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Revenue from Contracts with Customers (Tables)
9 Months Ended
Sep. 30, 2020
Revenue from Contract with Customer [Abstract]  
Disaggregation of Revenue
The following table summarizes revenue:
Three Months EndedNine Months Ended
(in thousands, except percentages)September 30,
2020
September 30,
2019
September 30,
2020
September 30,
2019
Revenue:
Lease licenses$78,917 $70,693 $237,000 $239,953 
Perpetual licenses62,705 66,451 161,793 190,734 
Software licenses141,622 137,144 398,793 430,687 
Maintenance211,942 193,189 615,609 559,768 
Service13,401 13,566 43,209 39,209 
Maintenance and service225,343 206,755 658,818 598,977 
Total revenue$366,965 $343,899 $1,057,611 $1,029,664 
Direct revenue, as a percentage of total revenue74.9 %76.8 %75.7 %75.9 %
Indirect revenue, as a percentage of total revenue25.1 %23.2 %24.3 %24.1 %
Changes in Deferred Revenue
The changes in deferred revenue, inclusive of both current and long-term deferred revenue, during the nine months ended September 30, 2020 and 2019 were as follows:
(in thousands)20202019
Beginning balance – January 1$365,274 $343,174 
Acquired deferred revenue1,405 3,266 
Deferral of revenue1,025,057 991,524 
Recognition of revenue(1,057,611)(1,029,664)
Currency translation4,307 (4,985)
Ending balance – September 30$338,432 $303,315 
Remaining Performance Obligations, Expected Timing of Satisfaction
Total revenue allocated to remaining performance obligations as of September 30, 2020 will be recognized as revenue as follows:
(in thousands) 
Next 12 months$570,236 
Months 13-24180,873 
Months 25-3661,069 
Thereafter67,734 
Total revenue allocated to remaining performance obligations$879,912