We had other income of $4,000 for the three months ended September 30, 2021, compared to other income of $40,000 in the same period of the prior year. The decrease was primarily due to lower miscellaneous income.
Pre-tax net income
For the foregoing reasons, we had pre-tax net income of $5.3 million, or $0.78 per basic share and $0.65 per diluted share, for the three months ended September 30, 2021, a decrease of $0.3 million, or 6%, compared to a pre-tax net income of $5.6 million, or $0.85 per basic share and $0.70 per diluted share for the same period of the prior year.
Income tax expense
We had income tax expense of $1.1 million for the three months ended September 30, 2021, compared to income tax expense of $0.7 million for the three months ended September 30, 2020. Increase of tax expense in the current quarter was due to lower tax benefits relating to employee stock plans, federal and state research and development credit.
Net income
For the foregoing reasons, we had net income of $4.2 million, or $0.61 per basic share and $0.51 per diluted share, for the three months ended September 30, 2021, a decrease of $0.7 million, or 15%, compared to a net income of $4.9 million, or $0.74 per basic share and $0.61 per diluted share, for the same period of the prior year.
Nine Months Ended September 30, 2021 Compared to Nine Months Ended September 30, 2020
Revenues
We had revenues of $41.5 million for the nine months ended September 30, 2021, an increase of $15.0 million, or 56%, compared to $26.5 million in the same period in 2020. Our revenues are primarily from fees charged to customers for use of our vascular testing products and from sales of accessories used with these products. We recognized revenues of $40.7 million from fees for our vascular testing products for the nine months ended September 30, 2021, consisting of $22.7 million from fixed-fee licenses and $18.0 million from variable-fee licenses, compared to $25.8 million in the same period of the prior year, consisting of $18.7 million from fixed-fee licenses and $7.1 million from variable-fee licenses. The remainder was from sales of other products, which were $0.8 million compared to $0.7 million in the same period of the prior year.
We experienced the effects of COVID-19 beginning late in the first quarter and primarily during the second quarter of 2020, which decreased our revenues, in particular, revenue from variable-fee licenses. However, in the third quarter of 2020, our business returned to and even exceeded pre-COVID-19 levels, and we experienced even higher test volumes as our customers accelerated usage due to a backlog of untested patients. This increased testing volume continued in the first half of 2021, until a slowing of sequential growth in the third quarter of 2021, which we believe may be either due to effects of the Delta variant of COVID-19 during the third quarter of 2021, or due to a new seasonality in the home-testing market, which it hasn’t seen in prior periods, or due to both.
Revenues from fees for vascular testing products are recognized monthly for each unit installed with a customer, usually billed as a fixed monthly fee, or as a variable monthly fee dependent on usage. The primary reason for the increase in revenues was growth in the number of installed units from both new customers and established customers, which we believe is the result of our sales and marketing efforts, partially offset by some effects from the COVID-19 pandemic in the third quarter of 2021.
Operating expenses
We had total operating expenses of $23.8 million for the nine months ended September 30, 2021, an increase of $7.2 million or 43%, compared to $16.6 million in the same period in the prior year. The primary reasons for this change were due to increased expenses associated with our expanding business, such as increased personnel expenses, including stock-based compensation, partially offset by payroll tax reductions available in the first half as compared to the prior year period. As a percentage of revenues, operating expenses decreased to 57% in the first nine months of 2021 as compared to 62% in the prior year period. The changes in the various components of our operating expenses are described below.