EX-99.1 2 ny20044174x2_ex99-1.htm EXHIBIT 99.1

Exhibit 99.1

REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

To the Stockholders and the Board of Directors of ANSYS, Inc.

Opinion on the Financial Statements

We have audited the accompanying consolidated balance sheets of ANSYS, Inc. and subsidiaries (the “Company”) as of December 31, 2024 and 2023, the related consolidated statements of income, comprehensive income, stockholders’ equity, and cash flows for each of the three years in the period ended December 31, 2024, and the related notes in the Index at Item 15 (collectively referred to as the “financial statements”). In our opinion, the financial statements present fairly, in all material respects, the financial position of the Company as of December 31, 2024 and 2023, and the results of its operations and its cash flows for each of the three years in the period ended December 31, 2024, in conformity with accounting principles generally accepted in the United States of America.

Basis for Opinion

These financial statements are the responsibility of the Company’s management. Our responsibility is to express an opinion on the Company’s financial statements based on our audits. We are a public accounting firm registered with the PCAOB and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB.

We conducted our audits in accordance with the standards of the PCAOB. Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free of material misstatement, whether due to error or fraud. Our audits included performing procedures to assess the risks of material misstatement of the financial statements, whether due to error or fraud, and performing procedures that respond to those risks. Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the financial statements. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that our audits provide a reasonable basis for our opinion.

Critical Audit Matter

The critical audit matter communicated below is a matter arising from the current‐period audit of the financial statements that was communicated or required to be communicated to the audit committee and that (1) relates to accounts or disclosures that are material to the financial statements and (2) involved our especially challenging, subjective, or complex judgments. The communication of critical audit matters does not alter in any way our opinion on the financial statements, taken as a whole, and we are not, by communicating the critical audit matter below, providing a separate opinion on the critical audit matter or on the accounts or disclosures to which it relates.

Revenue—Time-Based Subscription Lease Licenses—Refer to Notes 2 and 3 to the financial statements

Critical Audit Matter Description

The Company sells time‐based subscription lease license contracts with customers that are sold as a bundled arrangement that include the rights to a term software license as well as post‐contract support (PCS). Revenue is recognized up front at the commencement of the lease for the term software license and recognized ratably over the term of the contract for the PCS in the arrangement. Utilizing observable inputs, the Company determined that 50% of the estimated standalone selling price of the subscription lease license is attributable to the term license, while 50% is attributable to PCS. This determination involved judgment, particularly as it relates to the value relationship between the Company’s PCS to subscription lease licenses, the value relationship between PCS and the Company’s perpetual licenses and its linkage to the shortened term of a subscription lease license, the average economic life of the Company’s software, renewal rates of its customers, and the price of the bundled arrangement in relation to the perpetual licensing approach.


Given the judgments necessary to determine the allocation between the term software license and PCS, auditing this estimate involved a high degree of auditor judgment.

How the Critical Audit Matter Was Addressed in the Audit
 
Our audit procedures related to management’s estimate of the allocation between the term software license and PCS in a subscription lease license included the following, among others:


We tested the effectiveness of controls over subscription lease license revenue, including those over the determination of the estimated standalone selling price of the Company’s licenses and services, as well as the allocation of this standalone selling price within the arrangement.


We evaluated the pricing relationship between PCS and perpetual licenses on the net licensing fee of the arrangement, as well as the Company’s renewal rate of PCS sales on perpetual licenses through those arrangements selected for testing that contained both elements as a consideration point of the value relationship between the term software license and PCS when a customer purchases a bundled subscription lease license.


We evaluated the estimated economic life of the Company’s software through observable data points.


Through our current and historical audit procedures, we confirmed that the term software license portion and PCS portion of an arrangement are not sold separately from one another.


We selected a sample of arrangements and performed the following:


Compared the list price of the subscription lease license to the consideration received from the customer and recalculated the discount from list price for each arrangement.


Evaluated whether management appropriately calculated the estimated standalone selling price for the subscription lease license.


Tested management’s identification of distinct performance obligations.


Tested the mathematical accuracy of revenue recognized at a point in time or over time based upon the identification of subscription lease licenses within the arrangement.

/s/ Deloitte & Touche LLP
Pittsburgh, Pennsylvania
February 19, 2025

We have served as the Company's auditor since 2002.


 
ANSYS, INC. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS

   
December 31,
 
(in thousands, except share and per share data)
 
2024
   
2023
 
ASSETS
           
Current assets:
           
Cash and cash equivalents
 
$
1,446,743
   
$
860,201
 
Short-term investments
   
50,774
     
189
 
Accounts receivable, less allowance for doubtful accounts of $16,500 and $20,700, respectively
   
1,022,850
     
864,526
 
Other receivables and current assets
   
311,126
     
324,651
 
Total current assets
   
2,831,493
     
2,049,567
 
Long-term assets:
               
Property and equipment, net
   
89,646
     
77,780
 
Operating lease right-of-use assets
   
105,122
     
116,980
 
Goodwill
   
3,778,128
     
3,805,874
 
Other intangible assets, net
   
716,244
     
835,417
 
Other long-term assets
   
308,333
     
273,030
 
Deferred income taxes
   
222,465
     
164,227
 
Total long-term assets
   
5,219,938
     
5,273,308
 
Total assets
 
$
8,051,431
   
$
7,322,875
 
LIABILITIES AND STOCKHOLDERS' EQUITY
               
Current liabilities:
               
Accounts payable
 
$
27,062
   
$
22,772
 
Accrued bonuses and commissions
   
189,521
     
170,909
 
Accrued income taxes
   
15,105
     
22,454
 
Other accrued expenses and liabilities
   
204,969
     
215,645
 
Deferred revenue
   
504,527
     
457,514
 
Total current liabilities
   
941,184
     
889,294
 
Long-term liabilities:
               
Deferred income taxes
   
55,863
     
75,301
 
Long-term operating lease liabilities
   
86,936
     
100,505
 
Long-term debt
   
754,208
     
753,891
 
Other long-term liabilities
   
126,800
     
113,520
 
Total long-term liabilities
   
1,023,807
     
1,043,217
 
Commitments and contingencies
               
Stockholders' equity:
               
Preferred stock, $0.01 par value; 2,000,000 shares authorized; zero shares issued or outstanding
   
     
 
Common stock, $0.01 par value; 300,000,000 shares authorized; 95,267,307 shares issued
   
953
     
953
 
Additional paid-in capital
   
1,790,688
     
1,670,450
 
Retained earnings
   
5,859,034
     
5,283,342
 
Treasury stock, at cost: 7,731,667 and 8,361,447 shares, respectively
   
(1,416,655
)
   
(1,474,110
)
Accumulated other comprehensive loss
   
(147,580
)
   
(90,271
)
Total stockholders' equity
   
6,086,440
     
5,390,364
 
Total liabilities and stockholders' equity
 
$
8,051,431
   
$
7,322,875
 

The accompanying notes are an integral part of the consolidated financial statements.


ANSYS, INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME

   
Year Ended December 31,
 
(in thousands, except per share data)
 
2024
   
2023
   
2022
 
Revenue:
                 
Software licenses
 
$
1,263,916
   
$
1,088,748
   
$
988,978
 
Maintenance and service
   
1,280,893
     
1,181,201
     
1,076,575
 
Total revenue
   
2,544,809
     
2,269,949
     
2,065,553
 
Cost of sales:
                       
Software licenses
   
45,367
     
40,004
     
33,081
 
Amortization
   
88,560
     
80,990
     
69,372
 
Maintenance and service
   
145,892
     
150,304
     
148,188
 
Total cost of sales
   
279,819
     
271,298
     
250,641
 
Gross profit
   
2,264,990
     
1,998,651
     
1,814,912
 
Operating expenses:
                       
Selling, general and administrative
   
995,340
     
855,135
     
772,871
 
Research and development
   
528,014
     
494,869
     
433,661
 
Amortization
   
23,748
     
22,512
     
15,722
 
Total operating expenses
   
1,547,102
     
1,372,516
     
1,222,254
 
Operating income
   
717,888
     
626,135
     
592,658
 
Interest income
   
51,131
     
19,588
     
5,717
 
Interest expense
   
(47,849
)
   
(47,145
)
   
(22,726
)
Other expense, net
   
(3,132
)
   
(6,440
)
   
(334
)
Income before income tax provision
   
718,038
     
592,138
     
575,315
 
Income tax provision
   
142,346
     
91,726
     
51,605
 
Net income
 
$
575,692
   
$
500,412
   
$
523,710
 
Earnings per share – basic:
                       
Earnings per share
 
$
6.59
   
$
5.76
   
$
6.02
 
Weighted average shares
   
87,313
     
86,833
     
87,051
 
Earnings per share – diluted:
                       
Earnings per share
 
$
6.55
   
$
5.73
   
$
5.99
 
Weighted average shares
   
87,895
     
87,386
     
87,490
 

The accompanying notes are an integral part of the consolidated financial statements.


ANSYS, INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Net income
 
$
575,692
   
$
500,412
   
$
523,710
 
Other comprehensive (loss) income:
                       
Foreign currency translation adjustments
   
(57,298
)
   
32,451
     
(66,610
)
Unrealized losses on available-for-sale securities, net of tax
   
(11
)
   
     
 
Comprehensive income
 
$
518,383
   
$
532,863
   
$
457,100
 

The accompanying notes are an integral part of the consolidated financial statements.


ANSYS, INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS

   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Cash flows from operating activities:
                 
Net income
 
$
575,692
   
$
500,412
   
$
523,710
 
Adjustments to reconcile net income to net cash provided by operating activities:
                       
Depreciation and amortization
   
142,672
     
132,504
     
114,563
 
Operating lease right-of-use assets expense
   
22,620
     
23,514
     
22,721
 
Deferred income tax benefit
   
(80,403
)
   
(91,306
)
   
(130,716
)
Provision for bad debts
   
2,598
     
2,704
     
6,222
 
Stock-based compensation expense
   
270,900
     
221,891
     
168,128
 
Other
   
1,242
     
1,238
     
4,680
 
Changes in operating assets and liabilities:
                       
Accounts receivable
   
(231,900
)
   
(102,516
)
   
(114,986
)
Other receivables and current assets
   
4,910
     
(30,204
)
   
30,259
 
Other long-term assets
   
6,841
     
(8,563
)
   
(3,613
)
Accounts payable, accrued expenses and current liabilities
   
23,620
     
27,853
     
(8,250
)
Accrued income taxes
   
(6,917
)
   
13,731
     
99
 
Deferred revenue
   
62,005
     
34,507
     
33,003
 
Other long-term liabilities
   
1,860
     
(8,643
)
   
(14,817
)
Net cash provided by operating activities
   
795,740
     
717,122
     
631,003
 
Cash flows from investing activities:
                       
Acquisitions, net of cash acquired
   
(1,586
)
   
(208,911
)
   
(386,264
)
Capital expenditures
   
(44,045
)
   
(25,318
)
   
(24,370
)
Purchases of short-term investments
   
(53,415
)
   
(172
)
   
(230
)
Other investing activities
   
(516
)
   
(5,641
)
   
(504
)
Net cash used in investing activities
   
(99,562
)
   
(240,042
)
   
(411,368
)
Cash flows from financing activities:
                       
Purchase of treasury stock
   
     
(196,494
)
   
(205,571
)
Restricted stock withholding taxes paid in lieu of issued shares
   
(106,097
)
   
(63,645
)
   
(64,242
)
Proceeds from shares issued for stock-based compensation
   
10,475
     
30,114
     
25,595
 
Other financing activities
   
(2,922
)
   
(1,294
)
   
(1,290
)
Net cash used in financing activities
   
(98,544
)
   
(231,319
)
   
(245,508
)
Effect of exchange rate fluctuations on cash and cash equivalents
   
(11,092
)
   
49
     
(27,403
)
Net increase (decrease) in cash and cash equivalents
   
586,542
     
245,810
     
(53,276
)
Cash and cash equivalents, beginning of period
   
860,201
     
614,391
     
667,667
 
Cash and cash equivalents, end of period
 
$
1,446,743
   
$
860,201
   
$
614,391
 
Supplemental disclosures of cash flow information:
                       
Income taxes paid
 
$
184,415
   
$
144,117
   
$
115,339
 
Interest paid
 
$
47,081
   
$
46,069
   
$
20,844
 
Non-cash and unpaid consideration in connection with acquisitions
 
$
   
$
5,056
   
$
5,391
 

The accompanying notes are an integral part of the consolidated financial statements.


ANSYS, INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY

   
Common Stock
           
Treasury Stock
         
(in thousands)
 
Shares
   
Amount
   
Additional
Paid-In
Capital
   
Retained
Earnings
   
Shares
   
Amount
   
Accumulated
Other
Comprehensive (Loss)/Income
   
Total
Stockholders'
Equity
 
Balance, January 1, 2022
   
95,267
   
$
953
   
$
1,465,694
   
$
4,259,220
     
8,188
   
$
(1,185,707
)
 
$
(56,112
)
 
$
4,484,048
 
Acquisition of Analytical Graphics Inc.
                   
511
             
(3
)
   
300
             
811
 
Treasury shares acquired
                                   
725
     
(205,571
)
           
(205,571
)
Stock-based compensation activity
                   
74,112
             
(593
)
   
55,351
             
129,463
 
Other comprehensive loss
                                                   
(66,610
)
   
(66,610
)
Net income for the year
                           
523,710
                             
523,710
 
Balance, December 31, 2022
   
95,267
     
953
     
1,540,317
     
4,782,930
     
8,317
     
(1,335,627
)
   
(122,722
)
   
4,865,851
 
Treasury shares acquired, including excise tax
                                   
650
     
(196,609
)
           
(196,609
)
Stock-based compensation activity
                   
130,133
             
(606
)
   
58,126
             
188,259
 
Other comprehensive income
                                                   
32,451
     
32,451
 
Net income for the year
                           
500,412
                             
500,412
 
Balance, December 31, 2023
   
95,267
     
953
     
1,670,450
     
5,283,342
     
8,361
     
(1,474,110
)
   
(90,271
)
   
5,390,364
 
Acquisition activity of previously acquired businesses
                   
1,818
             
(8
)
   
719
             
2,537
 
Stock-based compensation activity
                   
118,420
             
(621
)
   
56,736
             
175,156
 
Other comprehensive loss, net of tax effects
                                                   
(57,309
)
   
(57,309
)
Net income for the year
                           
575,692
                             
575,692
 
Balance, December 31, 2024
   
95,267
   
$
953
   
$
1,790,688
   
$
5,859,034
     
7,732
   
$
(1,416,655
)
 
$
(147,580
)
 
$
6,086,440
 

The accompanying notes are an integral part of the consolidated financial statements.


ANSYS, INC. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
December 31, 2024
 
1.
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 high-tech, aerospace and defense, automotive, energy, industrial equipment, materials and chemicals, consumer products, healthcare and construction.
 
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.
 
Pending Acquisition
 
On January 15, 2024, we entered into the Merger Agreement with Synopsys and Merger Sub, under which Synopsys will acquire Ansys. The transaction is anticipated to close in the first half of 2025, subject to the receipt of required regulatory approvals and other customary closing conditions. As part of our efforts to obtain regulatory approval for the merger, we have entered into a definitive agreement with Keysight Technologies, Inc. for the sale of our PowerArtist RTL business. The transaction is subject to customary closing conditions, including review by regulatory authorities, and the closing of Synopsys' proposed acquisition of Ansys. As such, the assets and liabilities of the PowerArtist RTL business have not been classified as assets held for sale in the consolidated balance sheets. The PowerArtist RTL business has not materially contributed to our financial results.
 
2.
Accounting Policies
 
Accounting Principles
 
The consolidated financial statements and accompanying notes are prepared in accordance with accounting principles generally accepted in the United States. Certain items in the consolidated statement of cash flows and notes to the consolidated financial statements of prior years have been conformed to the current year's presentation. These presentation changes 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
 
Segment reporting: In November 2023, the FASB issued ASU No. 2023-07, Segment Reporting (Topic 280): Improvements to Reportable Segment Disclosures (ASU 2023-07). ASU 2023-07 requires enhanced disclosures related to segment information, including for entities with one reportable segment. It does not change the determination of reportable segments. The enhanced disclosures in accordance with the new guidance are required to be reported in the annual period beginning after December 15, 2023. The standard only impacts footnote disclosures. We have adopted the reporting requirements in the report herein. See Note 21, "Segment Disclosure."


Accounting Guidance Issued and Not Yet Adopted
 
Income tax disclosures: In December 2023, the Financial Accounting Standards Board (FASB) issued ASU No. 2023-09, Income Taxes (Topic 740): Improvements to Income Tax Disclosures (ASU 2023-09). ASU 2023-09 requires disclosure of greater disaggregation of information in the rate reconciliation and income taxes paid disaggregated by jurisdiction. It also includes certain other amendments to improve the effectiveness of income tax disclosures. The standard is effective for annual periods beginning after December 15, 2024. Early adoption is permitted. The standard only impacts footnote disclosures.
 
Expense disaggregation disclosures: In November 2024, the FASB issued ASU No. 2024-03, Income Statement - Reporting Comprehensive Income - Expense Disaggregation Disclosures (Topic 220): Disaggregation of Income Statement Expenses (ASU 2024-03). ASU 2024-03 requires disclosure of disaggregation of expense captions. It also includes certain other disclosure requirements to improve the reporting of expense information. The standard is effective for annual periods beginning after December 15, 2026. Early adoption is permitted. The standard only impacts footnote disclosures.
 
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 or impacting these consolidated financial statements include:
 

Contract revenue
 

Standalone selling prices of our products and services
 

Allowance for doubtful accounts receivable
 

Valuation of goodwill and other intangible assets
 

Useful lives for depreciation and amortization
 

Operating lease assets and liabilities
 

Fair values of stock awards
 

Income taxes
 

Uncertain tax positions
 

Tax valuation reserves
 

Contingencies and litigation
 
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.


In addition to perpetual licenses, we sell time-based subscription lease licenses. Subscription 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 subscription 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 subscription 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.
 
Revenue from training, consulting 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.
 
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 sales facilitated by channel partners, the channel partner is the principal to the transaction with the end user. 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, Cash Equivalents and Short-Term Investments
 
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 money market fund balances were held in various funds of a single issuer at December 31, 2024.
 
Short-term investments consist of available-for-sale debt securities with remaining maturities greater than three months at the date of purchase and time deposits. Investments in debt securities with remaining maturities greater than three months at the date of purchase are designated as short-term available-for-sale securities, as we may convert these investments into cash at any time, including to fund general operations. We invest in debt securities that have an effective maturity term of less than three years. The debt securities are carried at fair value, with unrealized gains and losses included in the consolidated balance sheets as a component of accumulated other comprehensive (loss) income. For available-for-sale debt securities in an unrealized loss position, we evaluate whether a current expected credit loss exists based on available information relevant to the credit rating of the security, current economic conditions and reasonable and supportable forecasts. The allowance for any credit loss will be recorded in other expense, net, on the condensed consolidated statements of income, not to exceed the amount of the unrealized loss. Any excess unrealized loss other than the credit loss is generally recognized in accumulated other comprehensive loss. The cost of securities sold is based on the specific identification method and realized gains and losses are included in other expense, net. To date, we have not recorded any credit loss or realized gains or losses.
 
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.
 
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 acquired software and technology, customer lists and trade names. 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 $112.3 million, $103.5 million and $85.1 million for the years ended December 31, 2024, 2023 and 2022, 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 2024, 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, 2024. No other events or circumstances changed during the year ended December 31, 2024 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 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)
 
2024
   
2023
   
2022
 
Revenue from channel partners
   
25
%
   
26
%
   
24
%

No single customer or channel partner accounted for more than 5% of our revenue in 2024, 2023 or 2022.
 
In addition to the concentration of credit risk with respect to trade receivables, our cash, cash equivalents and short-term investments 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, cash equivalents and short-term investments:
 
   
As of December 31,
 
(in thousands)
 
2024
   
2023
 
Cash, cash equivalents and short-term investments held domestically
 
$
1,052,003
   
$
529,092
 
Cash, cash equivalents and short-term investments held by foreign subsidiaries
   
445,514
     
331,298
 
                 
Cash and cash equivalents held in excess of deposit insurance, foreign and domestic
   
1,434,694
     
846,723
 
Largest balance of cash and cash equivalents held with one financial institution, foreign and domestic
   
720,577
     
359,362
 

Allowance for Doubtful Accounts
 
ASU No. 2016-13, Financial Instruments - Credit Losses (Topic 326): Measurement of Credit Losses on Financial Instruments  requires us to use the current expected credit loss 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 years ended December 31, 2024, 2023 and 2022 were as follows:
 
(in thousands)
 
2024
   
2023
   
2022
 
Beginning balance – January 1
 
$
20,700
   
$
18,300
   
$
14,600
 
Additions: Charges to expense
   
2,598
   
$
2,704
     
6,222
 
Deductions: Write-offs
   
(6,798
)
   
(304
)
   
(2,522
)
Ending balance – December 31
 
$
16,500
   
$
20,700
   
$
18,300
 
 
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 converted to the functional currency in the period in which they occur. 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 expense, net. We recorded net foreign exchange losses of $3.1 million and $4.0 million for the years ended December 31, 2024 and 2023, respectively, and net foreign exchange gains of $1.6 million for the year ended December 31, 2022.
 
The financial statements of our foreign subsidiaries are translated from the functional 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 of foreign currency translation adjustments and unrealized losses on available-for-sale securities, net of tax effects.
 
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)
 
2024
   
2023
   
2022
 
Net income
 
$
575,692
   
$
500,412
   
$
523,710
 
Weighted average shares outstanding – basic
   
87,313
     
86,833
     
87,051
 
Dilutive effect of stock plans
   
582
     
553
     
439
 
Weighted average shares outstanding – diluted
   
87,895
     
87,386
     
87,490
 
Basic earnings per share
 
$
6.59
   
$
5.76
   
$
6.02
 
Diluted earnings per share
 
$
6.55
   
$
5.73
   
$
5.99
 
Anti-dilutive shares
   
43
     
218
     
300
 


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, accounts receivable, accounts payable, accrued expenses, other accrued liabilities, fixed forward contracts and short-term obligations are deemed to be reasonable estimates of their fair values because of their short-term nature. Our term loan is a variable rate debt obligation and, therefore, the carrying amount approximates the fair value.
 

3.
Revenue from Contracts with Customers
 
Disaggregation of Revenue
 
The following table summarizes revenue:
 
   
Year Ended December 31,
 
(in thousands, except percentages)
 
2024
   
2023
   
2022
 
Revenue:
                 
Subscription lease licenses
 
$
948,831
   
$
786,050
   
$
687,665
 
Perpetual licenses
   
315,085
     
302,698
     
301,313
 
Software licenses
   
1,263,916
     
1,088,748
     
988,978
 
Maintenance
   
1,209,217
     
1,103,523
     
1,004,245
 
Service
   
71,676
     
77,678
     
72,330
 
Maintenance and service
   
1,280,893
     
1,181,201
     
1,076,575
 
Total revenue
 
$
2,544,809
   
$
2,269,949
   
$
2,065,553
 
                         
Direct revenue, as a percentage of total revenue
   
75.2
%
   
73.9
%
   
76.1
%
Indirect revenue, as a percentage of total revenue
   
24.8
%
   
26.1
%
   
23.9
%

Our software licenses revenue is recognized up front, while maintenance and service revenue is 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, 2024 and 2023 were as follows:
 
(in thousands)
 
2024
   
2023
 
Beginning balance – January 1
 
$
479,754
   
$
435,758
 
Acquired deferred revenue
   
     
8,030
 
Deferral of revenue
   
2,617,131
     
2,305,294
 
Recognition of deferred revenue
   
(2,544,809
)
   
(2,269,949
)
Currency translation
   
(15,771
)
   
621
 
Ending balance – December 31
 
$
536,305
   
$
479,754
 
 
Total revenue allocated to remaining performance obligations as of December 31, 2024 will be recognized as revenue as follows:
 
(in thousands)
     
Next 12 months
 
$
1,029,144
 
Months 13-24
   
419,744
 
Months 25-36
   
206,327
 
Thereafter
   
63,052
 
Total revenue allocated to remaining performance obligations
 
$
1,718,267
 

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 deferred revenue associated with installment billings for periods beyond the current quarterly billing cycle and committed contracts with start dates beyond the end of the current period. Revenue recognized during the years ended December 31, 2024 and 2023 included amounts in deferred revenue and backlog at the beginning of the period of $897.4 million, of which $457.5 million was in deferred revenue, and $846.3 million, of which $414.0 million was in deferred revenue, respectively.

4.
Acquisitions
 
During the year ended December 31, 2024, we incurred acquisition-related expenses of $52.8 million, primarily consisting of costs related to the Merger Agreement with Synopsys. Acquisition-related expenses are recognized as selling, general and administrative and research and development expenses on the consolidated statements of income.
 
On December 5, 2023, we entered into an agreement to make a strategic equity investment in Humanetics in the amount of $300.0 million, subject to receipt of regulatory approvals among other customary closing conditions. As a result of our interactions with regulators, the parties mutually agreed to terminate the investment agreement in July 2024.


2023 Acquisitions
 
On January 3, 2023, we completed the acquisition of DYNAmore for a purchase price of $140.8 million, or $128.0 million net of cash acquired. The acquisition expands our position as a simulation solution provider within the automotive industry. The effects of the acquisition were not material to our consolidated results of operations.
 
Additionally, during the year ended December 31, 2023, we completed other acquisitions to expand our solution offerings and enhance our customers' experience. These acquisitions were not significant, individually or in the aggregate. The combined purchase price of these acquisitions during the year ended December 31, 2023 was approximately $94.4 million, or $88.3 million net of cash acquired.
 
During the year ended December 31, 2023, we incurred acquisition-related expenses of $9.4 million. Acquisition-related expenses are recognized as selling, general and administrative and research and development expenses on the consolidated statements of income.
 
The assets acquired and liabilities assumed in connection with 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 value of consideration and the fair values of identified assets acquired and liabilities assumed at each respective date of acquisition:
 
Fair Value of Consideration:

(in thousands)
     
Cash
 
$
230,106
 
Non-cash consideration
   
5,056
 
Total consideration
 
$
235,162
 
         
Recognized Amounts of Identifiable Assets Acquired and Liabilities Assumed:
       
         
(in thousands)
       
Cash
 
$
18,870
 
Accounts receivable and other tangible assets
   
19,294
 
Developed software and core technologies
   
28,110
 
Customer lists
   
83,790
 
Trade names
   
2,910
 
Accounts payable and other liabilities
   
(8,845
)
Deferred revenue
   
(8,030
)
Net deferred tax liabilities
   
(31,980
)
Total identifiable net assets
 
$
104,119
 
Goodwill
 
$
131,043
 
 
The goodwill, which is generally not tax-deductible, is attributed to intangible assets that do not qualify for separate recognition, including the assembled workforces of the acquired businesses and the synergies expected to arise as a result of the acquisitions.
 
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, attrition rate and obsolescence rate.


The weighted-average useful life, valuation method and assumptions used to determine the fair value of the intangible assets related to the 2023 acquisitions are as follows:
 
Intangible Asset
 
Weighted-Average
Useful Life
 
Valuation Method
 
Assumptions
Developed software and core technologies
 
5 years
 
Relief-from-royalty or multi-period excess earnings
 
Royalty rate: 20.0%
Obsolescence rate: 15.0% - 20.0%
Discount rate: 12.5% - 22.0%
Trade names
 
5 years
 
Relief-from-royalty
 
Royalty rate:  1.0% - 2.0%
Discount rate: 15.5% - 22.0%
Customer lists
 
13 years
 
Multi-period excess earnings
 
Attrition rate: 5.0%
Discount rate: 15.5% - 22.0%
 
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 or in the aggregate during 2023.

5.   Cash Equivalents and Short-Term Investments
 
During the year ended December 31, 2024, we invested in available-for-sale debt securities, which are included in short-term investments in the consolidated balance sheets. As of December 31, 2024, our cash equivalents and short-term investments were as follows:
 
(in thousands)
 
Amortized Cost
   
Gross Unrealized
Gains
   
Gross Unrealized
Losses Less Than
12 Continuous
Months
   
Estimated Fair
Value(1)
 
Cash equivalents:
                       
Money market funds
 
$
410,515
   
$
   
$
   
$
410,515
 
Total cash equivalents
   
410,515
     
     
     
410,515
 
Short-term investments:
                               
Corporate debt securities
   
27,149
     
76
     
(20
)
   
27,205
 
Municipal bonds
   
18,402
     
39
     
(59
)
   
18,382
 
U.S. agency bonds
   
5,056
     
     
(51
)
   
5,005
 
Other short-term investments
   
182
     
     
     
182
 
Total short-term investments
   
50,789
     
115
     
(130
)
   
50,774
 
Total cash equivalents and short-term investments
 
$
461,304
   
$
115
   
$
(130
)
 
$
461,289
 
(1) See Note 9, "Fair Value Measurement" for further discussion on fair values.
 
Of the $27.2 million of corporate debt securities, $5.3 million are in a loss position at December 31, 2024. Of the $18.4 million of municipal bonds, $6.0 million are in a loss position at December 31, 2024. Of the $5.0 million of U.S. agency bonds, $5.0 million are in a loss position at December 31, 2024.
 
The unrealized losses presented above are primarily attributable to changes in interest rates. We believe that we have the ability to realize the full value of these investments upon maturity.


The following table outlines maturities of our available-for-sale debt securities as of December 31, 2024:
 
(in thousands)
 
Amortized Cost
   
Fair Value
 
Less than 1 year
 
$
16,796
   
$
16,822
 
1-3 years
   
33,811
     
33,770
 
Total
 
$
50,607
   
$
50,592
 
 
6.   Other Receivables and Current Assets
 
Our other receivables and current assets comprise the following balances:
 
   
December 31,
 
(in thousands)
 
2024
   
2023
 
Receivables related to unrecognized revenue
 
$
244,605
   
$
253,646
 
Income taxes receivable, including overpayments and refunds
   
7,755
     
22,104
 
Prepaid expenses and other current assets
   
58,766
     
48,901
 
Total other receivables and current assets
 
$
311,126
   
$
324,651
 

Receivables related to unrecognized revenue represent the current portion of billings made for customer contracts that have not yet been recognized as revenue.
 
7.   Property and Equipment
 
Property and equipment consists of the following:
 
      
December 31,
 
(in thousands)
Estimated Useful Lives
 
2024
   
2023
 
Equipment
1-15 years
 
$
149,765
   
$
136,112
 
Computer software
1-5 years
   
34,461
     
29,210
 
Buildings and improvements
2-40 years
   
41,880
     
39,728
 
Leasehold improvements
1-17 years
   
29,862
     
29,587
 
Furniture
1-10 years
   
15,693
     
15,921
 
Land
     
2,696
     
2,696
 
Property and equipment, gross
     
274,357
     
253,254
 
Less: Accumulated depreciation
     
(184,711
)
   
(175,474
)
Property and equipment, net
   
$
89,646
   
$
77,780
 

Depreciation expense related to property and equipment was $30.9 million, $29.0 million and $29.5 million for the years ended December 31, 2024, 2023 and 2022, respectively.
 
8.   Goodwill and Intangible Assets
 
Goodwill represents the excess of the fair value of consideration 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, 2024
   
December 31, 2023
 
(in thousands)
 
Gross
Carrying
Amount
   
Accumulated
Amortization
   
Gross
Carrying
Amount
   
Accumulated
Amortization
 
Finite-lived intangible assets:
                       
Developed software and core technologies
 
$
1,142,840
   
$
(635,450
)
 
$
1,146,022
   
$
(557,359
)
Customer lists
   
261,895
     
(91,769
)
   
289,874
     
(89,800
)
Trade names
   
189,017
     
(150,646
)
   
190,203
     
(143,880
)
Total
 
$
1,593,752
   
$
(877,865
)
 
$
1,626,099
   
$
(791,039
)
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.
 
As of December 31, 2024, estimated future amortization expense for the intangible assets reflected above is as follows:
 
(in thousands)
     
2025
 
$
114,392
 
2026
   
115,188
 
2027
   
118,417
 
2028
   
112,188
 
2029
   
98,453
 
Thereafter
   
157,249
 
Total intangible assets subject to amortization, net
   
715,887
 
Indefinite-lived trade name
   
357
 
Other intangible assets, net
 
$
716,244
 

The changes in goodwill during the years ended December 31, 2024 and 2023 were as follows:

(in thousands)
 
2024
   
2023
 
Beginning balance - January 1
 
$
3,805,874
   
$
3,658,267
 
Acquisitions and adjustments(1)
   
868
     
122,635
 
Currency translation
   
(28,614
)
   
24,972
 
Ending balance - December 31
 
$
3,778,128
   
$
3,805,874
 
(1) In addition to goodwill from acquisitions completed within the period, 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.
 
During the first quarter of 2024, 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, 2024. No other events or circumstances changed during the year ended December 31, 2024 that would indicate that the fair values of our reporting unit and indefinite-lived intangible asset are below their carrying amounts.


9.   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 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 debt approximates the estimated fair value. See Note 11, "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,
2024
   
Quoted Prices in
Active Markets
(Level 1)
   
Significant Other
Observable
Inputs
(Level 2)
   
Significant
Unobservable
Inputs
(Level 3)
 
Assets
                       
Cash equivalents:
                       
Money market funds
 
$
410,515
   
$
410,515
   
$
   
$
 
Short-term investments:
                               
Corporate debt securities
 
$
27,205
   
$
   
$
27,205
   
$
 
Municipal bonds
 
$
18,382
   
$
   
$
18,382
   
$
 
U.S. agency bonds
 
$
5,005
   
$
   
$
5,005
   
$
 
Other short-term investments
 
$
182
   
$
   
$
182
   
$
 
Deferred compensation plan investments
 
$
2,459
   
$
2,459
   
$
   
$
 
Equity securities
 
$
785
   
$
785
   
$
   
$
 

         
Fair Value Measurements at Reporting Date Using:
 
(in thousands)
 
December 31,
2023
   
Quoted Prices in
Active Markets
(Level 1)
   
Significant Other
Observable
Inputs
(Level 2)
   
Significant
Unobservable
Inputs
(Level 3)
 
Assets (Liabilities)
                       
Cash equivalents:
                       
Money market funds
 
$
170,821
   
$
170,821
   
$
   
$
 
Short-term investments:
                               
Other short-term investments
 
$
189
   
$
   
$
189
   
$
 
Deferred compensation plan investments
 
$
2,337
   
$
2,337
   
$
   
$
 
Equity securities
 
$
634
   
$
634
   
$
   
$
 
Forward contracts
 
$
(412
)
 
$
   
$
(412
)
 
$
 

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 available-for-sale securities and time deposits.
 
The deferred compensation plan investments in the preceding tables represent trading securities held in a rabbi trust for the benefit of 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.
 
The equity securities represent our investment in a publicly traded company. These securities are traded in an active market with quoted prices. As a result, the securities are classified as Level 1 in the fair value hierarchy. The securities are recorded within other long-term assets on our consolidated balance sheets.
 
The forward contracts represent currency hedges to mitigate exchange rate exposure. These contracts are classified within Level 2 because these contracts are not actively traded and the valuation inputs are based on quoted prices and market observable data of similar instruments. The liabilities associated with the forward contracts are recorded at fair value in other accrued expenses and liabilities in the consolidated balance sheets.
 
10.   Leases
 
Our right-of-use (ROU) assets and lease liabilities primarily include operating leases for office space. 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 an option to renew the contract through August 2044.  No options are included in the lease liability. Absent the exercise of options in the lease, our remaining base rent (inclusive of property taxes and certain operating costs) is $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, 2024, 2023 and 2022 are as follows:
 
(in thousands)
 
2024
   
2023
   
2022
 
Lease liability cost
 
$
28,385
   
$
28,481
   
$
27,543
 
Variable lease cost not included in the lease liability(1)
   
5,524
     
5,749
     
4,436
 
Total lease cost
 
$
33,909
   
$
34,230
   
$
31,979
 
 
(1) Variable lease cost includes common area maintenance, property taxes, utilities and fluctuations in rent due to a change in an index or rate.
 
Other information related to operating leases for the years ended December 31, 2024, 2023 and 2022 is as follows:
 
(in thousands)
 
2024
   
2023
   
2022
 
Cash paid for amounts included in the measurement of the lease liability:
                 
Operating cash flows from operating leases
 
$
(28,598
)
 
$
(28,281
)
 
$
(26,767
)
Right-of-use assets obtained in exchange for new operating lease liabilities
 
 
$
15,655
   
$
12,913
   
$
36,735
 

   
As of December 31,
 
   
2024
   
2023
 
Weighted-average remaining lease term of operating leases
 
5.8 years
   
6.4 years
 
Weighted-average discount rate of operating leases
   
3.3
%
   
3.4
%


The maturity schedule of the operating lease liabilities as of December 31, 2024 is as follows:

(in thousands)
     
2025
 
$
27,781
 
2026
   
23,395
 
2027
   
19,317
 
2028
   
17,644
 
2029
   
12,592
 
Thereafter
   
21,824
 
Total future lease payments
   
122,553
 
Less: Present value adjustment
   
(11,130
)
Present value of future lease payments(1)
 
$
111,423
 

(1)Includes the current portion of operating lease liabilities of $24.5 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, 2024.
 
11.   Debt
 
On June 30, 2022, we entered into a credit agreement (as amended, the 2022 Credit Agreement) with PNC Bank, National Association, as administrative agent, swing line lender, and an L/C issuer, the lenders party thereto, and the other L/C issuers party thereto. The 2022 Credit Agreement refinanced our previous credit agreements in their entirety. Terms used in this description of the 2022 Credit Agreement with initial capital letters that are not otherwise defined herein are as defined in the 2022 Credit Agreement.
 
The 2022 Credit Agreement provides for a $755.0 million unsecured term loan facility and a $500.0 million unsecured revolving loan facility, which includes a $50.0 million sublimit for the issuance of letters of credit. The revolving loan facility is available for working capital and general corporate purposes. Each of the term loan facility and the revolving loan facility matures on June 30, 2027.
 
Borrowings under the term loan and revolving loan facilities accrue interest at a rate that is based on the Term SOFR plus an applicable margin or at the base rate plus an applicable margin, at our election. The base rate is the highest of (i) the Overnight Bank Funding Rate, plus 0.500%, (ii) the PNC Bank, National Association prime rate, and (iii) Daily Simple SOFR plus an adjustment for SOFR plus 1.00%. The applicable margin for the borrowings is a percentage per annum based on the lower of (1) a pricing level determined by our then-current consolidated net leverage ratio and (2) a pricing level determined by our public debt rating (if available).
 
On September 29, 2023, the 2022 Credit Agreement was amended to provide for an interest rate adjustment (Sustainability Rate Adjustment) based upon the achievement of certain environmental, social and governance KPIs. The Sustainability Rate Adjustment range is +/- 0.05% and will be adjusted annually based on the KPIs of the preceding year.
 
The 2022 Credit Agreement also provides for the option to add certain foreign subsidiaries as borrowers and to borrow in Euros, Sterling, Yen and Swiss Francs under the revolving loan facility, up to a sublimit of $150.0 million. Borrowings under the revolving loan facility denominated in these currencies will accrue interest at a rate that is based on (a) for Euros, €STR, (b) for Sterling, SONIA, (c) for Yen, TONAR and (d) for Swiss Francs, SARON, plus an applicable margin calculated as described above.
 
Under the 2022 Credit Agreement, the weighted average interest rates in effect for the years ended December 31, 2024 and 2023 were 6.08% and 6.01%, respectively. The rate in effect as of December 31, 2024 and for the first quarter of 2025 under the 2022 Credit Agreement is 5.25%.
 
The 2022 Credit Agreement contains customary representations and warranties, affirmative and negative covenants and events of default. The 2022 Credit Agreement also contains a financial covenant requiring us and our subsidiaries to maintain a consolidated net leverage ratio not in excess of 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 net 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, 2024, we had $755.0 million of borrowings outstanding under the term loan, with a carrying value of $754.2 million, which is net of $0.8 million of unamortized debt discounts and issuance costs. The total amount was included in long-term debt. As of December 31, 2024, no borrowings were outstanding under the revolving loan facility.
 
As of December 31, 2023, we had $755.0 million of borrowings outstanding under the term loan, with a carrying value of $753.9 million, which is net of $1.1 million of unamortized debt discounts and issuance costs. The total amount was included in long-term debt. As of December 31, 2023, no borrowings were outstanding under the revolving loan facility.
 
We were in compliance with all covenants under the 2022 Credit Agreement as of December 31, 2024 and December 31, 2023, respectively.
 
As of December 31, 2024, all debt is scheduled to mature in 2027 with no principal payments required prior to the maturity date.
 
12.   Income Taxes
 
Income before income tax provision included the following components:
 
   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Domestic
 
$
544,979
   
$
458,581
   
$
504,797
 
Foreign
   
173,059
     
133,557
     
70,518
 
Total
 
$
718,038
   
$
592,138
   
$
575,315
 
 
The provision for income taxes was composed of the following:
 
   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Current:
                 
Federal
 
$
144,537
   
$
115,942
   
$
103,007
 
State
   
20,265
     
11,759
     
11,286
 
Foreign
   
57,947
     
55,332
     
68,028
 
Deferred:
                       
Federal
   
(78,139
)
   
(79,251
)
   
(94,398
)
State
   
(6,318
)
   
(8,145
)
   
(9,647
)
Foreign
   
4,054
     
(3,911
)
   
(26,671
)
Total
 
$
142,346
   
$
91,726
   
$
51,605
 
 

The reconciliation of the U.S. federal statutory tax rate to the consolidated effective tax rate was as follows:
 
   
Year Ended December 31,
 
   
2024
   
2023
   
2022
 
Federal statutory tax rate
   
21.0
%
   
21.0
%
   
21.0
%
Nondeductible expenses
   
3.5
     
2.1
     
2.3
 
State income taxes, net of federal benefit
   
1.5
     
0.6
     
0.9
 
Foreign rate differential
   
0.7
     
0.4
     
 
Stock-based compensation
   
0.3
     
     
(1.5
)
U.S. federal tax (benefit) expense on foreign earnings
   
0.1
     
(1.2
)
   
(2.4
)
Benefit from tax planning and entity structuring activities
   
     
(0.3
)
   
(2.5
)
Research and development credits
   
(3.0
)
   
(3.2
)
   
(3.2
)
Foreign-derived intangible income deduction
   
(4.2
)
   
(4.1
)
   
(5.7
)
Other
   
(0.1
)
   
0.2
     
0.1
 
     
19.8
%
   
15.5
%
   
9.0
%
 
The components of deferred tax assets and liabilities are as follows:
 
   
December 31,
 
(in thousands)
 
2024
   
2023
 
Deferred tax assets:
           
Research and experimentation capitalization
 
$
211,192
   
$
148,355
 
Uncertain tax positions
   
55,583
     
52,685
 
Net operating loss carryforwards
   
31,304
     
34,907
 
Stock-based compensation
   
29,712
     
33,473
 
Operating lease liabilities
   
24,967
     
28,380
 
Debt obligation basis difference
   
20,289
     
30,289
 
Employee benefits
   
12,066
     
13,662
 
Other
   
13,459
     
9,752
 
Valuation allowance
   
(16,892
)
   
(17,608
)
Total deferred tax assets
   
381,680
     
333,895
 
Deferred tax liabilities:
               
Other intangible assets
   
(177,270
)
   
(202,404
)
Operating lease right-of-use assets
   
(23,407
)
   
(26,878
)
Deferred revenue
   
(11,367
)
   
(12,080
)
Property and equipment
   
(3,034
)
   
(3,607
)
Other
   
     
 
Total deferred tax liabilities
   
(215,078
)
   
(244,969
)
Net deferred tax assets
 
$
166,602
   
$
88,926
 
 
The net decrease in the valuation allowance was primarily due to $0.9 million of currency fluctuations on balances relating to foreign jurisdictions, partially offset by a $0.2 million increase 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, 2024, we had federal net operating loss carryforwards of $0.7 million, which are subject to limitations of their utilization and expire between 2036 - 2037. Deferred tax assets of $0.9 million have been recorded for state operating loss carryforwards. These losses expire between 2027 - 2042, and are subject to limitations on their utilization. We had total foreign net operating loss carryforwards of $122.3 million, of which $89.1 million are not currently subject to expiration dates. The remainder, $33.2 million, expires between 2030 - 2039. We had tax credit carryforwards of $8.5 million, of which $1.9 million are not currently subject to expiration dates and $6.6 million expire in various years between 2025 - 2044. Of these tax credit carryforwards, $0.7 million are subject to limitations on their utilization.
 
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. Unrecognized provisions for taxes on indefinitely reinvested undistributed earnings of foreign subsidiaries would not be significant.
 
The following is a reconciliation of the total amounts of unrecognized tax benefits:
 
   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Unrecognized tax benefit as of January 1
 
$
54,884
   
$
45,772
   
$
39,641
 
Gross changes—acquisitions
   
     
     
 
Gross increases—tax positions in prior period
   
146
     
     
403
 
Gross decreases—tax positions in prior period
   
(267
)
   
(1,782
)
   
(2,780
)
Gross increases—tax positions in current period
   
12,302
     
14,814
     
13,905
 
Reductions due to a lapse of the applicable statute of limitations
   
(2,998
)
   
(3,236
)
   
(3,743
)
Changes due to currency fluctuation
   
(6,516
)
   
(684
)
   
(1,654
)
Settlements
   
     
     
 
Unrecognized tax benefit as of December 31
 
$
57,551
   
$
54,884
   
$
45,772
 

We believe that it is reasonably possible that $32.2 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, 2024 were to be recognized, a benefit of $13.0 million would impact the effective tax rate.
 
We recognize interest and penalties related to unrecognized tax benefits as income tax expense. We recorded penalty expense of $0.1 million, $0.7 million and $0.7 million for the years ended December 31, 2024, 2023 and 2022, respectively. We recorded interest income of $0.2 million for the year ended December 31, 2024, interest income of $0.3 million for the year ended December 31, 2023 and interest expense of $0.1 million for the year ended December 31, 2022. As of December 31, 2024, we accrued a liability for penalties of $8.8 million and interest of $2.3 million. As of December 31, 2023, we accrued a liability for penalties of $8.7 million and interest of $2.6 million.
 
The OECD has introduced a two-pillar approach to address the tax challenges arising from the digitalization of the economy. Pillar Two defines global minimum tax rules and includes a 15 percent minimum tax rate. We have not recorded any income tax provision related to Pillar Two for the year ended December 31, 2024 based on the laws currently enacted in the jurisdictions in which we operate.
 
We are subject to taxation in the United States and various states and foreign jurisdictions. In the United States, our only major tax jurisdiction, the 2017 - 2024 tax years are open to examination by the Internal Revenue Service.
 

13.  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. Domestic employees of acquired businesses may participate in the 401(k) plan when they become eligible. 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, 2024 and 2023, the total unfunded portions of the benefit obligations were $12.4 million and $11.8 million, respectively.
 
Expenses related to our retirement programs were $28.0 million in 2024, $25.9 million in 2023 and $21.9 million in 2022.
 
14.   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. Under the terms of the employment agreement, in the event that the Chief Executive Officer's employment with us is terminated by us without "Cause" or as a result of his resignation with "Good Reason" (each as defined in the agreement) the Chief Executive Officer will be entitled to (i) receive an amount equal to two times the sum of his then effective base salary plus his target bonus, payable over 24 months in equal installments, (ii) receive payment of the prior year's earned annual cash incentive, to the extent unpaid, (iii) receive payment of a pro-rated target annual cash incentive for the year of termination, (iv) in certain circumstances, receive a lump sum amount equal to 24 months of the COBRA premium applicable to the health, dental and vision plans in which the Chief Executive Officer was participating prior to termination, (v) have any outstanding performance-based and time-based equity awards receive accelerated vesting treatment equal to an additional two years after termination, and (vi) have the period of time during which the Chief Executive Officer may exercise his vested stock options be extended to the longer of (x) six months after his date of termination or (y) seven days after the commencement of our first open trading window that occurs after the date of termination, but in no event later than the 10-year expiration date of such options. 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.
 
If a termination under the circumstances described above occurs during the period beginning 60 days prior to the effective date of a definitive agreement that will result in a change in control and ending 18 months after the consummation (closing) of a change in control, then, in lieu of the benefits described in the foregoing paragraph, the Chief Executive Officer will be entitled to the amounts described in the paragraph above, except that (a) the amount described in clause (i) will be paid in a lump sum rather than over 24 months, and (b) instead of the two-year acceleration period described in clause (v), all outstanding performance-based and time-based equity awards held by the Chief Executive Officer shall immediately become fully exercisable, vested and/or non-forfeitable on an accelerated basis, subject to any performance or metric-based requirements set forth therein which shall be separately determined as set forth in the applicable award agreement.
 
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.
 

15.   Stock-Based Compensation
 
On May 14, 2021, our stockholders approved the ANSYS, Inc. 2021 Equity and Incentive Compensation Plan (the 2021 Plan). The 2021 Plan is a long-term incentive plan pursuant to which awards may be granted to directors, officers, other employees and certain consultants of Ansys and its subsidiaries. These awards may include stock option rights, stock appreciation rights, restricted stock, restricted stock units, cash incentives, performance shares, performance units and other awards. The 2021 Plan authorizes 4.4 million shares of common stock for issuance, plus 1.6 million shares that remained available for issuance under the Fifth Amended and Restated ANSYS, Inc. 1996 Stock Option and Grant Plan (the Predecessor Plan) as of the effective date of the 2021 Plan plus any shares relating to the outstanding awards under the Predecessor Plan or the 2021 Plan that are subsequently forfeited. As of the effective date of the 2021 Plan, grants were no longer made under the Predecessor Plan.
 
The 2021 Plan requires a minimum vesting period or performance period of one year for most award types and a maximum period for options to be exercisable as ten years from the grant date. Upon the death or disability of a participant, performance awards are vested pro-rata, subject to any performance target requirements, and all other awards become fully vested. 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 2021 Plan may vest in the event of a change in control or an employee's termination of employment. A change in control will result in awards either being assumed by the acquirer or the pre-existing awards becoming immediately vested and earned at target award levels. In the event an employee is terminated without cause within 18 months after the change in control, any assumed awards will become immediately vested.
 
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, 2024, 2023 and 2022 is as follows:
 
   
Year Ended December 31,
 
(in thousands, except per share amounts)
 
2024
   
2023
   
2022
 
Cost of sales:
                 
Maintenance and service
   
14,313
     
13,337
     
10,073
 
Operating expenses:
                       
Selling, general and administrative
   
161,905
     
126,175
     
93,117
 
Research and development
   
94,682
     
82,379
     
64,938
 
Stock-based compensation expense before taxes
   
270,900
     
221,891
     
168,128
 
Related income tax benefits
   
(65,647
)
   
(53,880
)
   
(50,209
)
Stock-based compensation expense, net of taxes
 
$
205,253
   
$
168,011
   
$
117,919
 

As of December 31, 2024, total unrecognized estimated compensation expense related to awards granted prior to that date was $352.8 million, which is expected to be recognized over a weighted average period of 1.5 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, 2024, there is no unrecognized estimated compensation cost related to unvested stock options.
 
Information regarding stock option transactions is summarized below:

   
Year Ended December 31,
 
   
2024
   
2023
   
2022
 
(options in thousands)
 
Options
   
Weighted-
Average
Exercise
Price
   
Options
   
Weighted-
Average
Exercise
Price
   
Options
   
Weighted-
Average
Exercise
Price
 
Outstanding, beginning of year
   
103
   
$
94.23
     
226
   
$
94.24
     
375
   
$
83.67
 
Granted
   
   
$
     
   
$
     
   
$
 
Exercised
   
(1
)
 
$
86.57
     
(123
)
 
$
94.32
     
(148
)
 
$
67.56
 
Forfeited
   
(2
)
 
$
86.01
     
   
$
     
(1
)
 
$
67.44
 
Outstanding, end of year
   
100
   
$
94.46
     
103
   
$
94.23
     
226
   
$
94.24
 
Vested and Exercisable, end of year
   
100
   
$
94.46
     
103
   
$
94.23
     
226
   
$
94.24
 
Nonvested
   
   
$
     
   
$
     
   
$
 

   
2024
   
2023
   
2022
 
Weighted Average Remaining Contractual Term (in years)
                 
Outstanding
   
1.59
     
2.52
     
3.53
 
Vested and Exercisable
   
1.59
     
2.52
     
3.53
 
Aggregate Intrinsic Value (in thousands)
                       
Exercised
 
$
83
   
$
28,231
   
$
30,358
 
Outstanding
 
$
24,370
   
$
27,717
   
$
33,361
 
Vested and Exercisable
 
$
24,370
   
$
27,717
   
$
33,361
 
Compensation Expense - Stock Options (in thousands)
 
$
   
$
   
$
 

Information regarding stock options outstanding as of December 31, 2024 is summarized below:
 
(options in thousands)
   
Options Outstanding & Exercisable
 
Exercise Price
   
Options
   
Weighted-
Average
Remaining
Contractual
Life (years)
 
$
86.57
     
7
     
0.67
 
$
94.15
     
1
     
0.58
 
$
95.09
     
92
     
1.67
 

There were no unvested stock options as of December 31, 2024.


Restricted Stock Units
 
Under the terms of the 2021 Plan, we have issued various restricted stock unit awards (RSUs). 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
Prior to March 2023, one third of the awards vested annually.  Commencing in March 2023, one third vests in the first year and then one eighth quarterly thereafter.
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 through the vesting period.
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.
Board of Director restricted stock unit awards
The earlier of one year or the next regular meeting of stockholders
Continued service on the Board of Directors through the vesting period. Directors that retire prior to the vest date receive a pro-rata portion of the RSUs.

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 straight-line 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 vesting period based on management's estimates concerning the probability of operating performance metric achievement.
 
The fair values of 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. Due to the pending merger with Synopsys, there were no RSUs with a market condition issued in 2024.
 
   
Year Ended December 31,
 
Assumptions used in Monte Carlo lattice pricing model
 
2023
   
2022
 
Risk-free interest rate
   
4.6
%
   
1.8
%
Expected dividend yield
   
%
   
%
Expected volatility—Ansys stock price
   
36
%
   
37
%
Expected volatility—Nasdaq Composite Index
   
25
%
   
26
%
Expected term
 
2.8 years
   
2.8 years
 
Correlation factor
   
0.83
     
0.84
 
Weighted average fair value per share
 
$
452.14
   
$
290.65
 
 
Total compensation expense for RSU awards recorded for the years ended December 31, 2024, 2023 and 2022 was $270.5 million, $213.5 million and $164.0 million, respectively.


Information regarding all employee and non-employee director RSU transactions is summarized below:

   
Year Ended December 31,
 
   
2024
   
2023
   
2022
 
(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
   
1,538
   
$
309.33
     
1,220
   
$
301.72
     
1,074
   
$
278.02
 
Granted(1)
   
948
   
$
339.43
     
867
   
$
314.04
     
861
   
$
299.08
 
Performance adjustment - awards with market condition(2)
   
(20
)
 
$
285.28
     
(11
)
 
$
279.42
     
(8
)
 
$
276.73
 
Performance adjustment - awards  with performance condition(2)
   
59
   
$
339.62
     
79
   
$
310.37
     
73
   
$
300.28
 
Vested
   
(894
)
 
$
310.84
     
(558
)
 
$
300.30
     
(598
)
 
$
257.51
 
Forfeited
   
(76
)
 
$
322.38
     
(59
)
 
$
313.58
     
(182
)
 
$
295.13
 
Nonvested, end of year
   
1,555
   
$
327.62
     
1,538
   
$
309.33
     
1,220
   
$
301.72
 

(1) Includes all RSUs granted during the year. RSUs with operating performance conditions 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.
 
Employee Stock Purchase Plan
 
On May 12, 2022, our stockholders approved the ANSYS, Inc. 2022 Employee Stock Purchase Plan (2022 ESPP) and the reservation by our Board of Directors of 750,000 shares of common stock for issuance under the 2022 ESPP. On October 27, 2022, our Board of Directors approved the amendment and restatement of the 2022 ESPP. The 2022 ESPP replaced the 1996 Employee Stock Purchase Plan (1996 Plan) in its entirety. Shares issued in 2024 were issued under the 2022 ESPP. The 2022 ESPP and 1996 Plan (Purchase Plans) allow our employees and employees of our designated subsidiaries to purchase shares of our common stock at a discount to fair market value. Due to the pending merger with Synopsys, there were no offering periods under the Purchase Plans in 2024 after the conclusion of the offering period ending January 31, 2024. There were 634,167 shares available for future purchases as of December 31, 2024.
 
The Purchase Plans are administered by the Compensation Committee. Offerings under the Purchase Plans commence on the first business day occurring on or before each February 1 and August 1, and end on the last business day occurring on or before the following July 31 and January 31, respectively. 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 Plans.
 
During each offering, an eligible employee may purchase shares 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. Subject to limitations within the Purchase Plans, each employee's accumulated payroll deductions will be used to purchase common stock on the last day of the applicable offering period at a price equal to 85% of the fair market value of the common stock on the first or last day of the applicable offering period, whichever is less. Under applicable tax rules, an employee may not accrue at a rate that exceeds $25,000 of the fair market value of our stock (determined on the option grant date or dates) for each calendar year in which the option to purchase shares is outstanding at any time. As of December 31, 2024, 115,833 shares of common stock had been issued under the 2022 ESPP. The total compensation expense recorded under the Purchase Plans during the years ended December 31, 2024, 2023 and 2022 was $0.3 million, $8.3 million and $4.2 million, respectively.
 

16.  Stock Repurchase Program
 
There were no share repurchases in 2024. For the year ended December 31, 2023, 650 thousand shares were repurchased at an average price of $302.34 per share, with a total cost of $196.5 million. For the year ended December 31, 2022, 725 thousand shares were repurchased at an average price of $283.38 per share, with a total cost of $205.6 million. As of December 31, 2024, 1.1 million shares remained available for repurchase under the program.
 
17.   Royalty Agreements
 
We 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 $44.1 million, $39.0 million and $32.0 million for the years ended December 31, 2024, 2023 and 2022, respectively.
 
18.   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)
 
2024
   
2023
   
2022
 
United States
 
$
1,251,892
   
$
1,058,293
   
$
932,587
 
Germany
   
209,714
     
199,068
     
198,612
 
Japan
   
184,547
     
203,013
     
186,199
 
China and Hong Kong
   
126,628
     
111,467
     
105,101
 
South Korea
   
112,895
     
106,261
     
127,948
 
Other EMEA
   
445,791
     
406,719
     
349,159
 
Other international
   
213,342
     
185,128
     
165,947
 
Total revenue
 
$
2,544,809
   
$
2,269,949
   
$
2,065,553
 

Property and equipment by geographic area was as follows:
 
   
December 31,
 
(in thousands)
 
2024
   
2023
 
United States
 
$
65,731
   
$
56,421
 
India
   
6,280
     
5,057
 
France
   
4,975
     
4,771
 
Other EMEA
   
6,279
     
6,924
 
Other international
   
6,381
     
4,607
 
Total property and equipment, net
 
$
89,646
   
$
77,780
 
 

19. Unconditional Purchase Obligations
 
We have entered into various unconditional purchase obligations which primarily include minimum royalty contracts and software licenses and support. We expended $66.4 million, $54.8 million and $54.8 million related to unconditional purchase obligations that existed as of the beginning of each year for the years ended December 31, 2024, 2023 and 2022, respectively. Future expenditures under unconditional purchase obligations in effect as of December 31, 2024 are as follows:
 
(in thousands)
     
2025
 
$
66,763
 
2026
   
16,115
 
2027
   
9,322
 
2028
   
3,896
 
2029
   
299
 
Total
 
$
96,395
 
 
20.   Contingencies and Commitments
 
We are subject to various claims, investigations, and legal and regulatory proceedings that arise in the ordinary course of business, including, but not limited to, commercial disputes, labor and employment matters, tax audits, alleged infringement of third parties' 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 consolidated 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 $7.2 million. As such charges are not probable at this time, a reserve has not been recorded on the consolidated balance sheet as of December 31, 2024. 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 of India by the Indian tax authority and a decision is still pending. We can provide no assurances on the impact that the 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 $7.2 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, by third parties, of infringement or misappropriation of their intellectual property rights 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.


21.   Segment Disclosure
 
We develop and globally market engineering simulation software. As defined by the accounting guidance for segment reporting, we operate as one segment. Our Chief Operating Decision Maker (CODM) is Ajei Gopal, President and Chief Executive Officer. The financial information provided to and used by the CODM assists in making operational decisions and allocating resources, such as the allocation of personnel. The annual budgeting process is the primary mechanism used to make these decisions. The financial information also helps in making performance assessments using budgeted versus actual results. The profit and loss measure reviewed by the CODM is net income. Segment disclosures, including significant segment expenses, are detailed below:
 
   
Year Ended December 31,
 
(in thousands)
 
2024
   
2023
   
2022
 
Revenue
 
$
2,544,809
   
$
2,269,949
   
$
2,065,553
 
Salaries
   
(620,815
)
   
(581,027
)
   
(511,776
)
Stock-based compensation
   
(270,900
)
   
(221,891
)
   
(168,128
)
Incentive compensation(1)
   
(219,557
)
   
(194,025
)
   
(195,524
)
Amortization
   
(112,308
)
   
(103,502
)
   
(85,094
)
Depreciation
   
(30,929
)
   
(29,002
)
   
(29,468
)
Interest income
   
51,131
     
19,588
     
5,717
 
Interest expense
   
(47,849
)
   
(47,145
)
   
(22,726
)
Other segment expenses, net(2)
   
(575,544
)
   
(520,807
)
   
(483,239
)
Income tax provision
   
(142,346
)
   
(91,726
)
   
(51,605
)
Net income
 
$
575,692
   
$
500,412
   
$
523,710
 

(1) Incentive compensation includes bonuses and commissions.
(2) Other segment expenses, net consists primarily of other headcount-related expenses, IT maintenance and software hosting costs, acquisition-related costs and consulting and professional fees.

The measure of segment assets is reported on the consolidated balance sheet as total assets. The measure of expenditures for long-lived assets is reported on the consolidated statements of cash flows as capital expenditures.