The increase in costs of revenues of $0.4 million for the three months ended March 31, 2023, compared to the three months ended March 31, 2022, was primarily due to (i) a $0.2 million increase in personnel-related costs due to stock-based compensation expense, (ii) a $0.1 million increase in third-party cloud-delivery costs, and (iii) a $0.1 million increase in subcontractor costs. These were partially offset by a $0.2 million decrease in facilities and IT-related costs.
Gross Margin
Gross margin increased 5 percentage points for the three months ended March 31, 2023, to 71%, compared to 66% for the three months ended March 31, 2022. The higher gross margin during the three months ended March 31, 2023, was primarily due to higher total revenue, including Gainshare, when compared to the year-ago period.
Operating Expenses:
Research and Development
| | | | | | | | | | | | |
| | Three Months Ended | | | | | | |
| | March 31, | | Change | |
(Dollars in thousands) | | 2023 | | 2022 | | $ | | % | |
Research and development | | $ | 13,051 | | $ | 14,089 | | $ | (1,038) | | (7) | % |
As a percentage of total revenues | | | 32 | % | | 42 | % | | | | | |
Research and development expenses consist primarily of personnel-related costs including compensation, employee benefits, bonus and stock-based compensation expense, outside development services, travel, third-party cloud-services related costs, IT and facilities cost allocations to support product development activities.
Research and development expenses decreased $1.0 million for the three months ended March 31, 2023, compared to the three months ended March 31, 2022, primarily due to (i) a $1.7 million decrease in personnel-related costs primarily resulting from a lower stock-based and other compensation expenses, partially offset by worldwide salary increases, (ii) a $0.2 million decrease in facilities and IT-related costs including depreciation expense. These were partially offset by (i) a $0.5 million increase in subcontractor expenses primarily related to DFI systems and Exensio and Cimetrix software, (ii) a $0.2 million increase in travel expenses, and (iii) a $0.1 million increase in third-party cloud-services related costs.
We anticipate our expenses in research and development will fluctuate in absolute dollars from period to period as a result of the size and the timing of product development projects.
Selling, General, and Administrative
| | | | | | | | | | | | |
| | Three Months Ended | | | | | | |
| | March 31, | | Change | |
(Dollars in thousands) | | 2023 | | 2022 | | $ | | % | |
Selling, general, and administrative | | $ | 15,645 | | $ | 10,839 | | $ | 4,806 | | 44 | % |
As a percentage of total revenues | | | 38 | % | | 32 | % | | | | | |
Selling, general, and administrative expenses consist primarily of personnel-related costs including compensation, employee benefits, bonus, commission and stock-based compensation expense for sales, marketing, and general and administrative personnel, legal, tax and accounting services, marketing communications expenses, third-party cloud-services related costs, travel, IT, and facilities cost allocations.
Selling, general, and administrative expenses increased $4.8 million for the three months ended March 31, 2023, compared to the three months ended March 31, 2022, primarily due to (i) a $2.9 million increase in personnel-related costs mainly resulting from increases in headcount, stock-based compensation expense, worldwide salary increases, commission expenses, and employee benefit costs, (ii) a $1.7 million increase in legal fees related to the arbitration proceeding over a disputed customer contract, (iii) a $0.3 million increase in facilities and IT-related costs including depreciation expense, and