The cost of services and other revenue increased by $1.0 million, or 18% during the three months ended September 30, 2021 compared to the three months ended September 30, 2020. For the nine months ended September 30, 2021, the cost of services and other revenue increased by $2.6 million, or 16% compared to the nine months ended September 30, 2020. The increase in cost of services and other revenue for both periods is reflective of higher subscription revenue, which has increased cloud-based infrastructure costs.
Gross profit increased $1.5 million, or 4% during the three months ended September 30, 2021 compared to the three months ended September 30, 2020. During the nine months ended September 30, 2021 gross profit decreased by $4.3 million, or 4% compared to the nine months ended September 30, 2020. Gross profit margin was 72% and 70% for the three and nine months ended September 30, 2021, respectively, compared to 70% and 69% for the three and nine months ended September 30, 2020, respectively. The increase in profit margins for the three months ended September 30, 2021 reflects a shift in product mix to increased term-based software and subscription revenue and lower hardware revenue.
The majority of our inventory purchases are denominated in U.S. Dollars. Our sales are denominated in various currencies including the Euro. The impact of changes in currency rates are estimated to have increased revenue by approximately $0.3 million and $4.8 million for the three and nine months ended September 30, 2021, respectively. Had currency rates in 2021 been equal to rates in 2020, the gross profit margin would have been approximately 3 percentage point lower for both the three and nine months ended September 30, 2021.
Operating Expenses
| | | | | | | | | | | | | |
| | Three months ended September 30, | | Nine months ended September 30, | |
| | 2021 | | 2020 | | 2021 | | 2020 | |
|
| | (in thousands) | | (in thousands) | |
Operating costs | | | | | | | | | | | | | |
Sales and marketing | | $ | 15,474 | | $ | 14,576 | | $ | 49,850 | | $ | 44,129 | |
Research and development | | | 11,359 | | | 10,643 | | | 35,699 | | | 31,178 | |
General and administrative | | | 11,207 | | | 10,737 | | | 38,797 | | | 33,851 | |
Amortization of intangible assets | | | 1,396 | | | 2,360 | | | 4,503 | | | 7,049 | |
Total operating costs | | $ | 39,436 | | $ | 38,316 | | $ | 128,849 | | $ | 116,207 | |
Sales and Marketing Expenses
Sales and marketing expenses for the three months ended September 30, 2021 were $15.5 million, an increase of $0.9 million or 6%, from the three months ended September 30, 2020. Sales and marketing expenses for the nine months ended September 30, 2021 were $49.9 million, an increase of $5.7 million or 13% from the same period in 2020. The increase in expense for the three and nine months ended September 30, 2021 compared to the same periods in 2020 was driven by higher headcount and an increase in the average cost per employee.
Average full-time sales, marketing, support, and operating employee headcount for the three and nine months ended September 30, 2021 was 363 and 368, respectively, compared to 353 and 345 for the three and nine months ended September 30, 2020, respectively. Headcount was 3% and 7% higher for the three and nine months ended September 30, 2021, respectively, compared to the same periods in 2020.
Research and Development Expenses
Research and development expenses for the three months ended September 30, 2021, were $11.4 million, an increase of $0.7 million, or 7%, from the three months ended September 30, 2020. Research and development expenses for the nine months ended September 30, 2021, were $35.7 million, an increase of $4.5 million, or 15%, from the nine months ended September 30, 2020. The increase in both periods was driven primarily by higher personnel costs due to higher headcount.