur when the uncertainty associated with the estimate is subsequently resolved. Potential fee reductions imposed by bankruptcy courts and other regulatory agencies or negotiated with specific clients are estimated on a specific identification basis. Our estimates may vary depending on the nature of the engagement, client economics, historical experience and other appropriate factors. When there are changes in our estimates of potential fee reductions, we record such changes to revenues with a corresponding offset to our billed and unbilled accounts receivable.
Revenues recognized during the current period may include revenues from performance obligations satisfied or partially satisfied in previous periods. This primarily occurs when the estimated transaction price has changed based on our current probability assessment over whether the agreed-upon outcome for our performance-based and contingent arrangements will be achieved. The aggregate amount of revenues recognized related to a change in the transaction price in the current period, which related to performance obligations satisfied or partially satisfied in a prior period, was $17.9 million and $16.7 million for the three and six months ended June 30, 2021, respectively, and $8.3 million and $14.1 million for the three and six months ended June 30, 2020, respectively.
Unfulfilled performance obligations primarily consist of fees not yet recognized on certain fixed-fee arrangements and performance-based and contingent arrangements. As of June 30, 2021 and December 31, 2020, the aggregate amount of the remaining contract transaction price allocated to unfulfilled performance obligations was $4.4 million and $8.5 million,
respectively. We expect to recognize the majority of the related revenues over the next 24 months. We elected to utilize the optional exemption to exclude from this disclosure fixed-fee and performance-based and contingent arrangements with an original expected duration of one year or less and to exclude our time and expense arrangements for which revenues are recognized using the right-to-invoice practical expedient.
Contract assets are defined as assets for which we have recorded revenues but are not yet entitled to receive our fees because certain events, such as completion of the measurement period or client approval, must occur. The contract asset balance was $1.4 million as of June 30, 2021 and $2.6 million as of December 31, 2020.
Contract liabilities are defined as liabilities incurred when we have received consideration but have not yet performed the agreed-upon services. This may occur when clients pay fees before work begins. The contract liability balance was immaterial as of June 30, 2021 and December 31, 2020.