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Revenues
6 Months Ended
Jun. 30, 2019
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 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 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.
Fixed fee arrangements require the client to pay a pre-established fee in exchange for a predetermined set of professional services. We recognize revenues for these arrangements based on the proportional performance related to
individual performance obligations within each arrangement; however, these arrangements generally 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 by applying the proportional performance method.
Revenues are recognized when we satisfy a performance obligation by transferring services promised in a contract to a customer and in an amount that reflects the consideration that we expect to receive in exchange for those services. Performance obligations in our contracts represent distinct or separate services that we provide to our customers.
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 was $21.2 million and $23.7 million for the three and six months ended June 30, 2019, respectively, and $4.5 million and $6.5 million for the three and six months ended June 30, 2018, respectively.
Unfulfilled performance obligations represent the remaining contract transaction prices allocated to the performance obligations that are unsatisfied. Unfulfilled performance obligations primarily consist of fees not yet recognized on a proportional performance basis for fixed fee arrangements and performance-based and contingent arrangements. As of June 30, 2019 and December 31, 2018, the aggregate amount of the remaining contract transaction price allocated to unfulfilled performance obligations was $9.5 million and $8.8 million, respectively. We expect to recognize the majority of the related revenues over the next 24 months.
Contract assets are defined as assets for which we have recorded revenue 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 $6.8 million as of June 30, 2019 and $2.4 million as of December 31, 2018.
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 us upfront fees before we begin work for them. The contract liability balance was immaterial as of June 30, 2019 and December 31, 2018.