0001013462-21-000009 | 10-K | XBRL Viewer

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Document - USD ($)	12 Months Ended
Document - USD ($)	Dec. 31, 2020	Feb. 17, 2021	Jun. 30, 2020
Entity Information [Line Items]
Document Type	10-K
Document Annual Report	true
Document Period End Date	Dec. 31, 2020
Document Transition Report	false
Entity File Number	0-20853
Entity Registrant Name	ANSYS, Inc.
Entity Incorporation, State or Country Code	DE
Entity Tax Identification Number	04-3219960
Entity Address, Address Line One	2600 ANSYS Drive,
Entity Address, City or Town	Canonsburg,
Entity Address, State or Province	PA
Entity Address, Postal Zip Code	15317
City Area Code	844
Local Phone Number	462-6797
Entity Well-known Seasoned Issuer	Yes
Entity Voluntary Filers	No
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
ICFR Auditor Attestation Flag	true
Entity Shell Company	false
Entity Public Float			$ 20,712,000,000
Entity Common Stock, Shares Outstanding		86,751,764
Amendment Flag	false
Document Fiscal Year Focus	2020
Document Fiscal Period Focus	FY
Entity Central Index Key	0001013462
Current Fiscal Year End Date	--12-31
Nasdaq Stock Market LLC
Entity Information [Line Items]
Title of 12(b) Security	Common Stock, $0.01 par value per share
Trading Symbol	ANSS
Security Exchange Name	NASDAQ

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Current assets:
Cash and cash equivalents	$ 912,672	$ 872,094
Short-term investments	479	288
Accounts receivable, less allowance for doubtful accounts of $14,000 and $8,700, respectively	537,564	433,479
Other receivables and current assets	268,522	249,619
Total current assets	1,719,237	1,555,480
Long-term assets:
Property and equipment, net	96,503	83,636
Operating lease right-of-use assets	137,730	105,671
Goodwill	3,038,306	2,413,280
Other intangible assets, net	694,865	476,711
Other long-term assets	225,119	180,032
Deferred income taxes	28,830	24,077
Total long-term assets	4,221,353	3,283,407
Total assets	5,940,590	4,838,887
Current liabilities:
Accounts payable	18,691	14,298
Accrued bonuses and commissions	112,491	101,546
Accrued income taxes	26,116	9,996
Current portion of long-term debt	0	75,000
Other accrued expenses and liabilities	199,466	142,947
Deferred revenue	372,061	351,353
Total current liabilities	728,825	695,140
Long-term liabilities:
Deferred income taxes	110,321	78,643
Long-term operating lease liabilities	120,940	91,768
Long-term debt	798,118	423,531
Other long-term liabilities	84,514	96,426
Total long-term liabilities	1,113,893	690,368
Commitments and contingencies
Stockholders’ equity:
Preferred stock, $0.01 par value; 2,000,000 shares authorized; zero shares issued or outstanding	0	0
Common stock, $0.01 par value; 300,000,000 shares authorized; 95,266,320 and 94,627,585 shares issued, respectively	953	946
Additional paid-in capital	1,434,203	1,188,939
Retained earnings	3,804,593	3,370,706
Treasury stock, at cost: 8,693,809 and 8,893,177 shares, respectively	(1,124,102)	(1,041,831)
Accumulated other comprehensive loss	(17,775)	(65,381)
Total stockholders’ equity	4,097,872	3,453,379
Total liabilities and stockholders’ equity	$ 5,940,590	$ 4,838,887

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Statement of Financial Position [Abstract]
Allowance for doubtful accounts	$ 14,000	$ 8,700
Preferred stock, par value	$ 0.01	$ 0.01
Preferred stock, shares authorized	2,000,000	2,000,000
Preferred stock, shares issued	0	0
Preferred stock, shares outstanding	0	0
Common stock, par value	$ 0.01	$ 0.01
Common stock, shares authorized	300,000,000	300,000,000
Common stock, shares issued	95,266,320	94,627,585
Treasury stock, shares	8,693,809	8,893,177

CONSOLIDATED STATEMENTS OF INCOME - USD ($) shares in Thousands, $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Revenue:
Total revenue	$ 1,681,297	$ 1,515,892	$ 1,293,636
Cost of sales:
Amortization	40,642	21,710	27,034
Total cost of sales	225,264	166,273	155,885
Gross profit	1,456,033	1,349,619	1,137,751
Operating expenses:
Selling, general and administrative	587,707	521,200	413,580
Research and development	355,371	298,210	233,802
Amortization	16,599	15,169	13,795
Total operating expenses	959,677	834,579	661,177
Operating income	496,356	515,040	476,574
Interest income	5,073	12,796	11,419
Interest expense	(10,988)	(3,461)	(59)
Other income (expense), net	3,484	(1,792)	(849)
Income before income tax provision	493,925	522,583	487,085
Income tax provision	60,038	71,288	67,710
Net income	$ 433,887	$ 451,295	$ 419,375
Earnings per share – basic:
Earnings per share	$ 5.05	$ 5.36	$ 4.99
Weighted average shares	85,840	84,259	83,973
Earnings per share – diluted:
Earnings per share	$ 4.97	$ 5.25	$ 4.88
Weighted average shares	87,288	85,925	85,913
Software licenses
Revenue:
Total revenue	$ 780,850	$ 699,630	$ 576,717
Cost of sales:
Total cost of sales	30,618	23,944	18,619
Maintenance and service
Revenue:
Total revenue	900,447	816,262	716,919
Cost of sales:
Total cost of sales	$ 154,004	$ 120,619	$ 110,232

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Net income	$ 433,887	$ 451,295	$ 419,375
Other comprehensive income (loss):
Foreign currency translation adjustments	47,606	(3,002)	(24,535)
Comprehensive income	$ 481,493	$ 448,293	$ 394,840

- Definition

The portion of profit or loss for the period, net of income taxes, which is attributable to the parent.

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+ Details

CONSOLIDATED STATEMENTS OF CASH FLOWS - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cash flows from operating activities:
Net income	$ 433,887	$ 451,295	$ 419,375
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation and amortization	85,275	60,516	59,255
Operating lease right-of-use assets amortization	20,971	18,459
Deferred income tax benefit	(30,932)	(14,511)	(33,675)
Provision for bad debts	6,438	2,928	1,577
Stock-based compensation expense	145,615	116,190	83,346
Other	2,180	2,778	410
Changes in operating assets and liabilities:
Accounts receivable	(160,319)	(154,403)	(74,455)
Other receivables and current assets	(2,312)	(26,182)	(30,241)
Other long-term assets	(14,818)	(5,622)	1,839
Accounts payable, accrued expenses and current liabilities	21,362	38,543	19,920
Accrued income taxes	19,713	575	1,086
Deferred revenue	5,448	17,245	56,213
Other long-term liabilities	14,802	(7,875)	(19,662)
Net cash provided by operating activities	547,310	499,936	484,988
Cash flows from investing activities:
Acquisitions, net of cash acquired	(572,328)	(787,196)	(283,026)
Capital expenditures	(35,370)	(44,940)	(21,762)
Other investing activities	(6,555)	(1,412)	(7,443)
Net cash used in investing activities	(614,253)	(833,548)	(312,231)
Cash flows from financing activities:
Proceeds from long-term debt	375,000	500,000	0
Principal payments on long-term debt	(75,000)	0	0
Purchase of treasury stock	(161,029)	(59,116)	(269,801)
Restricted stock withholding taxes paid in lieu of issued shares	(71,019)	(42,431)	(28,879)
Proceeds from shares issued for stock-based compensation	29,560	34,093	41,019
Other financing activities	(915)	(3,137)	(5,014)
Net cash provided by (used in) financing activities	96,597	429,409	(262,675)
Effect of exchange rate fluctuations on cash and cash equivalents	10,924	(842)	(14,444)
Net increase (decrease) in cash and cash equivalents	40,578	94,955	(104,362)
Cash and cash equivalents, beginning of period	872,094	777,139	881,501
Cash and cash equivalents, end of period	912,672	872,094	777,139
Supplemental disclosures of cash flow information:
Income taxes paid	54,174	86,770	87,244
Interest paid	11,941	787	114
Fair value of common stock issued and unpaid consideration in connection with acquisitions	$ 232,690	$ 307,173	$ 0

CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY - USD ($) shares in Thousands, $ in Thousands	Total	Livermore Software Technology Corporation	Analytical Graphics, Inc.	Cumulative Effect, Period of Adoption, Adjustment	Common Stock	Common Stock Livermore Software Technology Corporation	Common Stock Analytical Graphics, Inc.	Additional Paid-In Capital	Additional Paid-In Capital Livermore Software Technology Corporation	Additional Paid-In Capital Analytical Graphics, Inc.	Retained Earnings	Retained Earnings Cumulative Effect, Period of Adoption, Adjustment	Treasury Stock	Treasury Stock Livermore Software Technology Corporation	Treasury Stock Analytical Graphics, Inc.	Accumulated Other Comprehensive (Loss)/Income
Beginning balance at Dec. 31, 2017	$ 2,245,831			$ 183,120	$ 932			$ 873,357			$ 2,316,916	$ 183,120	$ (907,530)			$ (37,844)
Beginning balance, shares at Dec. 31, 2017					93,236								9,044
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Treasury shares acquired	$ (269,801)												$ (269,801)
Treasury shares acquired, shares	1,674												1,674
Stock-based compensation, activity								(5,895)
Stock-based compensation activity	$ 95,557												$ 101,452
Stock-based compensation activity, shares													(1,116)
Other comprehensive (loss)/income	(24,535)															(24,535)
Net income for the year	419,375										419,375
Ending balance at Dec. 31, 2018	2,649,547				$ 932			867,462			2,919,411		$ (1,075,879)			(62,379)
Ending balance, shares at Dec. 31, 2018					93,236								9,602
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Acquisition activity		$ 307,173				$ 14			$ 307,159
Acquisition activity, common shares						1,392
Treasury shares acquired	$ (59,116)												$ (59,116)
Treasury shares acquired, shares	330												330
Stock-based compensation, activity								14,318
Stock-based compensation activity	$ 107,482												$ 93,164
Stock-based compensation activity, shares													(1,039)
Other comprehensive (loss)/income	(3,002)															(3,002)
Net income for the year	451,295										451,295
Ending balance at Dec. 31, 2019	3,453,379				$ 946			1,188,939			3,370,706		$ (1,041,831)			(65,381)
Ending balance, shares at Dec. 31, 2019					94,628								8,893
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Acquisition activity		$ 1,531	$ 218,348				$ 7		$ 1,030	$ 218,108				$ 501	$ 233
Acquisition activity, common shares							638
Acquisition activity, treasury shares														(6)	(3)
Treasury shares acquired	$ (161,029)												$ (161,029)
Treasury shares acquired, shares	690												690
Stock-based compensation, activity								26,126
Stock-based compensation activity	$ 104,150												$ 78,024
Stock-based compensation activity, shares													(880)
Other comprehensive (loss)/income	47,606															47,606
Net income for the year	433,887										433,887
Ending balance at Dec. 31, 2020	$ 4,097,872				$ 953			$ 1,434,203			$ 3,804,593		$ (1,124,102)			$ (17,775)
Ending balance, shares at Dec. 31, 2020					95,266								8,694

Organization	12 Months Ended
Organization	Dec. 31, 2020
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Organization	Organization We develop and globally market engineering simulation software and services widely used by engineers, designers, researchers and students across a broad spectrum of industries and academia, including aerospace and defense, automotive, electronics, semiconductors, energy, materials and chemical processing, turbomachinery, consumer products, healthcare, and sports. As defined by the accounting guidance for segment reporting, we operate as one segment. Given the integrated approach to the multi-discipline problem-solving needs of our customers, a single sale of software may contain components from multiple product areas and include combined technologies. We also have a multi-year product and integration strategy that will result in new, combined products or changes to the historical product offerings. As a result, it is impracticable for us to provide accurate historical or current reporting among our various product lines. We are closely monitoring the spread of COVID-19 and continually mitigating its potential effects on our business. The COVID-19 pandemic has had, and is expected to continue to have, an adverse impact on our business and our employees.

Accounting Policies

12 Months Ended

Dec. 31, 2020

Accounting Policies [Abstract]

Accounting Policies

Accounting Principles

The financial statements and accompanying notes are prepared in accordance with accounting principles generally accepted in the United States. Certain items in the consolidated financial statements and the notes to the consolidated financial statements of prior years have been reclassified to conform to the current year's presentation. These reclassifications had no effect on reported net income, comprehensive income, cash flows, total assets or total liabilities and stockholders' equity.

Principles of Consolidation

The accompanying consolidated financial statements include our accounts and those of our wholly owned subsidiaries. All intercompany accounts and transactions have been eliminated.

Recently Adopted Accounting Guidance

Leases: In February 2016, the Financial Accounting Standards Board (FASB) issued Accounting Standards Update (ASU) No. 2016-02, Leases (Topic 842) (ASU 2016-02). We adopted ASU 2016-02 and its related amendments (collectively known as Accounting Standards Codification (ASC) 842) on January 1, 2019 using the modified retrospective approach. Results for reporting periods beginning after January 1, 2019 are presented under ASC 842, while prior period amounts are not adjusted and continue to be reported in accordance with ASC 840, Leases. ASC 842 requires virtually all leases, other than leases of intangible assets, to be recorded on the balance sheet with a right-of-use (ROU) asset and a corresponding lease liability.

We elected the package of practical expedients permitted under the transition guidance within the new standard, which allowed us to carry forward our historical assessments of whether a contract contains a lease, lease classification and initial direct costs. In addition, we elected the accounting policy to combine the lease and nonlease components as a single component for all asset classes.

We determine if an arrangement is a lease at inception. Leases are classified as either operating or finance leases based on certain criteria. This classification determines the timing and presentation of expenses on the income statement, as well as the presentation of the related cash flows and balance sheet. Operating leases are recorded on the balance sheet as operating lease right-of-use assets, other accrued expenses and liabilities, and long-term operating lease liabilities. We currently have no finance leases.

ROU assets and related liabilities are recorded at lease commencement based on the present value of the lease payments over the expected lease term. Lease payments include future increases unless the increases are based on changes in an index or rate. As our leases do not usually provide an implicit rate, our incremental borrowing rate is used to calculate ROU assets and related liabilities. The incremental borrowing rate is determined based on our estimated credit rating, the term of the lease, the economic environment where the asset resides and full collateralization. The ROU assets and related lease liabilities include

optional renewals for which we are reasonably certain to exercise; whereas, optional terminations are included unless it is reasonably certain not to be elected.

The adoption of the new standard resulted in the recognition of ROU assets of $90.9 million and lease liabilities of $92.5 million, and corresponding deferred tax assets and liabilities, on our consolidated balance sheet as of January 1, 2019. The adoption had no impact on our consolidated statements of income or cash flows.

Credit losses: In June 2016, the FASB issued ASU No. 2016-13, Financial Instruments - Credit Losses (Topic 326): Measurement of Credit Losses on Financial Instruments (ASU 2016-13), which modifies the measurement of expected credit losses of certain financial instruments. We adopted ASU 2016-13 on January 1, 2020 with no material impact to our condensed consolidated financial statements. Previous guidance required the allowance for doubtful accounts to be estimated based on an incurred loss model, which considered past and current conditions. ASU 2016-13 requires us to use an expected loss model that also considers reasonable and supportable forecasts of future conditions, referred to as the current expected credit loss (CECL) methodology.

Under ASU 2016-13, we make judgments as to our ability to collect outstanding receivables and provide allowances for a portion of receivables over the lifetime of the receivables. Provisions are made based upon a specific review of all significant outstanding invoices from both value and delinquency perspectives. For those invoices not specifically reviewed, provisions are estimated at differing rates based upon the age of the receivable. In determining these percentages, we consider our historical loss experience, current economic trends and future conditions.

Accounting Guidance Issued and Not Yet Adopted

Income taxes: In December 2019, the FASB issued ASU No. 2019-12, Income Taxes (Topic 740): Simplifying the Accounting for Income Taxes (ASU 2019-12), as part of its initiative to reduce complexity in the accounting standards. The amendments in ASU 2019-12 eliminate certain exceptions related to the approach for intraperiod tax allocation, the methodology for calculating income taxes in an interim period and the recognition of deferred tax liabilities for outside basis differences. ASU 2019-12 also clarifies and simplifies other aspects of the accounting for income taxes. ASU 2019-12 is effective for fiscal years, and interim periods within those fiscal years, beginning after December 15, 2020. Early adoption is permitted, including adoption in any interim period. We do not expect the adoption of the new standard to have a material effect on our consolidated financial statements.

Use of Estimates

The preparation of financial statements in conformity with accounting principles generally accepted in the United States requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements. Estimates also affect the amounts of revenue and expenses during the reported periods. Significant estimates included in these consolidated financial statements include:

•Allowances for doubtful accounts receivable

•Income tax accruals

•Uncertain tax positions

•Tax valuation reserves

•Fair value of stock-based compensation and probabilities of performance award attainment

•Contract revenue

•Standalone selling prices of our products and services

•Acquired deferred revenue

•Useful lives for depreciation and amortization

•Valuations of goodwill and other intangible assets

•Deferred compensation

•Loss contingencies

•Operating lease assets and liabilities

Actual results could differ from these estimates. Changes in estimates are recorded in the results of operations in the period that the changes occur.

Revenue Recognition

Our revenue is derived principally from the licensing of computer software products and from related maintenance contracts. We enter into contracts that include combinations of products, maintenance and services, which are accounted for as separate performance obligations with differing revenue recognition patterns.

Revenue from perpetual licenses is classified as software license revenue. Software license revenue is recognized up front upon delivery of the licensed product and/or the utility that enables the customer to access authorization keys, provided that an enforceable contract has been received. Typically, our perpetual licenses are sold with post-contract support (PCS), which includes unspecified technical enhancements and customer support. We allocate value in bundled perpetual and PCS arrangements based on the standalone selling prices of the perpetual license and PCS. Revenue from PCS is classified as maintenance revenue and is recognized ratably over the term of the contract, as we satisfy the PCS performance obligation over time.

In addition to perpetual licenses, we sell time-based lease licenses. Lease licenses are sold only as a bundled arrangement that includes the rights to a term software license and PCS. Utilizing observable inputs, we determined that 50% of the estimated standalone selling price of the lease license is attributable to the term license and 50% is attributable to the PCS. This determination considered the value relationship for our products between PCS and time-based lease licenses, the value relationship between PCS and perpetual licenses, the average economic life of our products, software renewal rates and the price of the bundled arrangement in relation to the perpetual licensing approach. Consistent with the perpetual sales, the license component is classified as software license revenue and recognized as revenue up front at the commencement of the lease upon delivery of the licensed product and/or utility that enables the customer to access authorization keys. The PCS is classified as maintenance revenue and is recognized ratably over the term of the contract, as we satisfy the PCS performance obligation over time.

Revenue from training, support and other services is recognized as the services are performed. For contracts in which the service consists of a single performance obligation, such as providing a training class to a customer, we recognize revenue upon completion of the performance obligation. For service contracts that are longer in duration and often include multiple performance obligations (for example, both training and consulting), we measure the progress toward completion of the obligations and recognize revenue accordingly. In measuring progress towards the completion of performance obligations, we typically utilize output-based estimates for services with contractual billing arrangements that are not based on time and materials, and estimate output based on the total tasks completed as compared to the total tasks required for each work contract. Input-based estimates are utilized for services that involve general consultations with contractual billing arrangements based on time and materials, utilizing direct labor as the input measure. Proceeds from customers for the purpose of expediting roadmap items, developing new products or creating specific features and functionality for existing products is classified as revenue.

We also execute arrangements through independent channel partners in which the channel partners are authorized to market and distribute our software products to end users of our products and services in specified territories. In sales facilitated by channel partners, the channel partner bears the risk of collection from the end-user customer. We recognize revenue from transactions with channel partners in a manner consistent with the direct sales described above for both perpetual and time-based licenses. Revenue from channel partner transactions is the amount remitted to us by the channel partners. This amount includes a fee for PCS that is compensation for providing technical enhancements and the second level of technical support to the end user, which is recognized over the period that PCS is to be provided.

Non-income related taxes collected from customers and remitted to governmental authorities are recorded on the consolidated balance sheet as accounts receivable and accrued expenses. The collection and payment of these amounts are reported on a net basis in the consolidated statements of income and do not impact reported revenues or expenses.

We do not offer right of return. We warrant to our customers that our software will perform substantially as specified in our current user manuals. We have not experienced significant claims related to software warranties beyond the scope of maintenance support, which we are already obligated to provide. The warranty is not sold, and cannot be purchased, separately.

The warranty does not provide any type of additional service to the customer or performance obligation for us.

Our agreements with our customers generally require us to indemnify the customer against claims that our software infringes third-party patent, copyright, trademark or other proprietary rights. Such indemnification obligations are generally limited in a variety of industry-standard respects, including our right to replace an infringing product.

Significant Judgments

Our contracts with customers typically include promises to transfer licenses and services to a customer. Judgment is required to determine if the promises are separate performance obligations, and if so, to allocate the transaction price to each performance obligation. We use the estimated standalone selling price method to allocate the transaction price for each performance obligation. The estimated standalone selling price is determined using all information reasonably available to us, including market conditions and other observable inputs. The corresponding revenues are recognized as the related performance obligations are satisfied.

We apply a practical expedient to expense sales commissions as incurred when the amortization period would have been one year or less. Sales commissions associated with the initial year of multi-year contracts are expensed as incurred due to their immateriality. Sales commissions associated with multi-year contracts beyond the initial year are subject to an employee service requirement and are expensed as incurred as they are not considered incremental costs to obtain a contract.

We are required to adjust promised amounts of consideration for the effects of the time value of money if the timing of the payments provides the customer or us with a significant financing benefit. We consider various factors in assessing whether a financing component exists, including the duration of the contract, market interest rates and the timing of payments. Our contracts do not include a significant financing component requiring adjustment to the transaction price.

Cash and Cash Equivalents

Cash and cash equivalents consist primarily of highly liquid investments such as deposits held at major banks and money market funds. Cash equivalents are carried at cost, which approximates fair value. Our cash and cash equivalents balances comprise the following:


	December 31, 2020			December 31, 2019
(in thousands, except percentages)	Amount		% of Total	Amount		% of Total
Cash accounts	$	571,587	62.6	$	549,639	63.0
Money market funds	341,085		37.4	322,455		37.0
Total	$	912,672		$	872,094

Our money market fund balances are held in various funds of two issuers.

Property and Equipment

Property and equipment is stated at cost. Depreciation is computed using the straight-line method over the estimated useful lives of the various classes of assets, which range from one year to forty years. Repairs and maintenance are charged to expense as incurred. Gains or losses from the sale or retirement of property and equipment are included in operating income.

Research and Development

Research and development costs are expensed as incurred. Internally developed software costs required to be capitalized as defined by the accounting guidance are not material to our consolidated financial statements.

Business Combinations

When we consummate an acquisition, the assets acquired and the liabilities assumed are recognized separately from goodwill at their acquisition date fair values. Goodwill as of the acquisition date is measured as the excess of the fair value of consideration transferred over the acquisition date fair value of the net identifiable assets acquired. While best estimates and assumptions are used to accurately value assets acquired and liabilities assumed at the acquisition date as well as contingent consideration, where applicable, our estimates are inherently uncertain and subject to refinement. As a result, during the measurement period, which may be up to one year from the acquisition date, we record adjustments to the assets acquired and liabilities assumed with the corresponding offset to goodwill as we obtain new information about facts and circumstances that existed as of the acquisition date that, if known, would have affected the measurement of the amounts recognized as of that date. Upon the earlier of the conclusion of the measurement period or final determination of the values of assets acquired or liabilities assumed, any subsequent adjustments are recorded in the consolidated statements of income.

Goodwill and Other Intangible Assets

Goodwill represents the excess of the fair value of consideration transferred over the fair value of net identifiable assets acquired. Other intangible assets consist of trade names, customer lists, contract backlog and acquired software and technology. Intangible assets that are not considered to have an indefinite useful life are amortized over their useful lives, which range from two years to seventeen years. Amortization expense for intangible assets was $57.2 million, $36.9 million and $40.8 million for the years ended December 31, 2020, 2019 and 2018, respectively.

We test goodwill and indefinite-lived intangible assets for impairment at least annually by performing a quantitative assessment of whether the fair value of each reporting unit or asset exceeds its carrying amount. We have one reporting unit. Goodwill is tested at this reporting unit level and indefinite-lived intangible assets are tested at the individual asset level. This requires us to assess and make judgments regarding a variety of factors which impact the fair value of the reporting unit or asset being tested, including business plans, anticipated future cash flows, economic projections and other market data.

During the first quarter of 2020, we completed the annual impairment test for goodwill and the indefinite-lived intangible asset and determined that these assets had not been impaired as of the test date, January 1, 2020. Given the adverse economic and market conditions caused by COVID-19, we considered a variety of qualitative factors to determine if an additional quantitative impairment test was required subsequent to our annual impairment test. Based on a variety of factors, including the excess of the fair values over the carrying amounts in the most recent impairment test, we determined it was not more likely than not that an impairment existed as of March 31, 2020. No other events or circumstances changed during the year ended December 31, 2020 that would indicate that the fair values of our reporting unit and indefinite-lived intangible asset are below their carrying amounts.

Concentrations of Credit Risk

We have a concentration of credit risk with respect to revenue and trade receivables due to the use of certain significant channel partners to market and sell our products. We perform periodic credit evaluations of our customers' financial condition and generally do not require collateral. The following table outlines concentrations of risk with respect to our revenue:


	Year Ended December 31,
(as a % of revenue)	2020		2019		2018
Revenue from channel partners	22	%	23	%	22	%
Largest channel partner	3	%	4	%	4	%
2nd largest channel partner	2	%	2	%	2	%

No single customer accounted for more than 5% of our revenue in 2020, 2019 or 2018.

In addition to the concentration of credit risk with respect to trade receivables, our cash and cash equivalents are also exposed to concentration risk. Our cash and cash equivalent accounts are insured through various public and private bank deposit insurance programs, foreign and domestic; however, a significant portion of our funds are not insured. The following table outlines concentrations of risk with respect to our cash and cash equivalents:


	As of December 31,
(in thousands)	2020		2019
Cash and cash equivalents held domestically	$	582,882	$	626,433
Cash and cash equivalents held by foreign subsidiaries	329,790		245,661
Cash and cash equivalents held in excess of deposit insurance, foreign and domestic	887,886		855,721
Largest balance of cash and cash equivalents held with one financial institution, foreign and domestic	396,430		330,551

Allowance for Doubtful Accounts

Allowance for Doubtful Accounts Policy 2020

We adopted ASU 2016-13 on January 1, 2020. ASU 2016-13 requires us to use the CECL methodology to make judgments as to our ability to collect outstanding receivables and provide allowances for a portion of receivables over the lifetime of the receivables. Provisions are made based upon a specific review of all significant outstanding invoices from both value and delinquency perspectives. For those invoices not specifically reviewed, provisions are estimated at differing rates based upon the age of the receivable. In determining these percentages, we consider our historical loss experience, current economic trends and future conditions.

The changes in the allowance for doubtful accounts during the year ended December 31, 2020 were as follows:


(in thousands)	Year Ended December 31, 2020
Beginning balance – January 1	$	8,700
Additions: Charges to costs and expenses	6,438
Deductions: Write-offs	(1,138)
Ending balance – December 31	$	14,000

The increase in the allowance for doubtful accounts was driven by expected losses related to COVID-19.

Allowance for Doubtful Accounts Policy 2019 and 2018

Under previous guidance, we made judgments as to our ability to collect outstanding receivables and provided allowances for a portion of receivables when collection became doubtful. Provisions were made based upon a specific review of all significant outstanding invoices from both value and delinquency perspectives. For those invoices not specifically reviewed, provisions were estimated at differing rates based upon the age of the receivable and the geographic area of origin. In determining these percentages, we considered our historical collection experience and current economic trends in the customer's industry and geographic region.

We recorded provisions for bad debts of $6.4 million, $2.9 million and $1.6 million for the years ended December 31, 2020, 2019 and 2018, respectively.

Income Taxes

We account for income taxes under the asset and liability method, which requires the recognition of deferred tax assets and liabilities for the expected future tax consequences of events that have been included in the financial statements. Under this method, deferred tax assets and liabilities are determined based on the differences between the financial statement and tax bases of assets and liabilities using enacted tax rates in effect for the year in which the differences are expected to reverse. The effect of a change in tax rates on deferred tax assets and liabilities is recognized in income in the period of the enactment date.

We record net deferred tax assets to the extent we believe these assets will more likely than not be realized. In making such determination, we consider all available positive and negative evidence, including scheduled reversals of deferred tax liabilities, projected future taxable income, tax planning strategies and recent financial operations. In the event we determine that we will be able to realize deferred tax assets for which a valuation allowance was used to reduce their carrying value, the adjustment to the valuation allowance will be recorded as a reduction to the provision for income taxes.

Tax benefits related to uncertain tax positions taken or expected to be taken on a tax return are recorded when such benefits meet a more-likely-than-not threshold. Otherwise, these tax benefits are recorded when a tax position has been effectively settled, which means that the statute of limitations has expired or the appropriate taxing authority has completed its examination even though the statute of limitations remains open.

We recognize interest and penalties related to income taxes within the income tax expense line in the consolidated statements of income. Accrued interest and penalties are included within the related tax liability line in the consolidated balance sheets.

Foreign Currencies

Certain of our sales and intercompany transactions are denominated in foreign currencies. These transactions are translated to the functional currency at the exchange rate on the transaction date. Assets and liabilities denominated in a currency other than

our functional currency or our subsidiaries' functional currencies are translated at the effective exchange rate on the balance sheet date. Gains and losses resulting from foreign exchange transactions are included in other income (expense), net. We recorded net foreign exchange losses of $0.2 million, $2.5 million and $3.1 million for the years ended December 31, 2020, 2019 and 2018, respectively.

The financial statements of our foreign subsidiaries are translated from the functional (local) currency to U.S. Dollars. Assets and liabilities are translated at the exchange rates on the balance sheet date. Results of operations are translated at average exchange rates, which approximate rates in effect when the underlying transactions occurred.

Accumulated Other Comprehensive Loss

Accumulated other comprehensive loss is composed entirely of foreign currency translation adjustments.

Earnings Per Share

Basic earnings per share (EPS) amounts are computed by dividing earnings by the weighted average number of common shares outstanding during the period. Diluted EPS amounts assume the issuance of common stock for all potentially dilutive equivalents outstanding. To the extent stock awards are anti-dilutive, they are excluded from the calculation of diluted EPS.

The details of basic and diluted EPS are as follows:


	Year Ended December 31,
(in thousands, except per share data)	2020		2019		2018
Net income	$	433,887	$	451,295	$	419,375
Weighted average shares outstanding – basic	85,840		84,259		83,973
Dilutive effect of stock plans	1,448		1,666		1,940
Weighted average shares outstanding – diluted	87,288		85,925		85,913
Basic earnings per share	$	5.05	$	5.36	$	4.99
Diluted earnings per share	$	4.97	$	5.25	$	4.88
Anti-dilutive shares	23		14		7

Stock-Based Compensation

We account for stock-based compensation in accordance with share-based payment accounting guidance. The guidance requires an entity to measure the cost of employee services received in exchange for an award of equity instruments based on the grant-date fair value of the award. The cost is recognized over the period during which an employee is required to provide services in exchange for the award, typically the vesting period.

Fair Value of Financial Instruments

We account for certain assets and liabilities at fair value in accordance with the accounting guidance applicable to fair value measurements and disclosures. The carrying values of cash, cash equivalents, short-term investments, accounts receivable, accounts payable, accrued expenses, other accrued liabilities and short-term obligations are deemed to be reasonable estimates of their fair values because of their short-term nature. Our term loans are variable rate debt obligations and, therefore, the carrying amounts approximate the fair values.

Revenue from Contracts with Customers

12 Months Ended

Dec. 31, 2020

Revenue from Contract with Customer [Abstract]

Revenue from Contracts with Customers

Disaggregation of Revenue

The following table summarizes revenue:


	Year Ended December 31,
(in thousands)	2020			2019			2018
Revenue:
Lease licenses	$	500,105		$	406,043		$	275,619
Perpetual licenses	280,745			293,587			301,098
Software licenses	780,850			699,630			576,717
Maintenance	840,597			760,574			676,883
Service	59,850			55,688			40,036
Maintenance and service	900,447			816,262			716,919
Total revenue	$	1,681,297		$	1,515,892		$	1,293,636

Direct revenue, as a percentage of total revenue	77.8		%	77.1		%	77.6		%
Indirect revenue, as a percentage of total revenue	22.2		%	22.9		%	22.4		%

Our software licenses revenue is recognized up front, while maintenance and service revenue is generally recognized over the term of the contract.

Deferred Revenue

Deferred revenue consists of billings made or payments received in advance of revenue recognition from customer agreements. The timing of revenue recognition may differ from the timing of billings to customers. Payment terms vary by the type and location of customer and the products or services offered. The time between invoicing and when payment is due is not significant.

The changes in deferred revenue, inclusive of both current and long-term deferred revenue, during the years ended December 31, 2020 and 2019 were as follows:


(in thousands)	2020		2019
Beginning balance – January 1	$	365,274	$	343,174
Acquired deferred revenue	6,872		6,880
Deferral of revenue	1,687,907		1,532,549
Recognition of deferred revenue	(1,681,297)		(1,515,892)
Currency translation	10,054		(1,437)
Ending balance – December 31	$	388,810	$	365,274

Total revenue allocated to remaining performance obligations as of December 31, 2020 will be recognized as revenue as follows:


(in thousands)
Next 12 months	$	606,780
Months 13-24	199,909
Months 25-36	80,304
Thereafter	80,134
Total revenue allocated to remaining performance obligations	$	967,127

Revenue allocated to remaining performance obligations represents contracted revenue that has not yet been recognized, which includes both deferred revenue and backlog. Our backlog represents installment billings for periods beyond the current

quarterly billing cycle. Revenue recognized during the years ended December 31, 2020 and 2019 included amounts in deferred revenue and backlog at the beginning of the period of $569.8 million and $475.9 million, respectively.

- Definition

The entire disclosure of revenue from contract with customer to transfer good or service and to transfer nonfinancial asset. Includes, but is not limited to, disaggregation of revenue, credit loss recognized from contract with customer, judgment and change in judgment related to contract with customer, and asset recognized from cost incurred to obtain or fulfill contract with customer. Excludes insurance and lease contracts.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-URI http://asc.fasb.org/topic&trid=49130388

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130551-203045

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 13
-Subparagraph (b)(2)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130556-203045

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 12
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130554-203045

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 9
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130550-203045

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 12
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130554-203045

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 12
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130554-203045

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 12
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130554-203045

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130558-203045

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 12
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130554-203045

+ Details

Acquisitions

12 Months Ended

Dec. 31, 2020

Business Combinations [Abstract]

Acquisitions

2020 Acquisitions

On December 1, 2020, we acquired 100% of the shares of AGI, a premier provider of mission-simulation, modeling, testing and analysis software for aerospace, defense and intelligence applications. The acquisition expands the scope of our offerings, empowering users to solve challenges by simulating from the chip level all the way to a customer's entire mission. The transaction closed with a purchase price of $722.5 million.

On April 1, 2020, we acquired 100% of the shares of Lumerical, a leading developer of photonic design and simulation tools, for a purchase price of approximately $107.5 million, paid in cash. The acquisition adds best-in-class photonic products to our multiphysics portfolio, providing customers with a full set of solutions to solve their next-generation product challenges.

During the year ended December 31, 2020, we incurred $5.1 million in acquisition-related expenses, recognized as selling, general and administrative expense on the consolidated statements of income.

The assets and liabilities of AGI and Lumerical have been recorded based upon management's estimates of their fair market values as of each respective date of acquisition. The following tables summarize the fair value of consideration transferred and the fair values of identified assets acquired and liabilities assumed at each respective date of acquisition:

Fair Value of Consideration Transferred:


(in thousands)	AGI		Lumerical		Total
Cash	$	489,797	$	107,545	$	597,342
Ansys common stock(1)	218,348		—		218,348
Consideration not yet paid	14,342		—		14,342
Total consideration transferred at fair value	$	722,487	$	107,545	$	830,032

(1)We issued 0.6 million shares of our common stock in an unregistered offering to the prior owners of AGI with a fair value of $217.4 million, and we issued $0.9 million from shares held in treasury.

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	AGI		Lumerical		Total
Cash	$	17,663	$	11,844	$	29,507
Accounts receivable and other tangible assets	29,456		4,244		33,700
Developed software and core technologies	184,100		31,614		215,714
Customer lists	25,400		1,616		27,016
Trade names	18,200		1,756		19,956
Accounts payable and other liabilities	(23,279)		(1,106)		(24,385)
Deferred revenue	(5,467)		(1,405)		(6,872)
Net deferred tax liabilities	(50,207)		(7,452)		(57,659)
Total identifiable net assets	$	195,866	$	41,111	$	236,977
Goodwill	$	526,621	$	66,434	$	593,055

The goodwill, which is generally not tax-deductible, is attributed to intangible assets that do not qualify for separate recognition, including the assembled workforce of the acquired business and the synergies expected to arise as a result of the acquisitions.

The fair values of the assets acquired and liabilities assumed are based on preliminary calculations. The estimates and assumptions for these items are subject to change as additional information about what was known and knowable at the acquisition date is obtained during the measurement period (up to one year from the acquisition date).

We determined the fair value of our intangible assets using various valuation techniques, including the relief-from-royalty method and the multi-period excess earnings method. These models utilize certain unobservable inputs classified as Level 3 measurements as defined by ASC 820, Fair Value Measurements and Disclosures. The determination of fair value requires considerable judgment and is sensitive to changes in underlying assumptions, estimates and market factors. Estimating fair value requires us to make assumptions and estimates regarding our future plans, as well as industry and economic conditions. These assumptions and estimates include, but are not limited to: selection of a valuation methodology, royalty rate, discount rate and attrition rate.

The weighted-average useful life, valuation method and assumptions used to determine the fair value of the intangible assets acquired with the AGI acquisition are as follows:

Intangible Asset

Weighted-Average Useful Life

Valuation Method

Assumptions

Developed software and core technologies

10 years

Relief-from-royalty

Royalty rate: 40.0%

Discount rate: 11.0%

Trade names

9 years

Relief-from-royalty

Royalty rate: 1.0% - 2.0%

Discount rate: 11.0%

Customer lists

15 years

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 12.0%

The weighted-average useful life, valuation method and assumptions used to determine the fair value of the intangible assets acquired with the Lumerical acquisition are as follows:

Intangible Asset

Weighted-Average Useful Life

Valuation Method

Assumptions

Developed software and core technologies

10 years

Multi-period excess earnings

Discount rate: 16.5%

Trade names

6 years

Relief-from-royalty

Royalty rate: 2.0%

Discount rate: 16.5%

Customer lists

10 years

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 12.5%

2019 Acquisitions

On November 1, 2019, we completed the acquisition of 100% of the shares of LST, the premier provider of explicit dynamics and other advanced finite element analysis technology, for a purchase price of $781.5 million, inclusive of final net working capital adjustments. The acquisition empowers our customers to solve a new class of engineering challenges, including developing safer automobiles, aircraft and trains while reducing or even eliminating the need for costly physical testing. The purchase price was paid with $472.8 million in cash and 1.4 million shares of our common stock valued at $308.7 million. We issued $307.2 million of common stock in an unregistered offering to the prior owners of LST and the remaining $1.5 million was issued from shares held in treasury.

On February 1, 2019, we completed the acquisition of 100% of the shares of Granta Design for a purchase price of $208.7 million, paid in cash and inclusive of final net working capital adjustments. The acquisition of Granta Design, the premier provider of materials information technology, expands our portfolio into this important area, giving customers access to materials intelligence, including data that is critical to successful simulations.

Additionally, during the year ended December 31, 2019, we acquired Dynardo, Helic and DfR Solutions to combine the acquired technologies with our existing comprehensive multiphysics portfolio. These acquisitions were not individually significant. The combined purchase price of these other acquisitions was $138.5 million, paid in cash and inclusive of final net working capital adjustments.

During the year ended December 31, 2019, we incurred $6.6 million in acquisition-related expenses, recognized as selling, general and administrative expense on the consolidated statements of income.

The assets and liabilities of the acquisitions have been recorded based upon management's estimates of their fair market values as of each respective date of acquisition. The following tables summarize the fair values of consideration transferred and the fair values of identified assets acquired and liabilities assumed at each respective date of acquisition:

Fair Value of Consideration Transferred:


(in thousands)	LST		Granta Design		Other Acquisitions		Total
Cash	$	472,800	$	208,736	$	138,548	$	820,084
Ansys common stock	308,704		—		—		308,704
Total consideration transferred at fair value	$	781,504	$	208,736	$	138,548	$	1,128,788

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	LST		Granta Design		Other Acquisitions		Total
Cash	$	8,520	$	13,644	$	6,231	$	28,395
Accounts receivable and other tangible assets	20,569		6,941		10,734		38,244
Developed software and core technologies (10-year weighted-average life)	167,700		32,445		25,018		225,163
Customer lists (15-year weighted-average life)	25,900		20,016		15,743		61,659
Trade names (10-year weighted-average life)	10,600		4,579		2,051		17,230
Accounts payable and other liabilities	(3,887)		(5,164)		(5,946)		(14,997)
Deferred revenue	(3,565)		(1,426)		(1,889)		(6,880)
Uncertain tax positions	—		—		(257)		(257)
Net deferred tax liabilities	(47,412)		(8,976)		(8,151)		(64,539)
Total identifiable net assets	$	178,425	$	62,059	$	43,534	$	284,018
Goodwill	$	603,079	$	146,677	$	95,014	$	844,770

At the closing of the transaction, LST had uncertain tax positions inclusive of interest and penalties of $34.0 million and a corresponding indemnification asset. The uncertain tax positions reflected potential federal and state tax liabilities associated with tax years 2016 to 2019. As all tax positions have been resolved, the uncertain tax positions and the corresponding indemnification asset recorded at closing have been removed.

The valuation method and assumptions used to determine the fair value of the significant intangible assets acquired in 2019 are as follows:

Intangible Asset

Valuation Method

LST Assumptions

Granta Design Assumptions

Developed software and core technologies

Relief-from-royalty

Royalty rate: 50.0%

Discount rate: 10.0%

Royalty rate: 8.0% - 10.0%

Discount rate: 12.5%

Trade names

Relief-from-royalty

Royalty rate: 2.0%

Discount rate: 10.0%

Royalty rate: 2.0%

Discount rate: 14.0%

Customer lists

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 11.0%

Attrition rate: 10.0%

Discount rate: 12.5%

The operating results of each acquisition have been included in our consolidated financial statements since each respective date of acquisition. The effects of the business combinations were not material to our consolidated results of operations individually. The table presented below reflects the aggregate impact on our results of operations of the 2019 acquisitions from the date of acquisition to December 31, 2019. The operating income does not include integration costs borne directly by us and our non-acquired subsidiaries as a result of the acquisitions.


(in thousands)	Year Ended December 31, 2019
Revenue	$	44,079
Operating income	$	6,733

2018 Acquisition

On May 2, 2018, we completed the acquisition of 100% of the shares of OPTIS, a premier provider of software for scientific simulation of light, human vision and physics-based visualization, for a purchase price of $291.0 million, paid in cash. The acquisition extends our portfolio into the area of optical simulation to provide comprehensive sensor solutions, covering visible and infrared light, electromagnetics and acoustics for camera, radar and lidar.

The operating results of OPTIS have been included in our consolidated financial statements since May 2, 2018, the date of acquisition.

During the year ended December 31, 2018, we incurred $3.5 million in acquisition-related expenses, recognized as selling, general and administrative expense on the consolidated statements of income.

The assets and liabilities of OPTIS have been recorded based upon management's estimates of their fair market values as of the acquisition date. The following tables summarize the fair value of consideration transferred and the fair values of identified assets acquired and liabilities assumed at the acquisition date:

Fair Value of Consideration Transferred:


(in thousands)	OPTIS
Cash	$	290,983

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	OPTIS
Cash	$	7,957
Accounts receivable and other tangible assets	15,910
Developed software and core technologies (10-year weighted-average life)	47,597
Customer lists (12-year weighted-average life)	41,303
Trade names (9-year weighted-average life)	10,749
Accounts payable and other liabilities	(11,941)
Deferred revenue	(2,470)
Net deferred tax liabilities	(23,438)
Total identifiable net assets	$	85,667
Goodwill	$	205,316

During the one-year measurement period since the OPTIS acquisition date, we adjusted the fair values of the assets acquired and liabilities assumed, with the offset recorded as a $2.6 million increase to goodwill. These adjustments were made as we obtained new information about facts and circumstances that existed as of the acquisition date that, if known, would have affected the measurement of the amounts recognized as of that date.

Full pro forma results of operations have not been presented as the effects of the OPTIS business combination were not material to our consolidated results of operations. The table presented below reflects the impact of OPTIS from the date of acquisition to December 31, 2018. The operating loss does not include integration costs borne directly by us and our non-OPTIS subsidiaries as a result of the acquisition.


(in thousands)	Year Ended December 31, 2018
Revenue	$	18,532
Operating loss	$	(5,462)

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities

12 Months Ended

Dec. 31, 2020

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities [Abstract]

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities

Our other receivables and current assets, and other accrued expenses and liabilities, comprise the following balances:


	December 31,
(in thousands)	2020		2019
Receivables related to unrecognized revenue	$	192,154	$	177,679
Income taxes receivable, including overpayments and refunds	31,628		26,672
Prepaid expenses and other current assets	44,740		45,268
Total other receivables and current assets	$	268,522	$	249,619

Consumption, sales and VAT tax liabilities	$	45,156	$	36,398
Accrued expenses and other current liabilities	154,310		106,549
Total other accrued expenses and liabilities	$	199,466	$	142,947

Receivables related to unrecognized revenue represent the current portion of billings made for customer contracts that have not yet been recognized as revenue.

Property and Equipment

12 Months Ended

Dec. 31, 2020

Property, Plant and Equipment [Abstract]

Property and Equipment

Property and equipment consists of the following:


		December 31,
(in thousands)	Estimated Useful Lives	2020		2019
Equipment	1-15 years	$	123,139	$	105,428
Computer software	1-5 years	34,469		33,878
Buildings and improvements	2-40 years	38,332		38,095
Leasehold improvements	1-17 years	25,237		19,876
Furniture	1-13 years	14,902		12,766
Land		2,696		2,696
Property and equipment, gross		238,775		212,739
Less: Accumulated depreciation		(142,272)		(129,103)
Property and equipment, net		$	96,503	$	83,636

Depreciation expense related to property and equipment was $28.0 million, $23.6 million and $18.4 million for the years ended December 31, 2020, 2019 and 2018, respectively.

Goodwill and Intangible Assets

12 Months Ended

Dec. 31, 2020

Goodwill and Intangible Assets Disclosure [Abstract]

Goodwill and Intangible Assets

Goodwill and Intangible AssetsGoodwill represents the excess of the fair value of consideration transferred over the fair value of net identifiable assets acquired. Identifiable intangible assets acquired in business combinations are recorded based on their fair values on the date of acquisition.

Intangible assets are classified as follows:


	December 31, 2020				December 31, 2019
(in thousands)	Gross Carrying Amount		Accumulated Amortization		Gross Carrying Amount		Accumulated Amortization
Finite-lived intangible assets:
Developed software and core technologies	$	859,620	$	(370,338)	$	635,063	$	(332,622)
Customer lists and contract backlog	288,085		(136,093)		269,629		(132,596)
Trade names	175,626		(122,392)		154,259		(117,379)
Total	$	1,323,331	$	(628,823)	$	1,058,951	$	(582,597)
Indefinite-lived intangible asset:
Trade name	$	357			$	357

Finite-lived intangible assets are amortized over their estimated useful lives of two years to seventeen years. Amortization expense for the intangible assets reflected above was $57.2 million, $36.9 million and $40.8 million for the years ended December 31, 2020, 2019 and 2018, respectively.

As of December 31, 2020, estimated future amortization expense for the intangible assets reflected above is as follows:


(in thousands)
2021	$	74,981
2022	77,300
2023	78,426
2024	77,399
2025	74,805
Thereafter	311,597
Total intangible assets subject to amortization, net	694,508
Indefinite-lived trade name	357
Other intangible assets, net	$	694,865

The changes in goodwill during the years ended December 31, 2020 and 2019 were as follows:


(in thousands)	2020		2019
Beginning balance - January 1	$	2,413,280	$	1,572,455
Acquisitions and adjustments(1)	596,054		842,588

Currency translation	28,972		(1,763)
Ending balance - December 31	$	3,038,306	$	2,413,280

(1) In accordance with the accounting for business combinations, we recorded adjustments to goodwill for the effect of changes in the provisional fair values of the assets acquired and liabilities assumed during the measurement period (up to one year from the acquisition date) as we obtained new information about facts and circumstances that existed as of the acquisition date that, if known, would have affected the measurement of the amounts recognized as of that date. Such adjustments are not material to our consolidated financial statements.

Fair Value Measurement

12 Months Ended

Dec. 31, 2020

Fair Value Disclosures [Abstract]

Fair Value Measurement

The valuation hierarchy for disclosure of assets and liabilities reported at fair value prioritizes the inputs for such valuations into three broad levels:

•Level 1: quoted prices (unadjusted) in active markets for identical assets or liabilities;

•Level 2: quoted prices for similar assets and liabilities in active markets or inputs that are observable for the asset or liability, either directly or indirectly through market corroboration, for substantially the full term of the financial instrument; or

•Level 3: unobservable inputs based on our own assumptions used to measure assets and liabilities at fair value.

A financial asset's or liability's classification within the hierarchy is determined based on the lowest level input that is significant to the fair value measurement.

Our current and long-term debt is classified within Level 2 of the fair value hierarchy because these borrowings are not actively traded and have a variable interest rate structure based upon market rates. The carrying amount of our current and long-term debt approximates the estimated fair value. See Note 10, “Debt”, for additional information on these borrowings.

The following tables provide the assets carried at fair value and measured on a recurring basis:


			Fair Value Measurements at Reporting Date Using:
(in thousands)	December 31, 2020		Quoted Prices in Active Markets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets
Cash equivalents	$	341,085	$	341,085	$	—	$	—
Short-term investments	$	479	$	—	$	479	$	—
Deferred compensation plan investments	$	1,602	$	1,602	$	—	$	—


			Fair Value Measurements at Reporting Date Using:
(in thousands)	December 31, 2019		Quoted Prices in Active Markets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets
Cash equivalents	$	322,455	$	322,455	$	—	$	—
Short-term investments	$	288	$	—	$	288	$	—
Deferred compensation plan investments	$	1,110	$	1,110	$	—	$	—

The cash equivalents in the preceding tables represent money market funds, valued at net asset value, with carrying values which approximate their fair values because of their short-term nature.

The short-term investments in the preceding tables represent deposits held by certain foreign subsidiaries. The deposits have fixed interest rates with original maturities ranging from three months to one year.

The deferred compensation plan investments in the preceding tables represent trading securities held in a rabbi trust for the benefit of the non-employee directors. These securities consist of mutual funds traded in an active market with quoted prices. As a result, the plan assets are classified as Level 1 in the fair value hierarchy. The plan assets are recorded within other long-term assets on our consolidated balance sheets.

Leases

12 Months Ended

Dec. 31, 2020

Leases [Abstract]

Leases

LeasesWe primarily have operating leases for office space included in our ROU assets and lease liabilities. Our executive offices and those related to certain domestic product development, marketing, production and administration are located in a 186,000 square foot office facility in Canonsburg, Pennsylvania. The term of the lease is 183 months, which began on October 1, 2014 and expires on December 31, 2029. The lease agreement includes options to renew the contract through August 2044, an option to lease additional space in January 2025 and an option to terminate the lease in December 2025. No options are included in the

lease liability as renewal is not reasonably certain. In addition, we are reasonably certain we will not terminate the lease agreement. Absent the exercise of options in the lease, our remaining base rent (inclusive of property taxes and certain operating costs) is $4.5 million per annum through 2024 and $4.7 million per annum for 2025 - 2029.

The components of our global lease cost reflected in the consolidated statements of income for the years ended December 31, 2020 and 2019 are as follows:


(in thousands)	2020		2019
Lease liability cost	$	24,818	$	22,507
Variable lease cost not included in the lease liability(1)	5,067		3,754

Total lease cost	$	29,885	$	26,261

(1) Variable lease cost includes common area maintenance, property taxes, utilities and fluctuations in rent due to a change in an index or rate.

For the year ended December 31, 2018, lease cost totaled $21.3 million.

Other information related to operating leases for the years ended December 31, 2020 and 2019 is as follows:


(in thousands)	2020		2019
Cash paid for amounts included in the measurement of the lease liability:
Operating cash flows from operating leases	$	(22,470)	$	(20,031)
Right-of-use assets obtained in exchange for new operating lease liabilities	$	48,248	$	35,191


	As of December 31,
	2020		2019
Weighted-average remaining lease term of operating leases	7.3 years		7.7 years
Weighted-average discount rate of operating leases	2.9	%	3.7	%

The maturity schedule of the operating lease liabilities as of December 31, 2020 is as follows:


(in thousands)
2021	$	27,311
2022	24,712
2023	21,522
2024	20,264
2025	17,076
Thereafter	50,438
Total future lease payments	161,323
Less: Present value adjustment	(16,792)
Present value of future lease payments(1)	$	144,531

(1)Includes the current portion of operating lease liabilities of $23.6 million, which is reflected in other accrued expenses and liabilities in the consolidated balance sheets.

There were no material leases that have been signed but not yet commenced as of December 31, 2020.

Debt

12 Months Ended

Dec. 31, 2020

Debt Disclosure [Abstract]

Debt

In February 2019, we entered into a credit agreement for a $500.0 million unsecured revolving credit facility, which includes a $50.0 million sublimit for the issuance of letters of credit (Revolving Credit Facility), with Bank of America, N.A. as the Administrative Agent. The Revolving Credit Facility becomes payable in full on February 22, 2024 and is available for general corporate purposes, including, among others, to finance acquisitions and capital expenditures. The Revolving Credit Facility was not utilized in 2020 or 2019.

In connection with the acquisition of LST, we amended our credit agreement (Amended Credit Agreement) on October 16, 2019. The amendment provided for a new $500.0 million unsecured term loan facility to finance the acquisition. The term loan was funded on November 1, 2019 and matures on November 1, 2024. Principal on the term loan will be payable on the last business day of each fiscal quarter commencing with the ninth full fiscal quarter after the funding date at a rate of 1.25% per quarter, increasing to 2.50% per quarter after the next four fiscal quarters. We repaid $75.0 million of the unsecured term loan balance in January 2020 prior to the scheduled maturity dates in 2022 ($25.0 million) and 2023 ($50.0 million).

In connection with the acquisition of AGI, we entered into a credit agreement (AGI Credit Agreement) on November 9, 2020, with Bank of America, N.A. as the Administrative Agent. The AGI Credit Agreement provided for a new $375.0 million unsecured term loan facility to finance a portion of the cash consideration for the acquisition. The term loan was funded on December 1, 2020 and matures on November 1, 2024. Principal on the term loan will be payable on the last business day of each fiscal quarter commencing with the fifth full fiscal quarter after the funding date at a rate of 1.25% per quarter, increasing to 2.50% per quarter after the next four fiscal quarters.

Borrowings under the Amended Credit Agreement and the AGI Credit Agreement (Credit Agreements) accrue interest at the Eurodollar rate plus an applicable margin or at the base rate, at our election. For the quarter ended December 31, 2020, we elected to apply the Eurodollar rate. The base rate is the applicable margin plus the highest of (i) the federal funds rate plus 0.500%, (ii) the Bank of America prime rate and (iii) the Eurodollar rate plus 1.000%. The applicable margin for these borrowings is a percentage per annum based on the lower of (1) a pricing level determined by our then-current consolidated leverage ratio and (2) a pricing level determined by our debt ratings (if such debt ratings exist). This results in a margin ranging from 1.125% to 1.750% and 0.125% to 0.750% for the Eurodollar rate and base rate, respectively.

The weighted-average interest rates in effect for the years ended December 31, 2020 and 2019 were 2.09% and 2.96%, respectively. As of December 31, 2020, the rates in effect for the Amended Credit Agreement and the AGI Credit Agreement were 1.38% and 1.50%, respectively.

The Credit Agreements contain language in the event the Eurodollar rate is not available due to LIBOR changes. If this occurs, the base rate will be used for borrowings. However, we may work with the Administrative Agent to amend the Credit Agreements to replace the Eurodollar rate with (i) one or more rates based on the Secured Overnight Financing Rate (SOFR); or (ii) another alternative benchmark rate, subject to the lenders' approval.

The Credit Agreements contain customary representations and warranties, affirmative and negative covenants and events of default. The Credit Agreements also each contain a financial covenant requiring us to maintain a consolidated leverage ratio of indebtedness to earnings before interest, taxes, depreciation and amortization not exceeding 3.50 to 1.00 as of the end of any fiscal quarter (for the four-quarter period ending on such date) with an opportunity for a temporary increase in such consolidated leverage ratio to 4.00 to 1.00 upon the consummation of certain qualified acquisitions for which the aggregate consideration is at least $250.0 million.

As of December 31, 2020 and December 31, 2019, there were no outstanding borrowings under the unsecured Revolving Credit Facility, and the carrying values of the term loans were $798.1 million, which is net of $1.9 million of unamortized debt issuance costs, and $498.5 million, which is net of $1.5 million of unamortized debt issuance costs, respectively. We were in compliance with all covenants as of December 31, 2020 and December 31, 2019.

As of December 31, 2020, scheduled maturities of total debt for each of the five succeeding fiscal years are as follows:


(in thousands)
2021	$	—
2022	18,750
2023	37,500
2024	743,750
2025	—
Total	$	800,000

Income Taxes

12 Months Ended

Dec. 31, 2020

Income Tax Disclosure [Abstract]

Income Taxes

Income before income taxes included the following components:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Domestic	$	465,382	$	448,271	$	455,478
Foreign	28,543		74,312		31,607
Total	$	493,925	$	522,583	$	487,085

The provision for income taxes was composed of the following:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Current:
Federal	$	26,855	$	44,824	$	58,138
State	12,738		9,554		12,888
Foreign	51,377		31,421		30,359
Deferred:
Federal	(12,203)		(8,833)		(20,764)
State	(2,119)		(965)		(2,901)
Foreign	(16,610)		(4,713)		(10,010)
Total	$	60,038	$	71,288	$	67,710

The reconciliation of the U.S. federal statutory tax rate to the consolidated effective tax rate was as follows:


	Year Ended December 31,
	2020		2019		2018
Federal statutory tax rate	21.0	%	21.0	%	21.0	%
State income taxes, net of federal benefit	1.6		1.5		1.5
Foreign rate differential	0.4		0.8		0.8
Uncertain tax positions	0.1		(0.2)		0.5

Valuation allowance release	(0.8)		(1.3)		—

Benefit from entity structuring activities	(1.5)		—		(1.4)
Foreign-derived intangible income deduction	(2.8)		(3.8)		(3.9)
Research and development credits	(3.2)		(2.2)		(2.3)
Stock-based compensation	(3.6)		(3.1)		(3.3)
Other	1.0		0.9		1.0
	12.2	%	13.6	%	13.9	%

The components of deferred tax assets and liabilities are as follows:


	December 31,
(in thousands)	2020		2019
Deferred tax assets:
Net operating loss carryforwards	$	47,551	$	35,044
Operating lease liabilities	34,803		26,628
Stock-based compensation	24,738		24,254
Uncertain tax positions	18,565		19,227
Employee benefits	13,290		9,392
Research and development credits	9,847		5,865
Allowance for doubtful accounts	3,193		1,841
Other	6,856		4,468
Valuation allowance	(15,398)		(17,524)
Total deferred tax assets	143,445		109,195
Deferred tax liabilities:
Other intangible assets	(147,960)		(99,193)
Operating lease right-of-use assets	(33,304)		(25,648)
Deferred revenue	(26,839)		(13,744)
Accounting method change	(10,781)		(21,396)
Property and equipment	(6,052)		(3,780)
Total deferred tax liabilities	(224,936)		(163,761)
Net deferred tax liabilities	$	(81,491)	$	(54,566)

The valuation allowance decreased by $2.1 million for the year ended December 31, 2020. Intercompany debt restructuring resulted in the ability to utilize losses in a foreign jurisdiction where we previously determined that utilization was remote, resulting in the release of $2.3 million of valuation allowance. In addition, a favorable tax ruling in a foreign jurisdiction resulted in the release of $1.8 million of valuation allowance recorded against losses where we previously determined that utilization was remote. These decreases in the valuation allowance are offset by other increases in unrealizable tax assets. As of each reporting date, management considers new evidence, both positive and negative, that could affect the future realization of deferred tax assets. If management determines it is more likely than not that an asset, or a portion of an asset, will not be realized, a valuation allowance is recorded.

As of December 31, 2020, we had federal net operating loss carryforwards of $28.3 million, which are subject to limitations of their utilization. Losses totaling $25.6 million are not currently subject to expiration dates, while the remaining $2.7 million of losses expire between 2025 - 2037. Deferred tax assets of $1.9 million have been recorded for state operating loss carryforwards. These losses expire between 2030 - 2042, and are subject to limitations on their utilization. We had total foreign net operating loss carryforwards of $166.1 million, of which $141.7 million are not currently subject to expiration dates. The remainder, $24.4 million, expires between 2025 - 2036. We had tax credit carryforwards of $11.2 million, of which $6.9 million are subject to limitations on their utilization. Approximately $0.7 million of these tax credit carryforwards are not currently subject to expiration dates. The remainder, $10.5 million, expires in various years between 2021 - 2040.

In general, it is our intention to permanently reinvest all earnings in excess of previously taxed amounts. Substantially all of the pre-2018 earnings of our non-U.S. subsidiaries were taxed through the transition tax and post-2018 current earnings are taxed as part of global intangible low-taxed income tax expense. These taxes increase our previously taxed earnings and allow for the repatriation of the majority of our foreign earnings without any residual U.S. federal tax. While we believe that the financial reporting bases may be greater than the tax bases of investments in foreign subsidiaries for any earnings in excess of previously taxed amounts, such amounts are considered permanently reinvested. The cumulative temporary difference related to such permanently reinvested earnings is approximately $93.0 million and we would anticipate the tax effect on those earnings to be immaterial.

The following is a reconciliation of the total amounts of unrecognized tax benefits:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Unrecognized tax benefit as of January 1	$	49,085	$	22,827	$	19,657
Gross changes—acquisitions	(24,963)		26,914		—
Gross increases—tax positions in prior period	1,572		207		1,229
Gross decreases—tax positions in prior period	—		(1,743)		(376)
Gross increases—tax positions in current period	1,281		3,563		4,014
Reductions due to a lapse of the applicable statute of limitations	(3,502)		(2,230)		(994)
Changes due to currency fluctuation	994		(453)		(703)
Settlements	(392)		—		—
Unrecognized tax benefit as of December 31	$	24,075	$	49,085	$	22,827

We believe that it is reasonably possible that approximately $5.0 million of uncertain tax positions included in the table above may be resolved within the next twelve months as a result of settlement with a taxing authority or a lapse of the statute of limitations. If the unrecognized tax benefit as of December 31, 2020 were to be recognized, a benefit of $16.3 million would impact the effective tax rate.

We recognize interest and penalties related to income taxes as income tax expense. We recorded penalty expense of $0.2 million, $0.5 million and $0.8 million for the years ended December 31, 2020, 2019 and 2018, respectively. We recorded interest expense of $0.3 million and less than $0.1 million for the years ended December 31, 2020 and 2019, respectively, and interest income of $0.1 million for the year ended December 31, 2018. As of December 31, 2020, we accrued a liability for penalties of $5.5 million and interest of $5.4 million. As of December 31, 2019, we accrued a liability for penalties of $11.7 million and interest of $6.6 million.

We are subject to taxation in the U.S. and various states and foreign jurisdictions. In the U.S., our only major tax jurisdiction, the 2017 - 2020 tax years are open to examination by the Internal Revenue Service.

- Definition

The entire disclosure for income taxes. Disclosures may include net deferred tax liability or asset recognized in an enterprise's statement of financial position, net change during the year in the total valuation allowance, approximate tax effect of each type of temporary difference and carryforward that gives rise to a significant portion of deferred tax liabilities and deferred tax assets, utilization of a tax carryback, and tax uncertainties information.

+ References + Details

Pension And Profit-Sharing Plans	12 Months Ended
Pension And Profit-Sharing Plans	Dec. 31, 2020
Retirement Benefits [Abstract]
Pension And Profit-Sharing Plans	Pension and Profit-Sharing Plans We have a 401(k) plan for all qualifying domestic employees that permits participants to defer a portion of their pay pursuant to Section 401(k) of the Internal Revenue Code. We make matching contributions on behalf of each eligible participant in an amount equal to 100% of the first 3% and an additional 25% of the next 5%, for a maximum total of 4.25% of the employee's eligible compensation. We may make discretionary matching contributions. We may also make discretionary nonelective contributions in an amount to be determined by the Board of Directors for each Plan Year, provided the employee is employed at the end of the year and has worked at least 1,000 hours. We also maintain and contribute to various defined contribution and defined benefit pension arrangements for our international employees. We meet the minimum statutory funding requirements for our foreign plans. As of December 31, 2020 and 2019, the total unfunded portions of the defined benefit obligations were $13.5 million and $11.2 million, respectively. Expenses related to our retirement programs were $18.7 million in 2020, $16.3 million in 2019 and $12.4 million in 2018.

- Definition

The entire disclosure for retirement benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
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-Name Accounting Standards Codification
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Reference 3: http://www.xbrl.org/2003/role/disclosureRef
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Reference 7: http://www.xbrl.org/2003/role/disclosureRef
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Reference 8: http://www.xbrl.org/2003/role/disclosureRef
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+ Details

Non-Compete and Employment Agreements	12 Months Ended
Non-Compete and Employment Agreements	Dec. 31, 2020
Non-Compete and Employment Agreements [Abstract]
Non-Compete and Employment Agreements	Non-Compete and Employment Agreements Our employees have signed agreements under which they have agreed not to disclose trade secrets or confidential information that, where legally permitted, restrict engagement in or connection with any business that is competitive with us anywhere in the world while employed by us (and, in some cases, for specified periods thereafter in relevant geographic areas), and that any products or technology created by them during their term of employment are our property. In addition, we require all channel partners to enter into agreements not to disclose our trade secrets and other proprietary information. We have an employment agreement with our Chief Executive Officer. This agreement provides for, among other things, in the case of termination by us other than for Cause (as defined therein) or by the Chief Executive Officer for Good Reason (as defined therein) and subject to his execution and delivery of a release of claims against us, he will receive minimum severance payments equal to the sum of two times his base salary and target bonus to be paid out over two years from the date of termination and up to two years of COBRA payments for health care coverage after termination. During his employment with us and for two years thereafter, following termination of employment under certain circumstances described in the contract, he will be subject to non-competition and non-solicitation obligations. We also have employment agreements with several other employees, primarily in foreign jurisdictions. The terms of these employment agreements generally include annual compensation and non-compete clauses.

Stock-Based Compensation

12 Months Ended

Dec. 31, 2020

Share-based Payment Arrangement [Abstract]

Stock-Based Compensation

We have an equity incentive plan - the Fifth Amended and Restated ANSYS, Inc. 1996 Stock Option and Grant Plan (Stock Plan). The Stock Plan, as amended, authorizes the grant of approximately 39.8 million shares of our common stock in the form of: (i) incentive stock options (ISOs), (ii) nonqualified stock options, (iii) common stock with or without vesting or other restrictions, (iv) common stock upon the attainment of specified performance goals, (v) restricted stock awards, (vi) the right to receive cash dividends with the holders of the common stock as if the recipient held a specified number of shares of the common stock, (vii) deferred stock awards, (viii) restricted stock unit awards, (ix) stock appreciation rights and (x) cash-based awards.

The Stock Plan provides that: (i) the exercise price of any stock option must be no less than the fair value of the stock at the date of grant and (ii) the exercise price of an ISO held by an optionee who possesses more than 10% of the total combined voting power of all classes of stock must be no less than 110% of the fair market value of the stock at the time of grant. The Compensation Committee of the Board of Directors has the authority to set expiration dates that are no later than ten years from the date of grant (or five years for an optionee who meets the 10% criterion), payment terms, and other provisions for each grant. Shares associated with unexercised options or reacquired shares of common stock (except those shares withheld as a result of tax withholding, shares used to pay an option exercise price or pursuant to a net issuance) become available again for option grants and common stock-related awards under the Stock Plan.

The Compensation Committee of the Board of Directors may, at its sole discretion, accelerate the date or dates on which an award granted under the Stock Plan may vest or extend, in the case of a stock option, the exercise period up to the expiration date of the option, subject to the terms and conditions of the Stock Plan. Upon termination of service of a participant due to the participant’s death or disability, the vesting of restricted stock units held by the participant accelerates (in case of performance-based vesting, subject to the attainment of the performance requirement).

In the event of a "sale event," defined in the Stock Plan as a "Transaction," all outstanding awards will be assumed or continued by the successor entity, with appropriate adjustment in the awards to reflect the transaction. In such event, except as the Compensation Committee may otherwise specify with respect to particular awards in the award agreements, if the service relationship of the holder of an award is terminated without cause on or within 18 months after the sale event, then all awards held by such holder will become fully vested and exercisable at that time. If there is a sale event in which the successor entity refuses to assume or continue outstanding awards, then subject to the consummation of the sale event, all awards with time-based vesting conditions will become fully vested and exercisable at the effective time of the sale event and all awards with performance-based vesting conditions may become vested at the discretion of the Compensation Committee and then all such awards will terminate at the time of the sale event. In the event of the termination of stock options or stock appreciation rights in connection with a sale event, the Compensation Committee may either make or provide for a cash payment to the holders of such awards equal to the difference between the per share transaction consideration and the exercise price of such awards or permit each holder to have at least a 15-day period to exercise such awards prior to their termination.

We currently issue shares related to exercised stock options or vested awards from our existing pool of treasury shares and have no specific policy to repurchase treasury shares as stock options are exercised or as awards vest. If the treasury pool is depleted, we will issue new shares.

Total stock-based compensation expense recognized for the years ended December 31, 2020, 2019 and 2018 is as follows:


	Year Ended December 31,
(in thousands, except per share amounts)	2020		2019		2018
Cost of sales:
Maintenance and service	13,626		8,494		5,224
Operating expenses:
Selling, general and administrative	73,491		60,639		47,099
Research and development	58,498		47,057		31,023
Stock-based compensation expense before taxes	145,615		116,190		83,346
Related income tax benefits	(56,485)		(47,454)		(34,518)
Stock-based compensation expense, net of taxes	$	89,130	$	68,736	$	48,828
Net impact on earnings per share:
Basic earnings per share	$	(1.04)	$	(0.82)	$	(0.58)
Diluted earnings per share	$	(1.02)	$	(0.80)	$	(0.57)

As of December 31, 2020, total unrecognized estimated compensation expense related to awards granted prior to that date was $160.7 million, which is expected to be recognized over a weighted average period of 1.4 years. Forfeitures of awards are accounted for as they occur.

Stock Options

Prior to 2017, we granted stock option awards. The value of each stock option award was estimated on the date of grant, or date of acquisition for options issued in a business combination, using the Black-Scholes option pricing model (Black-Scholes model). The determination of the fair value of stock-based payment awards using an option pricing model was affected by our stock price as well as assumptions regarding a number of complex and subjective variables. These variables included our stock volatility during the preceding six years, actual and projected employee stock option exercise behaviors, interest rate assumptions using the five-year U.S. Treasury Note yield on the date of grant or acquisition date, and expected dividends. The stock-based compensation expense for options was recorded ratably over the requisite service period.

As of December 31, 2020, there is no unrecognized estimated compensation cost related to unvested stock options.

Information regarding stock option transactions is summarized below:


	Year Ended December 31,
	2020			2019			2018
(options in thousands)	Options	Weighted- Average Exercise Price		Options	Weighted- Average Exercise Price		Options	Weighted- Average Exercise Price
Outstanding, beginning of year	984	$	67.49	1,484	$	62.80	2,170	$	59.17
Granted	—	$	—	—	$	—	—	$	—
Exercised	(336)	$	54.43	(495)	$	53.53	(679)	$	50.92
Forfeited	—	$	—	(5)	$	64.21	(7)	$	86.28
Outstanding, end of year	648	$	74.26	984	$	67.49	1,484	$	62.80
Vested and Exercisable, end of year	648	$	74.26	924	$	65.71	1,347	$	59.69
Nonvested	—	$	—	60	$	94.77	137	$	93.44


	2020		2019		2018
Weighted Average Remaining Contractual Term (in years)
Outstanding	2.93		3.18		3.55
Vested and Exercisable	2.93		2.95		3.14
Nonvested	0.00		6.71		7.60
Aggregate Intrinsic Value (in thousands)
Exercised	$	78,269	$	72,098	$	78,648
Outstanding	$	187,679	$	186,926	$	118,908
Vested and Exercisable	$	187,679	$	177,111	$	112,133
Nonvested	$	—	$	9,815	$	6,775
Compensation Expense - Stock Options (in thousands)	$	1,030	$	1,709	$	2,006

Information regarding stock options outstanding as of December 31, 2020 is summarized below:


(options in thousands)	Options Outstanding & Exercisable
Range of Exercise Prices	Options	Weighted- Average Remaining Contractual Life (years)	Weighted- Average Exercise Price
$12.26 - $24.42	13	0.40	$	22.10
$58.67	167	0.86	$	58.67
$67.44	226	1.85	$	67.44
$78.56 - $95.09	242	5.48	$	94.15

There were no unvested stock options as of December 31, 2020.

Restricted Stock Units

Under the terms of the Fifth Amended and Restated ANSYS, Inc. 1996 Stock Option and Grant Plan, we issue various restricted stock unit awards. The following table summarizes the types of awards and vesting conditions:


Award	Vesting Period	Vesting Condition
Restricted stock units with a service condition only	Three years	Continued employment through the vesting period. One third vests annually.
Restricted stock units with an operating performance and service condition	Three years	Operating performance metrics as defined at the beginning of each sub-performance period and subject to continued employment.
Restricted stock units with a market and service condition	Three years	Our performance measured by total stockholder return relative to the Nasdaq Composite Index for the performance period and subject to continued employment through the vesting period.

The fair value of RSUs with only a service condition is based on the fair market value of our stock on the date of the grant and is recognized over the vesting period.

The fair value of RSUs with operating performance metrics is based on the fair market value of our stock on the date of the grant and is recognized from the grant date through the conclusion of the performance period associated with each operating performance metric based on management's estimates concerning the probability of vesting.

The fair values of restricted stock units (RSUs) with a market condition were estimated using a Monte Carlo simulation model and are recognized over the vesting period. The determination of the fair values of the awards was affected by the grant date and several variables, each of which has been identified in the chart below:


	Year Ended December 31,
Assumptions used in Monte Carlo lattice pricing model	2020	2019	2018
Risk-free interest rate	0.7%	2.5%	2.4%
Expected dividend yield	—%	—%	—%
Expected volatility—Ansys stock price	25%	23%	21%
Expected volatility—Nasdaq Composite Index	18%	16%	15%
Expected term	2.8 years	2.8 years	2.8 years
Correlation factor	0.77	0.71	0.65
Weighted average fair value per share	$245.08	$238.99	$191.76

Total compensation expense for employee RSU awards recorded for the years ended December 31, 2020, 2019 and 2018 was $138.3 million, $109.9 million and $77.4 million, respectively.

Information regarding all employee RSU transactions is summarized below:


	Year Ended December 31,
	2020			2019			2018
(RSUs in thousands)	RSUs	Weighted- Average Grant Date Fair Value		RSUs	Weighted- Average Grant Date Fair Value		RSUs	Weighted- Average Grant Date Fair Value
Nonvested, beginning of year	1,618	$	165.26	1,522	$	129.96	1,361	$	100.66
Granted(1)	501	$	256.47	843	$	192.37	681	$	163.67
Performance adjustment - awards with market condition(2)	18	$	191.76	12	$	120.96	10	$	78.71
Performance adjustment - awards with performance condition(2)	(10)	$	279.08	62	$	176.89	66	$	162.64
Vested	(742)	$	158.13	(704)	$	125.84	(524)	$	101.38
Forfeited	(62)	$	193.28	(117)	$	140.43	(72)	$	125.29
Nonvested, end of year	1,323	$	201.98	1,618	$	165.26	1,522	$	129.96

(1) Includes all RSUs granted during the year. RSUs with operating performance conditions are issued annually and have one performance cycle or three sub-performance cycles. Performance conditions are assigned near the beginning of each performance cycle or sub-performance cycle, as applicable, and awards are reflected as grants at the target number of units at that time.

(2) RSUs with a market or performance condition are granted at target and vest based on achievement of the market or operating performance and service conditions. The actual number of RSUs issued may be more or less than the target RSUs depending on the achievement of the market or operating performance conditions.

Board of Directors

During and prior to 2015, we granted deferred stock awards to non-employee Directors, which are rights to receive shares of common stock upon termination of service as a Director. Associated with these awards, we established a non-qualified 409(a) deferred compensation plan with assets held under a rabbi trust to provide Directors an opportunity to diversify their vested awards. During open trading windows and at their elective option, the Directors may convert their Ansys shares into a variety of non-Ansys-stock investment options in order to diversify a portion of their holdings, subject to meeting ownership guidelines.

Information regarding deferred stock awards to non-employee Directors is summarized below:


	Year Ended December 31, 2020
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	5,598	60,081	65,679
Shares Diversified	1,400	(1,400)	—
Deferred Awards Outstanding, end of year	6,998	58,681	65,679


	Year Ended December 31, 2019
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	12,250	120,449	132,699
Shares Diversified	13,348	(13,348)	—
Shares Issued Upon Retirement	(20,000)	(47,020)	(67,020)
Deferred Awards Outstanding, end of year	5,598	60,081	65,679


	Year Ended December 31, 2018
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	29,500	159,599	189,099
Shares Diversified	6,105	(6,105)	—
Shares Issued Upon Retirement	(23,355)	(33,045)	(56,400)
Deferred Awards Outstanding, end of year	12,250	120,449	132,699

Information regarding RSU awards to non-employee Directors is summarized below:


	Year Ended December 31,
	2020			2019			2018
(RSUs in thousands)	BOD RSUs	Weighted- Average Grant Date Fair Value		BOD RSUs	Weighted- Average Grant Date Fair Value		BOD RSUs	Weighted- Average Grant Date Fair Value
Nonvested, beginning of year	9,688	$	187.53	13,632	$	165.71	18,018	$	123.38
Granted	9,664	$	253.40	11,259	$	187.53	13,632	$	165.71
Vested	(10,704)	$	193.35	(14,287)	$	166.71	(18,018)	$	123.38
Forfeited	(577)	$	253.93	(916)	$	187.53	—	$	—
Nonvested, end of year	8,071	$	253.93	9,688	$	187.53	13,632	$	165.71

The RSUs to non-employee Directors vest in full upon the earlier of one year from the date of grant or the date of the next regular meeting of stockholders. If a non-employee Director retires prior to the vest date, the non-employee Director receives a pro-rata portion of the RSUs. Total compensation expense associated with the awards recorded for the years ended December 31, 2020, 2019 and 2018 was $2.2 million, $2.5 million and $2.3 million, respectively.

Employee Stock Purchase Plan

Our 1996 Employee Stock Purchase Plan (the “Purchase Plan”) was adopted by the Board of Directors on April 19, 1996 and was subsequently approved by our stockholders. The stockholders approved an amendment to the Purchase Plan in May 2016 to increase the number of shares available for offerings to 1.8 million shares of which 0.1 million shares are available for future purchases as of December 31, 2020. The Purchase Plan is administered by the Compensation Committee. Offerings under the Purchase Plan commence on each February 1 and August 1, and have a duration of six months. An employee who owns or is deemed to own shares of stock representing in excess of 5% of the combined voting power of all classes of our stock may not participate in the Purchase Plan.

During each offering, an eligible employee may purchase shares under the Purchase Plan by authorizing payroll deductions of up to 10% of his or her cash compensation during the offering period. The maximum number of shares that may be purchased by any participating employee during any offering period is limited to 3,840 shares (as adjusted by the Compensation Committee from time to time). Unless the employee has previously withdrawn from the offering, his or her accumulated payroll

deductions will be used to purchase common stock on the last business day of the period at a price equal to 90% of the fair market value of the common stock on the first or last day of the offering period, whichever is lower. Under applicable tax rules, an employee may not accrue the right to purchase more than $25,000 of common stock, based on the grant-date fair value, in any calendar year in which the option is outstanding at any time. As of December 31, 2020, 1.7 million shares of common stock had been issued under the Purchase Plan. The total compensation expense recorded under the Purchase Plan during the years ended December 31, 2020, 2019 and 2018 was $4.1 million, $2.0 million and $1.8 million, respectively.

Stock Repurchase Program

12 Months Ended

Dec. 31, 2020

Class of Stock Disclosures [Abstract]

Stock Repurchase Program

Under our stock repurchase program, we repurchased shares as follows:


	Year Ended December 31,
(in thousands, except per share data)	2020		2019		2018
Number of shares repurchased	690		330		1,674
Average price paid per share	$	233.48	$	179.41	$	161.12
Total cost	$	161,029	$	59,116	$	269,801

All of the shares of common stock repurchased during the year ended December 31, 2020 were repurchased in the first quarter of 2020. As of December 31, 2020, 2.8 million shares remained available for repurchase under the program.

Royalty Agreements	12 Months Ended
Royalty Agreements	Dec. 31, 2020
Royalty Agreements [Abstract]
Royalty Agreements	Royalty AgreementsWe have entered into various renewable license agreements under which we have been granted access to the licensor's technology and the right to sell the technology in our product line. Royalties are payable to developers of the software at various rates and amounts, which generally are based upon unit sales, revenue or flat fees. Royalty fees are reported in cost of software licenses and were $29.6 million, $22.4 million and $16.9 million for the years ended December 31, 2020, 2019 and 2018, respectively.

Geographic Information

12 Months Ended

Dec. 31, 2020

Segments, Geographical Areas [Abstract]

Geographic Information

Revenue to external customers is attributed to individual countries based upon the location of the customer. Revenue by geographic area was as follows:


	Year Ended December 31,
(in thousands)	2020		2019		2018
United States	$	776,716	$	637,916	$	506,335
Japan	183,117		162,154		145,951
Germany	160,771		158,809		140,506
South Korea	74,953		90,082		72,724
France	71,255		68,551		67,657
Other EMEA	236,678		211,193		193,317
Other international	177,807		187,187		167,146
Total revenue	$	1,681,297	$	1,515,892	$	1,293,636

Property and equipment by geographic area was as follows:


	December 31,
(in thousands)	2020		2019
United States	$	65,633	$	59,473
India	7,408		5,660
France	5,749		3,657
Germany	5,277		4,237
United Kingdom	3,765		4,194
Other EMEA	2,082		1,875
Other international	6,589		4,540
Total property and equipment, net	$	96,503	$	83,636

Unconditional Purchase Obligations

12 Months Ended

Dec. 31, 2020

Unconditional Purchase Obligations (Excluding Capital Stock Redemptions) [Abstract]

Unconditional Purchase Obligations

We have entered into various unconditional purchase obligations which primarily include royalties and software licenses and services. We expended $37.2 million, $24.2 million and $22.4 million related to unconditional purchase obligations that existed as of the beginning of each year for the years ended December 31, 2020, 2019 and 2018, respectively. Future expenditures under unconditional purchase obligations in effect as of December 31, 2020 are as follows:


(in thousands)
2021	$	44,865
2022	20,751
2023	6,758
2024	2,525
2025	26
Total	$	74,925

Contingencies and Commitments	12 Months Ended
Contingencies and Commitments	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Contingencies and Commitments	Contingencies and Commitments We are subject to various investigations, claims and legal proceedings that arise in the ordinary course of business, including commercial disputes, labor and employment matters, tax audits, alleged infringement of intellectual property rights and other matters. In our opinion, the resolution of pending matters is not expected to have a material adverse effect on our consolidated results of operations, cash flows or financial position. However, each of these matters is subject to various uncertainties and it is possible that an unfavorable resolution of one or more of these proceedings could materially affect our results of operations, cash flows or financial position. Our Indian subsidiary has several service tax audits pending that have resulted in formal inquiries being received on transactions through mid-2012. We could incur tax charges and related liabilities of approximately $7.3 million. As such charges are not probable at this time, a reserve has not been recorded on the condensed consolidated balance sheet as of December 31, 2020. The service tax issues raised in our notices and inquiries are very similar to the case, M/s Microsoft Corporation (I) (P) Ltd. Vs. Commissioner of Service Tax, New Delhi, wherein the Delhi Customs, Excise and Service Tax Appellate Tribunal (CESTAT) issued a favorable ruling to Microsoft. The Microsoft ruling was subsequently challenged in the Supreme Court by the Indian tax authority and a decision is still pending. We can provide no assurances on the impact that the present Microsoft case’s decision will have on our cases, however, an unfavorable ruling in the Microsoft case may impact our assessment of probability and result in the recording of a $7.3 million reserve. We are uncertain as to when these service tax matters will be concluded. We sell software licenses and services to our customers under contractual agreements. Such agreements generally include certain provisions indemnifying the customer against claims of intellectual property infringement or non-compliance to contractual terms and conditions by third parties arising from such customer’s usage of our products or services. To date, payments related to these indemnification provisions have been immaterial. For several reasons, including the lack of prior material indemnification claims, we cannot determine the maximum amount of potential future payments, if any, related to such indemnification provisions.

Schedule II - Valuation and Qualifying Accounts

12 Months Ended

Dec. 31, 2020

SEC Schedule, 12-09, Valuation and Qualifying Accounts [Abstract]

Valuation and Qualifying Accounts

ANSYS, INC. AND SUBSIDIARIES

Valuation and Qualifying Accounts


(in thousands) Description	Balance at Beginning of Year		Additions: Charges to Costs and Expenses		Deductions: Write-Offs		Balance at End of Year
Year ended December 31, 2020 Allowance for doubtful accounts	$	8,700	$	6,438	$	1,138	$	14,000
Year ended December 31, 2019 Allowance for doubtful accounts	$	8,000	$	2,928	$	2,228	$	8,700
Year ended December 31, 2018 Allowance for doubtful accounts	$	6,800	$	1,577	$	377	$	8,000

Accounting Policies (Policies)

12 Months Ended

Dec. 31, 2020

Accounting Policies [Abstract]

Accounting Principles

Principles Of Consolidation

Principles of Consolidation

The accompanying consolidated financial statements include our accounts and those of our wholly owned subsidiaries. All intercompany accounts and transactions have been eliminated.

Recently Adopted Accounting Guidance

optional renewals for which we are reasonably certain to exercise; whereas, optional terminations are included unless it is reasonably certain not to be elected.

Accounting Guidance Issued And Not Yet Adopted

Accounting Guidance Issued and Not Yet Adopted

Use Of Estimates

Use of Estimates

•Allowances for doubtful accounts receivable

•Income tax accruals

•Uncertain tax positions

•Tax valuation reserves

•Fair value of stock-based compensation and probabilities of performance award attainment

•Contract revenue

•Standalone selling prices of our products and services

•Acquired deferred revenue

•Useful lives for depreciation and amortization

•Valuations of goodwill and other intangible assets

•Deferred compensation

•Loss contingencies

•Operating lease assets and liabilities

Actual results could differ from these estimates. Changes in estimates are recorded in the results of operations in the period that the changes occur.

Revenue Recognition

The warranty does not provide any type of additional service to the customer or performance obligation for us.

Significant Judgments

Cash And Cash Equivalents

Cash and Cash Equivalents


	December 31, 2020			December 31, 2019
(in thousands, except percentages)	Amount		% of Total	Amount		% of Total
Cash accounts	$	571,587	62.6	$	549,639	63.0
Money market funds	341,085		37.4	322,455		37.0
Total	$	912,672		$	872,094

Our money market fund balances are held in various funds of two issuers.

Property And Equipment

Property and Equipment

Research And Development

Research and Development

Business Combinations

Goodwill And Other Intangible Assets

Goodwill and Other Intangible Assets

Concentrations Of Credit Risk

Concentrations of Credit Risk


	Year Ended December 31,
(as a % of revenue)	2020		2019		2018
Revenue from channel partners	22	%	23	%	22	%
Largest channel partner	3	%	4	%	4	%
2nd largest channel partner	2	%	2	%	2	%

No single customer accounted for more than 5% of our revenue in 2020, 2019 or 2018.


	As of December 31,
(in thousands)	2020		2019
Cash and cash equivalents held domestically	$	582,882	$	626,433
Cash and cash equivalents held by foreign subsidiaries	329,790		245,661
Cash and cash equivalents held in excess of deposit insurance, foreign and domestic	887,886		855,721
Largest balance of cash and cash equivalents held with one financial institution, foreign and domestic	396,430		330,551

Allowance For Doubtful Accounts

Allowance for Doubtful Accounts

Allowance for Doubtful Accounts Policy 2020

The changes in the allowance for doubtful accounts during the year ended December 31, 2020 were as follows:


(in thousands)	Year Ended December 31, 2020
Beginning balance – January 1	$	8,700
Additions: Charges to costs and expenses	6,438
Deductions: Write-offs	(1,138)
Ending balance – December 31	$	14,000

The increase in the allowance for doubtful accounts was driven by expected losses related to COVID-19.

Allowance for Doubtful Accounts Policy 2019 and 2018

We recorded provisions for bad debts of $6.4 million, $2.9 million and $1.6 million for the years ended December 31, 2020, 2019 and 2018, respectively.

Income Taxes

Foreign Currencies

Accumulated Other Comprehensive Loss

Accumulated other comprehensive loss is composed entirely of foreign currency translation adjustments.

Earnings Per Share

The details of basic and diluted EPS are as follows:


	Year Ended December 31,
(in thousands, except per share data)	2020		2019		2018
Net income	$	433,887	$	451,295	$	419,375
Weighted average shares outstanding – basic	85,840		84,259		83,973
Dilutive effect of stock plans	1,448		1,666		1,940
Weighted average shares outstanding – diluted	87,288		85,925		85,913
Basic earnings per share	$	5.05	$	5.36	$	4.99
Diluted earnings per share	$	4.97	$	5.25	$	4.88
Anti-dilutive shares	23		14		7

Stock-Based Compensation

Fair Value Of Financial Instruments

Fair Value of Financial InstrumentsWe account for certain assets and liabilities at fair value in accordance with the accounting guidance applicable to fair value measurements and disclosures. The carrying values of cash, cash equivalents, short-term investments, accounts receivable, accounts payable, accrued expenses, other accrued liabilities and short-term obligations are deemed to be reasonable estimates of their fair values because of their short-term nature. Our term loans are variable rate debt obligations and, therefore, the carrying amounts approximate the fair values.

Accounting Policies (Tables)

12 Months Ended

Dec. 31, 2020

Summary Of Cash And Cash Equivalents

Our cash and cash equivalents balances comprise the following:


	December 31, 2020			December 31, 2019
(in thousands, except percentages)	Amount		% of Total	Amount		% of Total
Cash accounts	$	571,587	62.6	$	549,639	63.0
Money market funds	341,085		37.4	322,455		37.0
Total	$	912,672		$	872,094

Allowance for Doubtful Accounts Rollforward

The changes in the allowance for doubtful accounts during the year ended December 31, 2020 were as follows:


(in thousands)	Year Ended December 31, 2020
Beginning balance – January 1	$	8,700
Additions: Charges to costs and expenses	6,438
Deductions: Write-offs	(1,138)
Ending balance – December 31	$	14,000

Basic And Diluted Earnings Per Share

The details of basic and diluted EPS are as follows:


	Year Ended December 31,
(in thousands, except per share data)	2020		2019		2018
Net income	$	433,887	$	451,295	$	419,375
Weighted average shares outstanding – basic	85,840		84,259		83,973
Dilutive effect of stock plans	1,448		1,666		1,940
Weighted average shares outstanding – diluted	87,288		85,925		85,913
Basic earnings per share	$	5.05	$	5.36	$	4.99
Diluted earnings per share	$	4.97	$	5.25	$	4.88
Anti-dilutive shares	23		14		7

Customer Concentration Risk

Schedule Of Risk Concentration

The following table outlines concentrations of risk with respect to our revenue:


	Year Ended December 31,
(as a % of revenue)	2020		2019		2018
Revenue from channel partners	22	%	23	%	22	%
Largest channel partner	3	%	4	%	4	%
2nd largest channel partner	2	%	2	%	2	%

Credit Concentration Risk

Schedule Of Risk Concentration

The following table outlines concentrations of risk with respect to our cash and cash equivalents:


	As of December 31,
(in thousands)	2020		2019
Cash and cash equivalents held domestically	$	582,882	$	626,433
Cash and cash equivalents held by foreign subsidiaries	329,790		245,661
Cash and cash equivalents held in excess of deposit insurance, foreign and domestic	887,886		855,721
Largest balance of cash and cash equivalents held with one financial institution, foreign and domestic	396,430		330,551

Revenue from Contracts with Customers (Tables)

12 Months Ended

Dec. 31, 2020

Revenue from Contract with Customer [Abstract]

Disaggregation of Revenue

The following table summarizes revenue:


	Year Ended December 31,
(in thousands)	2020			2019			2018
Revenue:
Lease licenses	$	500,105		$	406,043		$	275,619
Perpetual licenses	280,745			293,587			301,098
Software licenses	780,850			699,630			576,717
Maintenance	840,597			760,574			676,883
Service	59,850			55,688			40,036
Maintenance and service	900,447			816,262			716,919
Total revenue	$	1,681,297		$	1,515,892		$	1,293,636

Direct revenue, as a percentage of total revenue	77.8		%	77.1		%	77.6		%
Indirect revenue, as a percentage of total revenue	22.2		%	22.9		%	22.4		%

Changes in Deferred Revenue

The changes in deferred revenue, inclusive of both current and long-term deferred revenue, during the years ended December 31, 2020 and 2019 were as follows:


(in thousands)	2020		2019
Beginning balance – January 1	$	365,274	$	343,174
Acquired deferred revenue	6,872		6,880
Deferral of revenue	1,687,907		1,532,549
Recognition of deferred revenue	(1,681,297)		(1,515,892)
Currency translation	10,054		(1,437)
Ending balance – December 31	$	388,810	$	365,274

Remaining Performance Obligations, Expected Timing of Satisfaction

Total revenue allocated to remaining performance obligations as of December 31, 2020 will be recognized as revenue as follows:


(in thousands)
Next 12 months	$	606,780
Months 13-24	199,909
Months 25-36	80,304
Thereafter	80,134
Total revenue allocated to remaining performance obligations	$	967,127

Acquisitions (Tables)

12 Months Ended

Dec. 31, 2020

Business Combinations [Abstract]

Fair Value of Consideration Transferred

Fair Value of Consideration Transferred:


(in thousands)	AGI		Lumerical		Total
Cash	$	489,797	$	107,545	$	597,342
Ansys common stock(1)	218,348		—		218,348
Consideration not yet paid	14,342		—		14,342
Total consideration transferred at fair value	$	722,487	$	107,545	$	830,032

Fair Value of Consideration Transferred:


(in thousands)	LST		Granta Design		Other Acquisitions		Total
Cash	$	472,800	$	208,736	$	138,548	$	820,084
Ansys common stock	308,704		—		—		308,704
Total consideration transferred at fair value	$	781,504	$	208,736	$	138,548	$	1,128,788

Fair Value of Consideration Transferred:


(in thousands)	OPTIS
Cash	$	290,983

Schedule of Recognized Identified Assets Acquired and Liabilities Assumed

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	AGI		Lumerical		Total
Cash	$	17,663	$	11,844	$	29,507
Accounts receivable and other tangible assets	29,456		4,244		33,700
Developed software and core technologies	184,100		31,614		215,714
Customer lists	25,400		1,616		27,016
Trade names	18,200		1,756		19,956
Accounts payable and other liabilities	(23,279)		(1,106)		(24,385)
Deferred revenue	(5,467)		(1,405)		(6,872)
Net deferred tax liabilities	(50,207)		(7,452)		(57,659)
Total identifiable net assets	$	195,866	$	41,111	$	236,977
Goodwill	$	526,621	$	66,434	$	593,055

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	LST		Granta Design		Other Acquisitions		Total
Cash	$	8,520	$	13,644	$	6,231	$	28,395
Accounts receivable and other tangible assets	20,569		6,941		10,734		38,244
Developed software and core technologies (10-year weighted-average life)	167,700		32,445		25,018		225,163
Customer lists (15-year weighted-average life)	25,900		20,016		15,743		61,659
Trade names (10-year weighted-average life)	10,600		4,579		2,051		17,230
Accounts payable and other liabilities	(3,887)		(5,164)		(5,946)		(14,997)
Deferred revenue	(3,565)		(1,426)		(1,889)		(6,880)
Uncertain tax positions	—		—		(257)		(257)
Net deferred tax liabilities	(47,412)		(8,976)		(8,151)		(64,539)
Total identifiable net assets	$	178,425	$	62,059	$	43,534	$	284,018
Goodwill	$	603,079	$	146,677	$	95,014	$	844,770

Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:


(in thousands)	OPTIS
Cash	$	7,957
Accounts receivable and other tangible assets	15,910
Developed software and core technologies (10-year weighted-average life)	47,597
Customer lists (12-year weighted-average life)	41,303
Trade names (9-year weighted-average life)	10,749
Accounts payable and other liabilities	(11,941)
Deferred revenue	(2,470)
Net deferred tax liabilities	(23,438)
Total identifiable net assets	$	85,667
Goodwill	$	205,316

Schedule of Finite-Lived Intangible Assets Acquired as Part of Business Combination

The weighted-average useful life, valuation method and assumptions used to determine the fair value of the intangible assets acquired with the AGI acquisition are as follows:

Intangible Asset

Weighted-Average Useful Life

Valuation Method

Assumptions

Developed software and core technologies

10 years

Relief-from-royalty

Royalty rate: 40.0%

Discount rate: 11.0%

Trade names

9 years

Relief-from-royalty

Royalty rate: 1.0% - 2.0%

Discount rate: 11.0%

Customer lists

15 years

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 12.0%

The weighted-average useful life, valuation method and assumptions used to determine the fair value of the intangible assets acquired with the Lumerical acquisition are as follows:

Intangible Asset

Weighted-Average Useful Life

Valuation Method

Assumptions

Developed software and core technologies

10 years

Multi-period excess earnings

Discount rate: 16.5%

Trade names

6 years

Relief-from-royalty

Royalty rate: 2.0%

Discount rate: 16.5%

Customer lists

10 years

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 12.5%

The valuation method and assumptions used to determine the fair value of the significant intangible assets acquired in 2019 are as follows:

Intangible Asset

Valuation Method

LST Assumptions

Granta Design Assumptions

Developed software and core technologies

Relief-from-royalty

Royalty rate: 50.0%

Discount rate: 10.0%

Royalty rate: 8.0% - 10.0%

Discount rate: 12.5%

Trade names

Relief-from-royalty

Royalty rate: 2.0%

Discount rate: 10.0%

Royalty rate: 2.0%

Discount rate: 14.0%

Customer lists

Multi-period excess earnings

Attrition rate: 10.0%

Discount rate: 11.0%

Attrition rate: 10.0%

Discount rate: 12.5%

Business Acquisition, Pro Forma Information

The table presented below reflects the aggregate impact on our results of operations of the 2019 acquisitions from the date of acquisition to December 31, 2019. The operating income does not include integration costs borne directly by us and our non-acquired subsidiaries as a result of the acquisitions.


(in thousands)	Year Ended December 31, 2019
Revenue	$	44,079
Operating income	$	6,733

The table presented below reflects the impact of OPTIS from the date of acquisition to December 31, 2018. The operating loss does not include integration costs borne directly by us and our non-OPTIS subsidiaries as a result of the acquisition.


(in thousands)	Year Ended December 31, 2018
Revenue	$	18,532
Operating loss	$	(5,462)

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities (Tables)

12 Months Ended

Dec. 31, 2020

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities [Abstract]

Schedule of Other Receivables and Current Assets and Other Accrued Expenses and Liabilities

Our other receivables and current assets, and other accrued expenses and liabilities, comprise the following balances:


	December 31,
(in thousands)	2020		2019
Receivables related to unrecognized revenue	$	192,154	$	177,679
Income taxes receivable, including overpayments and refunds	31,628		26,672
Prepaid expenses and other current assets	44,740		45,268
Total other receivables and current assets	$	268,522	$	249,619

Consumption, sales and VAT tax liabilities	$	45,156	$	36,398
Accrued expenses and other current liabilities	154,310		106,549
Total other accrued expenses and liabilities	$	199,466	$	142,947

Property and Equipment (Tables)

12 Months Ended

Dec. 31, 2020

Property, Plant and Equipment [Abstract]

Components Of Property and Equipment

Property and equipment consists of the following:


		December 31,
(in thousands)	Estimated Useful Lives	2020		2019
Equipment	1-15 years	$	123,139	$	105,428
Computer software	1-5 years	34,469		33,878
Buildings and improvements	2-40 years	38,332		38,095
Leasehold improvements	1-17 years	25,237		19,876
Furniture	1-13 years	14,902		12,766
Land		2,696		2,696
Property and equipment, gross		238,775		212,739
Less: Accumulated depreciation		(142,272)		(129,103)
Property and equipment, net		$	96,503	$	83,636

Goodwill and Intangible Assets (Tables)

12 Months Ended

Dec. 31, 2020

Goodwill and Intangible Assets Disclosure [Abstract]

Intangible Assets (Finite-Lived)

Intangible assets are classified as follows:


	December 31, 2020				December 31, 2019
(in thousands)	Gross Carrying Amount		Accumulated Amortization		Gross Carrying Amount		Accumulated Amortization
Finite-lived intangible assets:
Developed software and core technologies	$	859,620	$	(370,338)	$	635,063	$	(332,622)
Customer lists and contract backlog	288,085		(136,093)		269,629		(132,596)
Trade names	175,626		(122,392)		154,259		(117,379)
Total	$	1,323,331	$	(628,823)	$	1,058,951	$	(582,597)
Indefinite-lived intangible asset:
Trade name	$	357			$	357

Intangible Assets (Indefinite-Lived)

Intangible assets are classified as follows:


	December 31, 2020				December 31, 2019
(in thousands)	Gross Carrying Amount		Accumulated Amortization		Gross Carrying Amount		Accumulated Amortization
Finite-lived intangible assets:
Developed software and core technologies	$	859,620	$	(370,338)	$	635,063	$	(332,622)
Customer lists and contract backlog	288,085		(136,093)		269,629		(132,596)
Trade names	175,626		(122,392)		154,259		(117,379)
Total	$	1,323,331	$	(628,823)	$	1,058,951	$	(582,597)
Indefinite-lived intangible asset:
Trade name	$	357			$	357

Estimated Future Amortization Expense for Intangible Assets

As of December 31, 2020, estimated future amortization expense for the intangible assets reflected above is as follows:


(in thousands)
2021	$	74,981
2022	77,300
2023	78,426
2024	77,399
2025	74,805
Thereafter	311,597
Total intangible assets subject to amortization, net	694,508
Indefinite-lived trade name	357
Other intangible assets, net	$	694,865

Changes in Goodwill

The changes in goodwill during the years ended December 31, 2020 and 2019 were as follows:


(in thousands)	2020		2019
Beginning balance - January 1	$	2,413,280	$	1,572,455
Acquisitions and adjustments(1)	596,054		842,588

Currency translation	28,972		(1,763)
Ending balance - December 31	$	3,038,306	$	2,413,280

Fair Value Measurement (Tables)

12 Months Ended

Dec. 31, 2020

Fair Value Disclosures [Abstract]

Fair Value of Assets and Liabilities Measured on Recurring Basis

The following tables provide the assets carried at fair value and measured on a recurring basis:


			Fair Value Measurements at Reporting Date Using:
(in thousands)	December 31, 2020		Quoted Prices in Active Markets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets
Cash equivalents	$	341,085	$	341,085	$	—	$	—
Short-term investments	$	479	$	—	$	479	$	—
Deferred compensation plan investments	$	1,602	$	1,602	$	—	$	—


			Fair Value Measurements at Reporting Date Using:
(in thousands)	December 31, 2019		Quoted Prices in Active Markets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets
Cash equivalents	$	322,455	$	322,455	$	—	$	—
Short-term investments	$	288	$	—	$	288	$	—
Deferred compensation plan investments	$	1,110	$	1,110	$	—	$	—

Leases (Tables)

12 Months Ended

Dec. 31, 2020

Leases [Abstract]

Schedule of Lease Cost

The components of our global lease cost reflected in the consolidated statements of income for the years ended December 31, 2020 and 2019 are as follows:


(in thousands)	2020		2019
Lease liability cost	$	24,818	$	22,507
Variable lease cost not included in the lease liability(1)	5,067		3,754

Total lease cost	$	29,885	$	26,261

(1) Variable lease cost includes common area maintenance, property taxes, utilities and fluctuations in rent due to a change in an index or rate.

Lessee, Operating Lease Other Information

Other information related to operating leases for the years ended December 31, 2020 and 2019 is as follows:


(in thousands)	2020		2019
Cash paid for amounts included in the measurement of the lease liability:
Operating cash flows from operating leases	$	(22,470)	$	(20,031)
Right-of-use assets obtained in exchange for new operating lease liabilities	$	48,248	$	35,191


	As of December 31,
	2020		2019
Weighted-average remaining lease term of operating leases	7.3 years		7.7 years
Weighted-average discount rate of operating leases	2.9	%	3.7	%

Schedule of Maturity of Operating Lease Liabilities

The maturity schedule of the operating lease liabilities as of December 31, 2020 is as follows:


(in thousands)
2021	$	27,311
2022	24,712
2023	21,522
2024	20,264
2025	17,076
Thereafter	50,438
Total future lease payments	161,323
Less: Present value adjustment	(16,792)
Present value of future lease payments(1)	$	144,531

(1)Includes the current portion of operating lease liabilities of $23.6 million, which is reflected in other accrued expenses and liabilities in the consolidated balance sheets.

Debt (Table)

12 Months Ended

Dec. 31, 2020

Debt Disclosure [Abstract]

Schedule of Maturities of Debt

As of December 31, 2020, scheduled maturities of total debt for each of the five succeeding fiscal years are as follows:


(in thousands)
2021	$	—
2022	18,750
2023	37,500
2024	743,750
2025	—
Total	$	800,000

Income Taxes (Tables)

12 Months Ended

Dec. 31, 2020

Income Tax Disclosure [Abstract]

Components Of Income Before Income Taxes

Income before income taxes included the following components:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Domestic	$	465,382	$	448,271	$	455,478
Foreign	28,543		74,312		31,607
Total	$	493,925	$	522,583	$	487,085

Components Of Provision For Income Taxes

The provision for income taxes was composed of the following:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Current:
Federal	$	26,855	$	44,824	$	58,138
State	12,738		9,554		12,888
Foreign	51,377		31,421		30,359
Deferred:
Federal	(12,203)		(8,833)		(20,764)
State	(2,119)		(965)		(2,901)
Foreign	(16,610)		(4,713)		(10,010)
Total	$	60,038	$	71,288	$	67,710

Reconciliation Of U.S. Federal Statutory Tax Rate To Consolidated Effective Tax Rate

The reconciliation of the U.S. federal statutory tax rate to the consolidated effective tax rate was as follows:


	Year Ended December 31,
	2020		2019		2018
Federal statutory tax rate	21.0	%	21.0	%	21.0	%
State income taxes, net of federal benefit	1.6		1.5		1.5
Foreign rate differential	0.4		0.8		0.8
Uncertain tax positions	0.1		(0.2)		0.5

Valuation allowance release	(0.8)		(1.3)		—

Benefit from entity structuring activities	(1.5)		—		(1.4)
Foreign-derived intangible income deduction	(2.8)		(3.8)		(3.9)
Research and development credits	(3.2)		(2.2)		(2.3)
Stock-based compensation	(3.6)		(3.1)		(3.3)
Other	1.0		0.9		1.0
	12.2	%	13.6	%	13.9	%

Components Of Deferred Tax Assets And Liabilities

The components of deferred tax assets and liabilities are as follows:


	December 31,
(in thousands)	2020		2019
Deferred tax assets:
Net operating loss carryforwards	$	47,551	$	35,044
Operating lease liabilities	34,803		26,628
Stock-based compensation	24,738		24,254
Uncertain tax positions	18,565		19,227
Employee benefits	13,290		9,392
Research and development credits	9,847		5,865
Allowance for doubtful accounts	3,193		1,841
Other	6,856		4,468
Valuation allowance	(15,398)		(17,524)
Total deferred tax assets	143,445		109,195
Deferred tax liabilities:
Other intangible assets	(147,960)		(99,193)
Operating lease right-of-use assets	(33,304)		(25,648)
Deferred revenue	(26,839)		(13,744)
Accounting method change	(10,781)		(21,396)
Property and equipment	(6,052)		(3,780)
Total deferred tax liabilities	(224,936)		(163,761)
Net deferred tax liabilities	$	(81,491)	$	(54,566)

Reconciliation Of Unrecognized Tax Benefits

The following is a reconciliation of the total amounts of unrecognized tax benefits:


	Year Ended December 31,
(in thousands)	2020		2019		2018
Unrecognized tax benefit as of January 1	$	49,085	$	22,827	$	19,657
Gross changes—acquisitions	(24,963)		26,914		—
Gross increases—tax positions in prior period	1,572		207		1,229
Gross decreases—tax positions in prior period	—		(1,743)		(376)
Gross increases—tax positions in current period	1,281		3,563		4,014
Reductions due to a lapse of the applicable statute of limitations	(3,502)		(2,230)		(994)
Changes due to currency fluctuation	994		(453)		(703)
Settlements	(392)		—		—
Unrecognized tax benefit as of December 31	$	24,075	$	49,085	$	22,827

Stock-Based Compensation (Tables)

12 Months Ended

Dec. 31, 2020

Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]

Stock-Based Compensation Expense

Total stock-based compensation expense recognized for the years ended December 31, 2020, 2019 and 2018 is as follows:


	Year Ended December 31,
(in thousands, except per share amounts)	2020		2019		2018
Cost of sales:
Maintenance and service	13,626		8,494		5,224
Operating expenses:
Selling, general and administrative	73,491		60,639		47,099
Research and development	58,498		47,057		31,023
Stock-based compensation expense before taxes	145,615		116,190		83,346
Related income tax benefits	(56,485)		(47,454)		(34,518)
Stock-based compensation expense, net of taxes	$	89,130	$	68,736	$	48,828
Net impact on earnings per share:
Basic earnings per share	$	(1.04)	$	(0.82)	$	(0.58)
Diluted earnings per share	$	(1.02)	$	(0.80)	$	(0.57)

Summary of Stock Options

Information regarding stock option transactions is summarized below:


	Year Ended December 31,
	2020			2019			2018
(options in thousands)	Options	Weighted- Average Exercise Price		Options	Weighted- Average Exercise Price		Options	Weighted- Average Exercise Price
Outstanding, beginning of year	984	$	67.49	1,484	$	62.80	2,170	$	59.17
Granted	—	$	—	—	$	—	—	$	—
Exercised	(336)	$	54.43	(495)	$	53.53	(679)	$	50.92
Forfeited	—	$	—	(5)	$	64.21	(7)	$	86.28
Outstanding, end of year	648	$	74.26	984	$	67.49	1,484	$	62.80
Vested and Exercisable, end of year	648	$	74.26	924	$	65.71	1,347	$	59.69
Nonvested	—	$	—	60	$	94.77	137	$	93.44


	2020		2019		2018
Weighted Average Remaining Contractual Term (in years)
Outstanding	2.93		3.18		3.55
Vested and Exercisable	2.93		2.95		3.14
Nonvested	0.00		6.71		7.60
Aggregate Intrinsic Value (in thousands)
Exercised	$	78,269	$	72,098	$	78,648
Outstanding	$	187,679	$	186,926	$	118,908
Vested and Exercisable	$	187,679	$	177,111	$	112,133
Nonvested	$	—	$	9,815	$	6,775
Compensation Expense - Stock Options (in thousands)	$	1,030	$	1,709	$	2,006

Summary of Types of Awards and Vesting Conditions

The following table summarizes the types of awards and vesting conditions:


Award	Vesting Period	Vesting Condition
Restricted stock units with a service condition only	Three years	Continued employment through the vesting period. One third vests annually.
Restricted stock units with an operating performance and service condition	Three years	Operating performance metrics as defined at the beginning of each sub-performance period and subject to continued employment.
Restricted stock units with a market and service condition	Three years	Our performance measured by total stockholder return relative to the Nasdaq Composite Index for the performance period and subject to continued employment through the vesting period.

Summary of Restricted Stock Units

Information regarding all employee RSU transactions is summarized below:


	Year Ended December 31,
	2020			2019			2018
(RSUs in thousands)	RSUs	Weighted- Average Grant Date Fair Value		RSUs	Weighted- Average Grant Date Fair Value		RSUs	Weighted- Average Grant Date Fair Value
Nonvested, beginning of year	1,618	$	165.26	1,522	$	129.96	1,361	$	100.66
Granted(1)	501	$	256.47	843	$	192.37	681	$	163.67
Performance adjustment - awards with market condition(2)	18	$	191.76	12	$	120.96	10	$	78.71
Performance adjustment - awards with performance condition(2)	(10)	$	279.08	62	$	176.89	66	$	162.64
Vested	(742)	$	158.13	(704)	$	125.84	(524)	$	101.38
Forfeited	(62)	$	193.28	(117)	$	140.43	(72)	$	125.29
Nonvested, end of year	1,323	$	201.98	1,618	$	165.26	1,522	$	129.96

Employee Stock Option

Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]

Information Regarding Stock Options Outstanding

Information regarding stock options outstanding as of December 31, 2020 is summarized below:


(options in thousands)	Options Outstanding & Exercisable
Range of Exercise Prices	Options	Weighted- Average Remaining Contractual Life (years)	Weighted- Average Exercise Price
$12.26 - $24.42	13	0.40	$	22.10
$58.67	167	0.86	$	58.67
$67.44	226	1.85	$	67.44
$78.56 - $95.09	242	5.48	$	94.15

Restricted Stock Units (RSUs)

Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]

Assumptions to Estimate Fair Value of Stock Awards

The determination of the fair values of the awards was affected by the grant date and several variables, each of which has been identified in the chart below:


	Year Ended December 31,
Assumptions used in Monte Carlo lattice pricing model	2020	2019	2018
Risk-free interest rate	0.7%	2.5%	2.4%
Expected dividend yield	—%	—%	—%
Expected volatility—Ansys stock price	25%	23%	21%
Expected volatility—Nasdaq Composite Index	18%	16%	15%
Expected term	2.8 years	2.8 years	2.8 years
Correlation factor	0.77	0.71	0.65
Weighted average fair value per share	$245.08	$238.99	$191.76

Diversified Deferred Stock Award

Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]

Summary of Stock Awards To Non-Employee Directors

Information regarding deferred stock awards to non-employee Directors is summarized below:


	Year Ended December 31, 2020
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	5,598	60,081	65,679
Shares Diversified	1,400	(1,400)	—
Deferred Awards Outstanding, end of year	6,998	58,681	65,679


	Year Ended December 31, 2019
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	12,250	120,449	132,699
Shares Diversified	13,348	(13,348)	—
Shares Issued Upon Retirement	(20,000)	(47,020)	(67,020)
Deferred Awards Outstanding, end of year	5,598	60,081	65,679


	Year Ended December 31, 2018
	Diversified	Undiversified	Total
Deferred Awards Outstanding, beginning of year	29,500	159,599	189,099
Shares Diversified	6,105	(6,105)	—
Shares Issued Upon Retirement	(23,355)	(33,045)	(56,400)
Deferred Awards Outstanding, end of year	12,250	120,449	132,699

Director Restricted Stock Units

Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]

Summary of Stock Awards To Non-Employee Directors

Information regarding RSU awards to non-employee Directors is summarized below:


	Year Ended December 31,
	2020			2019			2018
(RSUs in thousands)	BOD RSUs	Weighted- Average Grant Date Fair Value		BOD RSUs	Weighted- Average Grant Date Fair Value		BOD RSUs	Weighted- Average Grant Date Fair Value
Nonvested, beginning of year	9,688	$	187.53	13,632	$	165.71	18,018	$	123.38
Granted	9,664	$	253.40	11,259	$	187.53	13,632	$	165.71
Vested	(10,704)	$	193.35	(14,287)	$	166.71	(18,018)	$	123.38
Forfeited	(577)	$	253.93	(916)	$	187.53	—	$	—
Nonvested, end of year	8,071	$	253.93	9,688	$	187.53	13,632	$	165.71

Stock Repurchase Program (Tables)

12 Months Ended

Dec. 31, 2020

Class of Stock Disclosures [Abstract]

Stock Repurchase Program

Under our stock repurchase program, we repurchased shares as follows:


	Year Ended December 31,
(in thousands, except per share data)	2020		2019		2018
Number of shares repurchased	690		330		1,674
Average price paid per share	$	233.48	$	179.41	$	161.12
Total cost	$	161,029	$	59,116	$	269,801

Geographic Information (Tables)

12 Months Ended

Dec. 31, 2020

Segments, Geographical Areas [Abstract]

Revenue By Geographic Area

Revenue by geographic area was as follows:


	Year Ended December 31,
(in thousands)	2020		2019		2018
United States	$	776,716	$	637,916	$	506,335
Japan	183,117		162,154		145,951
Germany	160,771		158,809		140,506
South Korea	74,953		90,082		72,724
France	71,255		68,551		67,657
Other EMEA	236,678		211,193		193,317
Other international	177,807		187,187		167,146
Total revenue	$	1,681,297	$	1,515,892	$	1,293,636

Property and Equipment by Geographic Area

Property and equipment by geographic area was as follows:


	December 31,
(in thousands)	2020		2019
United States	$	65,633	$	59,473
India	7,408		5,660
France	5,749		3,657
Germany	5,277		4,237
United Kingdom	3,765		4,194
Other EMEA	2,082		1,875
Other international	6,589		4,540
Total property and equipment, net	$	96,503	$	83,636

Unconditional Purchase Obligations (Tables)

12 Months Ended

Dec. 31, 2020

Unconditional Purchase Obligations (Excluding Capital Stock Redemptions) [Abstract]

Unconditional Purchase Obligations

Future expenditures under unconditional purchase obligations in effect as of December 31, 2020 are as follows:


(in thousands)
2021	$	44,865
2022	20,751
2023	6,758
2024	2,525
2025	26
Total	$	74,925

Organization - Additional Information (Detail)	12 Months Ended
Organization - Additional Information (Detail)	Dec. 31, 2020 Segment
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Number of operating segments	1

Accounting Policies - Additional Information (Details) $ in Thousands	12 Months Ended
	Dec. 31, 2020 USD ($)	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Jan. 01, 2019 USD ($)
Operating lease right-of-use assets	$ 137,730	$ 105,671		$ 90,900
Operating lease liabilities	$ 144,531			$ 92,500
Lease license to license revenue	50.00%
Lease license to maintenance revenue	50.00%
Amortization of intangible assets	$ 57,200	36,900	$ 40,800
Provision for bad debts	6,438	2,928	1,577
Net foreign exchange loss	$ (200)	$ (2,500)	$ (3,100)
Money Market Funds
Concentration risk, % of money market funds with two issuers	100.00%
Minimum
Property and equipment, estimated useful lives (years)	1 year
Finite-lived intangible asset, useful life	2 years
Maximum
Property and equipment, estimated useful lives (years)	40 years
Finite-lived intangible asset, useful life	17 years
Customer Concentration Risk
Number of customers with more than five percent of revenue	0	0	0
Concentration risk, % of money market funds with two issuers	22.00%	23.00%	22.00%

Accounting Policies - Summary of Cash and Cash Equivalents (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Cash accounts, Amount	$ 571,587	$ 549,639
Money market funds, Amount	341,085	322,455
Total	$ 912,672	$ 872,094
Cash
Percent Of Cash And Cash Equivalents	62.60%	63.00%
Money Market Funds
Percent Of Cash And Cash Equivalents	37.40%	37.00%

Accounting Policies - Schedule of Risk Concentration (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Concentration Risk [Line Items]
Total	$ 912,672	$ 872,094
Customer Concentration Risk
Concentration Risk [Line Items]
Concentration risk, percentage	22.00%	23.00%	22.00%
Credit Concentration Risk
Concentration Risk [Line Items]
Cash and cash equivalents held in excess of deposit insurance, foreign and domestic	$ 887,886	$ 855,721
Largest balance of cash and cash equivalents held with one financial institution, foreign and domestic	$ 396,430	$ 330,551
1st Largest Channel Partner \| Customer Concentration Risk
Concentration Risk [Line Items]
Concentration risk, percentage	3.00%	4.00%	4.00%
2nd Largest Channel Partner \| Customer Concentration Risk
Concentration Risk [Line Items]
Concentration risk, percentage	2.00%	2.00%	2.00%
United States \| Credit Concentration Risk
Concentration Risk [Line Items]
Total	$ 582,882	$ 626,433
Foreign \| Credit Concentration Risk
Concentration Risk [Line Items]
Total	$ 329,790	$ 245,661

Accounting Policies - Allowance for Doubtful Accounts Rollforward (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Accounts Receivable, Allowance for Credit Loss [Roll Forward]
Beginning balance - January 1	$ 8,700
Additions: Charges to costs and expenses	6,438	$ 2,928	$ 1,577
Deductions: Write-offs	(1,138)
Ending balance - December 31	$ 14,000	$ 8,700

Accounting Policies - Basic and Diluted Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Accounting Policies [Abstract]
Net income	$ 433,887	$ 451,295	$ 419,375
Weighted average shares outstanding - basic	85,840	84,259	83,973
Dilutive effect of stock plans	1,448	1,666	1,940
Weighted average shares outstanding - diluted	87,288	85,925	85,913
Basic earnings per share	$ 5.05	$ 5.36	$ 4.99
Diluted earnings per share	$ 4.97	$ 5.25	$ 4.88
Anti-dilutive shares	23	14	7

- Definition

The amount of net income (loss) for the period per each share of common stock or unit outstanding during the reporting period.

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- Definition

The amount of net income (loss) for the period available to each share of common stock or common unit outstanding during the reporting period and to each share or unit that would have been outstanding assuming the issuance of common shares or units for all dilutive potential common shares or units outstanding during the reporting period.

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+ Details

- Definition

The portion of profit or loss for the period, net of income taxes, which is attributable to the parent.

+ References

+ Details

Revenue from Contracts with Customers - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Revenue from Contract with Customer [Abstract]
Amounts of revenue recognized from beginning deferred revenue and backlog	$ 569.8	$ 475.9

Revenue from Contracts with Customers - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Statement [Line Items]
Total revenue	$ 1,681,297	$ 1,515,892	$ 1,293,636
Lease license
Statement [Line Items]
Total revenue	500,105	406,043	275,619
Perpetual license
Statement [Line Items]
Total revenue	280,745	293,587	301,098
Software licenses
Statement [Line Items]
Total revenue	780,850	699,630	576,717
Maintenance
Statement [Line Items]
Total revenue	840,597	760,574	676,883
Service
Statement [Line Items]
Total revenue	59,850	55,688	40,036
Maintenance and service
Statement [Line Items]
Total revenue	$ 900,447	$ 816,262	$ 716,919
Direct revenue, as a percentage of total revenue
Statement [Line Items]
Concentration risk, percentage	77.80%	77.10%	77.60%
Indirect revenue, as a percentage of total revenue
Statement [Line Items]
Concentration risk, percentage	22.20%	22.90%	22.40%

Revenue from Contracts with Customers - Changes in Deferred Revenue (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Movement in Deferred Revenue [Roll Forward]
Beginning balance	$ 365,274	$ 343,174
Acquired deferred revenue	6,872	6,880
Deferral of revenue	1,687,907	1,532,549
Recognition of deferred revenue	(1,681,297)	(1,515,892)
Currency translation	10,054	(1,437)
Ending balance	$ 388,810	$ 365,274

Revenue from Contracts with Customers - Remaining Performance Obligations, Expected Timing of Satisfaction (Details) $ in Thousands	Dec. 31, 2020 USD ($)
Revenue from Contract with Customer [Abstract]
Revenue, remaining performance obligation, amount	$ 967,127
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2021-01-01
Revenue from Contract with Customer [Abstract]
Revenue, remaining performance obligation, amount	$ 606,780
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period	12 months
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2022-01-01
Revenue from Contract with Customer [Abstract]
Revenue, remaining performance obligation, amount	$ 199,909
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period	12 months
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2023-01-01
Revenue from Contract with Customer [Abstract]
Revenue, remaining performance obligation, amount	$ 80,304
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period	12 months
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2024-01-01
Revenue from Contract with Customer [Abstract]
Revenue, remaining performance obligation, amount	$ 80,134
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period

Acquisitions - Additional Information (Details) - USD ($) shares in Thousands, $ in Thousands						12 Months Ended
	Dec. 01, 2020	Apr. 01, 2020	Nov. 01, 2019	Feb. 01, 2019	May 02, 2018	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Acquisition costs						$ 5,100	$ 6,600	$ 3,500
Total consideration transferred at fair value						830,032	1,128,788
Fair value of common stock issued as consideration in connection with acquisitions						218,348	308,704
Analytical Graphics, Inc.
Percentage of shares acquired	100.00%
Payments to acquire businesses, gross	$ 722,500
Total consideration transferred at fair value	722,487
Fair value of common stock issued as consideration in connection with acquisitions	$ 218,348
Lumerical
Percentage of shares acquired		100.00%
Payments to acquire businesses, gross		$ 107,500
Total consideration transferred at fair value		$ 107,545
Livermore Software Technology Corporation
Percentage of shares acquired			100.00%
Payments to acquire businesses, gross			$ 472,800
Total consideration transferred at fair value			$ 781,504
Business acquisition, equity interest issued or Issuable, number of shares			1,400
Fair value of common stock issued as consideration in connection with acquisitions			$ 308,704
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Indemnification Asset, Resolved			34,000
Livermore Software Technology Corporation \| Common Stock
Fair value of common stock issued as consideration in connection with acquisitions			307,200
Livermore Software Technology Corporation \| Treasury Stock
Fair value of common stock issued as consideration in connection with acquisitions			$ 1,500
Granta Design
Percentage of shares acquired				100.00%
Payments to acquire businesses, gross				$ 208,700
Total consideration transferred at fair value				$ 208,736
Series of Individually Immaterial Business Acquisitions
Payments to acquire businesses, gross							138,500
Total consideration transferred at fair value							$ 138,548
OPTIS
Percentage of shares acquired					100.00%
Payments to acquire businesses, gross					$ 291,000
Goodwill, period increase (decrease)						$ 2,600

Acquisitions - Fair Value of Consideration Transferred 2020 (Details) - USD ($) shares in Thousands			12 Months Ended
	Dec. 01, 2020	Apr. 01, 2020	Dec. 31, 2020	Dec. 31, 2019
Cash			$ 597,342,000	$ 820,084,000
Ansys common stock			218,348,000	308,704,000
Consideration not yet paid			14,342,000
Total consideration transferred at fair value			830,032,000	$ 1,128,788,000
Analytical Graphics, Inc.
Cash	$ 489,797,000
Ansys common stock	218,348,000
Consideration not yet paid	14,342,000
Total consideration transferred at fair value	$ 722,487,000
Stock issued to prior owners of Analytical Graphics, Inc., amount			$ 218,348,000
Analytical Graphics, Inc. \| Common Stock
Common stock issued to prior owners of Analytical Graphics, Inc., shares	600		638
Stock issued to prior owners of Analytical Graphics, Inc., amount	$ 217,400,000		$ 7,000
Analytical Graphics, Inc. \| Treasury Stock
Stock issued to prior owners of Analytical Graphics, Inc., amount	$ 900,000		$ 233,000
Lumerical
Cash		$ 107,545,000
Total consideration transferred at fair value		$ 107,545,000

Acquisitions - Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed 2020 (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 01, 2020	Apr. 01, 2020	Dec. 31, 2019
Cash	$ 29,507			$ 28,395
Accounts receivable and other tangible assets	33,700			38,244
Accounts payable and other liabilities	(24,385)			(14,997)
Deferred revenue	(6,872)			(6,880)
Net deferred tax liabilities	(57,659)			(64,539)
Total identifiable net assets	236,977			284,018
Goodwill	593,055			844,770
Developed Software and Core Technologies
Finite-lived intangible assets	215,714			225,163
Customer Lists
Finite-lived intangible assets	27,016			61,659
Trade Names
Finite-lived intangible assets	$ 19,956			$ 17,230
Analytical Graphics, Inc.
Cash		$ 17,663
Accounts receivable and other tangible assets		29,456
Accounts payable and other liabilities		(23,279)
Deferred revenue		(5,467)
Net deferred tax liabilities		(50,207)
Total identifiable net assets		195,866
Goodwill		526,621
Analytical Graphics, Inc. \| Developed Software and Core Technologies
Finite-lived intangible assets		184,100
Analytical Graphics, Inc. \| Customer Lists
Finite-lived intangible assets		25,400
Analytical Graphics, Inc. \| Trade Names
Finite-lived intangible assets		$ 18,200
Lumerical
Cash			$ 11,844
Accounts receivable and other tangible assets			4,244
Accounts payable and other liabilities			(1,106)
Deferred revenue			(1,405)
Net deferred tax liabilities			(7,452)
Total identifiable net assets			41,111
Goodwill			66,434
Lumerical \| Developed Software and Core Technologies
Finite-lived intangible assets			31,614
Lumerical \| Customer Lists
Finite-lived intangible assets			1,616
Lumerical \| Trade Names
Finite-lived intangible assets			$ 1,756

Acquisitions - Fair Value of Consideration Transferred 2019 (Details) - USD ($) $ in Thousands			12 Months Ended
	Nov. 01, 2019	Feb. 01, 2019	Dec. 31, 2020	Dec. 31, 2019
Cash			$ 597,342	$ 820,084
Ansys common stock			218,348	308,704
Total consideration transferred at fair value			$ 830,032	1,128,788
Livermore Software Technology Corporation
Cash	$ 472,800
Ansys common stock	308,704
Total consideration transferred at fair value	$ 781,504
Granta Design
Cash		$ 208,736
Total consideration transferred at fair value		$ 208,736
Other Acquisitions
Cash				138,548
Total consideration transferred at fair value				$ 138,548

Acquisitions - Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed 2019 (Details) - USD ($)	Dec. 31, 2020	Dec. 31, 2019	Nov. 01, 2019	Feb. 01, 2019
Business Acquisition [Line Items]
Cash	$ 29,507,000	$ 28,395,000
Accounts receivable and other tangible assets	33,700,000	38,244,000
Accounts payable and other liabilities	(24,385,000)	(14,997,000)
Deferred revenue	(6,872,000)	(6,880,000)
Uncertain tax positions		(257,000)
Net deferred tax liabilities	(57,659,000)	(64,539,000)
Total identifiable net assets	236,977,000	284,018,000
Goodwill	593,055,000	844,770,000
Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets	215,714,000	225,163,000
Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets	27,016,000	61,659,000
Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets	$ 19,956,000	17,230,000
Livermore Software Technology Corporation
Business Acquisition [Line Items]
Cash			$ 8,520,000
Accounts receivable and other tangible assets			20,569,000
Accounts payable and other liabilities			(3,887,000)
Deferred revenue			(3,565,000)
Uncertain tax positions			0
Net deferred tax liabilities			(47,412,000)
Total identifiable net assets			178,425,000
Goodwill			603,079,000
Livermore Software Technology Corporation \| Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets			167,700,000
Livermore Software Technology Corporation \| Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets			25,900,000
Livermore Software Technology Corporation \| Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets			$ 10,600,000
Granta Design
Business Acquisition [Line Items]
Cash				$ 13,644,000
Accounts receivable and other tangible assets				6,941,000
Accounts payable and other liabilities				(5,164,000)
Deferred revenue				(1,426,000)
Uncertain tax positions				0
Net deferred tax liabilities				(8,976,000)
Total identifiable net assets				62,059,000
Goodwill				146,677,000
Granta Design \| Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets				32,445,000
Granta Design \| Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets				20,016,000
Granta Design \| Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets				$ 4,579,000
Other Acquisitions
Business Acquisition [Line Items]
Cash		6,231,000
Accounts receivable and other tangible assets		10,734,000
Accounts payable and other liabilities		(5,946,000)
Deferred revenue		(1,889,000)
Uncertain tax positions		(257,000)
Net deferred tax liabilities		(8,151,000)
Total identifiable net assets		43,534,000
Goodwill		95,014,000
Other Acquisitions \| Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets		25,018,000
Other Acquisitions \| Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets		15,743,000
Other Acquisitions \| Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets		$ 2,051,000

Acquisitions - Pro Forma Information 2019 (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Revenue	$ 1,681,297	$ 1,515,892	$ 1,293,636
Operating income	$ 496,356	515,040	$ 476,574
2019 Acquisitions
Revenue		44,079
Operating income		$ 6,733

- Definition

Amount of revenue recognized from goods sold, services rendered, insurance premiums, or other activities that constitute an earning process. Includes, but is not limited to, investment and interest income before deduction of interest expense when recognized as a component of revenue, and sales and trading gain (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-Subparagraph (a)
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Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 323
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-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=114001798&loc=d3e33918-111571

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 28
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=75031198&loc=d3e14064-108612

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
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Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
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Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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Reference 8: http://www.xbrl.org/2003/role/disclosureRef
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Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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Reference 10: http://www.xbrl.org/2003/role/disclosureRef
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Reference 13: http://www.xbrl.org/2003/role/disclosureRef
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-Name Accounting Standards Codification
-Topic 220
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-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(1))
-URI http://asc.fasb.org/extlink&oid=120395209&loc=SL114868664-224227

+ Details

Acquisitions - Fair Value of Consideration Transferred 2018 (Details) - USD ($) $ in Thousands		12 Months Ended
	May 02, 2018	Dec. 31, 2020	Dec. 31, 2019
Cash		$ 597,342	$ 820,084
OPTIS
Cash	$ 290,983

Acquisitions - Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed 2018 (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019	May 02, 2018
Business Acquisition [Line Items]
Cash	$ 29,507	$ 28,395
Accounts receivable and other tangible assets	33,700	38,244
Accounts payable and other liabilities	(24,385)	(14,997)
Deferred revenue	(6,872)	(6,880)
Net deferred tax liabilities	(57,659)	(64,539)
Total identifiable net assets	236,977	284,018
Goodwill	593,055	844,770
Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets	215,714	225,163
Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets	27,016	61,659
Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets	$ 19,956	$ 17,230
OPTIS
Business Acquisition [Line Items]
Cash			$ 7,957
Accounts receivable and other tangible assets			15,910
Accounts payable and other liabilities			(11,941)
Deferred revenue			(2,470)
Net deferred tax liabilities			(23,438)
Total identifiable net assets			85,667
Goodwill			205,316
OPTIS \| Developed Software and Core Technologies
Business Acquisition [Line Items]
Finite-lived intangible assets			47,597
OPTIS \| Customer Lists
Business Acquisition [Line Items]
Finite-lived intangible assets			41,303
OPTIS \| Trade Names
Business Acquisition [Line Items]
Finite-lived intangible assets			$ 10,749

Acquisitions - Pro Forma Information 2018 (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Revenue	$ 1,681,297	$ 1,515,892	$ 1,293,636
Operating income (loss)	$ 496,356	$ 515,040	476,574
OPTIS
Revenue			18,532
Operating income (loss)			$ (5,462)

- Definition

+ References

+ Details

Acquisitions - Valuation Assumptions and Weighted-Average Useful Life (Details)				12 Months Ended
	Dec. 01, 2020	Apr. 01, 2020	May 02, 2018	Dec. 31, 2020	Nov. 01, 2019	Feb. 01, 2019
Developed Software and Core Technologies
Finite-lived intangible asset, useful life				10 years
Trade Names
Finite-lived intangible asset, useful life				10 years
Customer Lists
Finite-lived intangible asset, useful life				15 years
Analytical Graphics, Inc. \| Developed Software and Core Technologies
Finite-lived intangible asset, useful life	10 years
Royalty Rate	40.00%
Discount Rate	11.00%
Analytical Graphics, Inc. \| Trade Names
Finite-lived intangible asset, useful life	9 years
Discount Rate	11.00%
Analytical Graphics, Inc. \| Customer Lists
Finite-lived intangible asset, useful life	15 years
Discount Rate	12.00%
Attrition Rate	10.00%
Analytical Graphics, Inc. \| Minimum \| Trade Names
Royalty Rate	1.00%
Analytical Graphics, Inc. \| Maximum \| Trade Names
Royalty Rate	2.00%
Lumerical \| Developed Software and Core Technologies
Finite-lived intangible asset, useful life		10 years
Discount Rate		16.50%
Lumerical \| Trade Names
Finite-lived intangible asset, useful life		6 years
Royalty Rate		2.00%
Discount Rate		16.50%
Lumerical \| Customer Lists
Finite-lived intangible asset, useful life		10 years
Discount Rate		12.50%
Attrition Rate		10.00%
Livermore Software Technology Corporation \| Developed Software and Core Technologies
Royalty Rate					50.00%
Discount Rate					10.00%
Livermore Software Technology Corporation \| Trade Names
Royalty Rate					2.00%
Discount Rate					10.00%
Livermore Software Technology Corporation \| Customer Lists
Discount Rate					11.00%
Attrition Rate					10.00%
Granta Design \| Developed Software and Core Technologies
Discount Rate						12.50%
Granta Design \| Trade Names
Royalty Rate						2.00%
Discount Rate						14.00%
Granta Design \| Customer Lists
Discount Rate						12.50%
Attrition Rate						10.00%
Granta Design \| Minimum \| Developed Software and Core Technologies
Royalty Rate						8.00%
Granta Design \| Maximum \| Developed Software and Core Technologies
Royalty Rate						10.00%
OPTIS \| Developed Software and Core Technologies
Finite-lived intangible asset, useful life			10 years
OPTIS \| Trade Names
Finite-lived intangible asset, useful life			9 years
OPTIS \| Customer Lists
Finite-lived intangible asset, useful life			12 years

Other Receivables and Current Assets and Other Accrued Expenses and Liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Other Receivables and Current Assets and Other Accrued Expenses and Liabilities [Abstract]
Receivables related to unrecognized revenue	$ 192,154	$ 177,679
Income taxes receivable, including overpayments and refunds	31,628	26,672
Prepaid expenses and other current assets	44,740	45,268
Total other receivables and current assets	268,522	249,619
Consumption, sales and VAT tax liabilities	45,156	36,398
Accrued expenses and other current liabilities	154,310	106,549
Total other accrued expenses and liabilities	$ 199,466	$ 142,947

Property and Equipment - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Property, Plant and Equipment [Abstract]
Depreciation expense related to property and equipment	$ 28.0	$ 23.6	$ 18.4

Property and Equipment - Components of Property and Equipment (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 238,775	$ 212,739
Less: Accumulated depreciation	(142,272)	(129,103)
Property and equipment, net	96,503	83,636
Equipment
Property, Plant and Equipment [Line Items]
Property and equipment, gross	123,139	105,428
Computer Software
Property, Plant and Equipment [Line Items]
Property and equipment, gross	34,469	33,878
Building and Building Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, gross	38,332	38,095
Leasehold Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, gross	25,237	19,876
Furniture
Property, Plant and Equipment [Line Items]
Property and equipment, gross	14,902	12,766
Land
Property, Plant and Equipment [Line Items]
Property and equipment, gross	$ 2,696	$ 2,696
Minimum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	1 year
Minimum \| Equipment
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	1 year
Minimum \| Computer Software
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	1 year
Minimum \| Building and Building Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	2 years
Minimum \| Leasehold Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	1 year
Minimum \| Furniture
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	1 year
Maximum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	40 years
Maximum \| Equipment
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	15 years
Maximum \| Computer Software
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	5 years
Maximum \| Building and Building Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	40 years
Maximum \| Leasehold Improvements
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	17 years
Maximum \| Furniture
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful lives (years)	13 years

Goodwill and Intangible Assets - Additional Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Amortization of intangible assets	$ 57,200	$ 36,900	$ 40,800
Minimum
Finite-lived intangible asset, useful life	2 years
Maximum
Finite-lived intangible asset, useful life	17 years

Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Intangible Assets [Line Items]
Amortized intangible assets, gross carrying amount	$ 1,323,331	$ 1,058,951
Amortized intangible assets, accumulated amortization	(628,823)	(582,597)
Indefinite-lived intangible assets (excluding goodwill)	357
Trade Names
Intangible Assets [Line Items]
Indefinite-lived intangible assets (excluding goodwill)	357	357
Developed Software and Core Technologies
Intangible Assets [Line Items]
Amortized intangible assets, gross carrying amount	859,620	635,063
Amortized intangible assets, accumulated amortization	(370,338)	(332,622)
Customer Lists
Intangible Assets [Line Items]
Amortized intangible assets, gross carrying amount	288,085	269,629
Amortized intangible assets, accumulated amortization	(136,093)	(132,596)
Trade Names
Intangible Assets [Line Items]
Amortized intangible assets, gross carrying amount	175,626	154,259
Amortized intangible assets, accumulated amortization	$ (122,392)	$ (117,379)

Goodwill and Intangible Assets - Estimated Future Amortization Expense for Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Goodwill and Intangible Assets Disclosure [Abstract]
2021	$ 74,981
2022	77,300
2023	78,426
2024	77,399
2025	74,805
Thereafter	311,597
Total intangible assets subject to amortization, net	694,508
Indefinite-lived trade name	357
Other intangible assets, net	$ 694,865	$ 476,711

Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Goodwill [Roll Forward]
Beginning balance	$ 2,413,280	$ 1,572,455
Acquisitions and adjustments	596,054	842,588
Currency translation	28,972	(1,763)
Ending balance	$ 3,038,306	$ 2,413,280

Fair Value Measurement - Fair Value of Assets and Liabilities Measured on Recurring Basis (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	$ 341,085	$ 322,455
Short-term investments	479	288
Deferred compensation plan investments	1,602	1,110
Quoted Prices in Active Markets (Level 1)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	341,085	322,455
Short-term investments	0	0
Deferred compensation plan investments	1,602	1,110
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	0	0
Short-term investments	479	288
Deferred compensation plan investments	0	0
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	0	0
Short-term investments	0	0
Deferred compensation plan investments	$ 0	$ 0

Fair Value Measurement - Additional Information (Details)	12 Months Ended
	Dec. 31, 2020
Minimum
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Short-term investments maturity	3 months
Maximum
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Short-term investments maturity	1 year

Leases - Additional Information (Details) $ in Thousands	12 Months Ended
Leases - Additional Information (Details) $ in Thousands	Dec. 31, 2020 USD ($) ft²	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)
Lessee, Lease, Description [Line Items]
Lease cost	$ 29,885	$ 26,261	$ 21,300
Current portion of operating lease liabilities	$ 23,600
Canonsburg Office, New Company Headquarters
Lessee, Lease, Description [Line Items]
Area of real estate property \| ft²	186,000
Period of leased property	183 months
Base rent through 2024	$ 4,500
Base rent 2025-2029	$ 4,700

Leases - Schedule of Lease Cost (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Leases [Abstract]
Lease liability cost	$ 24,818	$ 22,507
Variable lease cost not included in the lease liability	5,067	3,754
Total lease cost	$ 29,885	$ 26,261	$ 21,300

Leases - Lessee, Operating Lease Other Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Leases [Abstract]
Operating cash flows from operating leases	$ (22,470)	$ (20,031)
Right-of-use assets obtained in exchange for new operating lease liabilities	$ 48,248	$ 35,191
Weighted-average remaining lease term of operating leases	7 years 3 months 18 days	7 years 8 months 12 days
Weighted-average discount rate of operating leases	2.90%	3.70%

Leases - Schedule of Maturity of Operating Lease Liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Jan. 01, 2019
Leases [Abstract]
2021	$ 27,311
2022	24,712
2023	21,522
2024	20,264
2025	17,076
Thereafter	50,438
Total future lease payments	161,323
Present value adjustment	(16,792)
Present value of future lease payments	144,531	$ 92,500
Current portion of operating lease liabilities	$ 23,600
Operating Lease, Liability, Current, Statement of Financial Position [Extensible List]	us-gaap:OtherAccruedLiabilitiesCurrent

Debt (Details) - USD ($)	12 Months Ended
Debt (Details) - USD ($)	Dec. 31, 2020	Dec. 31, 2019	Dec. 01, 2020	Nov. 01, 2019
Line of Credit Facility [Line Items]
Unsecured debt	$ 798,100,000	$ 498,500,000
Term loan principal repayment rate, initial	1.25%
Term loan principal repayment rate, increased	2.50%
Early debt repayment	$ 75,000,000.0
Early repayment of debt due in 2022	25,000,000.0
Early repayment of debt due in 2023	$ 50,000,000.0
Weighted-average interest rate over time	2.09%	2.96%
Consolidated leverage ratio	3.50
Consolidated leverage ratio increased	4.00
Qualified acquisition amount	$ 250,000,000.0
Unamortized debt issuance cost	$ 1,900,000	$ 1,500,000
Livermore Software Technology Corporation
Line of Credit Facility [Line Items]
Unsecured debt				$ 500,000,000.0
Weighted-average interest rate at a point in time	1.38%
Analytical Graphics, Inc.
Line of Credit Facility [Line Items]
Unsecured debt			$ 375,000,000.0
Weighted-average interest rate at a point in time	1.50%
Revolving Credit Facility
Line of Credit Facility [Line Items]
Line of credit facility, maximum borrowing capacity	$ 500,000,000.0
Outstanding borrowings under the credit agreement	0
Letter of Credit
Line of Credit Facility [Line Items]
Line of credit facility, maximum borrowing capacity	$ 50,000,000.0
Base Rate
Line of Credit Facility [Line Items]
Debt instrument, basis spread on federal funds rate	0.50%
Debt instrument, basis spread on Eurodollar rate	1.00%
Base Rate \| Minimum
Line of Credit Facility [Line Items]
Debt instrument, basis spread on variable rate	0.125%
Base Rate \| Maximum
Line of Credit Facility [Line Items]
Debt instrument, basis spread on variable rate	0.75%
Eurodollar \| Minimum
Line of Credit Facility [Line Items]
Debt instrument, basis spread on variable rate	1.125%
Eurodollar \| Maximum
Line of Credit Facility [Line Items]
Debt instrument, basis spread on variable rate	1.75%

Debt - Schedule of Maturities of Debt (Details) $ in Thousands	Dec. 31, 2020 USD ($)
Debt Disclosure [Abstract]
2021	$ 0
2022	18,750
2023	37,500
2024	743,750
2025	0
Total	$ 800,000

Income Taxes - Additional Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Contingency [Line Items]
Valuation allowance, deferred tax asset, increase (decrease), amount	$ (2,100)
Deferred tax assets, operating loss carryforwards, state and local	1,900
Tax credit carryforwards	11,200
Cumulative temporary difference, permanently reinvested earnings	93,000
Significant change in unrecognized tax benefits is reasonably possible, amount of unrecorded benefit	5,000
Unrecognized tax benefits that would impact effective tax rate	16,300
Penalty expense	200	$ 500	$ 800
Interest (income) expense	300	100	$ (100)
Liability for penalties	5,500	11,700
Liability for interest	5,400	$ 6,600
Valuation Allowance Release, Foreign Jurisdiction, Debt Restructuring
Income Tax Contingency [Line Items]
Valuation allowance, deferred taxes, released	2,300
Valuation Allowance Release, Foreign Jurisdiction, Favorable Tax Ruling
Income Tax Contingency [Line Items]
Valuation allowance, deferred taxes, released	1,800
Subject To Expiration
Income Tax Contingency [Line Items]
Tax credit carryforwards	10,500
Subject To Utilization Limitations
Income Tax Contingency [Line Items]
Tax credit carryforwards	6,900
Not Subject To Expiration
Income Tax Contingency [Line Items]
Tax credit carryforwards	700
Foreign Country
Income Tax Contingency [Line Items]
Net operating loss carryforwards	166,100
Federal Domestic
Income Tax Contingency [Line Items]
Net operating loss carryforwards	28,300
Operating Loss Carryforward With No Expiration Date \| Foreign Country
Income Tax Contingency [Line Items]
Net operating loss carryforwards	141,700
Operating Loss Carryforward With No Expiration Date \| Federal Domestic
Income Tax Contingency [Line Items]
Net operating loss carryforwards	25,600
Subject To Expiration \| Foreign Country
Income Tax Contingency [Line Items]
Net operating loss carryforwards	24,400
Subject To Expiration \| Federal Domestic
Income Tax Contingency [Line Items]
Net operating loss carryforwards	$ 2,700

Income Taxes - Components of Income Before Income Taxes (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Disclosure [Abstract]
Domestic	$ 465,382	$ 448,271	$ 455,478
Foreign	28,543	74,312	31,607
Income before income tax provision	$ 493,925	$ 522,583	$ 487,085

Income Taxes - Components of Provision for Income Taxes (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Disclosure [Abstract]
Current, Federal	$ 26,855	$ 44,824	$ 58,138
Current, State	12,738	9,554	12,888
Current, Foreign	51,377	31,421	30,359
Deferred, Federal	(12,203)	(8,833)	(20,764)
Deferred, State	(2,119)	(965)	(2,901)
Deferred, Foreign	(16,610)	(4,713)	(10,010)
Total	$ 60,038	$ 71,288	$ 67,710

- Definition

Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References + Details

Income Taxes - Reconciliation of U.S. Federal Statutory Tax Rate to Consolidated Effective Tax Rate (Details)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Disclosure [Abstract]
Federal statutory tax rate	21.00%	21.00%	21.00%
State income taxes, net of federal benefit	1.60%	1.50%	1.50%
Foreign rate differential	0.40%	0.80%	0.80%
Uncertain tax positions	0.10%	(0.20%)	0.50%
Valuation allowance release	(0.80%)	(1.30%)	0.00%
Benefit from entity structuring activities	(1.50%)	0.00%	(1.40%)
Foreign-derived intangible income deduction	(2.80%)	(3.80%)	(3.90%)
Research and development credits	(3.20%)	(2.20%)	(2.30%)
Stock-based compensation	(3.60%)	(3.10%)	(3.30%)
Other	1.00%	0.90%	1.00%
Consolidated effective tax rate	12.20%	13.60%	13.90%

Income Taxes - Components of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Income Tax Disclosure [Abstract]
Net operating loss carryforwards	$ 47,551	$ 35,044
Operating lease liabilities	34,803	26,628
Stock-based compensation	24,738	24,254
Uncertain tax positions	18,565	19,227
Employee benefits	13,290	9,392
Research and development credits	9,847	5,865
Allowance for doubtful accounts	3,193	1,841
Other	6,856	4,468
Valuation allowance	(15,398)	(17,524)
Deferred tax assets	143,445	109,195
Other intangible assets	(147,960)	(99,193)
Operating lease right-of-use assets	(33,304)	(25,648)
Deferred revenue	(26,839)	(13,744)
Accounting method change	(10,781)	(21,396)
Property and equipment	(6,052)	(3,780)
Deferred tax liabilities	(224,936)	(163,761)
Net deferred tax liabilities	$ (81,491)	$ (54,566)

Income Taxes - Reconciliation of Unrecognized Tax Benefits (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Unrecognized tax benefit as of January 1	$ 49,085	$ 22,827	$ 19,657
Gross decreases - acquisitions	(24,963)
Gross increases-acquisitions		26,914	0
Gross increases-tax positions in prior period	1,572	207	1,229
Gross decreases-tax positions in prior period	0	(1,743)	(376)
Gross increases-tax positions in current period	1,281	3,563	4,014
Reductions due to a lapse of the applicable statute of limitations	(3,502)	(2,230)	(994)
Changes due to currency fluctuation		(453)	(703)
Changes due to currency fluctuation	994
Settlements	(392)	0	0
Unrecognized tax benefit as of December 31	$ 24,075	$ 49,085	$ 22,827

Pension And Profit-Sharing Plans - Defined Benefit Plan (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Retirement Benefits [Abstract]
Total unfunded portion of the defined benefit obligations	$ 13.5	$ 11.2

Pension And Profit-Sharing Plans (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Defined Contribution Plan Disclosure [Line Items]
Expenses related to retirement programs	$ 18.7	$ 16.3	$ 12.4
Four Zero One K Plan
Defined Contribution Plan Disclosure [Line Items]
Maximum annual contributions per employee, percent	4.25%
Minimum working hours per employee required to be eligible for discretionary contribution	1000 hours
First Three Percent Of Employee Pay \| Four Zero One K Plan
Defined Contribution Plan Disclosure [Line Items]
Percentage of employee contribution employer matches	100.00%
Percentage of employee pay employer matches	3.00%
More Than Three Percent Up To Eight Percent Of Employee Pay \| Four Zero One K Plan
Defined Contribution Plan Disclosure [Line Items]
Percentage of employee contribution employer matches	25.00%
Percentage of employee pay employer matches	5.00%

Stock-Based Compensation - Additional Information (Details) - USD ($)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Shares authorized for grant under the plan	39,800,000
Percentage of voting interest to be held by optionee	10.00%
Exercise price as a percentage of fair value at the time of grant	110.00%
Maximum months after sale event where awards fully vest when service relationship terminated without cause	18 months
Minimum number of days that may be granted to terminated employee to exercise awards prior to termination	15 days
Total unrecognized estimated unvested stock awards	$ 160,700,000
Weighted-average period of recognition of unrecognized compensation cost (years)	1 year 4 months 24 days
Stock-based compensation expense	$ 145,615,000	$ 116,190,000	$ 83,346,000
Performance Shares
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Restricted stock unit vesting period	3 years
Restricted Stock
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Stock-based compensation expense	$ 138,300,000	109,900,000	77,400,000
Restricted Stock Units (RSUs)
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Restricted stock unit vesting period	3 years
Director Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Stock-based compensation expense	$ 2,200,000	2,500,000	2,300,000
Market and Service Condition Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Restricted stock unit vesting period	3 years
Maximum
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Expiration period of options from the date of grant	10 years
Expiration period for optionee who meets the 10% criteria	5 years
ANSYS 1996 Employee Stock Purchase Plan \| Employee Stock
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Shares authorized for grant under the plan	1,800,000
Expiration period of options from the date of grant	6 months
Stock-based compensation expense	$ 4,100,000	$ 2,000,000.0	$ 1,800,000
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant	100,000
Share-based compensation arrangement by share-based payment award, maximum employee subscription rate	10.00%
Share-based compensation arrangement by share-based payment award, maximum number of shares per employee	3,840
Share-based compensation arrangement by share-based payment award, purchase price of common stock, percent	90.00%
Share-based compensation arrangement by share-based payment award, maximum dollar amount of common stock purchasable in a calendar year	$ 25,000
Share-based compensation arrangement by share-based payment award, shares issued as of date	1,700,000
ANSYS 1996 Employee Stock Purchase Plan \| Maximum \| Employee Stock
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Share-based compensation arrangement by share-based payment award, eligibility, ownership percentage	5.00%

Stock-Based Compensation - Stock-Based Compensation Expense (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense before taxes	$ 145,615	$ 116,190	$ 83,346
Related income tax benefits	(56,485)	(47,454)	(34,518)
Stock-based compensation expense, net of taxes	$ 89,130	$ 68,736	$ 48,828
Basic earnings per share (in dollars per share)	$ (1.04)	$ (0.82)	$ (0.58)
Diluted earnings per share (in dollars per share)	$ (1.02)	$ (0.80)	$ (0.57)
Maintenance and service
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense before taxes	$ 13,626	$ 8,494	$ 5,224
Selling, general and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense before taxes	73,491	60,639	47,099
Research and development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense before taxes	$ 58,498	$ 47,057	$ 31,023

Stock-Based Compensation - Summary of Stock Options (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Roll Forward]
Outstanding, beginning of year, Weighted-Average Exercise Price (in dollars per share)	$ 67.49	$ 62.80	$ 59.17
Granted, Weighted-Average Exercise Price (in dollars per share)	0	0	0
Exercised, Weighted-Average Exercise Price (in dollars per share)	54.43	53.53	50.92
Forfeited, Weighted-Average Exercise Price (in dollars per share)	0	64.21	86.28
Outstanding, end of year, Weighted-Average Exercise Price (in dollars per share)	74.26	67.49	62.80
Vested and Exercisable, end of year, Weighted-Average Exercise Price (in dollars per share)	74.26	65.71	59.69
Nonvested, Weighted-Average Exercise Price (in dollars per share)	$ 0	$ 94.77	$ 93.44
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Outstanding, beginning of year, Options (in shares)	984	1,484	2,170
Granted, Options (in shares)	0	0	0
Exercised, Options (in shares)	(336)	(495)	(679)
Forfeited, Options (in shares)	0	(5)	(7)
Outstanding, end of year, Options (in shares)	648	984	1,484
Vested and Exercisable, end of year, Options (in shares)	648	924	1,347
Nonvested, Options (in shares)	0	60	137
Outstanding, Weighted-Average Remaining Contractual Term (in years)	2 years 11 months 4 days	3 years 2 months 4 days	3 years 6 months 18 days
Vested and Exercisable, Weighted-Average Remaining Contractual Term (in years)	2 years 11 months 4 days	2 years 11 months 12 days	3 years 1 month 20 days
Nonvested, Weighted-Average Remaining Contractual Term (in years)	0 years	6 years 8 months 15 days	7 years 7 months 6 days
Exercised, Aggregate Intrinsic Value	$ 78,269	$ 72,098	$ 78,648
Outstanding, Aggregate Intrinsic Value	187,679	186,926	118,908
Vested and Exercisable, Aggregate Intrinsic Value	187,679	177,111	112,133
Nonvested, Aggregate Intrinsic Value	0	9,815	6,775
Compensation Expense - Stock Options (in thousands)	$ 1,030	$ 1,709	$ 2,006

Stock-Based Compensation - Information Regarding Stock Options Outstanding (Details)	12 Months Ended
	Dec. 31, 2020 $ / shares shares
$12.26 - $24.42
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]
Range of Exercise Prices, Lower Limit (in dollars per share)	$ 12.26
Range of Exercise Prices, Upper Limit (in dollars per share)	$ 24.42
Options Outstanding, Options (in shares) \| shares	13,000
Options Outstanding, Weighted-Average Remaining Contractual Life (years)	4 months 24 days
Options Outstanding, Weighted-Average Exercise Price (in dollars per share)	$ 22.10
$58.67
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]
Range of Exercise Prices, Lower Limit (in dollars per share)	58.67
Range of Exercise Prices, Upper Limit (in dollars per share)	$ 58.67
Options Outstanding, Options (in shares) \| shares	167,000
Options Outstanding, Weighted-Average Remaining Contractual Life (years)	10 months 9 days
Options Outstanding, Weighted-Average Exercise Price (in dollars per share)	$ 58.67
$67.44
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]
Range of Exercise Prices, Lower Limit (in dollars per share)	67.44
Range of Exercise Prices, Upper Limit (in dollars per share)	$ 67.44
Options Outstanding, Options (in shares) \| shares	226,000
Options Outstanding, Weighted-Average Remaining Contractual Life (years)	1 year 10 months 6 days
Options Outstanding, Weighted-Average Exercise Price (in dollars per share)	$ 67.44
$78.56 - $95.09
Share-based Payment Arrangement, Option, Exercise Price Range [Line Items]
Range of Exercise Prices, Lower Limit (in dollars per share)	78.56
Range of Exercise Prices, Upper Limit (in dollars per share)	$ 95.09
Options Outstanding, Options (in shares) \| shares	242,000
Options Outstanding, Weighted-Average Remaining Contractual Life (years)	5 years 5 months 23 days
Options Outstanding, Weighted-Average Exercise Price (in dollars per share)	$ 94.15

Stock-Based Compensation - Assumptions to Estimate Fair Value of Stock Awards (Details) - Restricted Stock Unit Compensation Expense - $ / shares	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Risk-free interest rate	0.70%	2.50%	2.40%
Expected dividend yield	0.00%	0.00%	0.00%
Expected term (in years)	2 years 9 months 18 days	2 years 9 months 18 days	2 years 9 months 18 days
Correlation factor	0.77	0.71	0.65
Weighted average fair value per share (in dollars per share)	$ 245.08	$ 238.99	$ 191.76
Ansys Stock Price
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Expected volatility	25.00%	23.00%	21.00%
Nasdaq Composite Index
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Expected volatility	18.00%	16.00%	15.00%

Stock-Based Compensation - Summary of Restricted Stock Units (Details) - $ / shares shares in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Nonvested, beginning of year, RSUs (in shares)	1,618	1,522	1,361
Granted, RSUs (in shares)	501	843	681
Performance adjustment, market condition, RSUs (in shares)	18	12	10
Performance adjustment, performance condition, RSUs (in shares)	(10)	62	66
Vested, RSUs (in shares)	(742)	(704)	(524)
Forfeited, RSUs (in shares)	(62)	(117)	(72)
Nonvested, end of year, RSUs (in shares)	1,323	1,618	1,522
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]
Nonvested, beginning of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 165.26	$ 129.96	$ 100.66
Granted, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	256.47	192.37	163.67
Performance adjustment, Market Condition, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	191.76	120.96	78.71
Performance adjustment, Performance Condition, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	279.08	176.89	162.64
Vested, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	158.13	125.84	101.38
Forfeited, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	193.28	140.43	125.29
Nonvested, end of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 201.98	$ 165.26	$ 129.96

Stock-Based Compensation - Summary of Deferred Stock Awards to Non-Employee Directors (Details) - shares shares in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]
Deferred awards outstanding, beginning of year (in shares)	65,679	132,699	189,099
Shares diversified (in shares)	0	0	0
Shares issued upon retirement (in shares)		(67,020)	(56,400)
Deferred awards outstanding, end of year (in shares)	65,679	65,679	132,699
Diversified Deferred Stock Award
Share-based Compensation Arrangement by Share-based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]
Deferred awards outstanding, beginning of year (in shares)	5,598	12,250	29,500
Shares diversified (in shares)	1,400	13,348	6,105
Shares issued upon retirement (in shares)		(20,000)	(23,355)
Deferred awards outstanding, end of year (in shares)	6,998	5,598	12,250
Undiversified Deferred Stock Award
Share-based Compensation Arrangement by Share-based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]
Deferred awards outstanding, beginning of year (in shares)	60,081	120,449	159,599
Shares diversified (in shares)	(1,400)	(13,348)	(6,105)
Shares issued upon retirement (in shares)		(47,020)	(33,045)
Deferred awards outstanding, end of year (in shares)	58,681	60,081	120,449

Stock-Based Compensation - Summary of Restricted Stock Units to Non-Employee Directors (Details) - $ / shares shares in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Nonvested, beginning of year, RSUs (in shares)	1,618	1,522	1,361
Granted, RSUs (in shares)	501	843	681
Vested, RSUs (in shares)	(742)	(704)	(524)
Forfeited, RSUs (in shares)	(62)	(117)	(72)
Nonvested, end of year, RSUs (in shares)	1,323	1,618	1,522
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]
Nonvested, beginning of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 165.26	$ 129.96	$ 100.66
Granted, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	256.47	192.37	163.67
Vested, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	158.13	125.84	101.38
Forfeited, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	193.28	140.43	125.29
Nonvested, end of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 201.98	$ 165.26	$ 129.96
Director Restricted Stock Units
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Nonvested, beginning of year, RSUs (in shares)	9,688	13,632	18,018
Granted, RSUs (in shares)	9,664	11,259	13,632
Vested, RSUs (in shares)	(10,704)	(14,287)	(18,018)
Forfeited, RSUs (in shares)	(577)	(916)	0
Nonvested, end of year, RSUs (in shares)	8,071	9,688	13,632
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]
Nonvested, beginning of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 187.53	$ 165.71	$ 123.38
Granted, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	253.40	187.53	165.71
Vested, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	193.35	166.71	123.38
Forfeited, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	253.93	187.53	0
Nonvested, end of year, Weighted-Average Grant Date Fair Value, RSUs (in dollars per share)	$ 253.93	$ 187.53	$ 165.71

Stock Repurchase Program (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Class of Stock Disclosures [Abstract]
Number of shares repurchased	690	330	1,674
Average price paid per share	$ 233.48	$ 179.41	$ 161.12
Total cost	$ 161,029	$ 59,116	$ 269,801

Stock Repurchase Program - Additional Information (Details) shares in Millions	Dec. 31, 2020 shares
Class of Stock Disclosures [Abstract]
Stock repurchase program, remaining number of shares authorized to be repurchased	2.8

Royalty Agreements (Details) - USD ($) $ in Thousands	12 Months Ended
Royalty Agreements (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cost of goods and services sold	$ 225,264	$ 166,273	$ 155,885
Royalty
Cost of goods and services sold	$ 29,600	$ 22,400	$ 16,900

Geographic Information - Revenue by Geographic Area (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	$ 1,681,297	$ 1,515,892	$ 1,293,636
United States
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	776,716	637,916	506,335
Japan
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	183,117	162,154	145,951
Germany
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	160,771	158,809	140,506
South Korea
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	74,953	90,082	72,724
France
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	71,255	68,551	67,657
Other EMEA
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	236,678	211,193	193,317
Other international
Revenues from External Customers and Long-Lived Assets [Line Items]
Total revenue	$ 177,807	$ 187,187	$ 167,146

- Definition

+ References

+ Details

Geographic Information - Property and Equipment by Geographic Area (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Dec. 31, 2019
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	$ 96,503	$ 83,636
United States
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	65,633	59,473
India
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	7,408	5,660
France
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	5,749	3,657
Germany
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	5,277	4,237
United Kingdom
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	3,765	4,194
Other EMEA
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	2,082	1,875
Other international
Revenues from External Customers and Long-Lived Assets [Line Items]
Total property and equipment, net	$ 6,589	$ 4,540

Unconditional Purchase Obligations (Details) $ in Thousands	Dec. 31, 2020 USD ($)
Unconditional Purchase Obligations (Excluding Capital Stock Redemptions) [Abstract]
2021	$ 44,865
2022	20,751
2023	6,758
2024	2,525
2025	26
Total	$ 74,925

Unconditional Purchase Obligations - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Unconditional Purchase Obligations (Excluding Capital Stock Redemptions) [Abstract]
Unconditional purchase obligations, beginning of year	$ 37.2	$ 24.2	$ 22.4

Contingencies and Commitments - Additional Information (Details) $ in Millions	Dec. 31, 2020 USD ($)
India Service Tax Audit
Loss Contingencies [Line Items]
Loss contingency, estimate of possible loss	$ 7.3

Schedule II - Valuation and Qualifying Accounts (Details) - Allowance for doubtful accounts rollforward - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]
Balance at beginning of year	$ 8,700	$ 8,000	$ 6,800
Additions: charges to costs and expenses	6,438	2,928	1,577
Deductions: write-offs	1,138	2,228	377
Balance at end of year	$ 14,000	$ 8,700	$ 8,000

Label	Element	Value
Accounting Standards Update [Extensible List]	us-gaap_AccountingStandardsUpdateExtensibleList	us-gaap:AccountingStandardsUpdate201409Member

- Definition

Indicates amendment to accounting standards.

+ References

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+ Details