Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes ☒ No ☐

Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the registrant was required to submit such files). Yes ☒ No ☐

Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer,” “smaller reporting company,” and “emerging growth company” in Rule 12b-2 of the Exchange Act.

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to section 13(a) of the Exchange Act ☐

Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes ☐ No ☒

Indicate the number of shares outstanding of each of the issuer’s classes of common stock, as of the latest practicable date.

On October ~~21, 2019~~19, 2020, there were ~~40,473,100~~43,242,211 shares of the registrant’s Class A common stock outstanding and ~~31,300,732~~30,415,116 shares of the registrant’s Class B common stock outstanding.

		September 30, 2019			December 31, 2018				September 30, 2020			December 31, 2019
(In thousands)		(Unaudited)							(Unaudited)
ASSETS
CURRENT ASSETS:
Cash and cash equivalents		$	246,937		$	35,345			$	245,364		$	223,117
Accounts receivable, net			84,062			96,803				88,514			104,984
Income tax receivable			11,551			4,431				7,091			7,264
Prepaid expenses and other current assets			18,398			17,455				18,834			17,092
Total current assets			360,948			154,034				359,803			352,457
Property and equipment, net			33,720			30,153				34,401			36,297
Operating lease right of use assets			26,507			—				33,302			28,134
Goodwill			210,500			210,532				270,651			233,683
Other intangible assets, net			60,956			69,836				56,741			67,075
Deferred tax assets			5,870			5,354				5,631			5,791
Other long-term assets			18,199			17,288				19,174			19,708
TOTAL ASSETS		$	716,700		$	487,197			$	779,703		$	743,145
LIABILITIES, MEZZANINE EQUITY AND STOCKHOLDERS’ EQUITY	LIABILITIES, MEZZANINE EQUITY AND STOCKHOLDERS’ EQUITY							LIABILITIES, MEZZANINE EQUITY AND STOCKHOLDERS’ EQUITY
CURRENT LIABILITIES:
Current portion of long-term debt		$	437		$	331			$	430		$	430
Accounts payable			8,286			8,357				5,413			8,585
Accrued compensation and benefits			28,839			31,740				33,932			30,676
Current portion of operating lease liabilities			8,891			—				10,062			9,141
Other accrued expenses and current liabilities			27,426			27,039				25,606			28,603
Deferred revenue			69,377			59,765				74,045			75,431
Total current liabilities			143,256			127,232				149,488			152,866
Long-term debt, net of current portion			175,624			31,417				215,945			178,238
Operating lease liabilities, net of current portion			18,831			—				24,395			20,174
Deferred revenue, non-current			7,666			6,754				8,513			8,136
Other long-term liabilities			25,630			25,756				21,123			26,672
TOTAL LIABILITIES			371,007			191,159				419,464			386,086
Commitments and contingencies
MEZZANINE EQUITY			2,352			2,352				784			2,352
STOCKHOLDERS’ EQUITY:
Preferred stock ($0.0001 par value), authorized 45,000 shares, NaN issued and outstanding			—			—				—			—
Common stock ($0.0001 par value)
Class A common stock, authorized 513,797 shares, issued and outstanding 40,354 and 38,349 shares as of September 30, 2019 and December 31, 2018, respectively			4			4
Class B common stock, authorized 41,203 shares, issued and outstanding 31,391 and 32,171 shares as of September 30, 2019 and December 31, 2018, respectively			3			3
Class A common stock, authorized 513,797 shares, issued and outstanding 42,870 and 41,271 shares as of September 30, 2020 and December 31, 2019, respectively										4			4
Class B common stock, authorized 41,203 shares, issued and outstanding 30,591 and 31,131 shares as of September 30, 2020 and December 31, 2019, respectively										3			3
Additional paid-in capital			436,197			379,832				464,803			446,633
Accumulated deficit			(80,903	)		(74,863	)			(95,491	)		(82,405	)
Accumulated other comprehensive loss			(11,960	)		(11,290	)			(9,864	)		(9,528	)
TOTAL STOCKHOLDERS’ EQUITY			343,341			293,686				359,455			354,707
TOTAL LIABILITIES, MEZZANINE EQUITY AND STOCKHOLDERS’ EQUITY		$	716,700		$	487,197			$	779,703		$	743,145

	Three Months Ended September 30,						Nine Months Ended September 30,						Three Months Ended September 30,						Nine Months Ended September 30,
(in thousands, except per share data)	2019			2018			2019			2018			2020			2019			2020			2019
Revenue
License	$	46,853		$	40,880		$	180,127		$	154,515		$	55,023		$	46,853		$	183,584		$	180,127
Maintenance and other services		30,963			23,302			85,388			69,943			32,787			30,963			94,502			85,388
Total software		77,816			64,182			265,515			224,458			87,810			77,816			278,086			265,515
Software related services		7,956			8,692			25,635			26,872			6,170			7,956			18,548			25,635
Total software and related services		85,772			72,874			291,150			251,330			93,980			85,772			296,634			291,150
Client engineering services		12,803			12,155			37,265			36,652			10,868			12,803			34,386			37,265
Other		1,831			1,722			6,623			5,386			1,608			1,831			5,460			6,623
Total revenue		100,406			86,751			335,038			293,368			106,456			100,406			336,480			335,038
Cost of revenue
License		4,371			2,736			13,146			10,534			4,477			4,371			12,851			13,146
Maintenance and other services		9,548			7,095			27,509			22,202			9,626			9,548			28,583			27,509
Total software		13,919			9,831			40,655			32,736			14,103			13,919			41,434			40,655
Software related services		6,013			6,352			19,143			19,573			4,996			6,013			15,141			19,143
Total software and related services		19,932			16,183			59,798			52,309			19,099			19,932			56,575			59,798
Client engineering services		10,160			9,817			29,993			29,977			8,510			10,160			27,617			29,993
Other		1,649			1,204			5,858			3,416			1,427			1,649			4,422			5,858
Total cost of revenue		31,741			27,204			95,649			85,702			29,036			31,741			88,614			95,649
Gross profit		68,665			59,547			239,389			207,666			77,420			68,665			247,866			239,389
Operating expenses:
Research and development		29,667			24,301			87,012			71,748			30,678			29,667			91,115			87,012
Sales and marketing		25,790			19,243			78,462			57,849			26,998			25,790			80,903			78,462
General and administrative		20,706			17,234			60,886			51,636			20,905			20,706			63,499			60,886
Amortization of intangible assets		3,545			1,739			10,673			5,665			3,858			3,545			11,390			10,673
Other operating income, net		(536	)		(4,850	)		(1,702	)		(7,433	)		(1,596	)		(536	)		(3,431	)		(1,702	)
Total operating expenses		79,172			57,667			235,331			179,465			80,843			79,172			243,476			235,331
Operating (loss) income		(10,507	)		1,880			4,058			28,201			(3,423	)		(10,507	)		4,390			4,058
Interest expense		2,726			31			3,586			92			2,934			2,726			8,590			3,586
Other income, net		(588	)		(970	)		(703	)		(2,046	)		(782	)		(588	)		(1,852	)		(703	)
(Loss) income before income taxes		(12,645	)		2,819			1,175			30,155			(5,575	)		(12,645	)		(2,348	)		1,175
Income tax expense		3,294			1,885			7,215			5,617			2,930			3,294			10,350			7,215
Net (loss) income	$	(15,939	)	$	934		$	(6,040	)	$	24,538
Income per share:
Net (loss) income per share attributable to common stockholders, basic	$	(0.22	)	$	0.01		$	(0.08	)	$	0.37
Net (loss) income per share attributable to common stockholders, diluted	$	(0.22	)	$	0.01		$	(0.08	)	$	0.33
Net loss													$	(8,505	)	$	(15,939	)	$	(12,698	)	$	(6,040	)
Loss per share:
Net loss per share attributable to common stockholders, basic and diluted													$	(0.12	)	$	(0.22	)	$	(0.17	)	$	(0.08	)
Weighted average shares outstanding:
Weighted average number of shares used in computing net (loss) income per share, basic		71,770			70,001			71,313			66,429
Weighted average number of shares used in computing net (loss) income per share, diluted		71,770			76,709			71,313			74,182
Weighted average number of shares used in computing net loss per share, basic and diluted														73,311			71,770			72,979			71,313

															Accumulated																				Accumulated
	Common stock									Additional					other			Total			Common stock									Additional					other			Total
	Class A				Class B					paid-in		Accumulated			comprehensive			stockholders’			Class A				Class B					paid-in		Accumulated			comprehensive			stockholders’
(in thousands)	Shares		Amount		Shares			Amount		capital		deficit			loss			equity			Shares		Amount		Shares			Amount		capital		deficit			loss			equity
Balance at January 1, 2019		38,349	$	4		32,171		$	3	$	379,832	$	(74,863	)	$	(11,290	)	$	293,686
Balance at January 1, 2020																						41,271	$	4		31,131		$	3	$	446,633	$	(82,405	)	$	(9,528	)	$	354,707
Cumulative effect of an accounting change																						—		—		—			—		—		(388	)		—			(388	)
Net income		—		—		—			—		—		13,019			—			13,019			—		—		—			—		—		6,030			—			6,030
Exercise of stock options		397		—		—			—		458		—			—			458
Vesting of restricted stock		14		—		—			—		—		—			—			—
Stock-based compensation		—		—		—			—		869		—			—			869
Foreign currency translation, net of tax		—		—		—			—		—		—			337			337
Retirement related benefit plans, net of tax		—		—		—			—		—		—			228			228
Balance at March 31, 2019		38,760		4		32,171			3		381,159		(61,844	)		(10,725	)		308,597
Net loss		—		—		—			—		—		(3,120	)		—			(3,120	)
Equity component of convertible senior notes, net of issuance costs		—		—		—			—		50,009		—			—			50,009
Exercise of stock options		608		—		—			—		812		—			—			812			285		—		—			—		194		—			—			194
Vesting of restricted stock		34		—		—			—		—		—			—			—			143		—		—			—		—		—			—			—
Conversion from Class B to Class A common stock		270		—		(270	)		—		—		—			—			—			80		—		(80	)		—		—		—			—			—
Stock-based compensation		—		—		—			—		1,922		—			—			1,922			—		—		—			—		3,043		—			—			3,043
Foreign currency translation, net of tax		—		—		—			—		—		—			1,605			1,605			—		—		—			—		—		—			(7,578	)		(7,578	)
Retirement related benefit plans, net of tax		—		—		—			—		—		—			16			16			—		—		—			—		—		—			137			137
Balance at June 30, 2019		39,672		4		31,901			3		433,902		(64,964	)		(9,104	)		359,841
Balance at March 31, 2020																						41,779		4		31,051			3		449,870		(76,763	)		(16,969	)		356,145
Net loss		—		—		—			—		—		(15,939	)		—			(15,939	)		—		—		—			—		—		(10,223	)		—			(10,223	)
Exercise of stock options																						197		—		—			—		283		—			—			283
Vesting of restricted stock																						52		—		—			—		—		—			—			—
Conversion from Class B to Class A common stock																						80		—		(80	)		—		—		—			—			—
Stock-based compensation																						—		—		—			—		4,586		—			—			4,586
Reclassification of mezzanine equity to permanent equity																						—		—		—			—		1,568		—			—			1,568
Foreign currency translation, net of tax																						—		—		—			—		—		—			2,560			2,560
Retirement related benefit plans, net of tax																						—		—		—			—		—		—			31			31
Balance at June 30, 2020																						42,108		4		30,971			3		456,307		(86,986	)		(14,378	)		354,950
Net loss																						—		—		—			—		—		(8,505	)		—			(8,505	)
Issuance of common stock for acquisitions																						40		—		—			—		1,638		—			—			1,638
Exercise of stock options		165		—		—			—		169		—			—			169			328		—		—			—		618		—			—			618
Vesting of restricted stock		7		—		—			—		—		—			—			—			14		—		—			—		—		—			—			—
Conversion from Class B to Class A common stock		510		—		(510	)		—		—		—			—			—			380		—		(380	)		—		—		—			—			—
Stock-based compensation		—		—		—			—		2,126		—			—			2,126			—		—		—			—		6,240		—			—			6,240
Foreign currency translation, net of tax		—		—		—			—		—		—			(2,988	)		(2,988	)		—		—		—			—		—		—			4,572			4,572
Retirement related benefit plans, net of tax		—		—		—			—		—		—			132			132			—		—		—			—		—		—			(58	)		(58	)
Balance at September 30, 2019		40,354	$	4		31,391		$	3	$	436,197	$	(80,903	)	$	(11,960	)	$	343,341
Balance at September 30, 2020																						42,870	$	4		30,591		$	3	$	464,803	$	(95,491	)	$	(9,864	)	$	359,455

																	Accumulated																				Accumulated
	Common stock										Additional						other			Total			Common stock									Additional					other			Total
	Class A				Class B						paid-in			Accumulated			comprehensive			stockholders’			Class A				Class B					paid-in		Accumulated			comprehensive			stockholders’
(in thousands)	Shares		Amount		Shares			Amount			capital			deficit			loss			equity			Shares		Amount		Shares			Amount		capital		deficit			loss			equity
Balance at January 1, 2018		26,725	$	2		36,508		$	4		$	232,156		$	(168,141	)	$	(5,072	)	$	58,949
Cumulative effect of an accounting change, net of tax		—		—		—			—			—			77,744			—			77,744
Balance at January 1, 2019																								38,349	$	4		32,171		$	3	$	379,832	$	(74,863	)	$	(11,290	)	$	293,686
Net income		—		—		—			—			—			24,684			—			24,684			—		—		—			—		—		13,019			—			13,019
Adjustment for acquisitions		—		—		—			—			(96	)		—			—			(96	)
Exercise of stock options		632		1		—			—			300			—			—			301			397		—		—			—		458		—			—			458
Vesting of restricted stock																								14		—		—			—		—		—			—			—
Stock-based compensation		—		—		—			—			216			—			—			216			—		—		—			—		869		—			—			869
Foreign currency translation, net of tax		—		—		—			—			—			—			1,255			1,255			—		—		—			—		—		—			337			337
Retirement related benefit plans, net of tax		—		—		—			—			—			—			(12	)		(12	)		—		—		—			—		—		—			228			228
Balance at March 31, 2018		27,357		3		36,508			4			232,576			(65,713	)		(3,829	)		163,041
Balance at March 31, 2019																								38,760		4		32,171			3		381,159		(61,844	)		(10,725	)		308,597
Net loss		—		—		—			—			—			(1,080	)		—			(1,080	)		—		—		—			—		—		(3,120	)		—			(3,120	)
Follow-on public offering, net of offering costs of $370		5,731		1		(1,675	)		(1	)		135,201			—			—			135,201
Equity component of convertible senior notes, net of issuance costs																								—		—		—			—		50,009		—			—			50,009
Exercise of stock options		1,768		—		—			—			1,368			—			—			1,368			608		—		—			—		812		—			—			812
Vesting of restricted stock																								34		—		—			—		—		—			—			—
Conversion from Class B to Class A common stock		1,662		—		(1,662	)		—			—			—			—			—			270		—		(270	)		—		—		—			—			—
Stock-based compensation		—		—		—			—			434			—			—			434			—		—		—			—		1,922		—			—			1,922
Foreign currency translation, net of tax		—		—		—			—			—			—			(4,267	)		(4,267	)		—		—		—			—		—		—			1,605			1,605
Retirement related benefit plans, net of tax		—		—		—			—			—			—			118			118			—		—		—			—		—		—			16			16
Balance at June 30, 2018		36,518		4		33,171			3			369,579			(66,793	)		(7,978	)		294,815
Net income		—		—		—			—			—			934			—			934
Balance at June 30, 2019																								39,672		4		31,901			3		433,902		(64,964	)		(9,104	)		359,841
Net loss																								—		—		—			—		—		(15,939	)		—			(15,939	)
Exercise of stock options		602		—		—			—			260			—			—			260			165		—		—			—		169		—			—			169
Vesting of restricted stock																								7		—		—			—		—		—			—			—
Conversion from Class B to Class A common stock		1,000		—		(1,000	)		—			—			—			—			—			510		—		(510	)		—		—		—			—			—
Stock-based compensation		—		—		—			—			563			—			—			563			—		—		—			—		2,126		—			—			2,126
Foreign currency translation, net of tax		—		—		—			—			—			—			(1,149	)		(1,149	)		—		—		—			—		—		—			(2,988	)		(2,988	)
Retirement related benefit plans, net of tax		—		—		—			—			—			—			36			36			—		—		—			—		—		—			132			132
Balance at September 30, 2018		38,120	$	4		32,171		$	3		$	370,402		$	(65,859	)	$	(9,091	)	$	295,459
Balance at September 30, 2019																								40,354	$	4		31,391		$	3	$	436,197	$	(80,903	)	$	(11,960	)	$	343,341

	Nine Months Ended September 30,						Nine Months Ended September 30,
(In thousands)	2019			2018			2020			2019
OPERATING ACTIVITIES:
Net (loss) income	$	(6,040	)	$	24,538
Adjustments to reconcile net (loss) income to net cash provided by operating activities:
Net loss							$	(12,698	)	$	(6,040	)
Adjustments to reconcile net loss to net cash provided by operating activities:
Depreciation and amortization		15,836			10,895			16,916			15,836
Provision for bad debt		472			455
Provision for credit loss								930			472
Amortization of debt discount and issuance costs		3,044			18			8,067			3,044
Stock-based compensation expense		5,584			1,213			13,939			5,584
Gain on sale of assets held for sale and other		—			(4,544	)
Impairment of intangibles		—			608
Deferred income taxes		(741	)		706			(5,441	)		(741	)
Other, net		(16	)		(134	)		13			(16	)
Changes in assets and liabilities:
Accounts receivable		10,185			15,674			16,213			10,185
Prepaid expenses and other current assets		(8,718	)		(6,821	)		(1,055	)		(8,718	)
Other long-term assets		(1,443	)		44			867			(1,443	)
Accounts payable		(420	)		796			(3,321	)		(420	)
Accrued compensation and benefits		(2,111	)		2,650			1,274			(2,111	)
Other accrued expenses and current liabilities		2,110			(4,781	)		(5,847	)		2,110
Operating lease right-of-use assets and liabilities, net		188			—			(26	)		188
Deferred revenue		12,075			(895	)		(2,452	)		12,075
Net cash provided by operating activities		30,005			40,422			27,379			30,005
INVESTING ACTIVITIES:
Payments for acquisition of businesses, net of cash acquired								(32,279	)		(709	)
Capital expenditures		(8,120	)		(5,333	)		(4,006	)		(8,120	)
Payments for acquisition of developed technology		(473	)		(2,738	)		(433	)		(473	)
Payments for acquisition of businesses, net of cash acquired		(709	)		(15,950	)
Proceeds from the sale of assets held for sale and other		—			6,613
Other investing activities, net		16			—			152			16
Net cash used in investing activities		(9,286	)		(17,408	)		(36,566	)		(9,286	)
FINANCING ACTIVITIES:
Borrowings under revolving commitment								30,000			96,991
Proceeds from the exercise of stock options								1,094			1,441
Proceeds from issuance of convertible senior notes, net of underwriters' discount and commissions		223,101			—			—			223,101
Payments on revolving commitment		(127,941	)		—			—			(127,941	)
Borrowings under revolving commitment		96,991			—
Proceeds from the exercise of stock options		1,441			1,929
Payments for issuance costs of convertible senior notes		(1,233	)		—			—			(1,233	)
Payments for follow-on public offering and initial public offering costs		—			(541	)
Proceeds from issuance of Class A common stock in follow-on public offering, net of underwriters' discounts and commissions		—			135,572
Other financing activities		(399	)		(446	)		(401	)		(399	)
Net cash provided by financing activities		191,960			136,514			30,693			191,960
Effect of exchange rate changes on cash, cash equivalents and restricted cash		(1,065	)		(1,354	)		676			(1,065	)
Net increase in cash, cash equivalents and restricted cash		211,614			158,174			22,182			211,614
Cash, cash equivalents and restricted cash at beginning of year		35,685			39,578			223,497			35,685
Cash, cash equivalents and restricted cash at end of period	$	247,299		$	197,752		$	245,679		$	247,299
Supplemental disclosure of cash flow:
Interest paid	$	385		$	70		$	320		$	385
Income taxes paid	$	7,163		$	5,900		$	12,142		$	7,163
Supplemental disclosure of non-cash investing and financing activities:
Issuance of common stock in connection with acquisitions							$	1,638		$	—
Finance leases	$	588		$	995		$	117		$	588
Property and equipment in accounts payable, other current liabilities and other liabilities	$	1,827		$	228		$	208		$	1,827
Follow-on public offering costs in accounts payable	$	—		$	15
Promissory notes issued and deferred payment obligations for acquisitions	$	—		$	278

Altair Engineering Inc. (“Altair” or the “Company”) is incorporated in the state of Delaware. The Company is a global technology company providing software and cloud solutions in the areas of ~~product design~~simulation, data analytics, and ~~development, high performance~~high-performance computing ~~and data intelligence.~~(HPC). Altair enables organizations across broad industry segments to compete more effectively in a connected world while creating a more sustainable future. The Company is headquartered in Troy, Michigan.

In connection with the preparation of its financial statements for the quarter ended June 30, 2019, the Company identified and corrected certain errors that were immaterial to previously-reported consolidated financial statements. No such adjustments are necessary for the quarter ended September 30, 2019, nor does the Company anticipate any further adjustments based on these errors. These historical errors related primarily to i) the cumulative effective adjustment for the income tax effect of intercompany transactions resulting from the adoption of Accounting Standards Codification (“ASC”) No. 606, ~~Revenue from Contracts with Customers~~ (ASC 606) on January 1, 2018, and ii) income tax accounting for acquisitions. The Company evaluated the materiality of these errors both qualitatively and quantitatively in accordance with Staff Accounting Bulletin (“SAB”) No. 99, ~~Materiality, and SAB No. 108,~~ ~~Considering the Effects of Prior Year Misstatements When Quantifying Misstatements in Current Year Financial Statements~~, and determined the effect of these corrections were not material to the previously issued financial statements. However, the effect of correcting these errors in the current period would be material to the current period financial statements. Therefore, the amounts in the previous periods have been revised to reflect the correction of these errors. These revisions do not impact amounts previously reported in the consolidated statements of operations for the three months ended March 31, 2019 and 2018, the three and six months ended June 30, 2018, the three and nine months ended September 30, 2018, or for total operating, investing, or financing activities on the consolidated statements of cash flows for any previously reported period.

~~The following table presents the effect of the error corrections on the Company’s consolidated balance sheet for the period indicated (in thousands):~~

The adjustments for amounts similar to the above were also made to the Company’s consolidated balance sheets as of March 31, 2018, June 30, 2018, September 30, 2018, and March 31, 2019, respectively.Additionally, the Company revised goodwill, total assets, and total liabilities, mezzanine equity and stockholders’ equity on the consolidated balance sheet as of December 31, 2017, to correct these errors, resulting in a decrease of $1.6 million from the previously reported amounts. The consolidated statements of changes in stockholders’ equity (deficit) for the three month periods ended March 31, 2018 and 2019 have been corrected to reflect the adjustments described herein.

~~The following tables present the effect of the error corrections on the consolidated statements of operations for the periods indicated (in thousands, except per share data):~~

Additionally, the Company revised income tax expense, net income, and net income per share attributable to common stockholders (basic and diluted) on the consolidated statement of operations for the year ended December 31, 2016, to correct these errors, resulting in an increase of $0.2 million, a decrease of $0.2 million and a decrease of $0.01, respectively, from the previously reported amounts.

The accompanying unaudited consolidated financial statements have been prepared in accordance with United States generally accepted accounting principles (“GAAP”) and applicable rules and regulations of the Securities and Exchange Commission (“SEC”) regarding interim financial information. Accordingly, the accompanying statements do not include all the information and notes required by GAAP for complete financial statements. The accompanying unaudited consolidated financial statements should be read in conjunction with the Company’s audited consolidated financial statements (and notes thereto) for the year ended December 31, ~~2018,~~2019, included in the most recent Annual Report on Form 10-K filed with the SEC. In the opinion of management, all adjustments considered necessary for a fair presentation of the financial statements have been included, and all adjustments are of a normal and recurring nature. The preparation of the financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities, and disclosures of contingent assets and liabilities at the date of the financial statements and reported amounts of revenue and expenses during the reporting periods. Considerable judgment is often involved in making these determinations; use of different assumptions could result in significantly different results. Management believes its assumptions and estimates are reasonable and appropriate. However, actual results may differ from those estimates. In addition, the results of operations for the three and nine months ended September 30, ~~2019,~~2020, are not necessarily indicative of the results that may be expected for any future period.

~~The Company adopted Accounting Standards Update (“ASU”) No. 2016-02,~~ ~~Leases (Topic 842),~~ and its related amendments, on January 1, 2019. See Note 3 – Recent accounting guidance and Note 9 – Leases for additional information. There have been no other material changes to Altair’s significant accounting policies as compared to the significant accounting policies described in the Company’s Annual Report on Form 10-K for the year ended December 31, 2018.

In the fourth quarter of fiscal 2018, the Company adopted ASC 606 effective on January 1, 2018, using the modified retrospective approach for all contracts not completed as of the date of adoption. Results for the three and nine months ended September 30, 2018, have been modified to reflect the adoption of ASC 606 on January 1, 2018.

~~The Company recorded a decrease to accumulated deficit of $84.6 million, or $77.7 million net of tax, on January 1, 2018,~~ due to the cumulative effect of the ASC 606 adoption, with the impact primarily derived from revenue related to software licenses recognized at a point in time under ASC 606 that were historically recognized over time. There was no impact on Client Engineering Services or Other revenue upon the adoption of ASC 606.

~~The Company has concluded that all material transactions that have occurred that require disclosure or adjustments to the consolidated financial statements have been reported herein.~~

Certain prior period amounts included in the 2018 consolidated statement of operations, consolidated balance sheet and consolidated statement of cash flows have been reclassified to conform to the current year presentation.

The preparation of the consolidated financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosures of contingent assets and liabilities at the date of the financial statements and reported amounts of revenue and expenses during the reporting periods. On an ongoing basis, management evaluates its significant estimates including the stand alone selling price, or SSP, for each distinct performance obligation included in customer contracts with multiple performance obligations, valuation of acquired intangible assets in business combinations, the incremental borrowing rate used in the valuation of lease liabilities, the determination of the period of benefit for capitalized costs to obtain a contract, fair value of convertible senior notes, provision for ~~doubtful accounts,~~credit loss, tax valuation allowances, liabilities for uncertain tax provisions, impairment of goodwill and intangible assets, retirement obligations, useful lives of intangible assets, revenue for fixed price contracts, ~~valuation of common stock,~~ and stock-based compensation. Actual results could differ from those estimates.

In March 2020, The World Health Organization declared the outbreak of COVID-19 a pandemic, and a public health emergency of international concern. The global spread of COVID-19 created significant volatility and uncertainty. Such conditions are expected to continue. To limit the spread of COVID-19, governments have taken various actions, from time to time, including the issuance of travel restrictions, complete or partial prohibitions of non-essential activities, restrictions or shutdowns of non-essential businesses, stay-at-home orders, and social distancing guidelines. Some of these actions have varied from initial responses, pivoting between full or complete to partial or limited restrictions depending upon local or regional conditions. Accordingly, many businesses have adjusted to these actions by reducing or suspending operating or other activities. This has negatively impacted several of the markets the Company serves, including the automotive and aerospace markets.

The Company continues to robustly engage with its customers, primarily virtually. While the Company believes this active level of engagement may mitigate potential and evolving negative impacts from COVID-19, existing and potential customers may choose to reduce or delay technology spending in response to COVID-19, or attempt to renegotiate contracts and obtain concessions, which may materially and negatively impact the Company’s operating results, financial condition and new business. In certain cases, the Company has provided longer than normal payment terms to certain of its customers; however, the terms are less than one year, and the Company does not expect this to materially affect its consolidated financial statements. COVID-19’s

impact on some of the Company’s customers has primarily contributed to the decrease in revenue for software related and client engineering services. The Company’s software product revenue has been affected by elongated sales cycles for some of its customers along with greater challenges in securing new and expansion business. The Company is unable to accurately predict the full impact that COVID-19 will have due to numerous uncertainties, including the full scope of the disease, the duration of the initial outbreak or the number and intensity of subsequent waves of infections, actions that may be taken by governmental authorities, the impact to the businesses of the Company’s customers and partners, and the development of treatments and vaccines. Even after the COVID-19 pandemic subsides, the Company may experience material adverse impacts to its business as a result of any economic recession or depression that has occurred or may occur in the future. The Company will continue to evaluate the nature and extent of the impact to its business, consolidated results of operations, and financial condition.

The Company considers all highly liquid investments with original or remaining maturities of 90 days or less at the date of purchase to be cash equivalents. Cash and cash equivalents are recorded at cost, which approximates fair value.

Restricted cash is included in other long-term assets on the consolidated balance sheets. The following table provides a reconciliation of cash, cash equivalents and restricted cash reported in the consolidated balance ~~sheet~~sheets that sum to the total of the amounts reported in the consolidated statement of cash flows (in thousands):

	September 30, 2019		December 31, 2018		September 30, 2020		December 31, 2019
Cash and cash equivalents	$	246,937	$	35,345	$	245,364	$	223,117
Restricted cash included in other long-term assets		362		340		315		380
Total cash, cash equivalents, and restricted cash	$	247,299	$	35,685	$	245,679	$	223,497

Restricted cash represents amounts required for a contractual agreement with an insurer for the payment of potential health insurance claims, and term deposits for bank guarantees.

Inventory was $3.4 million and $2.0 million at September 30, 2019 and December 31, 2018, respectively, and is included in prepaid expenses and other current assets in the consolidated balance sheets. Inventory consistconsists of finished goods and is stated at the lower of cost and net realizable value. Cost is determined using the first-in, first-out method. Net realizable value is the estimated selling prices in the ordinary course of business, less reasonable predictable costs of completion, disposal, and transportation. The valuation of inventory requires management to estimate excess inventory as well as inventory that is not of saleable quality. The determination of obsolete or excess inventory requires management to estimate market conditions and future demand for the Company’s products. Inventory was $2.7 million and $2.4 million at September 30, 2020 and December 31, 2019, respectively, and is included in prepaid expenses and other current assets in the consolidated balance sheets.

The French government provides a research and development (“R&D”) tax credit known as Credit Impôt Recherche, or CIR, in order to encourage Companies to invest in R&D activities. The tax credit is deductible from French income tax and any excess is carried forward three years. After three years, any unused credit may be reimbursed to the Company by the French government. As of September 30, ~~2019,~~2020, the Company had approximately ~~$11.1~~$12.6 million ~~receivable~~of receivables from the French government related to CIR, of which ~~$2.4~~$3.1 million was recorded in income tax receivable and the remaining ~~$8.7~~$9.5 million was recorded in other long-term assets. As of December 31, ~~2018,~~2019, the Company had approximately ~~$11.7~~$12.1 million ~~receivable~~of receivables from the French government related to CIR, of which ~~$2.6~~$2.5 million was recorded in income tax receivable and the remaining ~~$9.1~~$9.6 million was recorded in other long-term assets. CIR is subject to customary audit by French tax authorities.

In 2017, the Company issued 200,000 shares of Class A common stock to a third party as partial consideration for the purchase of developed technology. These shares have a put right that can be exercised by the holder five years from date of purchase at $12.50 per share that requires the shares to be recorded at fair value at the issuance date and classified as mezzanine equity in the consolidated balance sheet. The put right option is terminated if the shareholders sell their shares. As of December 31, 2017, the Company concluded that it is no longer probable that the put option will be exercised as the put value is substantially below market value and subsequent adjustment is not required.

During the quarter ended June 30, 2020, the third party holder sold 133,336 shares on the open market and as a result, the issuance value of ~~the of instrument shall remain~~those shares was reclassified into permanent equity from mezzanine equity. The remaining 66,664 shares continue to be classified as mezzanine equity until one of the following three events take place: (1) the shares are sold on the open market; (2) a redemption feature lapses; or (3) there is a modification of the terms of the instrument. ~~As none of these events have taken place as of September 30, 2019, the classification remains as mezzanine equity.~~

The Company determines if an arrangement is a lease at inception. Operating leases are included in operating lease right-of-use (“ROU”) assets, current portion of operating lease liabilities, and operating lease liabilities, net of current portion on the Company’s consolidated balance sheets. Finance leases are included in property and equipment, current portion of long-term debt, and long-term debt, net of current portion on the consolidated balance sheets. The Company did not receive any lease concessions related to COVID-19 that had a material effect on the Company’s consolidated financial statements.

~~Basic (loss)~~Other income, per share attributable to common stockholders is computed using the weighted average number of shares of common stock outstanding for the period, excluding stock options and restricted stock units (“RSUs”). Diluted (loss) income per share attributable to common stockholders is based upon the weighted average number of shares of common stock outstanding for the period and potentially dilutive common shares, including the effect of stock options and RSUs under the treasury stock method. The following table sets forth the computationnet consists of the ~~numerators and denominators used in the basic and diluted (loss) income per share amounts~~following (in ~~thousands, except per share data)~~thousands):

The computation of diluted (loss) income per share does not include shares that are anti-dilutive under the treasury stock method because their exercise prices are higher than the average fair value of the Company’s stock during the period or due to a net loss in the period. For the three and nine months ended September 30, 2019, respectively, there were 5.3 million and 5.8 million anti-dilutive stock options excluded from the computation of (loss) income per share. For the three and nine months ended September 30, 2018, there were 0 anti-dilutive shares excluded from the computation of (loss) income per share.

The Company expects to settle the principal amount of the Convertible Notes (as defined in Note 8) in cash, and therefore, the Company uses the treasury stock method for calculating any potential dilutive effect of the Conversion Option (as defined in Note 8) on diluted net (loss) income per share, if applicable. The Conversion Option will have a dilutive impact on net income per share of common stock when the average market price of the Company’s Class A common stock for a given period exceeds the conversion price of the Convertible Notes of $46.50 per share. During the three and nine months ended September 30, 2019, the Company's weighted average common stock price was below the conversion price of the Convertible Notes.

~~Leases~~ ~~—In February 2016, the Financial Accounting Standard Board, or “FASB”, issued Accounting Standards Update, or “ASU”, No. 2016-02,~~ ~~Leases (ASC 842)~~. This standard amends various aspects of existing accounting guidance for leases, including the recognition of a right-of-use (ROU) asset and a lease liability on the balance sheet for all leases with terms longer than 12 months. The Company adopted ASU 2016-02 and its related amendments, on January 1, 2019 and elected the optional transition method and the package of practical expedients on adoption. Accordingly, the prior period comparative information has not been restated and continues to be reported under the accounting guidance in effect for those periods, including the disclosure requirements. The most significant impact of the adoption of ASC 842 was the recognition of ROU assets and lease liabilities for operating leases on the Company’s consolidated balance sheet. On adoption, the Company recognized operating liabilities associated with leases of $30.1 million and corresponding ROU assets of $29.1 million, based on the present value of the remaining minimum rental payments under current leasing standards for existing operating leases. See Note 9 – Leases for further discussion. The Company’s accounting for finance leases~~(previously referred to as capital leases prior to the adoption of ASC 842) remained~~ ~~substantially unchanged. The standard had no impact on the Company’s consolidated net income or cash flows.~~

~~Derivatives and Hedging~~ – ~~In August 2017, the FASB issued ASU 2017-12,~~ ~~Derivatives and Hedging (Topic 815): Targeted Improvements to Accounting for Hedging Activities.~~ This ASU amends the guidance with the objective of improving the financial reporting of hedging relationships to better portray the economic results of an entity’s risk management activities in its financial statements. In addition, this ASU amends the current guidance to simplify the application of the hedge accounting guidance. The Company adopted ASU 2017-12 on January 1, 2019. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

~~Comprehensive Income~~ ~~– In February 2018, the FASB issued ASU 2018-02,~~ ~~Income Statement — Reporting Comprehensive Income (Topic 220): Reclassification of Certain Tax Effects from Accumulated Other Comprehensive Income (AOCI)~~, which gives entities the option to reclassify to retained earnings the tax effects resulting from the Tax Cuts and Jobs Act, or the “Tax Act”, related to items in AOCI that the FASB refers to as having been stranded in AOCI. The Company adopted this guidance on January 1, 2019 and elected not to reclassify amounts stranded in AOCI. ~~The Company reclassifies taxes from AOCI to earnings as the items to which the tax effects relate are similarly reclassified.~~ ~~The adoption of ASU 2018-02 did not have a material effect on the Company’s consolidated financial statements.~~

~~Stock Compensation~~ ~~– In June 2018, the FASB issued ASU 2018-07,~~ ~~Compensation – Stock Compensation (Topic 718): Improvements to Nonemployee Share-Based Payment Accounting.~~ This ASU simplifies the accounting for share-based payments to nonemployees by aligning it with the accounting for share-based payments to employees, with certain exceptions. The Company adopted this guidance on January 1, 2019, which did not have a material effect on the Company’s consolidated financial statements.

Credit Losses – In June 2016, the FASB issued ASU 2016-13, Financial Instruments — Credit Losses (Topic 326): Measurement of Credit Losses on Financial ~~Instruments.~~Instruments. The ASU significantly ~~changes~~changed how entities ~~will~~ measure credit losses on most financial assets. ~~This guidance is effective for annual periods beginning after December 15, 2019, and interim periods therein; early adoption is permitted.~~ The Company adopted ASU 2016-13 effective January 1, 2020 and recorded a cumulative effect adjustment to retained earnings of $0.4 million related to the adoption of ASU 2016-13; prior periods have not been adjusted. Under this new accounting standard, beginning January 1, 2020, a provision for expected credit losses for groups of billed and unbilled receivables and contract assets that share similar risk characteristics is ~~currently evaluating~~recorded based on an evaluation of historical loss experience, current conditions, and reasonable and supportable forecasts. Accounts are written off when it becomes apparent that such amounts will not be collected, generally when amounts are past due by greater than one year. Generally, the Company does not require collateral or charge interest on accounts receivable. Accounts receivable were reported net of a provision for credit loss of $2.8 million and $1.4 million at September 30, 2020 and December 31, 2019, respectively.

The change in the provision for credit loss was driven by the $0.4 million from the adoption of ASU 2016-13 and incremental losses in the current year including an immaterial impact of ~~this new guidance on its consolidated financial statements and related disclosures and does~~COVID-19 as the Company made an adjustment to increase expected credit loss rates subsequent to the adoption. The impact resulting from the increased credit loss rates did not ~~expect this guidance to~~ have a material effect on ~~its consolidated financial statements.~~

~~Goodwill Impairment~~ ~~—In January 2017, the FASB issued ASU No. 2017-04,~~ ~~Intangibles – Goodwill and Other (Topic 350): Simplifying the Test for Goodwill Impairment~~, which simplifies accounting for goodwill impairments by eliminating step two from the goodwill impairment test. This guidance is effective for annual or interim goodwill impairment tests in fiscal years beginning after December 15, 2019. Early adoption is permitted for interim and annual goodwill impairment tests performed on testing dates after January 1, 2017. The new standard must be applied on a prospective basis. The adoption of this guidance is not expected to have a material impact on the Company’s consolidated financial ~~statements.~~statements, and is reflected in the amounts noted above.

Fair Value – In August 2018, the FASB issued ASU 2018-13, Fair Value Measurement (Topic 820): Disclosure Framework – Changes to the Disclosure Requirements for Fair Value Measurement. This ASU modifies the disclosure requirements for fair value measurements, by removing, modifying, or adding certain disclosures. The Company adopted ASU 2018-13 on January 1, 2020. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

Intangibles – In August 2018, the FASB issued ASU 2018-15, Intangibles – Goodwill and Other – Internal-Use Software (Subtopic 350-40): Customer’s Accounting for Implementation Costs Incurred in a Cloud Computing Arrangement That is a Service Contract. This ASU clarifies and aligns the requirements for capitalizing implementation costs incurred in a hosting arrangement that is a service contract with the requirements for capitalizing implementation costs incurred to develop or obtain internal-use software. The Company adopted ASU 2018-15 on January 1, 2020, on a prospective basis. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

Retirement Benefits – In August 2018, the FASB issued ASU 2018-14, Compensation – Retirement Benefits- Defined Benefit Plans – General (Subtopic 715-20): Disclosure Framework – Changes to the Disclosure Requirements for Defined Benefit Plans. This ASU modifies the disclosure requirements for defined benefit pension or other postretirement plans. The amendments are effective for fiscal years ending after December 15, 2020; early adoption is permitted. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and related disclosures and does not expect this guidance to have a material effect on its consolidated financial statements.

Income Taxes – In December 2019, the FASB issued ASU 2019-12, Income Taxes (Topic 740): Simplifying the Accounting for Income Taxes. This ASU simplifies the accounting for income taxes by removing certain exceptions to the general principles in Topic 740 and improves consistent application of GAAP for other areas of Topic 740 by clarifying and amending existing guidance. The amendments are effective for fiscal years, and interim ~~reporting~~ periods within those fiscal years, beginning after December 15, ~~2019. Early~~2020; early adoption is ~~permitted for any removed or modified disclosures.~~ permitted. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and related disclosures and does not expect this guidance to have a material effect on its consolidated financial statements.

~~Retirement Benefits~~Reference Rate Reform – In ~~August 2018,~~March 2020, the FASB issued ASU ~~2018-14,~~2020-04. Reference Rate Reform (Topic 848) - ~~Compensation – Retirement Benefits- Defined Benefit Plans – General (Subtopic 715-20): Disclosure Framework – Changes to~~Facilitation of the ~~Disclosure Requirements for Defined Benefit Plans.~~ Effects of Reference Rate Reform on Financial Reporting. This ASU ~~modifies~~provides optional expedients and exceptions for applying U.S. GAAP to contract modifications and hedging relationships, subject to meeting certain criteria, that reference LIBOR or another rate that is expected to be discontinued. The amendments in the ~~disclosure requirements for defined benefit pension or other postretirement plans. The amendments~~guidance are optional and effective for ~~fiscal years ending after~~all entities as of March 12, 2020 through December ~~15, 2020; early adoption~~31, 2022. The Company is ~~permitted. The adoption~~ currently evaluating the impact of this new guidance ison its consolidated financial statements and related disclosures and does not ~~expected~~expect this guidance to have a material ~~impact~~effect on ~~the Company’s~~its consolidated financial statements.

~~Intangibles~~Debt – In August ~~2018,~~2020, the FASB issued ASU ~~2018-15,~~No. 2020-06, ~~Intangibles~~Debt – ~~Goodwill~~Debt with Conversion and Other Options (Subtopic 470-20) and Derivatives and Hedging – ~~Internal-Use Software~~Contracts in Entity’s Own Equity (Subtopic ~~350-40): Customer’s Accounting for Implementation Costs Incurred in a Cloud Computing Arrangement That is a Service Contract.~~ 815-40).This ASU ~~clarifies~~simplifies the accounting for convertible instruments by eliminating certain separation models. Under ASU 2020-06, a convertible debt instrument will generally be reported as a single liability at its amortized cost with no separate accounting for embedded conversion features. The update also requires the if-converted method to be used for convertible instruments and ~~aligns~~ the ~~requirements for capitalizing implementation costs incurred~~effect of potential share settlement be included in ~~a hosting arrangement that is a service contract with~~ the ~~requirements for capitalizing implementation costs incurred to develop~~diluted earnings per share calculation when an instrument may be settled in cash or ~~obtain internal-use software.~~shares. The amendments in this update are effective for fiscal years beginning after December 15, ~~2019,~~2021, and interim periods within those fiscal ~~years; early~~years. The guidance allows entities to use a modified or full retrospective transition method. Early adoption is ~~permitted.~~ permitted, but no earlier than fiscal years beginning after December 15, 2020, including interim periods within those fiscal years. The Company is currently evaluating the ~~impact~~timing and method of adoption and the related effect of the new guidance on its consolidated financial statements and ~~related disclosures.~~earnings per share attributable to common stockholders.

Revenue is derived principally from the licensing of software products and from related maintenance contracts. The Company enters 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 term-based software licenses is classified as software revenue. Term-based licenses are sold only as a bundled arrangement that includes the rights to a ~~term~~term-based software license and post-contract customer support (PCS), which includes unspecified technical enhancements and customer support. Maximizing the use of observable inputs, the Company determined that a majority of the estimated standalone selling prices of the term-based license is attributable to the ~~term~~term-based license and a minority is attributable to the PCS. The license component is classified as license revenue and recognized as revenue upon the later of delivery of the licensed product or the beginning of the license period. PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company provides the PCS benefit over time as a stand ready to perform obligation.

In addition to term-based software licenses, the Company sells perpetual licenses. Software revenue is recognized upon the later of delivery of the licensed product or the beginning of the license period. Typically, the Company’s perpetual licenses are sold with PCS. The Company allocates value in bundled perpetual and PCS arrangements based on the value relationship between the software license and maintenance. Revenue from PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company satisfies the PCS performance obligation over time as a stand ready to perform obligation.

Revenue from training, consulting and other services is recognized as the services are performed, and is classified as maintenance and other services in the consolidated statement of operations. For contracts in which the service consists of a single performance obligation, such as providing a training class to a customer, the Company recognizes revenue upon completion of the performance obligation. For service contracts that are longer in duration and often include multiple performance obligations (for example, point-in-time training and consulting), the Company measures the progress toward completion of the obligations and recognizes revenue accordingly. In measuring progress towards the completion of performance obligations, the Company typically utilizes output-based estimates for services with fixed fee arrangements, and estimates output based on the total tasks completed as compared to the total tasks required for each 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.

The Company also executes arrangements through indirect channel partners in which the channel partners are authorized to market and distribute the Company's software products to end users of the Company's products and services in specified territories. In sales facilitated by channel partners, the channel partner bears the risk of collection from the end-user customer. The Company recognizes revenue from transactions with channel partners when the channel partner submits a purchase commitment, collectability from the channel partner is probable, and the performance obligation is met, at a point in time or over time as appropriate, provided that all other revenue recognition criteria are satisfied. Revenue from channel partner transactions is the amount remitted to the Company 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. The Company does not offer right of return, product rotation, or price protection to any of its channel partners.

Non-income related taxes collected from customers and remitted to governmental authorities are recorded on the consolidated balance ~~sheet~~sheets as accounts receivable, net and other accrued expenses and current liabilities. These amounts are reported on a net basis in the consolidated statements of operations and do not impact reported revenues or expenses. Certain hardware revenue is included within software revenue and is recognized when all revenue recognition criteria stated above are met, which is generally when the products are delivered to end customers.

The Company’s 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 within the context of the arrangement, and if so, the allocation of the transaction price to each performance obligation. The Company’s determination of standalone selling price for performance obligations is based on the midpoint of the range of historical observable prices for goods and services sold separately. In addition, the Company estimates the standalone selling price for certain performance obligations where observable prices are not directly available, or a significant portion of historical prices are not within the range. In instances where standalone selling price was not determined based on the range of historical observable prices for goods and services sold separately, the Company used an adjusted market assessment approach to estimate the standalone selling price. In such cases the Company has considered market conditions and other observable inputs, such as internal price lists, peer data, and industry data for a similar or identical product. The Company estimates standalone selling price at contract inception considering all information that is reasonably available and is based on the amount of consideration for which the Company expects to be entitled in exchange for transferring the promised good or service to the customer. The corresponding revenues are recognized as the related performance obligations are satisfied.

The Company’s contracts do not include a significant financing component requiring adjustment to the transaction price. Payment terms vary by contract type; however, arrangements typically stipulate a requirement for the customer to pay within 30 to 60 days.

The Company rarely enters into agreements to modify previously executed contracts, which constitute contract modifications. The Company assesses each of these contract modifications to determine (i) if the additional products and services are distinct from the products and services in the original arrangement; and (ii) if the amount of consideration expected for the added products and services reflects the stand-alone selling price of those products and services, as adjusted for contract-specific circumstances. A contract modification meeting both criteria is accounted for as a separate contract. A contract modification not meeting both criteria is considered a change to the original contract and is accounted for on either (i) a prospective basis as a termination of the existing contract and the creation of a new contract; or (ii) a cumulative catch-up basis. Generally, the Company’s contract modifications meet both criteria and are accounted for as a separate contract, as adjusted for contract-specific circumstances.

Consulting services from product design and development projects are considered distinct performance obligations and are provided to customers on a time-and-materials (“T&M”) or fixed-price basis. ~~Altair~~The Company recognizes software services revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. Revenue from fixed-price engagements is recognized using the output method based on the ratio of costs incurred, to the total estimated project costs.

Client engineering services revenue are derived from professional services for staffing primarily representing engineers and data scientists located at a customer site. These professional services are considered distinct performance obligations and are provided to customers on a T&M basis. The Company recognizes this revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. No significant judgments were made for revenue recognition within Other revenue.

The Company disaggregates its software revenue by type of performance obligation and timing of revenue recognition as follows (in thousands):

	Three Months Ended September 30,				Nine Months Ended September 30,				Three Months Ended September 30,				Nine Months Ended September 30,
	2019		2018		2019		2018		2020		2019		2020		2019
Software revenue:
Term licenses	$	38,794	$	32,688	$	149,825	$	128,560	$	47,386	$	38,794	$	160,027	$	149,825
Perpetual licenses		8,059		8,192		30,302		25,955		7,637		8,059		23,557		30,302
Maintenance		26,898		21,588		74,983		63,285		29,374		26,898		86,467		74,983
Professional services and other		4,065		1,714		10,405		6,658		3,413		4,065		8,035		10,405
Total software revenue	$	77,816	$	64,182	$	265,515	$	224,458	$	87,810	$	77,816	$	278,086	$	265,515

The Company derived approximately 10% of its total revenue through indirect sales channels for the nine months ended September 30, ~~2019~~2020 and ~~2018.~~2019.

Software related services revenue, client engineering services revenue, and other revenue were categorized based on the nature and timing of revenue and cash flows.

The Company pays commissions for new software product and PCS sales as well as for renewals of existing software and PCS contracts. Commissions paid to obtain renewal contracts are not commensurate with the commissions paid for new product sales and therefore, a portion of the commissions paid for new contracts relate to future renewals.

The Company accounts for new product sales commissions using a portfolio approach and allocates the cost of commissions in proportion to the allocation of transaction price of license and PCS performance obligations. Commissions allocated to the license and license renewal components are expensed at the time the license revenue is recognized. Commissions allocated to PCS are capitalized and amortized on a straight-line basis over a period of four years, reflecting the Company’s estimate of the expected period that it will benefit from those commissions. As of September 30, ~~2019~~2020, and December 31, ~~2018,~~2019, capitalized costs to obtain a contract were ~~$2.2~~$2.7 million and ~~$2.0~~$2.3 million, respectively, recorded in prepaid and other current assets, and ~~$0.7~~$0.6 million and ~~$0.2~~$0.8 million, respectively, recorded in other long-term assets. Amortization expense was ~~$1.1 million, $1.1 million, $3.3~~$2.0 million and ~~$3.0~~$3.6 million for the three and nine months ended September 30, ~~2019~~2020, respectively, and ~~2018~~$1.1 million and $3.3 million for the three and nine months ended September 30, 2019, ~~and 2018, respectively, and~~respectively. Amortization expense was included in sales and marketing expense in the Company’s consolidated statement of operations.

At September 30, ~~2019~~2020 and December 31, ~~2018,~~2019, contract assets were ~~$6.0~~$6.7 million and ~~$3.7~~$4.5 million, respectively, recorded in accounts receivable, and ~~$3.8~~$2.4 million and $2.7 million, respectively, recorded in prepaid expenses and other current assets.

Deferred revenue consists of billings made or payments received in advance of revenue recognition from software license, PCS and professional services 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 term between invoicing and when payment is due is not significant. The Company generally invoices its customers annually for the forthcoming year of software licenses, and more frequently for other products and services. Accordingly, the Company’s deferred revenue balance does not include revenue for future years of multiple year non-cancellable contracts that have not yet been billed.

Approximately ~~$53.7~~$66.9 million of revenue recognized during the nine months ended September 30, ~~2019,~~2020, was included in the deferred revenue balances at the beginning of the year. Revenue allocated to remaining performance obligations represents contracted revenue that has not yet been recognized, which includes deferred revenue and amounts that will be invoiced and recognized as revenue in future periods. Contracted revenue not yet recognized was $120.3 million as of September 30, 2020, of which the Company expects to recognize approximately 80% of the revenue over the next 12 months and the remainder thereafter.

In ~~July 2019,~~September 2020, the Company decided to sunset operations of its WEYV business, a consumer music and content service. The Company concluded that this decision was not a strategic shift that has or will have a major effect on its operations and financial results, and therefore did not meet the accounting criteria to be classified as a discontinued operation.

The operations of WEYV terminated in the third quarter of 2019. The loss on disposal was not material, and is included in other operating income in the consolidated statement of operations. WEYV had a loss before income tax of $0.4 million, $3.0 million, $0.9 million and $4.0 million for the three and nine months ended September 30, 2019 and 2018, respectively. The WEYV business is reported in All Other within the Company’s segment information in Note 17.

On November 5, 2018, the Company entered into an Agreement and Plan of Merger (“Merger Agreement”) with Datawatch Corporation, a Delaware corporation (“Datawatch”), and Dallas Merger Sub, Inc., a Delaware corporation (“Purchaser”) and a wholly owned subsidiary of the Company.~~Pursuant to the Merger Agreement, the Purchaser commenced a tender offerto purchase~~acquired all of the ~~issued~~outstanding capital stock and ~~outstanding shares~~equity interests of ~~Datawatch common stock, (the “Shares”~~Univa Corporation (“Univa”) atfor a preliminary base purchase price of ~~$13.10 per share, net~~$30.1 million, subject to ~~seller~~certain adjustments. Univa is headquartered in ~~cash, without interest~~Chicago, with offices in Canada and ~~less any applicable withholding taxes (the “Offer”).~~

On December 13, 2018, the Company accepted and paid for all Shares that were validly tendered and completed the acquisition of Datawatch through the merger of Purchaser with and into Datawatch, with Datawatch surviving as a wholly owned subsidiary of the Company.

Altair completed the acquisition of Datawatch for consideration of approximately $183.4 million which consisted of consideration paid to former holders of common stock of Datawatch at $13.10 a share, or $168.2 million and approximately $6.7 million to former holders of outstanding Datawatch equity awards. In addition, Altair paid $8.0 million on the day of closing to settle all of Datawatch’s outstanding debt and incurred a liability of approximately $0.5 million payable to former holders of certain unvested Datawatch equity awards for which service had been rendered at the acquisition date. Altair financed the acquisition with cash on hand and a drawdown from its then existing credit facility.

Germany. The financial results of ~~Datawatch~~Univa have been included in the Company’s consolidated financial statements since the acquisition date.

~~The~~This acquisition ~~of Datawatch has been~~will be accounted for as a business combination under the acquisition method of ~~accounting, which results in acquired assets and assumed liabilities being measured at their estimated fair values as of December 13, 2018,~~accounting. At September 30, 2020, the ~~acquisition date. As of the acquisition date, goodwill is measured as the excess of consideration transferred, which is also generally measured at fair~~book value of ~~the net acquisition date fair values of the assets acquired and liabilities assumed.~~

~~The following table summarizes the preliminary purchase consideration transferred to acquire Datawatch and the amounts of identified~~ assets acquired and liabilities assumed atwere reported in the ~~acquisition date (in thousands):~~

Company’s consolidated balance sheet. The ~~excess of preliminary~~remaining purchase ~~consideration over~~price has been recorded in goodwill in the ~~preliminary~~consolidated balance sheet pending fair value of net tangible and identifiable intangible assets acquired was recorded as goodwill. The preliminary fair values assigned to tangible and identifiable intangible assets acquired and liabilities assumed are based on management’s estimates and assumptions. The deferred tax liability established was primarily a result of the difference in the book basis and tax basis related to the identifiable intangible assets. allocation.

The preliminary estimated fair values of assets acquired and liabilities assumed, ~~including current and noncurrent income taxes payable and deferred taxes, customer contract assets and liabilities~~ and identifiable intangible assets may be subject to change as additional information is ~~received~~received. The Company expects to finalize the valuation as soon as practicable, but not later than one year from the acquisition date. Until the finalization of this valuation, the area of income taxes is open within the business combination measurement period.

Univa is a leading innovator in enterprise-grade workload management, scheduling, and ~~certain tax returns are finalized. Thus,~~optimization solutions for HPC and artificial intelligence (AI) on-premises and in the ~~provisional measurements of fair value set forth above are subject~~cloud. Univa’s technology complements Altair’s HPC and data analytics solutions and enables the Company to ~~change.~~ ~~The primary areas~~further expand into life sciences and financial services.

During the nine months ended September 30, 2020, the Company completed other business acquisitions that ~~remain preliminary relate~~were individually insignificant to the ~~fair value~~Company’s consolidated financial statements. The aggregate purchase price of ~~intangible assets acquired, certain tangible assets and liabilities acquired, income taxes and residual goodwill.~~

~~In October 2018, the Company acquired~~ ~~all of the outstanding capital stock~~ ~~of SIMSOLID Corporation, a Canadian corporation (“SIMSOLID”), for aggregate consideration of $22.1~~these other acquisitions was $9.4 million. The ~~allocation~~financial results of ~~fair value of purchase consideration was finalized~~these acquisitions have been included in the ~~first quarter~~Company’s consolidated financial statements since the acquisition dates.

These acquisitions will be accounted for as business combinations under the acquisition method of ~~2019, and there were 0 changes to~~accounting. At September 30, 2020, the ~~fair~~book value of assets acquired and liabilities assumed in these business acquisitions were reported in the Company’s consolidated balance sheet. The remaining purchase price has been recorded in goodwill in the consolidated balance sheet pending fair value allocation.

The preliminary estimated fair values of assets acquired and liabilities assumed, and identifiable intangible assets may be subject to change as ~~previously reported.~~

additional information is received. The Company expects to finalize the valuation as soon as practicable, but not later than one year from the acquisition date. Until the finalization of this valuation, the area of income taxes is open within the business combination measurement period.

	September 30,		December 31,		September 30,		December 31,
	2019		2018		2020		2019
Land	$	7,994	$	7,994	$	9,927	$	9,942
Building and improvements		14,447		13,120		15,558		15,512
Computer equipment and software		36,754		34,582		39,425		37,361
Office furniture and equipment		7,668		7,958
Office furniture, equipment and other						8,736		8,029
Leasehold improvements		8,613		6,926		9,377		9,014
Right-of-use assets under finance leases		2,660		—		2,681		2,745
Total property and equipment		78,136		70,580		85,704		82,603
Less: accumulated depreciation and amortization		44,416		40,427		51,303		46,306
Property and equipment, net	$	33,720	$	30,153	$	34,401	$	36,297

Depreciation expense, including amortization of ~~ROU~~right-of-use assets under finance leases, was $1.7 million and $5.5 million for the three and nine months ended September 30, 2020, respectively, and $1.9 million and $5.2 million for the three and nine months ended September 30, 2019, ~~respectively, and $1.6 million and $5.2 million for the three and nine months ended September 30, 2018,~~ respectively.

The changes in the carrying amount of goodwill, which is attributable to the Software reporting segment, were as follows (in thousands):

	September 30, 2019							September 30, 2020
	Weighted average amortization period	Gross carrying amount		Accumulated amortization		Net carrying amount		Weighted average amortization period	Gross carrying amount		Accumulated amortization		Net carrying amount
Definite-lived intangible assets:
Developed technology	4-6 years	$	55,870	$	22,679	$	33,191	4-6 years	$	61,039	$	33,219	$	27,820
Customer relationships	7-10 years		28,454		10,317		18,137	7-10 years		32,983		14,819		18,164
Other intangibles	10 years		204		57		147	10 years		184		57		127
Total definite-lived intangible assets			84,528		33,053		51,475			94,206		48,095		46,111
Indefinite-lived intangible assets:
Trade names			9,481				9,481			10,630				10,630
Total other intangible assets		$	94,009	$	33,053	$	60,956		$	104,836	$	48,095	$	56,741

	December 31, 2018							December 31, 2019
	Weighted average amortization period	Gross carrying amount		Accumulated amortization		Net carrying amount		Weighted average amortization period	Gross carrying amount		Accumulated amortization		Net carrying amount
Definite-lived intangible assets:
Developed technology	4-6 years	$	54,530	$	15,517	$	39,013	4-6 years	$	60,916	$	25,838	$	35,078
Customer relationships	7-10 years		28,422		7,309		21,113	7-10 years		32,582		11,575		21,007
Other intangibles	10 years		109		56		53	10 years		111		62		49
Total definite-lived intangible assets			83,061		22,882		60,179			93,609		37,475		56,134
Indefinite-lived intangible assets:
Trade names			9,657				9,657			10,941				10,941
Total other intangible assets		$	92,718	$	22,882	$	69,836		$	104,550	$	37,475	$	67,075

Amortization expense related to intangible assets was $3.9 million and $11.4 million for the three and nine months ended September 30, 2020, respectively, and $3.5 million and $10.7 million for the three and nine months ended September 30, 2019, ~~respectively,~~respectively.

The Company continues to monitor the significant global economic uncertainty as a result of COVID-19 to assess the outlook for demand for its products and ~~$1.7 million~~the impact on its business. Based on the Company’s interim impairment assessment, there were no indicators of impairment identified during the third quarter of 2020. Notwithstanding this conclusion, if business conditions were to deteriorate in a significant manner or for an extended duration, the likelihood of impairment would increase, and ~~$5.7 million~~the Company would again assess whether events or changes in circumstances indicate that an asset impairment that is more likely than not exists. Specifically, certain indefinite-lived intangible assets from recent acquisitions valued on the basis of short-term forecasts of revenue will be re-assessed for indicators of impairment and it is possible that an impairment charge will be reflected in the ~~three~~future should COVID-19 business conditions worsen or extend further in duration.

The allocation of fair value of purchase consideration of the Company’s 2019 acquisitions was finalized in the first quarter of 2020, and ~~nine months ended September 30, 2018, respectively.~~there were no material changes to the fair value of assets acquired and liabilities assumed, as previously reported.

	September 30,		December 31,		September 30,		December 31,
	2019		2018		2020		2019
Convertible senior notes	$	230,000	$	—	$	230,000	$	230,000
Revolving credit facility		—		30,950		30,000		—
Obligations for finance leases		1,178		813		877		1,174
Other borrowings		—		75
Total debt		231,178		31,838		260,877		231,174
Less: unamortized debt discount		49,147		—		39,647		46,820
Less: unamortized debt issuance costs		5,970		90		4,855		5,686
Less: current portion of long-term debt		437		331		430		430
Long-term debt, net of current portion	$	175,624	$	31,417	$	215,945	$	178,238

In June 2019, the Company issued $230.0 million aggregate principal amount of 0.25% convertible senior notes due in 2024 (the "Convertible Notes"), which includes the underwriters’ exercise in full of their option to purchase an additional $30.0 million principal amount of the Convertible Notes, in a public offering. The net proceeds from the issuance of the Convertible Notes were $221.9 million after deducting the underwriting discounts and commissions and estimated issuance costs.

The Company entered into a First Supplemental Indenture relating to the issuance by the Company of the Convertible Notes (the “Supplemental Indenture”) supplementing the Indenture, dated June 10, 2019 (the “Base Indenture,” and together with the Supplemental Indenture, the “Indenture”), by and between the Company and U.S. Bank National Association, as trustee (the “Trustee”). The Indenture includes customary covenants and sets forth certain events of default after which the Convertible Notes may be declared immediately due and payable and sets forth certain types of bankruptcy or insolvency events of default involving the Company after which the Convertible Notes become automatically due and payable. The Convertible Notes are senior unsecured obligations of the Company.

The Convertible Notes bear interest at a rate of 0.25% per year, payable semi-annually in arrears on June 1 and December 1 of each year, commencing December 1, 2019. The Convertible Notes ~~will~~ mature on June 1, 2024, unless, earlier repurchased or redeemed by the Company or converted pursuant to their terms.

The Convertible Notes have an initial conversion rate of 21.5049 shares of the Company's Class A common stock per $1,000 principal amount of Convertible Notes, which is equivalent to an initial conversion price of approximately $46.50 per share of its Class A common stock. The conversion rate will be subject to adjustment upon the occurrence of certain events specified in the Indenture but will not be adjusted for any accrued and unpaid interest. In addition, upon the occurrence of a make whole fundamental change or a redemption period (each as defined in the Indenture), the Company will, in certain circumstances, increase the conversion rate by a specified number of additional shares for a holder who elects to convert its Convertible Notes in connection with such make whole fundamental change or during the relevant redemption period.

Holders of the Convertible Notes may convert all or any portion of their Convertible Notes at any time prior to the close of business on December 1, 2023, in integral multiples of $1,000 principal amount, only under the following circumstances:

On or after December 1, 2023 until the close of business on the business day immediately preceding the maturity date, holders may convert their Convertible Notes at any time, regardless of the foregoing circumstances. Upon conversion, the Company may satisfy its conversion obligation by paying and/or delivering, as the case may be, cash, shares of Class A Common Stock or a combination of cash and shares of the Class A Common Stock, at the Company’s election, in the manner and subject to the terms and conditions provided in the Indenture. The Company intends to settle the principal amount of the Convertible Notes in cash and the conversion spread in shares.

During the quarter ended September 30, ~~2019,~~ 2020, the conditions allowing holders of the Convertible Notes to convert were not met. Therefore, the Convertible Notes were classified as long-term debt on the consolidated balance sheet as of September 30, ~~2019.~~2020.

As of September 30, 2020, the “if converted value” did not exceed the principal amount of the Convertible Notes.

The Company accounts for the Convertible Notes as separate liability and equity components. The carrying amount of the liability component of the Convertible Notes was calculated by measuring the fair value of similar debt instruments that do not have an associated convertible feature. The ~~Company determined the~~ carrying amount of the ~~liability~~equity component asrepresenting the ~~present value of its cash flows using a discount rate of approximately 5.5%. The estimated interest rate~~conversion option was ~~applied to~~determined by deducting the ~~Convertible Notes, which resulted in a~~ fair value of the liability component ~~of $178.2 million upon issuance, calculated as~~from the ~~present~~par value of ~~future contractual payments based on~~ the ~~$230.0 million aggregate principal amount.~~Convertible Notes. The ~~excess of~~difference between the principal amount of the Convertible Notes and the liability component, ~~over its carrying amount, or the debt discount,~~equal to $51.8 million (the “debt discount”), is amortized to interest expense over the term of the Convertible Notes using the effective interest method. The $51.8 million difference between the gross proceeds received from issuance of the Convertible Notes of $230.0 million and the estimated fair value of the liability component represents the equity component, or the “Conversion Option”, of the Convertible Notes and was recorded in additional paid-in capital. The equity component is not remeasured as long as it continues to meet the conditions for equity classification.

The Company allocated issuance costs related to the issuance of the Convertible Notes to the liability and equity components using the same proportions as the initial carrying value of the Convertible Notes. Issuance costs attributable to the liability component ~~were $6.3 million and~~ are being amortized to interest expense using the effective interest method over the term of the Convertible Notes. Issuance costs attributable to the equity ~~components were $1.8 million and~~component are ~~netted~~included with the equity component ~~of the Convertible Notes~~ in stockholders’ ~~equity on the condensed consolidated balance sheets.~~

The net carrying value of the liability component of the Convertible Notes was as follows (in thousands):

	September 30,		September 30,		December 31,
	2019		2020		2019
Principal	$	230,000	$	230,000	$	230,000
Less: unamortized debt discount		49,147		39,647		46,820
Less: unamortized debt issuance costs		5,970		4,810		5,686
Net carrying amount	$	174,883	$	185,543	$	177,494

The net carrying value of the equity component of the Convertible Notes was ~~as follows (in thousands):~~

The interest expense recognized related to the Convertible Notes was as follows (in thousands):

	Three Months Ended September 30,		Nine Months Ended September 30,		Three Months Ended September 30,				Nine Months Ended September 30,
	2019		2019		2020		2019		2020		2019
Contractual interest expense	$	144	$	169	$	143	$	144	$	431	$	169
Amortization of debt issuance cost and discount		2,577		3,024		2,720		2,577		8,050		3,024
Total	$	2,721	$	3,193	$	2,863	$	2,721	$	8,481	$	3,193

The Company has a $150.0 million credit facility ~~that was amended on June 5, 2019, to permit the issuance of the Convertible Notes and extend the~~with a maturity date of ~~the credit facility to~~ December 15, 2023 (“2019 Amended Credit Agreement”). The 2019 Amended Credit Agreement provides for an accordion feature that allows the Company to expand the size of the revolving line of credit by an additional $50.0 million, subject to certain conditions, by obtaining additional commitments from the existing lenders or by causing a person acceptable to the administrative agent to become a lender (in each case subject to the terms and conditions set forth in the 2019 Amended Credit Agreement).

As of September 30, ~~2019,~~2020, the Company had 0$30.0 million of outstanding borrowings under the 2019 Amended Credit Agreement and there was ~~$150.0~~$120.0 million available for future borrowing. The 2019 Amended Credit Agreement is available for general corporate purposes, including working capital, capital expenditures, and permitted acquisitions.

Borrowings under the 2019 Amended Credit Agreement bear interest at a rate per annum equal to an agreed upon applicable margin plus, at the Company’s option, either the Alternate Base Rate (defined as the greatest of (1) the Prime Rate (as defined in the 2019 Amended Credit Agreement) in effect on such day, (2) the Federal Funds Effective Rate (as defined in the 2019 Amended Credit Agreement) in effect on such day plus 1/2 of 1.00% or (3) the Adjusted LIBO Rate (as defined in the 2019 Amended Credit Agreement) for a one month interest period on such day (or if such day is not a business day, the immediately preceding business day) plus 1.00%) or the Adjusted LIBO Rate. The applicable margin for borrowings under the 2019 Amended Credit Agreement is based on the Company’s most recently tested consolidated total net leverage ratio and will vary from (a) in the case of Eurodollar loans, 1.25% to 2.00%, and (b) in the case of ABR loans and swingline loans, 0.25% to 1.00%. The Company pays a commitment fee (based on the Company’s most recently tested consolidated total senior secured net leverage ratio) ranging from 0.15% to 0.30% on the unused portion of the 2019 Amended Credit Agreement.

The 2019 Amended Credit Agreement is secured by collateral including (i) substantially all of the Company’s properties and assets, and the properties and assets of the Company’s direct and indirect domestic subsidiaries but excluding any patents, copyrights, patent applications or copyright applications or any trade secrets or software products and (ii) pledges of the equity interests in all present and future direct and indirect domestic subsidiaries (subject in each case to certain exceptions as provided for under the 2019 Amended Credit Agreement). The Company’s direct and indirect domestic subsidiaries are guarantors of all the obligations under the 2019 Amended Credit Agreement.

The 2019 Amended Credit Agreement requires the Company to maintain the following financial covenants:

At September 30, ~~2019,~~2020, the Company was in compliance with all the above financial covenants.

The Company determines if an arrangement is a lease at inception. Operating leases are included in operating lease assets and operating lease obligations on the Company’s consolidated balance sheets. Finance leases are included in property and equipment, current portion of long-term debt, and long-term debt on the consolidated balance sheets.

ROU assets represent the Company’s right to use an underlying asset for the lease term and lease liabilities represent the Company’s obligation to make lease payments under the lease. Operating lease ROU assets and operating lease liabilities are recognized based on the present value of the future minimum lease payments over the lease term at commencement date. At commencement date, the ROU asset also includes adjustments for lease prepayments, lease incentives received and the lessee's initial direct costs, if applicable. As most of the Company’s leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at commencement date in determining the present value of future payments. The incremental borrowing rates are determined using rates specific to the term of the lease, economic environments where lease activity is concentrated, value of lease portfolio, and assuming full collateralization of the loans. Subsequent to the commencement date, the operating ROU asset is equal to the remeasured lease liability adjusted for cumulative prepaid or accrued rent if the lease payments are uneven throughout the lease term, unamortized lease incentives, unamortized initial direct costs and any impairment of the ROU assets. The lease terms may include options to extend or terminate the lease when it is reasonably certain that the Company will exercise that option. Lease cost for minimum lease payments is recognized on a straight-line basis over the lease term.

The Company has elected not to recognize a lease liability or ROU asset for short-term leases (leases with a term of twelve months or less). For contracts with lease and non-lease components, the Company has elected not to allocate the contract consideration, and account for the lease and non-lease components as a single lease component.

The Company’s operating leases consist of office facilities, office equipment and cars and the Company’s finance leases consist of office equipment and cars. The Company’s leases have remaining terms of less than one year to 8.1 years, some of which include one or more options to renew, with renewal terms up to six years and some of which include options to terminate the leases within the next four years.

Operating lease cost includes short-term leases and variable lease costs, which are immaterial. Rent cost related to operating leases for office facilities was $3.0 million and $9.0 million for the three and nine months ended September 30, 2019, respectively, and $2.4 million and $7.0 million for the three and nine months ended September 30, 2018, respectively.

~~Supplemental balance sheet information related to lease liabilities at September 30, 2019, was as follows:~~

~~Supplemental cash flow information related to leases for the nine months ended September 30, 2019, was as follows (in thousands):~~

~~Maturities of operating lease liabilities at September 30, 2019, were as follows (in thousands):~~

~~Total obligations for finance leases, previously referred to as capital leases prior to the adoption of~~ ~~Topic 842~~ ~~on January 1, 2019, were $0.8 million at December 31, 2018.~~

The following table provides the details of other accrued expenses and current liabilities (in thousands):

	September 30,		December 31,		September 30,		December 31,
	2019		2018		2020		2019
Income taxes payable	$	8,400	$	3,932	$	4,852	$	6,008
Accrued VAT						4,417		5,312
Accrued professional fees		4,232		3,165		3,997		2,581
Accrued VAT		2,907		4,536
Accrued royalties		1,888		2,613		2,063		2,314
Defined contribution plan liabilities		1,389		1,376		1,656		1,593
Obligations for acquisition of businesses						1,362		1,362
Billings in excess of cost						541		879
Non-income tax liabilities		1,024		853		898		1,253
Government grants		806		915
Billings in excess of cost		436		1,504
Other current liabilities		6,344		8,145		5,820		7,301
Total	$	27,426	$	27,039	$	25,606	$	28,603

The following table provides details of other long-term liabilities (in thousands):

	September 30,		December 31,		September 30,		December 31,
	2019		2018		2020		2019
Pension and other post retirement liabilities	$	9,766	$	9,111	$	11,430	$	10,379
Deferred tax liabilities		5,598		5,339		6,885		6,275
Other liabilities		10,266		11,306		2,808		10,018
Total	$	25,630	$	25,756	$	21,123	$	26,672

The accounting guidance for fair value, among other things, defines fair value, establishes a consistent framework for measuring fair value and expands disclosure for each major asset and liability category measured at fair value on either a recurring or nonrecurring basis. Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability (an exit price) in an orderly transaction between market participants at the reporting date. The framework for measuring fair value consists of a three-level valuation hierarchy that prioritizes the inputs to valuation techniques used to measure fair value based upon whether such inputs are observable or unobservable. Observable inputs reflect market data obtained from independent sources, while unobservable inputs reflect market assumptions made by the reporting entity. The three-level hierarchy for the inputs to valuation techniques is briefly summarized as follows:

Level 1 – Quoted prices in active markets for identical assets and liabilities at the measurement date;

Level 2 – Observable inputs, other than the quoted prices in active markets, that are observable either directly or indirectly; and

Level 3 – Unobservable inputs in which there is little or no market data, which require the reporting entity to develop its own assumptions.

An asset’s or liability’s fair value measurement level within the fair value hierarchy is based on the lowest level of any input that is significant to the fair value measurement. Valuation techniques used need to maximize the use of observable inputs and minimize the use of unobservable inputs.

The carrying value of cash and cash equivalents, accounts receivable and accounts payable approximate fair value due to their short maturities. Interest on the Company’s ~~long-term debt~~line of credit is at a variable rate, and as such the debt obligation outstanding approximates fair value.

~~As of September 30, 2019, the fair~~The carrying value of the Company’s Convertible Notes ~~was $232.0 million.~~are at face value less unamortized debt discount and issuance costs. The estimated fair values of the Convertible Notes, which the Company has classified as Level 2 financial instruments, were determined based on quoted bid prices of the Convertible Notes on the last trading day of each reporting period. ~~The Company carries the convertible senior notes at face value less unamortized debt discount and issuance costs on its consolidated balance sheet, and it presents~~At September 30, 2020, the fair value of the Convertible Notes was $255.3 million and is presented for required disclosure purposes only. For further information on the Convertible Notes, see Note 8.7. – Debt.

Basic net (loss) income per share attributable to common stockholders is computed using the weighted average number of shares of common stock outstanding for the period, excluding stock options and restricted stock units (“RSUs”). Diluted net (loss) income per share attributable to common stockholders is based upon the weighted average number of shares of common stock outstanding for the period and potentially dilutive common shares, including the effect of stock options and RSUs under the treasury stock method. The following table sets forth the computation of the numerators and denominators used in the basic and diluted net loss per share amounts (in thousands, except per share data):

Since the Company was in a net loss position for all periods presented, basic net loss per share attributable to common stockholders is the same as diluted loss per share for all periods as the inclusion of all potential common shares outstanding would have been anti-dilutive. For the three and nine months ended September 30, 2020, respectively, there were 3.7 million and 5.1 million anti-dilutive stock options excluded from the computation of loss per share.For the three and nine months ended September 30, 2019, respectively, there were 5.3 million and 5.8 million anti-dilutive stock options excluded from the computation of loss per share.

The Company expects to settle the principal amount of the Convertible Notes in cash, and therefore, the Company uses the treasury stock method for calculating any potential dilutive effect of the Conversion Option on diluted net income per share, if applicable. The Conversion Option will have a dilutive impact on net income per share of common stock when the average market price of the Company’s Class A common stock for a given period exceeds the conversion price of the Convertible Notes of $46.50 per share. During the three and nine months ended September 30, 2020, the Company's weighted average common stock price was below the conversion price of the Convertible Notes.

In 2001, the Company established the Nonqualified Stock Option Plan (“NSO Plan”) under which ~~3,736,947~~3,025,236 stock options with an exercise price of $0.000025 remain outstanding at September 30, ~~2019.~~2020. The NSO Plan was terminated in 2003. Stock options under the NSO plan were immediately vested and have a contractual term of 35 years from the date of grant. The outstanding awards will continue to be governed by their existing terms under the NSO Plan. The NSO Plan is accounted for as an equity plan.

The following table summarizes the stock option activity under the NSO Plan for the period:

	Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)		Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)
Outstanding at January 1, 2019		4,337,856		$	0.000025		18.0	$	119.6
Outstanding at January 1, 2020											3,557,436		$	0.000025		17.0	$	127.8
Exercised		(600,909	)	$	0.000025						(532,200	)	$	0.000025
Forfeited		—			—						0			0
Outstanding and exercisable at September 30, 2019		3,736,947		$	0.000025		17.3	$	129.4
Outstanding and exercisable at September 30, 2020											3,025,236		$	0.000025		16.3	$	127.0

The total intrinsic value of the NSO Plan stock options exercised during the nine months ended September 30, ~~2019,~~2020, was ~~$22.8~~$19.3 million.

Also in 2001, the Company established the Incentive and Nonqualified Stock-based Plan (“ISO Plan”) which was terminated in 2011 and was authorized to issue nonqualified stock options (“NQSO”) and incentive stock options (“ISO”) covering 11,153,872 shares of Class A common stock. The NQSO grants could be issued at less than the fair market value at date of grant under the terms of the ISO Plan, while ISO grants were issued at a price equal to or greater than the fair market value at date of grant. Options generally vested over a two to three-year period. All options have a contractual term of ten years from the date of grant.

The following table summarizes the stock option activity under the 2001 stock-based compensation plans for the period:

	Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)		Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)
Outstanding at January 1, 2019		532,220		$	0.65		1.4	$	14.3
Outstanding at January 1, 2020											103,000		$	0.64		1.0	$	3.6
Exercised		(271,278	)	$	0.66						(69,500	)	$	0.64
Forfeited		—			—						0			0
Outstanding and exercisable at September 30, 2019		260,942		$	0.64		0.6	$	8.9
Outstanding and exercisable at September 30, 2020											33,500		$	0.64		0.3	$	1.4

The total intrinsic value of the ISO Plan stock options exercised during the nine months ended September 30, ~~2019,~~2020, was ~~$9.3~~$2.0 million.

During 2012, the Company established the 2012 Incentive and Nonqualified Stock Option Plan (“2012 Plan”) which permits the issuance of 5,200,000 shares of Class A common stock for the grant of nonqualified stock options and incentive stock options for management, other employees, and board members of the Company. The options are issued at a price equal to or greater than fair market value at date of grant. All options have a contractual term of 10 years from date of grant.

The 2012 Plan is accounted for as an equity plan. For those options expected to vest, compensation expense is recognized on a straight-line basis over a four-year period, the total requisite service period of the awards. Total compensation cost related to nonvested awards not yet recognized as of September 30, ~~2019,~~2020, totaled ~~$0.5~~$0.2 million, and is expected to be recognized over a weighted average period of ~~1.3~~0.7 years.

The following table summarizes the stock option activity under the 2012 Plan for the period:

	Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)		Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)
Outstanding at January 1, 2019		1,541,165		$	4.12		6.9	$	36.2
Outstanding at January 1, 2020											1,183,817		$	4.23		6.1
Granted		—			—						0			0
Exercised		(299,089	)	$	3.76						(213,837	)	$	3.79
Forfeited		(6,772	)	$	4.56						(7,400	)	$	4.56
Outstanding at September 30, 2019		1,235,304		$	4.21		6.3
Exercisable at September 30, 2019		859,107		$	3.95		5.9	$	26.4
Outstanding at September 30, 2020											962,580		$	4.29		5.4
Exercisable at September 30, 2020											828,690		$	4.14		5.2	$	31.4

The total intrinsic value of the 2012 Plan stock options exercised during the nine months ended September 30, ~~2019,~~2020, was ~~$9.7~~$7.4 million.

In connection with the acquisition of Datawatch, all outstanding unvested Datawatch RSUs were converted into a right to receive cash (the “Replacement Awards”). The payment to the holders of unvested Datawatch RSUs will be payable on or after the date that such RSUs would have otherwise vested in accordance with its original terms.

The accounting treatment for the outstanding unvested Datawatch RSUs in the context of the business combination was to allocate the fair value of the RSUs at the date of consummation attributable to pre-combination service to the aggregate merger consideration. The difference between the fair value of the Replacement Awards and the amount allocable to pre-combination service was considered a post-combination expense to the Company after the consummation date.

The estimated post combination expense to the Company as a result of the business combination was approximately $3.4 million which will be recognized on a straight-line basis over the remaining service period that was stipulated in each holder’s original RSU agreement. The weighted average remaining service period is 1.25 years. Once the vesting conditions of the service period are met, Altair will cash-settle the Replacement Awards. The liability related to the Datawatch RSUs as of September 30, 2019 and December 31, 2018, was $0.3 million and $0.6 million, respectively, and is recorded in other accrued expenses and current liabilities.

In 2017, the Company’s board of directors adopted the 2017 Equity Incentive Plan (“2017 Plan”), which was approved by the Company’s stockholders. The 2017 Plan provides for the grant of incentive stock options to the Company’s employees and any parent and subsidiary corporations’ employees, and for the grant of nonstatutory stock options, stock appreciation rights, restricted stock, restricted stock units, performance units, performance shares, other cash-based awards and other stock-based awards to the Company’s employees, directors and consultants and the Company’s parent, subsidiary, and affiliate corporations’ employees and consultants. ~~The~~As of January 1, 2020, the 2017 Plan ~~has 8,104,971~~had 10,277,034 authorized shares of the Company’s Class A common stock reserved for issuance.

The following table summarizes the restricted stock units, or RSUs, awarded under the 2017 Plan for the period:

The weighted average grant date fair value of the RSUs was ~~$36.23~~$33.74 and the RSUs generally vest in 4 equal annual installments. Total compensation cost related to nonvested awards not yet recognized as of September 30, ~~2019,~~2020, totaled ~~$25.4~~$57.6 million, and is expected to be recognized over a weighted average period of approximately ~~four~~three years.

The following table summarizes the stock option activity under the 2017 Plan for the period:

	Number of options		Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)		Number of options			Weighted average exercise price per share		Weighted average remaining contractual term (years)		Aggregate intrinsic value (in millions)
Outstanding at January 1, 2019		—	$	—
Outstanding at January 1, 2020										20,000		$	38.11		9.2
Granted		20,000	$	38.11						2,127,454		$	39.49
Exercised		—	$	—						(5,000	)	$	38.11
Forfeited		—	$	—						(10,972	)	$	39.36
Outstanding at September 30, 2019		20,000	$	38.11		9.5
Exercisable at September 30, 2019		—	$	—		—	$	—
Outstanding at September 30, 2020										2,131,482		$	39.48		9.7
Exercisable at September 30, 2020										158		$	29.22		8.5	$	0.0

In addition to the stock options granted above, the Company expects to grant approximately 2.0 million additional stock options on December 2, 2020, with an exercise price reflecting the fair value on that date. Recipients of the December 2, 2020, deferred stock option award must be employed on that date in order to receive the grant. The Company has concluded that the grant date for this deferred award is December 2, 2020, and this grant will not be reflected in the table above until the fourth quarter of 2020.

The Company measures the fair value of its equity awards on the date of grant using the Black-Scholes option pricing model. This valuation model requires the Company to make certain estimates and assumptions, including assumptions related to the expected price volatility of the Company’s stock, the period under which the options will be outstanding, the rate of return on risk-free investments, and the expected dividend yield for the Company’s stock.

The fair values of the Company’s stock options granted during the nine months ended September 30, ~~2019,~~2020, were estimated using the following assumptions:

	Three Months Ended September 30,				Nine Months Ended September 30,				Three Months Ended September 30,				Nine Months Ended September 30,
	2019		2018		2019		2018		2020		2019		2020		2019
Cost of revenue – software	$	384	$	8	$	727	$	24	$	684	$	384	$	1,602	$	727
Research and development		674		175		1,611		330		2,428		674		5,686		1,611
Sales and marketing		625		140		1,562		315		1,949		625		3,949		1,562
General and administrative		609		240		1,684		544		1,173		609		2,702		1,684
Total stock-based compensation expense	$	2,292	$	563	$	5,584	$	1,213	$	6,234	$	2,292	$	13,939	$	5,584

At the end of each interim period, the Company makes its best estimate of the annual expected effective income tax rate and applies that rate to its ordinary year-to-date income (loss) before income taxes. The income tax provision or benefit related to unusual or infrequent items, if applicable, that will be separately reported or reported net of their related tax effects are individually computed and recognized in the interim period in which those items occur. In addition, the effect of changes in enacted tax laws or rates, tax status, judgment on the realizability of a beginning-of-the-year deferred tax asset in future years or income tax contingencies is recognized in the interim period in which the change occurs.

The computation of the annual expected effective income tax rate at each interim period requires certain estimates and assumptions including, but not limited to, the expected income (loss) before income taxes for the year, projections of the proportion of income (and/or loss) earned and taxed in respective tax jurisdictions, including applicable foreign taxes withheld at the source, permanent and temporary differences, and the likelihood of the realizability of deferred tax assets generated in the current year. Jurisdictions with a projected loss for the year or a year-to-date loss for which no tax benefit can be recognized due to a valuation allowance are excluded from the estimated annual effective tax rate. The impact of such an exclusion could result in a higher or lower effective tax rate during a particular quarter, based upon the composition and timing of actual earnings compared to annual projections. The estimates used to compute the provision or benefit for income taxes may change as new events occur, additional information is obtained or the Company’s tax environment changes. To the extent that the expected annual effective income tax rate changes, the effect of the change on prior interim periods is included in the income tax provision in the period in which the change in estimate occurs.

The Company’s income tax expense and effective tax rate for the three and nine months ended September 30, ~~2019~~2020 and ~~2018,~~2019, were as follows (in thousands, except percentages):

	Three Months Ended September 30,						Nine Months Ended September 30,						Three Months Ended September 30,						Nine Months Ended September 30,
	2019			2018			2019			2018			2020			2019			2020			2019
Income tax expense	$	3,294		$	1,885		$	7,215		$	5,617		$	2,930		$	3,294		$	10,350		$	7,215
Effective tax rate		(26	%)		67	%		614	%		19	%		(53	%)		(26	%)		(441	%)		614	%

The tax rate is affected by the Company being a U.S. resident taxpayer, the tax rates in the U.S. and other jurisdictions in which the Company operates, the relative amount of income earned by jurisdiction and the relative amount of losses or income for which no benefit or expense is ~~recognized.~~recognized due to a valuation allowance. The Company’s effective tax rate ~~was impacted by the geographic income mix in 2019 as compared to 2018, primarily related to United States pre-tax loss of $17.5 million and $12.3 million, respectively,~~ for the ~~three and~~ nine months ended September 30, 2020 and 2019, also includes net discrete expense of $5.3 million and net discrete expense of $3.3 million, respectively, primarily related to withholding taxes on royalties, changes in reserves, changes in accruals for ~~which a tax benefit~~unremitted earnings and other adjustments.

On March 27, 2020, the Coronavirus Aid, Relief, and Economic Security Act (“CARES Act”) was ~~not recognized due~~enacted in response to the ~~valuation allowance, compared~~COVID-19 pandemic. The CARES Act, among other things, permits NOL carryovers and carrybacks to ~~United States pre-tax~~offset 100% of taxable income for taxable years beginning before 2021. In addition, the CARES Act allows NOLs incurred in 2018, 2019, and 2020 to be carried back to each of ~~$2.8 million~~the five preceding taxable years to generate a refund of previously paid income taxes. The CARES Act also provides a temporary relaxation of the section 163(j) limitation on business interest expense deductions to 50% of adjusted taxable income for tax years beginning in 2019 and ~~$14.8 million~~2020, and an election to use 2019 adjusted taxable income for ~~the three and nine months ended September 30, 2018, for which~~ tax ~~expense was not recognized due to the valuation allowance. Partially offsetting~~years beginning in 2020. The Company is currently evaluating the impact of the CARES Act, but at present does not expect that the NOL carryback provision of the CARES Act would result in a material tax benefit. The Company also does not expect the relaxation of section 163(j) provisions to ~~the~~have a material tax ~~expense and the effective tax rate for September 30, 2019, was a reversal of a reserve recorded for uncertain tax positions of $1.1 million.~~

The components of accumulated other comprehensive loss were as follows (in thousands):

	Foreign currency translation			Retirement related benefit plans			Total			Foreign currency translation			Retirement related benefit plans			Total
Balance at January 1, 2019	$	(8,823	)	$	(2,467	)	$	(11,290	)
Other comprehensive (loss) income before reclassification		(1,046	)		87			(959	)
Balance at January 1, 2020										$	(6,928	)	$	(2,600	)	$	(9,528	)
Other comprehensive loss before reclassification											(446	)		(22	)		(468	)
Amounts reclassified from accumulated other comprehensive loss	—				289			289		—				132			132
Tax effects		—			—			—			—			—			—
Other comprehensive (loss) income		(1,046	)		376			(670	)		(446	)		110			(336	)
Balance at September 30, 2019	$	(9,869	)	$	(2,091	)	$	(11,960	)
Balance at September 30, 2020										$	(7,374	)	$	(2,490	)	$	(9,864	)

The Swedish Tax Authorities, or STA, ~~have~~ assessed tax (net of utilization of tax attributes), penalties and interest in the amount of ~~$6.6~~$6.2 million related to the acquisition of Panopticon AB by Datawatch Corporation, in 2013 for the years 2013, 2014 and 2015. The STA, upon auditing the acquisition transaction, reached a conclusion that post acquisition, certain assets were removed from Sweden, triggering the tax obligation. The STA is also of the opinion that some services related to product development provided to the new parent company in the U.S. were performed by Panopticon AB at a price below market price triggering tax obligations. Datawatch contested the findings by the STA throughout the audit process including contesting the STA position in the first level of administrative courts.~~An Administrative Court hearing was held on May 16, 2019.~~ On May 29, 2019, the Administrative Court issued its ruling in favor of Datawatch AB. On July 4, 2019, the STA filed an appeal of the Administrative Court ruling with the Administrative Court of ~~Appeal~~Appeals in Stockholm, effectively continuing to assert that the assessments are in fact appropriate. The Company continues to contest the assessment through the appeals process and in late September 2019, submitted its filing in response to the STA appeal with the Administrative Court of Appeal in Stockholm. The Company has determined that these events do not cause a change in the assessment of uncertain tax positions.

As previously disclosed on Form 8-K on May 10, 2019, the Company discovered potential violations of U.S. economic sanctions and export control laws and immediately filed preliminary self-disclosure notices with the U.S. Treasury Department’s Office of Foreign Assets Control (“OFAC”) and the U.S. Commerce Department’s Bureau of Industry & Security (“BIS”).

The Company subsequently conducted an internal investigation into these issues under the direction of outside legal counsel and filed voluntary self-disclosures with both agencies on July 25, 2019. These disclosures describe the unintentional transfer of commercial software and trial software licenses to various individuals located in Iran and other restricted countries. These transfers involved freeware, trial software licenses, and volunteer software testing communities. The Company did not discover any evidence indicating any commercial transactions with restricted parties or countries.

In addition to filing voluntary self-disclosures with OFAC and BIS, the Company has implemented a series of additional compliance measures to prevent unintentional transfers of the sort described above. These measures will further enhance the Company’s international trade compliance program, which is designed to assure that the Company does not conduct business directly or indirectly with any countries or parties subject to U.S. economic sanctions and export control laws.

~~On August 30, 2019, BIS notified the Company that it had completed its investigation of the potential violation of U.S. export control laws~~After relevant submissions by the Company and ~~concluded that no criminal or administrative prosecution was warranted and closed~~ the ~~matter.~~

~~Although OFAC has not notified~~STA, the Court of Appeals held a hearing on February 20, 2020. On March 27, 2020, the Court of Appeals issued its finding in favor of the STA. Pursuant to requirements in Sweden, the Company paid the assessed tax, penalties and interest on April 24, 2020. The Company, in accordance with its right to appeal the ruling to the Administrative Supreme Court of ~~its findings or~~Sweden, filed an appeal of the ~~completion~~Court of ~~its investigations,~~Appeals ruling citing specific grounds for reconsideration. On November 4, 2020, the ~~Company does~~Supreme Administrative Court issued a decision that they would not ~~currently have~~grant leave to appeal, effectively eliminating any reason to believe that its voluntary self-disclosures (or any related U.S. Government investigations) will have a meaningful impact on its operations, results of operations for any future period, or financial condition.further appeal rights in this matter.

From time to time, the Company may be subject to legal proceedings and claims in the ordinary course of business. The Company has received, and may in the future continue to receive, claims from third parties asserting, among other things, infringement of their intellectual property rights. Future litigation may be necessary to defend the Company, its partners and its customers by determining the scope, enforceability and validity of third party proprietary rights, or to establish and enforce the Company’s proprietary rights. The results of any current or future litigation cannot be predicted with certainty and regardless of the outcome, litigation can have an adverse impact on the Company because of defense and settlement costs, diversion of management resources and other factors.

The Company defines its operating segments as components of its business where separate financial information is available and used by the chief operating decision maker (“CODM”) in deciding how to allocate resources to its segments and in assessing performance. The Company’s CODM is its Chief Executive Officer.

The Company has identified 2 reportable segments for financial reporting purposes: Software and Client Engineering Services, or “CES”. The primary measure of segment operating performance is Adjusted EBITDA, which is defined as net income (loss) adjusted for income tax expense (benefit), interest expense, interest income and other, depreciation and amortization, stock-based compensation expense, restructuring charges, asset impairment charges and other special items as determined by management. Adjusted EBITDA includes an allocation of corporate headquarters costs.

The Software reportable segment derives revenue from the sale and ~~subscription~~lease of licenses for software products focused on the development and application of simulation, ~~high performance~~data analytics, and high-performance computing ~~and data intelligence~~ technology to synthesize and optimize designs, processes and decisions for improved business performance. The Software segment also derives revenue from software support, upgrades, training and consulting services focused on product design and development expertise ~~high performance computing, data intelligence,~~ and analysis support ~~throughout~~from the component level up to complete product ~~lifecycles.~~ engineering at any stage of the lifecycle.To a much lesser extent, the Software segment also includes revenue from the sale of hardware products, primarily as a result of ~~recent~~prior business acquisitions.

The Client Engineering Services reportable segment provides support to its customers with long-term ongoing product design and development expertise in its market segments of Solvers & Optimization, Modeling & Visualization, Industrial &and Concept Design, and ~~High Performance Computing.~~high performance computing. The Company hires simulation specialists, ~~industrial~~ designers, design engineers, materials experts, development and test specialists, manufacturing engineers ~~data scientists~~ and information technology and data analytics specialists for placement at customer sites for specific customer-directed assignments.

The “All other” represents innovative services and products, including toggled^®, the Company’s LED lighting business. toggled^® is focused on developing and selling next-generation solid state lighting technology along with communication and control protocols based on intellectual property for the direct replacement of fluorescent light tubes with LED ~~lamps.~~lamps, and for control of LED lighting. Other businesses combined within Other include the Company’s WEYV business, which ~~was terminated~~ceased operations in the third quarter of 2019, and potential services and product concepts that are still in their development stages. ~~See Note 5 for further information about the termination of the WEYV business.~~

Inter-segment sales are not significant for any period presented. The CODM does not review asset information by segment when assessing ~~performance;~~performance, therefore, no asset information is provided for reportable segments. The accounting policies of the segments are the same as those described in Note 1 – Organization and summary of significant accounting policies.


Three Months Ended September 30, 2019	Software			CES		All other			Total
Three months ended September 30, 2020												Software			CES		All other			Total
Revenue	$	85,772		$	12,803	$	1,831		$	100,406		$	93,980		$	10,868	$	1,608		$	106,456
Adjusted EBITDA	$	(2,834	)	$	1,707	$	(1,208	)	$	(2,335	)	$	7,071		$	1,607	$	(503	)	$	8,175


Three Months Ended September 30, 2018	Software			CES		All other			Total
Three months ended September 30, 2019												Software			CES		All other			Total
Revenue	$	72,874		$	12,155	$	1,722		$	86,751		$	85,772		$	12,803	$	1,831		$	100,406
Adjusted EBITDA	$	1,858		$	1,407	$	(866	)	$	2,399		$	(2,834	)	$	1,707	$	(1,208	)	$	(2,335	)


Nine Months Ended September 30, 2019	Software		CES		All other			Total
Nine months ended September 30, 2020										Software		CES		All other			Total
Revenue	$	291,150	$	37,265	$	6,623		$	335,038	$	296,634	$	34,386	$	5,460		$	336,480
Adjusted EBITDA	$	26,415	$	4,280	$	(3,881	)	$	26,814	$	32,637	$	4,086	$	(1,127	)	$	35,596


Nine Months Ended September 30, 2018	Software		CES		All other			Total
Nine months ended September 30, 2019										Software		CES		All other			Total
Revenue	$	251,330	$	36,652	$	5,386		$	293,368	$	291,150	$	37,265	$	6,623		$	335,038
Adjusted EBITDA	$	35,604	$	3,971	$	(2,323	)	$	37,252	$	26,415	$	4,280	$	(3,881	)	$	26,814

	Three Months Ended September 30,						Nine Months Ended September 30,						Three Months Ended September 30,						Nine Months Ended September 30,
	2019			2018			2019			2018			2020			2019			2020			2019
Reconciliation of Adjusted EBITDA to U.S. GAAP (Loss) income before income taxes:
Reconciliation of Adjusted EBITDA to U.S. GAAP income before income taxes:
Adjusted EBITDA	$	(2,335	)	$	2,399		$	26,814		$	37,252		$	8,175		$	(2,335	)	$	35,596		$	26,814
Stock-based compensation expense		(2,292	)		(563	)		(5,584	)		(1,213	)		(6,234	)		(2,292	)		(13,939	)		(5,584	)
Interest expense		(2,726	)		(31	)		(3,586	)		(92	)		(2,934	)		(2,726	)		(8,590	)		(3,586	)
Interest income and other ⁽¹⁾		76			4,384			(633	)		5,103			1,041			76			1,501			(633	)
Depreciation and amortization		(5,368	)		(3,370	)		(15,836	)		(10,895	)		(5,623	)		(5,368	)		(16,916	)		(15,836	)
(Loss) income before income taxes	$	(12,645	)	$	2,819		$	1,175		$	30,155		$	(5,575	)	$	(12,645	)	$	(2,348	)	$	1,175

In October ~~2019,~~2020, the Company ~~entered into~~acquired M-Base Engineering + Software GmbH, located in Aachen, Germany (“M-Base”). M-Base is a ~~stock purchase agreement (the “Stock Purchase Agreement”)~~leading international supplier of material database and ~~simultaneously acquired 97%~~material information systems, with a focus on plastics. The acquisition of ~~the outstanding capital stock of Polliwog Co. Ltd. (“Polliwog”), a software company based near Seoul, Korea, for aggregate consideration of $26.2 million. Simultaneously,~~M-Base will enable the Company ~~entered into~~to offer a ~~separate stock purchase agreement (the “Second Stock Purchase Agreement”) with one of Polliwog’s stockholders to acquire the remaining 3% of the outstanding Polliwog shares in October 2022.~~ ~~Polliwog is a supplier of Electronic Design Automation software to the global electronics industry,~~comprehensive, high-fidelity plastics database, which will ~~expand Altair’s ability to provide software for system-level design decisions. The Company believes Polliwog’s printed circuit board solvers and verification tools will integrate well~~directly connect with ~~Altair’s existing HyperWorks software solutions.~~

~~The consideration consisted of cash in the amount of $10.7 million, subject to a customary working capital adjustment, and an aggregate of 459,539 shares of~~ the Company’s Class A Common Stock, par value $0.0001 per share (the “SPA Stock Consideration”). NaN percent of the SPA Stock Consideration (183,815 shares) was issued at closing (which occurred concurrently with the execution of the Stock Purchase Agreement) and is subject to customary securities law restrictions on transferability for the first six months after the closing. The remaining 60 percent (an aggregate of 275,724 shares) of the SPA Stock Consideration will be issuable in equal installments of 91,908 shares on each of the one, two and three year anniversaries of the closing, subject to potential reduction in certain circumstances. The Company will pay an additional $0.3 million in cash and issue an additional 14,213 shares of its Class A Common Stock at the closing under the Second Stock Purchase Agreement, representing 3 percent of the aggregate consideration to be paid by Altair to acquire all of Polliwog’s outstanding capital stock.

In November 2019, the Company entered into a stock purchase agreement and simultaneously acquired 100% of the outstanding capital stock of DEM Solutions Limited, a company that provides market-leading Discrete Element Method (DEM) software for bulk material simulation, based in Edinburgh, UK.solvers.

Item 2. Management’s Discussion and Analysis of Financial Condition and Results of Operations

The following discussion and analysis of our financial condition and results of operations should be read in conjunction with our consolidated financial statements and related notes included elsewhere in this quarterly report and with our audited consolidated financial statements (and notes thereto) for the year ended December 31, ~~2018,~~2019, included in our Annual Report on Form 10-K filed with the SEC. This discussion contains forward-looking statements that involve risks and uncertainties. Our actual results could differ materially from those discussed below. All statements in this quarterly report regarding the future impact of COVID-19 are forward-looking in nature and thus subject to the safe harbor provisions described below.

This quarterly report on Form 10-Q contains forward-looking statements made pursuant to the safe harbor provisions of the Private Securities Litigation Reform Act of 1995 under Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. Forward-looking statements include statements with respect to our beliefs, plans, objectives, goals, expectations, anticipations, assumptions, estimates, intentions and future performance, and involve known and unknown risks, uncertainties and other factors, which may be beyond our control, and which may cause our actual results, performance or achievements to be materially different from future results, performance or achievements expressed or implied by such forward-looking statements. All statements other than statements of historical fact are statements that could be forward-looking statements. You can identify these forward-looking statements through our use of words such as “may,” “can,” “anticipate,” “assume,” “should,” “indicate,” “would,” “believe,” “contemplate,” “expect,” “seek,” “estimate,” “continue,” “plan,” “point to,” “project,” “predict,” “could,” “intend,” “target,” “potential” and other similar words and expressions of the future.

There are a number of important factors that could cause the actual results to differ materially from those expressed in any forward-looking statement made by us. These factors include, but are not limited to:

The foregoing does not represent an exhaustive list of matters that may be covered by the forward-looking statements contained herein or risk factors that we are faced with that may cause our actual results to differ from those anticipated in our forward-looking statements. For additional risks which could adversely impact our business and financial performance please see “Risk Factors” in our Annual Report on Form 10-K for the year ended December 31, ~~2018,~~2019, which was filed with the SEC, on March ~~1, 2019,~~2, 2020, and in Item 1A, Part II of this Quarterly Report on Form 10-Q and other information appearing elsewhere in our Annual Report on Form 10-K, this report on Form 10-Q and our other filings with the SEC.

All forward-looking statements are expressly qualified in their entirety by this cautionary notice. You are cautioned not to place undue reliance on any forward-looking statements, which speak only as of the date of this report or the date of the document incorporated by reference into this report. We have no obligation, and expressly disclaim any obligation, to update, revise or correct any of the forward-looking statements, whether as a result of new information, future events or otherwise. We have expressed our expectations, beliefs and projections in good faith, and we believe they have a reasonable basis. However, we cannot assure you that our expectations, beliefs or projections will result or be achieved or accomplished.

We are a global technology company providing software and cloud solutions in the areas of ~~product design~~simulation, data analytics, and ~~development, high performance computing, or HPC, and data intelligence.~~high-performance computing. We enable organizations across broad industry segments to compete more effectively in a connected world while creating a more sustainable future.

Our simulation-driven approach to innovation is powered by our broad portfolio of high-fidelity and high-performance physics solvers. Our integrated suite of software optimizes design performance across multiple disciplines encompassing structures, motion, fluids, thermal management, electromagnetics, system modeling, and embedded systems, while also providing data ~~intelligence~~analytics and true-to-life visualization and rendering.Our high performance computing solutions maximize the efficient utilization of complex compute resources and streamline the workflow management of compute-intensive tasks for applications including data analytics, modeling and simulation, and visualization. Our data analytics products include data preparation, data science and visualization solutions that fuel engineering, scientific, and business decisions.

Altair’s software products represent a comprehensive, open architecture solution for simulation, data ~~intelligence~~analytics and cloud computing to empower decision making for improved product development, manufacturing, energy management and exploration, financial services, health care, and retail operations. We believe our products offer a comprehensive set of technologies to design and optimize high performance, efficient, innovative and sustainable products and processes in an increasingly connected world. Our products are categorized by:

Altair also provides ~~client engineering services,~~Client Engineering Services, or CES, to support our customers with long-term ongoing expertise. This has the benefit of embedding us within customers, deepening our understanding of their processes, and allowing us to perceive trends more quickly ~~perceive trends~~ in the overall market. Our presence at our customers’ sites (currently substantially limited to remote presence in response to COVID-19) helps us to better tailor our software products’ research and development, or R&D, and sales initiatives.

In ~~October 2019,~~July 2020, we introduced Altair Units, our new, unified licensing system that gives access to every Altair product and the ~~Company~~power to solve on any scale. The new model delivers enhanced inclusivity at various price points and will allow customers to maximize their software value.

In March 2020, The World Health Organization declared the outbreak of COVID-19 a pandemic, and a public health emergency of international concern. ~~entered into a stock purchase agreement (the “Stock Purchase Agreement”)~~The global spread of COVID-19 has created significant volatility and ~~simultaneously~~ ~~acquired 97%~~uncertainty. Such conditions are expected to continue. To limit the spread of the outstanding capital stock of Polliwog Co. Ltd. (“Polliwog”), a software company based near Seoul, Korea, for aggregate consideration of $26.2 million. Simultaneously, the Company entered into a separate stock purchase agreement COVID-19,~~(the “Second Stock Purchase Agreement”)~~ ~~with one of Polliwog’s stockholders~~ governments have taken various actions, from time to ~~acquire the remaining 3% of the outstanding Polliwog shares in October 2022.~~ Polliwog is a supplier of Electronic Design Automation software to global electronics industry customers, which will expand Altair’s ability to provide software for system-level design decisions. The Company believes Polliwog ’s printed circuit board solvers and verification tools will integrate well with Altair’s existing HyperWorks software solutions.time, including

The consideration consisted of cash in the amount of $10.7 million, subject to a customary working capital adjustment, and an aggregate of 459,539 shares of the Company’s Class A Common Stock, par value $0.0001 per share (the “SPA Stock Consideration”). Forty percent of the SPA Stock Consideration (183,815 shares) was issued at closing (which occurred concurrently with the execution of the Stock Purchase Agreement) and is subject to customary securities law restrictions on transferability for the first six months after the closing. The remaining sixty percent (an aggregate of 275,724 shares) of the SPA Stock Consideration will be issuable in equal installments of 91,908 shares on each of the one, two and three year anniversaries of the closing, subject to potential reduction in certain circumstances. The Company will pay an additional $0.3 million in cash and issue an additional 14,213 shares of its Class A Common Stock at the closing under the Second Stock Purchase Agreement, representing three percent of the aggregate consideration to be paid by Altair to acquire all of Polliwog’s outstanding capital stock.

In June 2019, we issued $230.0 million aggregate principal amount of 0.25% convertible senior notes due in 2024 (the "Notes"), which includes the underwriters’ exercise in full of their option to purchase an additional $30.0 million principal amount of the Convertible Notes, in a public offering. The net proceeds from the issuance of travel restrictions, complete or partial prohibitions of non-essential activities, restrictions or shutdowns of non-essential businesses, stay-at-home orders and social distancing guidelines. Some of these actions have varied from initial responses, pivoting between full or complete to partial or limited restrictions depending upon local or regional conditions. Accordingly, many businesses have adjusted to these actions by reducing or suspending operating or other activities. This has negatively impacted several of the ~~Convertible Notes were $221.9 million after deducting~~markets we serve, including the ~~underwriting discounts~~automotive and ~~commissions and estimated issuance costs.~~aerospace markets.

~~In conjunction~~The ensuing discussion is provided to summarize the impacts of COVID-19 upon the Company, inclusive of some of the principal measures undertaken by the Company to date to respond to the pandemic. It is difficult to predict with any level of precision the broad effects of COVID-19 on specific industries or individual companies. Locally or regionally imposed restrictions in concert with the ~~issuance~~duration of pandemic conditions may create disparate impacts across the ~~Convertible Notes, we entered into a base indenture and a supplemental indenture by and between~~globe, including the primary countries or regions in which the Company and ~~U.S. Bank National Association (collectively,~~its customers operate.

The uncertain impact from the ~~“Indenture”). The Indenture includes customary covenants~~rapidly changing market and ~~sets forth~~economic conditions due to COVID-19 has disrupted the business of many of our customers and partners. These disruptions have had an adverse effect on our business and consolidated results of operations and could impact our financial condition in the future. For example, a negative impact on our customers may cause them to delay entering into new or expanded software licenses, request extended payment terms, delayed invoicing, higher discounts, lower renewal amounts or cancelations, and a reduction in demand for software related and client engineering services. These actions could have a negative impact on our financial results and liquidity. While adjustments to costs in previous periods have been undertaken to mitigate the potential loss of revenue, including through the reduction in use of outside contractors and furloughing those employees associated with client engineering services for whom their associated customer contracts were interrupted or terminated, we believe that it is important on a long term basis to retain much of the deeply technical and specialized engineering resources typically engaged in providing software related services.

We have adopted several measures in response to COVID-19 adhering to local and regional restrictions, including instructing employees to work from home, adjusting our expenses and cash flow to correlate with potential declines in billings and cash collections from customers, shifting certain of our customer events to online-only webcasts and restricting non-critical business travel by our employees. Historically, a portion of ~~default after which~~field sales, professional services and other activities were conducted in person. Currently, because of travel restrictions related to COVID-19, substantially all of our sales, professional services and other activities are being conducted virtually. We have developed contingency plans to reduce costs further if the ~~Convertible Notes~~current situation changes. We continue to actively monitor business conditions and government mandates related to COVID-19 and may take further actions that alter our business operations as may be ~~declared immediately due~~required by federal, state or local authorities or that we determine are in the best interests of our associates, customers, suppliers and ~~payable~~shareholders.

Throughout this period, our response is focused on maintaining the health and ~~sets forth~~safety of our employees, customers, and partners. We are committed to, and we believe we are capable of continuing to provide the same excellent level of service and technical support for our customers during these uncertain times. Our team is comfortable and highly experienced with remote collaboration, as it is a normal part of our global culture. During this crisis, customers working remotely can move their existing licenses from their on-premise servers to servers utilizing hosted Altair Units, or request temporary term-based software licenses for increased productivity and security. We are also providing access to an increased number of online training, marketing and sales resources.

We have almost entirely converted our business to being capable of operating nearly 100% “virtual” as required or recommended under COVID-19 restrictions, leveraging our global technology infrastructure. While we are capable of sustained operations primarily in a virtual environment, we expect that we will gradually resume normalized operations, when permitted, based on local conditions and restrictions, with the primary focus of preserving employee welfare, while continuing to support customers. We have undertaken certain ~~types~~measures to manage operating expenses given the uncertainties with the COVID-19 environment. Previously, we introduced temporary wage reductions, or other measures, in accordance with local labor laws and regulations, to reduce near term compensation costs. These adjustments, which were beneficial during the period of ~~bankruptcy or insolvency events~~heightened uncertainty early in COVID-19, have been rolled back, such that effective October 2020, the temporary wage reductions have been rescinded. We have, where possible, negotiated reductions in costs for consultants, professional and advisory fees, and other costs. Given global travel restrictions, we have substantially reduced expenses for travel related costs while many sales and marketing activities have reverted to being virtualized, further reducing certain expenditures on a net basis.

COVID-19 restrictions have begun to ease in certain jurisdictions, and we have been able to re-open offices in certain countries. On the other hand, certain jurisdictions that eased restrictions have subsequently heightened their restrictions.We have taken proactive steps to protect the health and safety of ~~default involving the Company after which the Convertible Notes become automatically due~~our employees, customers, and ~~payable. The Convertible Notes are senior unsecured obligations~~partners, preparing our offices for a safe return in compliance with local and regional regulations and requirements and enacting rigorous safety measures, including employee training and self-monitoring for symptoms of COVID-19. Adhering to local and regional requirements, these measures include a combination of the ~~Company.~~

~~The Convertible Notes bear interest at a rate~~taking of 0.25% per year, payable semi-annually in arrears on June 1 and December 1 of each year, commencing December 1, 2019. The Convertible Notes will mature on June 1, 2024, unless, earlier repurchased or redeemed by us or converted pursuantall employee temperatures upon reporting to ~~their terms.~~

~~The Convertible Notes have an initial conversion rate of 21.5049 shares of our Class A common stock per $1,000 principal amount of Convertible Notes, which is equivalent~~work, encouraging employees to ~~an initial conversion price of approximately $46.50 per share of our Class A common stock. The conversion rate will be subject~~continue to adjustment upon the occurrence of certain events specified in the Indenture but will not be adjusted for any accrued and unpaid interest. In addition, upon the occurrence of a make whole fundamental change or a redemption period (each as defined in the Indenture), we will, in certain circumstances, increase the conversion rate by a specified number of additional shares for a holder who elects to convert its Convertible Notes in connection with such make whole fundamental change or during the relevant redemption period.

Onfrom home, implementing social distancing protocols, maintaining suspension of travel, instituting facility protocols and cleaning guidelines, establishing hand sanitizer stations, disinfecting workspaces, and requiring the wearing of masks with respect to those employees who must be physically present in their workplace. In the event an employee contracts the virus and tests positive for COVID-19, we have mandated quarantining and have instructed employees not to return to work until such time that they have been cleared to do so. We expect to continue to practice these measures until we determine that COVID-19 is adequately contained for purposes of our business, and we may take further actions as government authorities require or ~~after December 1, 2023 until~~recommend or as we determine to be in the ~~close~~best interests of our employees, customers, and partners.

We derive a significant portion of our revenue from international operations, which are primarily conducted in foreign currencies. The value of the U.S. dollar has fluctuated in comparison to certain foreign currencies, including in Europe, driven in part by COVID-19 events and news. Since we have substantial international operations that arise from our normal business operations, our financial results in 2020 may be impacted by COVID-19 driven variations in foreign currency exchange rates, apart from the traditional elements that underlie foreign currency exchange rate changes.

We have performed an assessment of certain tangible and intangible assets to determine whether events or changes in circumstances caused by the COVID-19 pandemic resulted in indicators of impairment as of September 30, 2020. Based on present expectations, we determined that it is not more likely than not that indicators of impairment existed as of September 30, 2020. Notwithstanding this conclusion, if business conditions were to deteriorate in a significant manner or for an extended duration within our customer base, the likelihood of impairment would increase, and we would again assess whether events or changes in circumstances indicate that an asset impairment that is more likely than not exists. Specifically, certain non-amortizing intangible assets from recent acquisitions valued on the basis of short-term forecasts of revenue will be re-assessed for indicators of impairment and it is possible that an impairment charge will be reflected in the future should COVID-19 business ~~day immediately preceding~~conditions worsen or extend substantially in duration.

As reflected in our period to period analysis below, we believe the ~~maturity date, holders may convert their Convertible Notes at any time, regardless~~emergence of COVID-19 has negatively affected our results of operations. COVID-19’s impact on some of our customers has primarily contributed to the decrease in revenue for software related and client engineering services. Our software product revenue has been affected by elongated sales cycles, greater challenges in securing renewals, as well as new and expansion business. While we continue to robustly engage with our customers, primarily virtually, to mitigate the uncertain extent of the ~~foregoing circumstances. Upon conversion,~~negative impact of COVID-19 on our customers, our ability to attract, serve, retain, or expand customers will continue to be uncertain. Existing and potential customers may choose to reduce or delay technology spending in response to COVID-19, or attempt to renegotiate contracts and obtain concessions, which may materially and negatively impact our operating results, financial condition and prospects. In certain cases, we provided longer than normal payment terms to certain of our customers; however, the terms are less than one year, and we do not expect this to materially affect our consolidated financial statements. We are unable to accurately predict the full impact that COVID-19 will have due to numerous uncertainties, including the full scope of the disease, the duration of the outbreak, the number and intensity of subsequent waves of infections, actions that may be taken by governmental authorities, the impact to the businesses of our customers and partners, the development of treatments and vaccines, and other factors identified in Part II, Item 1A “Risk Factors” in this Form 10-Q. Even after the COVID-19 pandemic subsides, we may ~~satisfy~~experience material adverse impacts to our ~~conversion obligation by paying and/~~business as a result of any economic recession or ~~delivering, as~~depression that has occurred or may occur in the ~~case may be, cash, shares of Class A Common Stock or a combination of cash~~future. We will continue to evaluate the nature and ~~shares~~extent of the ~~Class A Common Stock, at~~impact to our ~~election, in the manner~~business, consolidated results of operations, and ~~subject to the terms and conditions provided in the Indenture.~~financial condition.

In June 2019, we amended our $150.0 million credit facility to, among other things, permit the issuance of the Convertible Notes and extend the maturity date of the credit facility to December 15, 2023.

We believe that our future success will depend on many factors, including those described below. While these areas present significant opportunity, they also present risks that we must manage to achieve successful results. If we are unable to address these challenges, our business, operating results and prospects could be harmed. Please see “Risk Factors” in our Annual Report on Form 10-K for the year ended December 31, ~~2018,~~2019, as filed with the SEC on March ~~1, 2019,~~2, 2020, and in Part II, Item 1A ~~Part II~~ of this Quarterly Report on Form 10-Q.

Our billings have historically been highest in the first and fourth quarters of any calendar year and may vary in future quarters. The timing of recording billings and the corresponding effect on our cash flows may vary due to the seasonality of the purchasing and payment patterns of our customers. In addition, the timing of the recognition of revenue, the amount and timing of operating expenses, including employee compensation, sales and marketing activities, and capital expenditures, may vary from quarter-to-quarter which may cause our reported results to fluctuate significantly. In addition, we may choose to grow our business for the long-term rather than to optimize for profitability or cash flows for a particular shorter-term period. This seasonality or the occurrence of any of the factors above may cause our results of operations to vary and our financial statements may not fully reflect the underlying performance of our business.

We believe that our recent and prior acquisitions result in certain benefits, including expanding our portfolio of software and products and enabling us to better serve our customer’s requests for data intelligence, simulation technology, and ~~simulation technology.~~high performance computing. However, to realize some of these anticipated benefits, the acquired businesses must be successfully integrated. The success of these acquisitions will depend in part on our ability to realize these anticipated benefits. We may fail to realize the anticipated benefits of these acquisitions for a variety of reasons.

Because of our substantial international operations, we are exposed to foreign currency risks that arise from our normal business operations, including in connection with our transactions that are denominated in foreign currencies, including the Euro, British Pound Sterling, Indian Rupee, Japanese Yen, and Chinese Yuan. To present the changes in our underlying business without regard to the impact of currency fluctuations, we evaluate certain of our operating results both on an as reported basis, as well as on a constant currency basis.

Constant currency amounts exclude the effect of foreign currency fluctuations on our reported results. Our comparative financial results were impacted by fluctuations in the value of the United States dollar relative to other currencies during the three and nine months ended September 30, ~~2019,~~2020, as compared to the three and nine months ended September 30, ~~2018.~~2019. To present this information, the results for ~~2019~~2020 for entities whose functional currency is a currency other than the United States dollar were converted to United States dollars at rates that were in effect for ~~2018.~~2019. These adjusted amounts are then compared to our current period reported amounts to provide operationally driven variances in our results.

The effects of currency fluctuations on our Revenue, Net income, Adjusted EBITDA and Billings, are reflected in the table below. Amounts in brackets indicate a net adverse impact from currency fluctuations.

Our ability to grow our revenue is affected, in part, by the pace at which our customers continue to expand their use of our design, simulation, optimization and analysis applications, our suite of data intelligence products and the degree to which prospective customers realize the benefit of using our software applications. To grow our presence within our customers and attract new customers, we devote substantial sales and marketing resources to drive increased adoption across our existing customers and encourage new customers to commence using our software. As a result of this “land and expand” business model, we expect to generate additional revenue from our current and future customer base. To the extent our sales and marketing efforts do not translate into customer retention or expansion, or if we do not allocate those expenses efficiently, our financial performance may be adversely affected. Therefore, our financial performance will depend in part on the degree to which our “land and expand” strategies are successful.

We have made and plan to continue to make investments for long-term growth, including investments in our ongoing research and development activities seeking to create new software and to enhance our existing applications to address emerging technology trends and additional customer needs. Generally, the development of new or improved applications in our software can result in the expansion of our user base within an organization and a potential increase in revenue over time, although the expenditures associated with such developments may adversely affect our performance in the near term. We intend to continue to invest resources in sales and marketing, by further expanding our sales teams and increasing our marketing activities. Our ability to continue to grow revenue from our current and potential customer base is dependent, in part, upon the success of our current and future research and development and sales and marketing activities.

We have identified two reportable segments: Software and Client Engineering Services:

Our other businesses which do not meet the criteria to be separate reportable segments are combined and reported as “Other” which represents innovative services and products, including toggled, our LED lighting business. toggled is focused on developing and selling next-generation solid state lighting technology along with communication and control protocols based on our intellectual property for the direct replacement of fluorescent light tubes with LED lamps. Other businesses combined within Other include our WEYV business, which ~~was terminated~~ceased operations in the third quarter of 2019, and potential services and product concepts that are still in development stages. ~~See Note 5 in the Notes to consolidated financial statements for further information about the termination of the WEYV business.~~

For additional information about our reportable segments and other businesses, see Note 1715 in the Notes to consolidated financial statements in Item 1, Part I of this Quarterly Report on Form 10-Q.

Comparison of the three and nine months ended September 30, ~~2019~~2020 and ~~2018~~2019

The following table sets forth the results of operations and the period-over-period percentage change in certain financial data for the three and nine months ended September 30, ~~2019~~2020 and ~~2018:~~2019:

	Three Months Ended September 30,						Increase / (decrease)			Nine Months Ended September 30,						Increase / (decrease)			Three Months Ended September 30,						Increase / (decrease)			Nine Months Ended September 30,						Increase / (decrease)
(in thousands)	2019			2018			%			2019			2018			%			2020			2019			%			2020			2019			%
Revenue:
Software	$	77,816		$	64,182			21	%	$	265,515		$	224,458			18	%	$	87,810		$	77,816			13	%	$	278,086		$	265,515			5	%
Software related services		7,956			8,692			(8	%)		25,635			26,872			(5	%)		6,170			7,956			(22	%)		18,548			25,635			(28	%)
Total software and related services		85,772			72,874			18	%		291,150			251,330			16	%		93,980			85,772			10	%		296,634			291,150			2	%
Client engineering services		12,803			12,155			5	%		37,265			36,652			2	%		10,868			12,803			(15	%)		34,386			37,265			(8	%)
Other		1,831			1,722			6	%		6,623			5,386			23	%		1,608			1,831			(12	%)		5,460			6,623			(18	%)
Total revenue		100,406			86,751			16	%		335,038			293,368			14	%		106,456			100,406			6	%		336,480			335,038			—	%
Cost of revenue:
Software		13,919			9,831			42	%		40,655			32,736			24	%		14,103			13,919			1	%		41,434			40,655			2	%
Software related services		6,013			6,352			(5	%)		19,143			19,573			(2	%)		4,996			6,013			(17	%)		15,141			19,143			(21	%)
Total software and related services		19,932			16,183			23	%		59,798			52,309			14	%		19,099			19,932			(4	%)		56,575			59,798			(5	%)
Client engineering services		10,160			9,817			3	%		29,993			29,977			—	%		8,510			10,160			(16	%)		27,617			29,993			(8	%)
Other		1,649			1,204			37	%		5,858			3,416			71	%		1,427			1,649			(13	%)		4,422			5,858			(25	%)
Total cost of revenue		31,741			27,204			17	%		95,649			85,702			12	%		29,036			31,741			(9	%)		88,614			95,649			(7	%)
Gross profit		68,665			59,547			15	%		239,389			207,666			15	%		77,420			68,665			13	%		247,866			239,389			4	%
Operating expenses:
Research and development		29,667			24,301			22	%		87,012			71,748			21	%		30,678			29,667			3	%		91,115			87,012			5	%
Sales and marketing		25,790			19,243			34	%		78,462			57,849			36	%		26,998			25,790			5	%		80,903			78,462			3	%
General and administrative		20,706			17,234			20	%		60,886			51,636			18	%		20,905			20,706			1	%		63,499			60,886			4	%
Amortization of intangible assets		3,545			1,739			104	%		10,673			5,665			88	%		3,858			3,545			9	%		11,390			10,673			7	%
Other operating income, net		(536	)		(4,850	)		(89	%)		(1,702	)		(7,433	)		(77	%)		(1,596	)		(536	)	NM				(3,431	)		(1,702	)		102	%
Total operating expenses		79,172			57,667			37	%		235,331			179,465			31	%		80,843			79,172			2	%		243,476			235,331			3	%
Operating (loss) income		(10,507	)		1,880		NM				4,058			28,201			(86	%)		(3,423	)		(10,507	)		(67	%)		4,390			4,058			8	%
Interest expense		2,726			31		NM				3,586			92		NM				2,934			2,726			8	%		8,590			3,586			140	%
Other income, net		(588	)		(970	)		(39	%)		(703	)		(2,046	)		(66	%)		(782	)		(588	)		33	%		(1,852	)		(703	)	NM
(Loss) income before income taxes		(12,645	)		2,819		NM				1,175			30,155			(96	%)		(5,575	)		(12,645	)		(56	%)		(2,348	)		1,175		NM
Income tax expense		3,294			1,885			75	%		7,215			5,617			28	%		2,930			3,294			(11	%)		10,350			7,215			43	%
Net (loss) income	$	(15,939	)	$	934		NM			$	(6,040	)	$	24,538		NM
Net loss																			$	(8,505	)	$	(15,939	)		(47	%)	$	(12,698	)	$	(6,040	)		110	%
Other financial information:
Billings⁽¹⁾	$	103,643		$	84,926			22	%	$	345,562		$	290,490			19	%	$	107,652		$	103,643			4	%	$	334,457		$	345,562			(3	%)
Adjusted EBITDA⁽²⁾	$	(2,335	)	$	2,399		NM			$	26,814		$	37,252			(28	%)	$	8,175		$	(2,335	)	NM			$	35,596		$	26,814			33	%
Net cash (used in) provided by operating activities	$	(1,863	)	$	3,109		NM			$	30,005		$	40,422			(26	%)	$	(6,022	)	$	(1,863	)		223	%	$	27,379		$	30,005			(9	%)
Free cash flow⁽³⁾	$	(3,316	)	$	906		NM			$	21,885		$	35,089			(38	%)	$	(7,498	)	$	(3,316	)		126	%	$	23,373		$	21,885			7	%

The following table sets forth our revenue ~~growth~~change on a constant currency basis for the three and nine months ended September 30, ~~2019,~~2020, compared to the three and nine months ended September 30, ~~2018:~~2019:

	Three Months Ended September 30,				Change			Constant currency change⁽¹⁾			Nine Months Ended September 30,				Change			Constant currency change⁽¹⁾			Three Months Ended September 30,				Change			Constant currency change⁽¹⁾			Nine Months Ended September 30,				Change			Constant currency change⁽¹⁾
(dollars in thousands)	2019		2018		%			%			2019		2018		%			%			2020		2019		%			%			2020		2019		%			%
Revenue:
Software	$	77,816	$	64,182		21	%		23	%	$	265,515	$	224,458		18	%		21	%	$	87,810	$	77,816		13	%		12	%	$	278,086	$	265,515		5	%		5	%
Software related services		7,956		8,692		(8	%)		(6	%)		25,635		26,872		(5	%)		—	%		6,170		7,956		(22	%)		(24	%)		18,548		25,635		(28	%)		(27	)%
Total software and related services		85,772		72,874		18	%		19	%		291,150		251,330		16	%		19	%		93,980		85,772		10	%		8	%		296,634		291,150		2	%		3	%
Client engineering services		12,803		12,155		5	%		5	%		37,265		36,652		2	%		2	%		10,868		12,803		(15	%)		(15	)%		34,386		37,265		(8	%)		(7	)%
Other		1,831		1,722		6	%		6	%		6,623		5,386		23	%		23	%		1,608		1,831		(12	%)		(12	%)		5,460		6,623		(18	%)		(18	%)
Total revenue	$	100,406	$	86,751		16	%		17	%	$	335,038	$	293,368		14	%		17	%	$	106,456	$	100,406		6	%		5	%	$	336,480	$	335,038		—	%		1	%

Total revenue increased by ~~$13.7~~$6.1 million, or ~~16%~~6%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. The increase was primarily attributable to an increase in software ~~revenue.~~revenue, partially offset by a decrease in software related services revenue and CES revenue as a result of the slowdown in economic activity by our customers due to COVID-19.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Software revenue	$	77,816		$	64,182		$	13,634		21	%	$	87,810		$	77,816		$	9,994		13	%
As a percent of software segment revenue		91	%		88	%							93	%		91	%
As a percent of consolidated revenue		78	%		74	%							82	%		78	%

The ~~21%~~13% increase in our software revenue for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018,~~2019, was primarily the result of an ~~expansion~~increase in ~~the number of units licensed by our existing customers under renewed~~ software license ~~agreements and licensing of units to new customers pursuant to new software license agreements. Also contributing to the increase~~revenue recognized in the current ~~year, was~~quarter.

Software related services revenue ~~attributable to recent acquisitions. Our performance~~decreased 22% for the three months ended September 30, ~~2019, was affected by adverse shifts in certain foreign currencies. On a constant currency basis, our software revenue increased by 23% for the three months ended September 30, 2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. This decrease was primarily the result of customers reducing their demand for these services due to COVID-19.

	Three Months Ended September 30,						Period-to-period change						Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$			%			2020			2019			$			%
Software related services revenue	$	7,956		$	8,692		$	(736	)		(8	%)
As a percent of software segment revenue		9	%		12	%
Client engineering services revenue													$	10,868		$	12,803		$	(1,935	)		(15	%)
As a percent of consolidated revenue		8	%		10	%								10	%		13	%

~~Software related services~~CES revenue decreased 8%15% for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018. This decrease was primarily~~2019. In response to COVID-19, some of our CES customers furloughed staff positions, while some other customers have reduced CES staff working hours or reduced billing rates. We have acted in concert with those customers to furlough or curtail the ~~result~~hours and compensation of ~~a decline in revenue from consulting services. On a constant currency basis,~~those impacted employees until such time as our ~~software related services revenue decreased by 6% for the three months ended September 30, 2019, as compared~~customers return to ~~the three months ended September 30, 2018.~~

~~Client engineering services~~normalized staffing, billing rates or required working hours.

The 5% increase in CES revenue for the three months ended September 30, 2019, as compared to the three months ended September 30, 2018, was primarily due to an increase in our ability to fulfill demand for our client engineering services. Our CES business is primarily affected by customer demand and our ability to fill customers’ open positions.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Other revenue	$	1,831		$	1,722		$	109		6	%	$	1,608		$	1,831		$	(223	)		(12	%)
As a percent of consolidated revenue		2	%		2	%							2	%		2	%

The ~~6% increase~~12% decrease in other revenue for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018,~~2019, was primarily due to ~~increased~~lower revenue from decreased unit sales from toggled, our LED lighting business, driven by ~~increased product unit sales.~~COVID-19.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Cost of software revenue	$	13,919		$	9,831		$	4,088		42	%	$	14,103		$	13,919		$	184		1	%
As a percent of software revenue		18	%		15	%							16	%		18	%
As a percent of consolidated revenue		14	%		11	%							13	%		14	%

Cost of software revenue ~~increased by $4.1 million, or 42%,~~ for the three months ended September 30, ~~2019, as compared to~~2020, was consistent with the three months ended September 30, ~~2018. This~~2019. The minor increase in the current year period was due to ~~increased employee compensation and related costs of $1.8~~a $0.4 million ~~increased~~increase in hardware costs ~~of $1.2~~offset by a $0.3 million ~~increased third party~~decrease in royalty ~~costs of $0.4 million and increased stock-based compensation expense of $0.4 million.~~fees.

	Three Months Ended September 30,						Period-to-period change						Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$			%			2020			2019			$			%
Cost of software related services revenue	$	6,013		$	6,352		$	(339	)		(5	%)	$	4,996		$	6,013		$	(1,017	)		(17	%)
As a percent of software related services revenue		76	%		73	%								81	%		76	%
As a percent of consolidated revenue		6	%		7	%								5	%		6	%

Cost of software related services revenue decreased 5%17% for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. The decrease in the current year period was primarily due to ~~fluctuations~~our efforts to reduce employee compensation and related costs due to a decline in ~~foreign currency.~~consulting services as a result of COVID-19.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Cost of client engineering services revenue	$	10,160		$	9,817		$	343		3	%	$	8,510		$	10,160		$	(1,650	)		(16	%)
As a percent of client engineering services revenue		79	%		81	%							78	%		79	%
As a percent of consolidated revenue		10	%		11	%							8	%		10	%

Cost of CES revenue ~~increased 3%~~decreased 16% for the three months ended September 30, ~~2019,~~2020, consistent with the decrease in revenue, as compared to the three months ended September 30, ~~2018, due~~2019. We have acted in concert with our customers reduced demand to furlough or curtail the hours and compensation ~~expenses associated with a larger number~~ of ~~placements~~employees until such time as our customers return to ~~meet customer demand.~~normal staffing, billing rates or required working hours.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Cost of other revenue	$	1,649		$	1,204		$	445		37	%	$	1,427		$	1,649		$	(222	)		(13	%)
As a percent of other revenue		90	%		70	%							89	%		90	%
As a percent of consolidated revenue		2	%		1	%							1	%		2	%

Cost of other revenue ~~increased $0.4 million, or 37%~~decreased 13%, for the three months ended September 30, ~~2019,~~2020, consistent with the decrease in revenue, as compared to the three months ended September 30, ~~2018. This increase is due to greater unit sales volumes at lower selling prices in excess of cost reductions for products sold for our LED lighting business.~~2019.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Gross profit	$	68,665		$	59,547		$	9,118		15	%	$	77,420		$	68,665		$	8,755		13	%
As a percent of consolidated revenue		68	%		69	%							73	%		68	%

Gross profit increased by ~~$9.1~~$8.8 million, or ~~15%~~13%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. This increase in gross profit was primarily attributable to the ~~growth of our~~increase in software revenue ~~of $13.6 million driven by the factors described above. The increase in revenue was partially offset by the~~without a corresponding increase in cost of ~~revenue as described above and resulted in the 1% decrease of gross margin in the current year.~~revenue.

Operating expenses, as discussed below, support all the products and services that we provide to our customers and, as a result, they are reported and discussed ~~here~~ in the aggregate.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Research and development	$	29,667		$	24,301		$	5,366		22	%	$	30,678		$	29,667		$	1,011		3	%
As a percent of consolidated revenue		30	%		28	%							29	%		30	%

Research and development expenses increased by ~~$5.4~~$1.0 million, or ~~22%~~3%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. This increase was primarily attributable to ~~higher employee costs of $3.1 million from an increase in our headcount, primarily due to acquisitions, an $0.9 million increase in outsourced development fees as~~ a ~~result of acquisitions, a $0.5~~$1.8 million increase in stock-based compensation expense, ~~and~~partially offset by a ~~$0.3~~$0.5 million ~~increase~~decrease in ~~software maintenance expense.~~travel expenses as a result of COVID-19 restrictions.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Sales and marketing	$	25,790		$	19,243		$	6,547		34	%	$	26,998		$	25,790		$	1,208		5	%
As a percent of consolidated revenue		26	%		22	%							25	%		26	%

Sales and marketing expenses increased by ~~$6.5~~$1.2 million, or ~~34%~~5%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018. Employee~~2019. This increase was primarily attributable to a $2.7 million increase in employee compensation and related expense, ~~increased $4.5 million,~~ primarily due to ~~acquisitions. Travel~~increased headcount and ~~trade show~~merit increases and a $1.3 million increase in stock-based compensation expense. These increases were partially offset by a $2.4 million decrease in travel and selling related expense ~~increased $0.9 million~~from suspension or cancellation of certain in-person sales and ~~stock-based compensation expense~~marketing activities as a result of COVID-19.

General and administrative expenses increased by ~~$0.5~~$0.2 million, inor 1%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. This increase was primarily attributable to a $0.7 million increase in software maintenance and a $0.5 million increase in stock-based compensation expense, partially offset by a $0.7 million decrease in healthcare costs and a $0.5 million decrease in professional fees.

	Three Months Ended September 30,						Period-to-period change					Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
General and administrative	$	20,706		$	17,234		$	3,472		20	%
Amortization of intangible assets												$	3,858		$	3,545		$	313		9	%
As a percent of consolidated revenue		21	%		20	%							4	%		4	%

~~General and administrative expenses~~Amortization of intangible assets increased by ~~$3.5~~$0.3 million, or ~~20%~~9%, for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, 2018. This increase was primarily attributable to a $1.4 million increase in employee compensation and related expenses, a $0.4 million increase in rent expense, a $0.4 million increase in stock-based compensation expense, a $0.3 million increase in professional fees and a $0.2 million increase in software maintenance expense.

~~Amortization of intangible assets increased by $1.8 million for the three months ended September 30, 2019, as compared to the three months ended September 30, 2018.~~2019. This was attributable to an increase in the amortization of developed technology ~~and customer relationships~~ in the current year period primarily as a result of ~~2018 acquisitions.~~acquisitions in the fourth quarter of 2019.

		Three Months Ended September 30,						Period-to-period change						Three Months Ended September 30,						Period-to-period change
(in thousands)		2019			2018			$			%			2020			2019			$		%
Other operating income, net		$	(536	)	$	(4,850	)	$	(4,314	)		(89	%)	$	(1,596	)	$	(536	)	$	1,060		198	%
As a percent of consolidated revenue	��		(1	%)		(6	%)								(1	%)		(1	%)

Other operating income, ~~decreased $4.3~~net increased $1.1 million for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. The ~~prior year period~~three months ended September 30, 2020, includes of a $1.0 million gain ~~on the sale of~~recognized from settlements related to a ~~building for $4.4 million, offset in part by impairment of trade names for $0.6 million as a result of rebranding certain products.~~historical acquisition.

	Three Months Ended September 30,						Period-to-period change			Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%	2020			2019			$		%
Interest expense	$	2,726		$	31		$	2,695	NM	$	2,934		$	2,726		$	208		8	%
As a percent of consolidated revenue		3	%		—	%					3	%		3	%

Interest expense increased ~~$2.7~~$0.2 million for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. The increase in interest expense was primarily the result of amortization of the debt discount and issuance costs on the Convertible Notes in the current year.

	Three Months Ended September 30,						Period-to-period change						Three Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$			%			2020			2019			$		%
Other income, net	$	(588	)	$	(970	)	$	(382	)		39	%	$	(782	)	$	(588	)	$	194		33	%
As a percent of consolidated revenue		(1	%)		(1	%)								(1	%)		(1	%)

Other income, net ~~decreased~~increased by ~~$0.4~~$0.2 million for the three months ended September 30, ~~2019,~~2020, as compared to the three months ended September 30, ~~2018.~~2019. This ~~decrease~~increase was ~~due to~~primarily a ~~$0.7~~result of a $1.2 million increase in gains from foreign currency ~~due to~~ fluctuations in the United States dollar relative to other functional currencies ~~offset by a $0.3 million increase in interest income~~ during the three months ended September 30, ~~2019,~~2020, compared to the three months ended September 30, ~~2018.~~2019. This increase was partially offset by a of $1.0 million decrease in interest income in the current year period due to lower interest rates as compared to the prior year period.

Three Months Ended September 30,

Period-to-period change

Three Months Ended

September 30,

Period-to-period change

(in thousands)

2019

2018

2020

2019

Income tax expense

3,294

1,885

1,409

2,930

3,294

(364

)

(11

The effective tax rate was ~~(26)%~~-53% and ~~67%~~-26% for the three months ended September 30, ~~2019~~2020 and ~~2018,~~2019, respectively. The tax rate is affected by the Company being a U.S. resident taxpayer, the tax rates in the U.S. and other jurisdictions in which the Company operates, the relative amount of income earned by jurisdiction and the relative amount of losses or income for which no benefit or expense is ~~recognized.~~recognized due to a valuation allowance. The Company’s effective tax rate ~~was impacted by~~for the ~~geographic income mix in~~three months ended September 30, 2020 and 2019, ~~as compared to 2018,~~also includes net discrete expense of $1.6 million and net discrete expense of $4.5 million, respectively, primarily related to ~~a United States pre-tax~~withholding taxes on royalties, changes in reserves, changes in accruals for unremitted earnings and other adjustments.

Net loss decreased by $7.4 million for the three months ended September 30, ~~2019, for which a tax benefit was not recognized due to the valuation allowance,~~2020, as compared to ~~a United States pre-tax income of $2.8 million for~~ the three months ended September 30, ~~2018, for which tax expense~~2019. This reduction in net loss was ~~not recognized due~~primarily attributable to an improvement in software revenue in the ~~valuation allowance.~~current period.

Total revenue increased by ~~$41.7~~$1.4 million ~~or 14%,~~ for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. The increase was primarily attributable to an increase in software ~~revenue.~~revenue, partially offset by a decrease in software related services revenue and CES revenue as a result of the slowdown in economic activity by our customers due to COVID-19.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Software revenue	$	265,515		$	224,458		$	41,057		18	%	$	278,086		$	265,515		$	12,571		5	%
As a percent of software segment revenue		91	%		89	%							94	%		91	%
As a percent of consolidated revenue		79	%		77	%							83	%		79	%

The ~~18%~~5% increase in our software revenue for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018,~~2019, was primarily the result of an ~~expansion~~increase in software maintenance revenue recognized, partially offset by a decrease in hardware revenue in the number of units licensed by our existing customers under renewed software license agreements, contributions from recent acquisitions and licensing of units to new customers pursuant to new software license agreements.current year.

	Nine Months Ended September 30,						Period-to-period change						Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$			%			2020			2019			$			%
Software related services revenue	$	25,635		$	26,872		$	(1,237	)		(5	%)	$	18,548		$	25,635		$	(7,087	)		(28	%)
As a percent of software segment revenue		9	%		11	%								6	%		9	%
As a percent of consolidated revenue		8	%		9	%								6	%		8	%

~~The 5% decrease in our software~~Software related services revenue decreased 28% for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018,~~2019. This decrease was primarily the result of ~~fluctuations in foreign currencies. On a constant currency basis, our software related~~customers reducing their demand for these services ~~revenue was relatively consistent with~~primarily due to the ~~prior year.~~

The 2% increase in CES revenue for the nine months ended September 30, 2019, as compared to the nine months ended September 30, 2018, was primarily due to an increase in demand for our consulting services. Client engineering services

Our CES business is primarily affected by customer demand and our ability to fill customers’ open positions. As noted above in response to COVID-19, in April some of our CES customers furloughed staff positions, while some other customers reduced CES staff working hours or reduced billing rates. We have acted in concert with those customers to furlough or curtail the hours and compensation of those impacted employees until such time as our customers return to normal staffing, billing rates, or required working hours. The 8% decrease in CES revenue for the nine months ended September 30, 2020, as compared to the nine months ended September 30, 2019, reflects those steps, offset in part by our ability to fulfill demand for our client engineering services in the first quarter of 2020.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Other revenue	$	6,623		$	5,386		$	1,237		23	%	$	5,460		$	6,623		$	(1,163	)		(18	%)
As a percent of consolidated revenue		2	%		2	%							2	%		2	%

The ~~23% increase~~18% decrease in other revenue for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018,~~2019, was primarily due to ~~increased~~lower revenue from decreased unit sales at lower selling prices from toggled, our LED lighting business, and decreased royalty income of $0.4 million. The decrease in unit sales was driven by ~~increased product unit sales.~~COVID-19.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Cost of software revenue	$	40,655		$	32,736		$	7,919		24	%	$	41,434		$	40,655		$	779		2	%
As a percent of software revenue		15	%		15	%							15	%		15	%
As a percent of consolidated revenue		12	%		11	%							12	%		12	%

Cost of software revenue increased by ~~$7.9~~$0.8 million, or ~~24%~~2%, for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. This increase in the current year was due to increased employee compensation and related costs of ~~$3.7~~$1.3 million, primarily due to increased ~~third party royalty costs of $0.8 million for software programs, $1.8 million in hardware costs, $0.7 million in~~headcount, increased stock-based compensation expense of $0.9 million and increased healthcare costs of $0.5 million. These increases in expenses were partially offset by decreases in travel expense and hardware costs of $1.3 million and $0.3 million, ~~in software maintenance.~~respectively, as compared to the nine months ended September 30, 2019.

	Nine Months Ended September 30,						Period-to-period change						Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$			%			2020			2019			$			%
Cost of software related services revenue	$	19,143		$	19,573		$	(430	)		(2	%)	$	15,141		$	19,143		$	(4,002	)		(21	%)
As a percent of software related services revenue		75	%		73	%								82	%		75	%
As a percent of consolidated revenue		6	%		7	%								4	%		6	%

Cost of software related services revenue decreased ~~$0.4 million, or 2%,~~21% for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. The decrease in the current year period was primarily ~~the~~due to a decrease in employee compensation and related costs due to a decline in consulting services and a decrease in travel expenses as a result of ~~fluctuations in foreign currencies.~~COVID-19 restrictions.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Cost of client engineering services revenue	$	29,993		$	29,977		$	16		0	%	$	27,617		$	29,993		$	(2,376	)		(8	%)
As a percent of client engineering services revenue		80	%		82	%							80	%		80	%
As a percent of consolidated revenue		9	%		10	%							8	%		9	%

Cost of CES revenue ~~was relatively consistent~~decreased 8% for the nine months ended September 30, ~~2019,~~2020, consistent with the decrease in revenue, as compared to the nine months ended September 30, ~~2018.~~2019. In response to reduced customer demand for these services, we furloughed or curtailed the hours and compensation of employees until such time as our customers return to normalized staffing or required working hours.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$			%
Cost of other revenue	$	5,858		$	3,416		$	2,442		71	%	$	4,422		$	5,858		$	(1,436	)		(25	%)
As a percent of other revenue		88	%		63	%							81	%		88	%
As a percent of consolidated revenue		2	%		1	%							1	%		2	%

~~The cost~~Cost of other revenue ~~increase of $2.4 million, or 71%~~decreased 25%, for the nine months ended September 30, ~~2019,~~2020, as a result of the decrease in revenue, as compared to the nine months ended September 30, ~~2018, was primarily~~2019. This decrease is due to ~~greater unit sales volumes at lower selling prices in excess of~~ cost reductions for products sold and lower sales volumes for our LED lighting ~~business, partially offset by decreased third party royalty income of $0.5 million..~~business.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Gross profit	$	239,389		$	207,666		$	31,723		15	%	$	247,866		$	239,389		$	8,477		4	%
As a percent of consolidated revenue		71	%		71	%							74	%		71	%

Gross profit increased ~~by $31.7~~$8.5 million, or ~~15%~~4%, for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. This increase in gross profit was primarily attributable to the ~~growth of our software revenue of $41.1 million driven by the factors described above. The~~ increase in ~~revenue was partially offset by the increase in cost of revenue as described above.~~software revenue.

Operating expenses, as discussed below, support all the products and services that we provide to our customers and, as a result, they are reported and discussed ~~here~~ in the aggregate.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Research and development	$	87,012		$	71,748		$	15,264		21	%	$	91,115		$	87,012		$	4,103		5	%
As a percent of consolidated revenue		26	%		24	%							27	%		26	%

Research and development expenses increased by ~~$15.3~~$4.1 million, or ~~21%~~5%, for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. This increase was primarily attributable to ~~higher employee costs of $9.6~~a $4.1 million resulting from annual compensation adjustments and an increase in our headcount, primarily due to acquisitions. In addition, there was an increase in outsourced development fees of $2.5 million as a result of acquisitions, an increase in stock-based compensation expense, ~~of $1.3~~a $0.6 million ~~and an~~ increase in software maintenance expense ofand a $0.8 million increase in healthcare costs, partially offset by a $1.4 million decrease in travel expense.

Sales and marketing expenses increased by $2.4 million, or 3%, for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~

~~Sales~~2019. Employee compensation and related expense increased $6.4 million, primarily due to increased headcount. Stock-based compensation expense increased by $2.4 million, and healthcare costs increased by $1.0 million. These increases were partially offset by a decrease in travel and selling related expenses of $7.1 million from suspension or cancellation of certain in-person sales and marketing activities as a result of COVID-19.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Sales and marketing	$	78,462		$	57,849		$	20,613		36	%
General and administrative												$	63,499		$	60,886		$	2,613		4	%
As a percent of consolidated revenue		23	%		20	%							19	%		18	%

~~Sales~~General and ~~marketing~~administrative expenses increased by ~~$20.6~~$2.6 million, or ~~36%~~4%, for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. This increase was primarily attributable to ~~higher employee costs of $13.5~~a $1.2 million ~~resulting from annual compensation adjustments and an~~ increase in ~~our headcount, primarily due to acquisitions. Travel and trade show related~~software maintenance expense, ~~increased $2.7~~a $1.0 million ~~and sales and marketing campaigns to support our direct sales force increased $0.8 million. In addition,~~increase in stock-based compensation expense, a $0.9 million increase in employee compensation and related expenses, a $0.7 million increase in consulting expense and a $0.3 million increase in healthcare costs, partially offset by a reduction in professional fees of $1.6 million.

Amortization of intangible assets increased by ~~$1.3~~$0.7 million ~~and $0.5 million, respectively.~~

~~General and administrative expenses increased by $9.3 million, or 18%,~~ for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, 2018. This increase was primarily attributable to higher employee costs of $3.8 million resulting from annual compensation adjustments and an increase in our headcount, primarily due to acquisitions, higher facility costs of $1.6 million, higher professional fees of $1.6 million, higher stock-based compensation expense of $1.1 million, and higher software maintenance expense of $0.6 million.

~~Amortization of intangible assets increased by $5.0 million for the nine months ended September 30, 2019, as compared to the nine months ended September 30, 2018.~~2019. This was attributable to an increase in the amortization of developed technology ~~and customer relationships~~ in the current year period primarily as a result of ~~2018 acquisitions.~~acquisitions in the fourth quarter of 2019.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Other operating income, net	$	(1,702	)	$	(7,433	)	$	5,731		(77	%)	$	(3,431	)	$	(1,702	)	$	1,729		102	%
As a percent of consolidated revenue		(1	%)		(3	%)							(1	%)		(1	%)

Other operating income, ~~decreased $5.7~~net increased by $1.7 million for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018. The prior year period includes~~2019. This increase was primarily the result of a $1.0 million gain onrecognized from settlements related to a historical acquisition in the ~~sale of a building for $4.4 million, a non-recurring adjustment for a change in estimated legal expenses of $2.0~~nine months ended September 30, 2020, and the $1.0 million of ~~income, offset~~non-recurring impairment charges for royalty contracts recognized in ~~part by impairment of trade names for $0.6 million as a result of rebranding certain products.~~the nine months ended September 30, 2019.

	Nine Months Ended September 30,						Period-to-period change			Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%	2020			2019			$		%
Interest expense	$	3,586		$	92		$	3,494	NM	$	8,590		$	3,586		$	5,004		140	%
As a percent of consolidated revenue		1	%		—	%					3	%		1	%

Interest expense increased ~~$3.5~~$5.0 million for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. The increase in interest expense was aprimarily the result of ~~the $2.9 million~~ amortization of the debt discount ~~related to~~and issuance costs on the Convertible Notes ~~and $0.4 million of increased interest expense due to increased borrowings under~~in the ~~line of credit during the nine months ended September 30, 2019.~~current year.

	Nine Months Ended September 30,						Period-to-period change					Nine Months Ended September 30,						Period-to-period change
(in thousands)	2019			2018			$		%			2020			2019			$		%
Other income, net	$	(703	)	$	(2,046	)	$	1,343		(66	%)	$	(1,852	)	$	(703	)	$	1,149		163	%
As a percent of consolidated revenue		(—	%)		(1	%)							(1	%)		—	%

Other income, net ~~decreased~~increased by ~~$1.3~~$1.1 million for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019. This ~~decrease~~increase was ~~due to~~primarily the result of foreign currency fluctuations in the United States dollar relative to other functional currencies during the nine months ended September 30, ~~2019,~~2020, compared to the nine months ended September 30, ~~2018.~~2019. This increase was partially offset by a decrease in interest income in the current year period due to lower interest rates as compared to the prior year period.

Nine Months Ended September 30,

Period-to-period change

Nine Months Ended

September 30,

Period-to-period change

(in thousands)

2019

2018

2020

2019

Income tax expense

7,215

5,617

1,598

10,350

7,215

3,135

The effective tax rate was ~~614%~~-441% and ~~19%~~614% for the nine months ended September 30, ~~2019~~2020 and ~~2018,~~2019, respectively. The tax rate is affected by the Company being a U.S. resident taxpayer, the tax rates in the U.S. and other jurisdictions in which the Company operates, the relative amount of income earned by jurisdiction and the relative amount of losses or income for which no benefit or expense is ~~recognized.~~recognized due to a valuation allowance. The Company’s effective tax rate ~~was impacted by~~for the ~~geographic income mix in~~nine months ended September 30, 2020 and 2019, ~~as compared to 2018,~~also includes net discrete expense of $5.3 million and net discrete expense of $3.3 million, respectively, primarily related to ~~a United States pre-tax~~withholding taxes on royalties, changes in reserves, changes in accruals for unremitted earnings and other adjustments.

Net loss increased by $6.7 million for the nine months ended September 30, ~~2019, for which a tax benefit was not recognized due to the valuation allowance,~~2020, as compared to ~~a United States pre-tax income of $14.8 million for~~ the nine months ended September 30, ~~2018, for which~~2019. This increase was primarily attributable to the increase in stock-based compensation expense, interest expense and tax expense was not recognized due to the valuation allowance. Offsetting the impact to the tax expense and the effective tax rate for September 30, 2019, was a reversal of reserve adjustments recorded for uncertain tax positions of $1.1 million.

In analyzing and planning for our business, we supplement our use of GAAP financial measures with non-GAAP financial measures, including Billings as a liquidity measure, Adjusted EBITDA ~~and Modified Adjusted EBITDA~~ as a performance ~~measures~~measure and Free Cash Flow as a liquidity measure.

	Three Months Ended September 30,					Nine Months Ended September 30,				Three Months Ended September 30,						Nine Months Ended September 30,
(in thousands)	2019			2018		2019		2018		2020			2019			2020		2019
Other financial data:
Billings	$	103,643		$	84,926	$	345,562	$	290,490	$	107,652		$	103,643		$	334,457	$	345,562
Adjusted EBITDA	$	(2,335	)	$	2,399	$	26,814	$	37,252	$	8,175		$	(2,335	)	$	35,596	$	26,814
Modified Adjusted EBITDA	$	(85	)	$	2,399	$	33,564	$	37,252
Free Cash Flow	$	(3,316	)	$	906	$	21,885	$	35,089	$	(7,498	)	$	(3,316	)	$	23,373	$	21,885

Billings. Billings consists of our total revenue plus the change in our deferred revenue, excluding deferred revenue from acquisitions during the period. Given that we generally bill our customers at the time of sale, but typically recognize a portion of the related revenue ratably over time, management believes that Billings is a meaningful way to measure and monitor our ability to provide our business with the working capital generated by upfront payments from our customers. ~~See the table below for information regarding the impact of ASC 606 on Billings for the nine months ended September 30, 2018.~~

Adjusted EBITDA. We define Adjusted EBITDA as net income (loss) adjusted for income tax expense (benefit), interest expense, interest income and other, depreciation and amortization, stock-based compensation expense, restructuring charges, asset impairment charges and other special items as determined by management. Our management team believes that Adjusted EBITDA is a meaningful measure of performance as it is commonly utilized by management and the investment community to analyze operating performance in our industry.

~~Modified Adjusted EBITDA.~~ Modified adjusted EBITDA is consistent with our definition of Adjusted EBITDA; however, it includes the revenue not recognized under GAAP due to acquisition accounting adjustments associated with accounting for deferred revenue in significant business combinations.

Free Cash Flow. Free Cash Flow is a non-GAAP measure that we calculate as cash flow provided by operating activities less capital expenditures. Management believes that Free Cash Flow is useful in analyzing our ability to service and repay debt, when applicable, and return value directly to stockholders.

These non-GAAP financial measures reflect an additional way of viewing aspects of our business that, when viewed with our GAAP results and the accompanying reconciliations to the corresponding GAAP financial measures included in the tables below, may provide a more complete understanding of factors and trends affecting our business. These non-GAAP financial measures should not be relied upon to the exclusion of GAAP financial measures and are by definition an incomplete understanding of the Company and must be considered in conjunction with GAAP measures.

We believe that the non-GAAP measures disclosed herein are only useful as an additional tool to help management and investors make informed decisions about our financial and operating performance and liquidity. By definition, non-GAAP measures do not give a full understanding of the Company. To be truly valuable, they must be used in conjunction with the comparable GAAP measures. In addition, non-GAAP financial measures are not standardized. It may not be possible to compare these financial measures with other companies’ non-GAAP financial measures having the same or similar names. We strongly encourage investors to review our consolidated financial statements and the notes thereto in their entirety and not rely on any single financial measure.

The following table provides a reconciliation of Billings to revenue, the most comparable GAAP financial measure, for each of the periods presented:

	Three Months Ended September 30,						Nine Months Ended September 30,						Three Months Ended September 30,						Nine Months Ended September 30,
(in thousands)	2019			2018			2019			2018			2020			2019			2020			2019
Revenue	$	100,406		$	86,751		$	335,038		$	293,368		$	106,456		$	100,406		$	336,480		$	335,038
Ending deferred revenue		77,043			53,975			77,043			53,975			82,558			77,043			82,558			77,043
Adoption of ASC 606 on beginning deferred revenue		—			—			—			82,909
Beginning deferred revenue		(73,806	)		(55,800	)		(66,519	)		(139,762	)		(80,348	)		(73,806	)		(83,567	)		(66,519	)
Acquisition related deferred revenue														(1,014	)		—			(1,014	)		—
Billings	$	103,643		$	84,926		$	345,562		$	290,490		$	107,652		$	103,643		$	334,457		$	345,562

The following table provides a reconciliation of ~~Modified Adjusted EBITDA and~~ Adjusted EBITDA to net ~~income (loss),~~loss, the most comparable GAAP financial measure, for each of the periods presented:

	Three Months Ended September 30,						Nine Months Ended September 30,						Three Months Ended September 30,						Nine Months Ended September 30,
(in thousands)	2019			2018			2019			2018			2020			2019			2020			2019
Net (loss) income	$	(15,939	)	$	934		$	(6,040	)	$	24,538
Net loss													$	(8,505	)	$	(15,939	)	$	(12,698	)	$	(6,040	)
Income tax expense		3,294			1,885			7,215			5,617			2,930			3,294			10,350			7,215
Stock-based compensation expense		2,292			563			5,584			1,213			6,234			2,292			13,939			5,584
Interest expense		2,726			31			3,586			92			2,934			2,726			8,590			3,586
Interest income and other ⁽¹⁾		(76	)		(4,384	)		633			(5,103	)		(1,041	)		(76	)		(1,501	)		633
Depreciation and amortization		5,368			3,370			15,836			10,895			5,623			5,368			16,916			15,836
Adjusted EBITDA		(2,335	)		2,399			26,814			37,252			8,175			(2,335	)		35,596			26,814
Acquisition related deferred revenue ⁽²⁾		2,250			—			6,750			—
Modified Adjusted EBITDA	$	(85	)	$	2,399		$	33,564		$	37,252

The following table provides a reconciliation of Free Cash Flow to net cash provided by operating activities, the most comparable GAAP financial measure, for each of the periods presented:

	Nine Months Ended September 30,						Nine Months Ended September 30,
(in thousands)	2019			2018			2020			2019
Net cash provided by operating activities	$	30,005		$	40,422		$	27,379		$	30,005
Capital expenditures		(8,120	)		(5,333	)		(4,006	)		(8,120	)
Free cash flow	$	21,885		$	35,089		$	23,373		$	21,885

Recurring Software License Rate. A key factor to our success is our recurring software license rate which we measure through Billings, primarily derived from annual renewals of our existing subscription customer agreements. We calculate our recurring software license rate for a particular period by dividing (i) the sum of software term-based license Billings, software license maintenance Billings, and 20% of software perpetual license Billings which we believe approximates maintenance as an element of the arrangement by (ii) the total software license Billings including all term-based subscriptions, maintenance, and perpetual license billings from all customers for that period. For the nine months ended September 30, 2020 and 2019, our recurring software license rate was 92% and 88%., respectively. The recurring software license rate may vary from period to period.

Our principal sources of liquidity have been the net payments received from global customers using our software and services and proceeds from our initial public offering, follow-on offering and ~~more recently~~ our convertible debt offering, as well as periodic draws on our credit facilities, when needed. We believe that funds generated from operations, with cash and cash equivalents and the amounts available to us to borrow under our credit facility, will be sufficient to meet our anticipated cash needs for at least the next 12 months.

In June 2019, we issued $230.0 million aggregate principal amount of Convertible Notes. See Note 8 in the Notes to consolidated financial statements in Item 1, Part I of this Quarterly Report on Form 10-Q.

We have commenced the ~~initial~~ planning to update zoning to allow for future expansion of our corporate headquarters facilities on the adjacent property we own to enable development consistent with our long-term needs. We have not yet determined the nature and scope of the overall timeline and investment beyond the immediate rezoning efforts necessary for our potential use in the future. Over the next 12 months, we expect to continue to advance this project, although we are considering the business impacts of COVID-19 on the nature and timing of this project.

We continue to evaluate possible acquisitions and other strategic transactions designed to expand our business. As a result, our expected uses of cash could change, our cash position could be reduced, or we may incur additional debt obligations to the extent we complete additional acquisitions.

Our existing cash and cash equivalents may fluctuate during fiscal 2020, due to changes in our planned cash expenditures, including changes in incremental costs such as direct costs and integration costs related to acquisitions. Cash from operations could also be affected by various risks and uncertainties, including, but not limited to, the effects of COVID-19. It is possible that certain customers may unilaterally decide to extend payments on accounts receivable, however the Company’s customer base is comprised primarily of larger organizations with previously strong liquidity and capital resources.

We believe that our existing cash balances, together with funds generated from operations and amounts available under our credit facility, will be sufficient to finance our operations and meet our foreseeable cash requirements for the next twelve months. We also believe that our financial resources,along with managing discretionary expenses,will allow us to manage the impact of COVID-19 on our business operations for the foreseeable future, which could include reductions in revenue and delays in payments from customers and partners. We will continue to evaluate our financial position as developments evolve relating to COVID-19.

We have a $150.0 million credit facility ~~that was amended on June 5, 2019, to permit the issuance of the Convertible Notes and extend the~~with a maturity date of ~~the credit facility to~~ December 15, 2023 (“2019 Amended Credit Agreement”). The 2019 Amended Credit Agreement allows us to request that the aggregate commitments under the 2019 Amended Credit Agreement be increased by up to $50.0 million for a total of $200.0 million, subject to certain conditions.

As of September 30, ~~2019,~~2020, we had no$30.0 million of outstanding borrowings under the 2019 Amended Credit Agreement and there was ~~$150.0~~$120.0 million available for future borrowing. The 2019 Amended Credit Agreement is available for general corporate purposes, including working capital, capital expenditures and permitted acquisitions. At September 30, ~~2019,~~2020, we were in compliance with the financial covenants.

For additional information about the 2019 Amended Credit Agreement, see Note 87 in the Notes to consolidated financial statements in Item 1, Part I of this Quarterly Report on Form 10-Q.

As of September 30, ~~2019,~~2020, we had aggregate cash and cash equivalents of ~~$246.9~~$245.4 million available for working capital purposes, acquisitions, and capital expenditures; ~~$210.3~~$187.3 million of this aggregate amount was held in the United States and ~~$31.6~~$49.3 million was held in the APAC and EMEA ~~regions.~~regions with the remainder held in Canada, Mexico and South America.

Other than statutory limitations, there are no significant restrictions on the ability of our subsidiaries to pay dividends or make other distributions to Altair. Based on our current liquidity needs and repatriation strategies, we expect that we can manage our global liquidity needs without material adverse tax implications. The 2017 changes in U.S. tax law could materially affect our tax obligations. For further discussion, please see our ~~2018~~2019 Annual Report on Form 10-K, “Item 1A. Risk Factors – New legislations or tax-reform policies that would change U.S. or foreign taxation of international business activities, including uncertainties in the interpretation and application of the 2017 Tax Cuts and Jobs Act, could materially affect our tax obligations and effective tax rate.”

	Nine Months Ended September 30,						Nine Months Ended September 30,
(in thousands)	2019			2018			2020			2019
Net cash provided by operating activities	$	30,005		$	40,422		$	27,379		$	30,005
Net cash used in investing activities		(9,286	)		(17,408	)		(36,566	)		(9,286	)
Net cash provided by financing activities		191,960			136,514			30,693			191,960
Effect of exchange rate changes on cash, cash equivalents and restricted cash		(1,065	)		(1,354	)		676			(1,065	)
Net increase in cash, cash equivalents and restricted cash	$	211,614		$	158,174		$	22,182		$	211,614

Net cash provided by operating activities for the nine months ended September 30, ~~2019~~2020 was ~~$30.0~~$27.4 million, which reflects a decrease of ~~$10.4~~$2.6 million compared to the nine months ended September 30, ~~2018.~~2019. This decrease was the result of ~~the reduction in net income and~~ changes to our working capital position, offset in part by an increase in our net loss for the nine months ended September 30, ~~2019,~~2020, as compared to the nine months ended September 30, ~~2018.~~2019.

Net cash used in investing activities for the nine months ended September 30, ~~2019~~2020 was ~~$9.3~~$36.6 million, which reflects ~~a decrease~~an increase of ~~$8.1~~$27.3 million compared to the nine months ended September 30, ~~2018.~~2019. This ~~decrease~~increase was primarily the result of ~~a decrease in~~net cash payments of $32.3 million for business acquisitions infor the nine months ended September 30, ~~2019,~~2020, partially offset by a $4.1 million reduction in cash ~~received from the sale of a building in~~payments for capital expenditures as compared to the nine months ended September 30, ~~2018.~~2019.

Net cash provided by financing activities for the nine months ended September 30, ~~2019~~2020 was $30.7 million, compared to cash provided by financing activities of $192.0 million ~~which reflects an increase in cash provided of $55.4 million compared with~~for the nine months ended September 30, ~~2018.~~2019. For the nine months ended September 30, 2020, we had cash borrowings on our revolving credit facility of $30.0 million. For the nine months ended September 30, 2019, we received aggregate proceeds of $223.1 million from our Convertible Notes offering, net of underwriters’ discounts and commissions, and we had net cash payments on our revolving ~~commitment~~credit facility of $31.0 million. For the nine months ended September 30, 2018, we received aggregate proceeds of $135.6 million from our follow-on public offering, net of underwriters’ discounts and commissions, and we did not have any borrowings.

There were favorable effects of exchange rate changes on cash, cash equivalents and restricted cash of $0.7 million for the nine months ended September 30, 2020, compared toadverse effects of exchange rate changes on cash, cash equivalents and restricted cash of $1.1 million for the nine months ended September 30, ~~2019,~~2019.

We borrowed $30.0 million ~~for~~against our revolving credit facility during the nine months ended September 30, ~~2018.~~

~~Contractual obligations and~~2020. There were no other material changes in our commitments

~~Our principal commitments and contractual obligations consist of our Convertible Notes due in 2024, and obligations~~ under ~~operating leases for office facilities. The following summarizes our non-cancelable~~ contractual obligations as ~~of September 30, 2019:~~disclosed in our Annual Report on Form 10-K for the year ended December 31, 2019.

Through September 30, ~~2019,~~2020, we did not have any relationships with unconsolidated organizations or financial partnerships, such as structured finance or special purpose entities that would have been established for the purpose of facilitating off-balance sheet arrangements or other contractually narrow or limited purposes.

See Note 32 in the Notes to consolidated financial statements in Item 1, Part I of this Quarterly Report on Form 10-Q for a full description of the recent accounting pronouncements and our expectation of their impact, if any, on our results of operations and financial condition.

We are exposed to certain global market risks, including foreign currency exchange risk and interest rate risk primarily associated with our ~~debt.~~revolving credit facility.

As a result of our substantial international operations, we are exposed to foreign currency risks that arise from our normal business operations, including in connection with our transactions that are denominated in foreign currencies. In addition, we translate sales and financial results denominated in foreign currencies into United States dollars for purposes of our consolidated financial statements. As a result, appreciation of the United States dollar against these foreign currencies generally will have a negative impact on our reported revenue and operating income while depreciation of the United States dollar against these foreign currencies will generally have a positive effect on reported revenue and operating income.

To date, we have not entered into any foreign currency hedging contracts, since exchange rate fluctuations have not had a material impact on our operating results and cash flows. Based on our current international structure, we do not plan on engaging in hedging activities in the near future.

In June 2019, we issued $230.0 million aggregate principal amount of 0.250% ~~Convertible Notes.~~convertible senior notes due 2024. Our Convertible Notes have fixed annual interest rates at 0.250% and, therefore, we do not have economic interest rate exposure on our Convertible Notes. However, the value of the Convertible Notes is exposed to interest rate risk. Generally, the fair market value of our fixed interest rate Convertible Notes will increase as interest rates fall and decrease as interest rates rise. In addition, the fair values of the Convertible Notes are affected by our stock price. The fair value of the Convertible Notes will generally increase as our Class A common stock price increases in value and will generally decrease as our Class A common stock price declines in value. Additionally, we carry the Convertible Notes at face value less unamortized discount and issuance costs on our balance sheet, and we present the fair value for required disclosure purposes only.

As of September 30, ~~2019,~~2020, we had cash, cash equivalents and restricted cash of ~~$247.3~~$245.7 million, consisting primarily of bank deposits and money market funds. ~~As of~~At September 30, ~~2019,~~2020, we had no$30.0 million of outstanding borrowings under our 2019 Amended Credit Agreement. Such interest-bearing instruments carry a degree of interest rate risk; however, historical fluctuations of interest expense have not been significant.

Interest rate risk relates to the gain/increase or loss/decrease we could incur on our debt balances and interest expense associated with changes in interest rates. Changes in interest rates would impact the amount of interest income we realize on our invested cash balances. It is our policy not to enter into derivative instruments for speculative purposes, and therefore, we hold no derivative instruments for trading purposes.

The Company maintains disclosure controls and procedures (as defined in Rule 13a-15(e) or 15d-15(e) of the Exchange Act) that are designed to ensure that information required to be disclosed in periodic reports filed with the SEC under the Securities Exchange Act of 1934 is recorded, processed, summarized and reported within the time periods specified in the SEC’s rules and forms, and that such information is accumulated and communicated to the Company’s management, including its Chief Executive Officer and Chief Financial Officer, as appropriate, to allow timely decisions regarding required disclosure.Under the supervision and with the participation of our management, including the Chief Executive Officer and Chief Financial Officer, we have evaluated the effectiveness of our disclosure controls and procedures as defined in Rule 13(a)-15(e) under the Exchange Act as of the end of the period covered by this report. Based on that evaluation, the Chief Executive Officer and Chief Financial Officer have concluded that ~~these~~our disclosure controls and procedures were ~~not~~ effective as of September 30, ~~2019, due to a material weakness identified in connection with the audit of our fiscal year 2018 financial statements.~~

~~The material weakness pertained to controls over accounting for income taxes.~~ We determined that management’s review controls over income taxes are not operating effectively to detect a material misstatement in the financial statements related to income tax accounting around acquisitions, as well as routine and non-routine transactions. ~~We have taken steps to remediate this material weakness by~~enhancing our preparation and review procedures around income tax accounting, which includes supplementing our resources by using an independent consultant with technical expertise in tax accounting for acquisitions and routine and non-routine transactions.

Effective internal control over financial reporting is necessary for us to provide reliable and timely financial reports and, together with adequate disclosure controls and procedures, are designed to reasonably detect and prevent fraud. Any failure to implement required new or improved controls, or difficulties encountered in their implementation could cause us to fail to meet our reporting obligations.2020.

There was no change in our internal control over financial reporting (as defined in Rules 13a-15(f) and 15d-15(f) under the Exchange Act) that occurred during the quarter ended September 30, ~~2019,~~2020, that has materially affected, or is reasonably likely to materially affect, our internal control over financial reporting.

The Swedish Tax Authorities, or STA, have assessed tax (net of utilization of tax attributes), penalties and interest in the amount of $6.2 million related to the acquisition of Panopticon AB by Datawatch Corporation, in 2013 for the years 2013, 2014 and 2015. The STA, upon auditing the acquisition transaction, reached a conclusion that post acquisition, certain assets were removed from Sweden, triggering the tax obligation. The STA is also of the opinion that some services related to product development provided to the new parent company in the U.S. were performed by Panopticon AB at a price below market price triggering tax obligations. Datawatch contested the findings by the STA throughout the audit process including contesting the STA position in the first level of administrative courts.On May ~~10,~~29, 2019, the ~~Company discovered potential violations~~Administrative Court issued its ruling in favor of ~~U.S. economic sanctions and export control laws and immediately~~Datawatch AB. On July 4, 2019, the STA filed ~~preliminary self-disclosure notices~~an appeal of the Administrative Court ruling with the ~~U.S. Treasury Department’s Office~~Administrative Court of ~~Foreign Assets Control (“OFAC”) and the U.S. Commerce Department’s Bureau of Industry & Security (“BIS”).~~

The Company subsequently conducted an internal investigation into these issues under the direction of outside legal counsel and filed voluntary self-disclosures with both agencies on July 25, 2019. These disclosures describe the unintentional transfer of commercial software and trial software licensesAppeals in Stockholm, effectively continuing to various individuals located in Iran and other restricted countries. These transfers involved freeware, trial software licenses, and volunteer software testing communities. The Company did not discover any evidence indicating any commercial transactions with restricted parties or countries.

In addition to filing voluntary self-disclosures with OFAC and BIS, the Company has implemented a series of additional compliance measures to prevent unintentional transfers of the sort described above. These measures will further enhance the Company’s international trade compliance program, which is designed to assureassert that the ~~Company does not conduct business directly or indirectly with any countries or parties subject to U.S. economic sanctions and export control laws.~~

~~On August 30, 2019, BIS notified the Company that it had completed its investigation of the potential violation of U.S. export control laws~~assessments are in fact appropriate. After relevant submissions by the Company and ~~concluded that no criminal or administrative prosecution was warranted and closed~~ the ~~matter.~~STA, the Court of Appeals held a hearing on February 20, 2020.

~~Although OFAC has not notified~~On March 27, 2020, the Court of Appeals issued its finding in favor of the STA. Pursuant to requirements in Sweden, the Company paid the assessed tax, penalties and interest on April 24, 2020. The Company, in accordance with its right to appeal the ruling to the Administrative Supreme Court of ~~its findings or~~Sweden, filed an appeal of the ~~completion~~Court of ~~its investigations,~~Appeals ruling citing specific grounds for reconsideration. On November 4, 2020, the ~~Company does~~Supreme Administrative Court issued a decision that they would not ~~currently have~~grant leave to appeal, effectively eliminating any reason to believe that its voluntary self-disclosures (or any related U.S. Government investigations) will have a meaningful impact on its operations, results of operations for any future period, or financial condition.further appeal rights in this matter.

As previously described in the Company’s Annual Report on Form 10-K for the year ended December 31, ~~2018,~~2019, the Company is subject to ~~other~~ legal ~~proceedings. Except as set forth above,~~proceedings for which there were no other material changes ~~in such matters~~ during the nine months ended September 30, ~~2019.~~2020.

The risk ~~factors~~factor set forth below ~~supplement~~supplements the risk factors previously disclosed in Part I, Item 1A. "Risk Factors" in ~~our~~the Company’s Annual Report on Form 10-K for the year ended December 31, ~~2018.~~

~~Our 0.250% Convertible Senior Notes due 2024, or the Convertible Notes, are effectively subordinated to our secured debt and any liabilities of our subsidiaries.~~2019.

The ~~Convertible Notes rank senior in right~~COVID-19 pandemic, or other potential future pandemics or events, may cause severe business interruptions either globally or regionally, that could have a negative impact on our financial results.

In March 2020, the World Health Organization declared the outbreak of ~~payment~~a novel coronavirus (COVID-19) pandemic. The outbreak of the COVID-19 pandemic has significantly affected our customers, the global economy and financial markets. The full extent to ~~any of our indebtedness that is expressly subordinated in right of payment to the Convertible Notes; equal in right of payment to any of our liabilities~~which COVID-19 will impact global or regional economies will depend on future developments that are ~~not so subordinated; effectively junior in right of payment~~highly uncertain and cannot be accurately predicted. New information is likely to any of our secured indebtedness (including all amounts outstanding under our revolving credit facility) to the extent of the value of the assets securing such indebtedness; and structurally junior to all indebtedness and other liabilities (including trade payables) of our subsidiaries. In the event of our bankruptcy, liquidation, reorganization or other winding up, our assets that secure debt ranking senior or equal in right of payment to the Convertible Notes (including all amounts outstanding under our revolving credit facility) will be available to pay obligations on the Convertible Notes only after the secured debt has been repaid in full from these assets,emerge concerning COVID-19 and the ~~assets of our subsidiaries will be available~~actions to ~~pay obligations~~contain it or treat it with uncertain economic impact on the Convertible Notes only after all claims senior to the Convertible Notes have been repaid in full. There may not be sufficient assets remaining to pay amounts due on any or all of the Convertible Notes then outstanding.local, regional, national, and international markets. The indenture governing the Convertible Notes will not prohibit us from incurring additional senior debt or secured debt, nor does it prohibit any of our subsidiaries from incurring additional liabilities.

~~The Convertible Notes are our obligations only and a substantial portion of our operations are conducted through, and a substantial portion of our consolidated assets are held by, our subsidiaries.~~

The Convertible Notes are our obligations exclusively and are not guaranteed by any of our operating subsidiaries. A substantial portion of our operations is conducted through, and a substantial portion of our consolidated assets is held by, our subsidiaries. Accordingly, our ability to service our debt, including the Convertible Notes, depends in part on theCompany's future results of operations, ~~of our subsidiaries~~financial condition and ~~upon~~cash flows could be materially adversely affected by COVID-19, particularly if the ability of such subsidiaries to provide us with cash, whether in the form of dividends, loans or otherwise, to pay amounts due on our obligations, including the Convertible Notes. Our subsidiaries are separate and distinct legal entities and have no obligation, contingent or otherwise, to make payments on the Convertible Notes or to make any funds availablepandemic persists for ~~that purpose. In addition, dividends, loans or other distributions to us from such subsidiaries may be subject to contractual and other restrictions and are subject to other business considerations.~~

~~Servicing our debt will require~~ a significant amount of ~~cash,~~time causing a substantial longer-term contraction in business for the Company’s customer base, prior to eventual recovery.

Many governments have enacted a rapid massive global response leveraging monetary and ~~we may not have sufficient cash flow from our business~~fiscal policy to ~~pay our substantial debt.~~

~~Our ability to make scheduled payments~~mitigate long term economic harm, while providing short term economic support. While the implementation of policy responses varies country by country, and regionally, the totality of the ~~principal~~global response is based upon expectations that the response will serve to minimize the chance for a deep prolonged negative economic impact from COVID-19. Certain jurisdictions have begun to “re-open” their economies, within a relatively short time period of having engaged in substantial closure of most economic activity. Other jurisdictions have begun to ~~pay interest on,~~consider moves to gradually “re-open” or have actually “re-opened”. In certain instances, governments deemed it necessary to ~~refinance our future indebtedness, including~~reverse re-opening planning. The long term outcome of mitigation efforts is presently uncertain.

Additional risks from COVID-19 include the amounts payable under our revolving credit facility and the Convertible Notes, depends on our future performance, which is subject to economic, financial, competitive and other factors beyond our control. Our business may not continue to generate cash flow from operations in the future sufficient to service our debt and make necessary capital expenditures. If we are unable to generate such cash flow, we may be required to adopt one or more alternatives, such as selling assets, restructuring debt or obtaining additional equity capital on terms that may be onerous or highly dilutive. Our ability to refinance our indebtedness will depend on the capital markets and our financial condition at such time. We may not be able to engage in any of these activities or engage in these activities on desirable terms, which could result in a default on our debt obligations. In addition, anyinability of our ~~future debt agreements may contain restrictive covenants~~employees and those businesses upon which we rely for operations to carry out their responsibilities at levels of performance necessary to maintain our performance undisturbed as a result of measures taken by governmental authorities to limit the spread of COVID-19. It is possible that ~~may prohibit us from adopting any of these alternatives. Our failure to comply with these covenants could result in an event of default which, if not cured or waived, could result in the acceleration~~some of our ~~debt.~~

~~We may still incur substantially more debt or take other actions which would intensify the risks discussed above.~~

We and our subsidiaries may be able to incur substantial additional debt in the future, subject to the restrictions contained in our debt instruments, some of which may be secured debt. We will not be restricted under the terms of the indenture governing the Convertible Notes from incurring additional debt, securing existing or future debt, recapitalizing our debt or taking a number of other actions that are not limited by the terms of the indenture governing the Convertible Notes that could have the effect of diminishing our ability to make payments on the Convertible Notes when due. Our existing revolving credit facility restricts our ability to incur additional indebtedness, including secured indebtedness, but if the facility matures or is repaid, we may not be subject to such restrictions under the terms of any subsequent indebtedness.

We may not have the ability to raise the funds necessary to settle conversions of the Convertible Notes in cash or to repurchase the Convertible Notes upon a fundamental change, and our current debt contains, and our future debt may contain, limitations on our ability to pay cash upon conversion or repurchase of the Convertible Notes.

Holders of the Convertible Notes will have the right to require us to repurchase their Convertible Notes upon the occurrence of a fundamental change at a defined repurchase price equal to 100% of the principal amount of the Convertible Notes to be repurchased, ~~plus~~ accrued and unpaid interest, if any. In addition, upon conversion of the Convertible Notes, unless we elect to deliver solely shares of our Class A common stock to settle such conversion (other than paying cash in lieu of delivering any fractional share), we will be required to make cash payments in respect of the Convertible Notes being converted. However, we may not have enough available cash or be able to obtain financing at the time we are required to make repurchases of Convertible Notes surrendered therefor or Convertible Notes being converted.

In addition, our ability to repurchase the Convertible Notes or to pay cash upon conversions of the Convertible Notes may be limited by law, by regulatory authority or by agreements governing our indebtedness including our existing revolving credit facility. Our failure to repurchase Convertible Notes at a time when the repurchase is required by the indenture or to pay any cash payable on future conversions of the Convertible Notes as required by the indenture would constitute a default under the indenture. A default under the indenture or the occurrence of a fundamental change itself would likely also lead to a default under our revolving credit facility, and may lead to a default under agreements governing our future indebtedness. If the repayment of the related indebtedness were to be accelerated after any applicable notice or grace periods, we may not have sufficient funds to repay the indebtedness and repurchase the Convertible Notes or make cash payments upon conversions thereof.

~~Our revolving credit facility limits our ability to pay any cash amount upon the conversion or repurchase of the Convertible Notes.~~

Our existing revolving credit facility prohibits us from making any cash payments on the conversion or repurchase of the Convertible Notes if a default under such credit facility exists or would be created thereby. In addition, our ability to make cash payments on the conversion or repurchase of the Convertible Notes will be limited to the extent wefurloughed CES personnel do not ~~satisfy certain financial covenant tests after giving effect~~return to ~~such payments. Any new credit facility that we~~work when their positions return. COVID-19 may enter into may have similar restrictions. Our failure to make cash payments upon the conversion or repurchase of the Convertible Notes as required under the terms of the Convertible Notes would permit holders of the Convertible Notes to accelerate our obligations under the Convertible Notes.

~~The conditional conversion feature of the Convertible Notes, if triggered, may adversely~~also affect our operating and financial ~~condition and operating results.~~

In the event the conditional conversion feature of the Convertible Notes is triggered, holders of Convertible Notes will be entitled to convert the Convertible Notes at any time during specified periods at their option. If one or more holders elect to convert their Convertible Notes, unless we elect to satisfy our conversion obligation by delivering solely shares of our Class A common stock (other than paying cash in lieu of delivering any fractional share), we would be required to settle a portion or all of our conversion obligation through the payment of cash, which could adversely affect our liquidity. In addition, even if holders of the Convertible Notes do not elect to convert their Convertible Notes, we could be required under applicable accounting rules to reclassify all or a portion of the outstanding principal of the Convertible Notes as a current rather than long-term liability, which would result in a material reduction of our net working capital.

~~The accounting method for convertible debt securities that may be settled in cash, such as the Convertible Notes, could have a material effect on our reported financial results.~~

Under Financial Accounting Standards Board Accounting Standards Codification 470-20, Debt with Conversion and Other Options (“ASC 470-20”), an entity must separately account for the liability and equity components of the convertible debt instruments (such as the Convertible Notes) that may be settled entirely or partially in cash upon conversionresults in a manner that ~~reflects the issuer’s economic interest cost. The effect of ASC 470-20 on the accounting for the Convertible Notes~~ is not presently known to us, or that ~~the equity component is required~~we currently to be included in the additional paid-in capital section of stockholders’ equity on our consolidated balance sheet, and the value of the equity component would be treated as debt discount for purposes of accounting for the debt component of the Convertible Notes. As a result, we will be required to record a greater amount of non-cash interest expense in current periods presented as a result of the amortization of the discounted carrying value of the Convertible Notes to their face amount over the term of the Convertible Notes. We will report larger net losses (or lower net income) in our financial results because ASC 470-20 will require interest to include both the current period’s amortization of the debt discount and the instrument’s coupon interest, which could adversely affect our reported or future financial results, the trading price of our Class A common stock and the trading price of the Convertible Notes.

In addition, under certain circumstances, convertible debt instruments (such as the Convertible Notes) that may be settled entirely or partly in cash are currently accounted for utilizing the treasury stock method, the effect of which is that the shares issuable upon conversion of the Convertible Notes aredo not included in the calculation of diluted earnings per share except to the extent that the conversion value of the Convertible Notes exceeds their principal amount. Under the treasury stock method, for diluted earnings per share purposes, the transaction is accounted for as if the number of shares of Class A common stock that would be necessary to settle such excess, if we elected to settle such excess in shares, are issued. We cannot be sure that the accounting standards in the future will continue to permit the use of the treasury stock method. If we are unable to use the treasury stock method in accounting for the shares issuable upon conversion of the Convertible Notes, then our diluted earnings per share would be adversely affected.

~~Transactions relating to the Convertible Notes may affect the value of our Class A common stock.~~

The conversion of some or all of the Convertible Notes would dilute the ownership interests of existing stockholders to the extent we satisfy our conversion obligation by delivering shares of our Class A common stock upon any conversion of the Convertible Notes. If holders of our Convertible Notes elect to convert their notes, we may settle our conversion obligation by delivering to them aconsider presenting significant ~~number of shares of our Class A common stock, which would cause dilution~~risks to our ~~existing stockholders.~~

On ~~October 7, 2019,~~September 9, 2020, in connection with the acquisition of ~~Polliwog Co. Ltd.~~Ellexus Limited (“~~Polliwog”~~Ellexus”), the Company issued ~~or agreed~~ to ~~issue, to shareholders~~the stockholders of ~~Polliwog~~Ellexus an aggregate of ~~459,539~~40,000 shares of the Company’s Class A Common Stock, par value $0.0001 per ~~share (the “SPA Stock Consideration”). Forty percent of~~share. Of those shares, 10,000 shares are subject to indemnification claims that the ~~SPA Stock Consideration (183,815 shares) was issued at closing and is~~Company may make in the future. All shares are subject to customary securities law restrictions on transferability for the first six months after the closing. The remaining sixty percent (an aggregate of 275,724 shares) of the SPA Stock Consideration will be issuable in equal installments of 91,908 shares on each of the one, two and three year anniversaries of the closing, subject to potential reduction in certain circumstances.transferability. All shares ~~of Class A Common Stock issued or to be issued as the SPA Stock Consideration~~ were ~~or will be~~ issued without registration under the Securities Act of 1933, as amended (the “Securities Act”), pursuant to Section 4(a)(2) of the Securities Act. ~~Polliwog’s~~Ellexus’ existing stockholders provided customary representations for a private placement of securities and agreed to customary restrictions on transferability.

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.

Delaware		38-2591828
(State or other jurisdiction of incorporation or organization)		(I.R.S. Employer Identification No.)

1820 East Big Beaver Road, Troy, Michigan		48083
(Address of principal executive offices)		(Zip Code)


Title of each class	Trading Symbol	Name of each exchange on which registered
Class A Common Stock $0.0001 par value per share	ALTR	The NASDAQ Stock Market

				Page

PART I.	FINANCIAL INFORMATION

	Item 1.	Financial Statements – Unaudited		3

		a)	Consolidated Balance Sheets	3

		b)	Consolidated Statements of Operations	4

		c)	Consolidated Statements of Comprehensive Income (Loss)	5

		d)	Consolidated Statements of Changes in Stockholders’ Equity	6

		e)	Consolidated Statements of Cash Flows	8

		f)	Notes to Consolidated Financial Statements	9

	Item 2.	Management’s Discussion and Analysis of Financial Condition and Results of Operations		3329

	Item 3.	Quantitative and Qualitative Disclosures About Market Risk		5148

	Item 4.	Controls and Procedures		5249

PART II.	OTHER INFORMATION

	Item 1.	Legal Proceedings		5350

	Item 1A.	Risk Factors		5350

	Item 2.	Unregistered Sales of Equity Securities and Use of Proceeds		5651

	Item 3.	Defaults Upon Senior Securities		5651

	Item 4.	Mine Safety Disclosures		5651

	Item 5.	Other Information		5651

	Item 6.	Exhibits		5752

SIGNATURES				5853

	December 31, 2018
	As Reported			Adjustments			As Corrected
Deferred tax assets	$	1,373		$	3,981		$	5,354
Total assets	$	483,216		$	3,981		$	487,197
Other accrued expenses and current liabilities	$	27,565		$	(526	)	$	27,039
Total current liabilities	$	127,758		$	(526	)	$	127,232
Other long-term liabilities	$	28,153		$	(2,397	)	$	25,756
Total liabilities	$	194,082		$	(2,923	)	$	191,159
Accumulated deficit	$	(82,005	)	$	7,142		$	(74,863	)
Accumulated other comprehensive loss	$	(11,052	)	$	(238	)	$	(11,290	)
Total stockholders' equity	$	286,782		$	6,904		$	293,686
Total liabilities, mezzanine equity and stockholders' equity	$	483,216		$	3,981		$	487,197

	Year Ended December 31, 2018
	As Reported		Adjustments			As Corrected
Income before income taxes	$	27,024	$	—		$	27,024
Income tax expense	$	13,309	$	(1,820	)	$	11,489
Net income	$	13,715	$	1,820		$	15,535
Net income per share attributable to common stockholders, basic	$	0.20	$	0.03		$	0.23
Net income per share attributable to common stockholders, diluted	$	0.18	$	0.03		$	0.21

Large accelerated filer	☒	Accelerated filer	☐
Non-accelerated filer	☐	Smaller reporting company	☐
		Emerging growth company	☐

	Year Ended December 31, 2017
	As Reported			Adjustments			As Corrected
Loss before income taxes	$	(36,411	)	$	—		$	(36,411	)
Income tax expense	$	62,996		$	2,534		$	65,530
Net loss	$	(99,407	)	$	(2,534	)	$	(101,941	)
Net income per share attributable to common stockholders, basic	$	(1.89	)	$	(0.05	)	$	(1.94	)
Net income per share attributable to common stockholders, diluted	$	(1.89	)	$	(0.05	)	$	(1.94	)

Fair value of consideration transferred	$	183,427
Recognized amounts of identifiable assets acquired and liabilities assumed:
Cash		8,278
Accounts receivable		10,384
Other assets		2,522
Property and equipment		980
Trade names		7,400
Developed technology (6-year life)		22,600
Customer relationships (10-year life)		16,700
Accounts payable and other liabilities		(5,041	)
Deferred revenue		(3,649	)
Other long-term liabilities		(8,340	)
Total net identifiable assets acquired and liabilities assumed		51,834
Goodwill ⁽¹⁾	$	131,593

Balance at December 31, 2018	$	210,532
Effects of foreign currency translation and other		(32	)
Balance at September 30, 2019	$	210,500

Balance at December 31, 2019	$	233,683
Acquisitions		36,998
Effects of foreign currency translation and other		(30	)
Balance at September 30, 2020	$	270,651

	September 30,
	2019
Proceeds allocated to the conversion option (debt discount)	$	51,842
Less: issuance costs		1,833
Net carrying amount	$	50,009

(in thousands, except lease term and discount rate)
Operating leases:
Operating lease ROU assets	$	26,507

Current portion of operating lease liabilities	$	8,891
Operating lease liabilities, net of current portion		18,831
Total operating lease liabilities	$	27,722

Weighted average remaining lease term	4.1 years
Weighted average discount rate		5.5	%

Finance leases:
Property and equipment	$	2,660
Accumulated depreciation		(1,287	)
Property and equipment, net	$	1,373

Current portion of long-term debt	$	437
Long-term debt, net of current portion		741
Total finance lease liabilities	$	1,178

Weighted average remaining lease term		2.9
Weighted average discount rate		3.5	%

Cash paid for amounts included in the measurement of lease liabilities:
Operating cash flows from operating leases	$	(8,489	)
Operating cash flows from finance leases	$	(36	)
Financing cash flows from finance leases	$	(323	)

ROU assets obtained in exchange for lease obligations:
Operating leases	$	7,304
Finance leases	$	588

Year ending December 31,
2019 (excluding the nine months ended September 30, 2019)	$	2,809
2020		9,483
2021		7,202
2022		4,954
2023		2,964
Thereafter		3,291
Total lease payments		30,703
Less: imputed interest		2,981
Total operating lease liabilities	$	27,722

	Number of RSUs
Outstanding at January 1, ~~2019~~2020		~~206,061~~781,301
Granted		~~689,642~~587,223
Vested		(~~54,388~~209,341	)
Forfeited		(~~39,330~~35,491	)
Outstanding at September 30, ~~2019~~2020		~~801,985~~1,123,692

	2019 grants
Weighted average grant date fair value per share	$	38.11
Expected volatility		42	%
Expected term (in years)	6.25
Risk-free interest rate		1.80	%
Expected dividend yield		0	%

	2020 grants
Weighted average grant date fair value per share	$ 38.11 - 39.82
Expected volatility	35 - 42%
Expected term (in years)	6.25
Risk-free interest rate	0.46 - 1.80%
Expected dividend yield		0	%

			Payments due by period
(in thousands)	Total		Less than 1 year		1-3 years		3-5 years		More than 5 years
Convertible senior notes	$	230,000	$	—	$	—	$	230,000	$	—
Aggregate interest obligations⁽¹⁾		2,875		575		1,725		575		—
Operating lease obligations		30,845		10,239		13,402		4,852		2,352
Royalties		644		239		405		—		—
Finance lease obligations		1,239		467		672		100		—
Other long-term liabilities		3,106		1,493		1,269		344		—
Total	$	268,709	$	13,013	$	17,473	$	235,871	$	2,352

No.		Description

10.1		Executive Severance Agreement dated August 17. 2020, between Altair Engineering, Inc., and James R. Scapa (incorporated by reference to Exhibit 10.1 of the Company’s Current Report on Form 8-K filed with the Securities and Exchange Commission on August 17, 2020.) †

10.2		Executive Severance Agreement dated August 17. 2020, between Altair Engineering, Inc., and Brett Chouinard (incorporated by reference to Exhibit 10.2 of the Company’s Current Report on Form 8-K filed with the Securities and Exchange Commission on August 17, 2020.) †

10.3		Executive Severance Agreement dated August 17. 2020, between Altair Engineering, Inc., and Dr. Uwe Schramm (incorporated by reference to Exhibit 10.3 of the Company’s Current Report on Form 8-K filed with the Securities and Exchange Commission on August 17, 2020.) †

10.4		Executive Severance Agreement dated August 17. 2020, between Altair Engineering, Inc., and Amy Messano (incorporated by reference to Exhibit 10.4 of the Company’s Current Report on Form 8-K filed with the Securities and Exchange Commission on August 17, 2020.) †

31.1*		Certification of the Chief Executive Officer of Altair Engineering Inc. pursuant to Rule 13a-14(a)/Rule 15d-14(a) under the Securities Exchange Act of 1934, as amended

31.2*		Certification of the Chief Financial Officer of Altair Engineering Inc. pursuant to Rule 13a-14(a)/Rule 15d-14(a) under the Securities Exchange Act of 1934, as amended

32.1**		Certification of the Chief Executive Officer and Chief Financial Officer of Altair Engineering Inc. pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

101.INS*		Inline XBRL Instance Document – the instance document does not appear in the Interactive Data File because its XBRL tags are embedded within the Inline XBRL document.

101.SCH*		Inline XBRL Taxonomy Extension Schema Document

101.CAL*		Inline XBRL Taxonomy Extension Calculation Linkbase Document

101.DEF*		Inline XBRL Taxonomy Extension Definition Linkbase Document

101.LAB*		Inline XBRL Taxonomy Extension Label Linkbase Document

101.PRE*		Inline XBRL Taxonomy Extension Presentation Linkbase Document

104		Cover Page Interactive Data File (formatted as Inline XBRL and contained in Exhibits 101).

	ALTAIR ENGINEERING INC.

Date: November ~~7, 2019~~5, 2020	By:	/s/ James Scapa
		James R. Scapa
		Chief Executive Officer (Principal Executive Officer)

Date: November ~~7, 2019~~5, 2020
	By:	/s/ Howard N. Morof
		Howard N. Morof
		Chief Financial Officer (Principal Financial and Accounting Officer)