Note 8 - Stock-based compensation and equity transactions

On December 13, 2017, the Company granted 80,000 incentive stock options to an employee. These options vested 8,000 shares on the date of grant, and the balance vests as to 8,000 shares per year thereafter on each of the next nine anniversaries of December 13, 2017, and expire ten years from the date of grant. On December 3, 2018, the Company granted each of two employees 25,000 incentive stock options. These options vested 5,000 each on the date of grant, and the balance vests as to 5,000 shares each per year thereafter on each of the next four anniversaries of December 3, 2018, and expire ten years from the date of grant. On December 3, 2018, the Company also granted one employee 10,000 incentive stock options. These options vested 2,000 shares on the date of grant, and the balance vests as to 2,000 shares per year thereafter on each of the next four anniversaries of December 3, 2018, and expire ten years from the date of grant. On March 8, 2019, the Company granted one employee 25,000 incentive stock options. These options vested 5,000 on the date of grant, and the balance vests as to 5,000 shares per year thereafter on each of the next four anniversaries of March 8, 2019, and expire ten years from the date of grant. No other incentive stock options were granted to Company employees during the three and nine months ended July 31, 2019 and 2018.

The weighted average fair value of employee and non-employee directors’ stock options granted by the Company during the nine months ended July 31, 2019 and 2018 was estimated to be $8.16 and $2.44, respectively, per share, using the Black-Scholes option pricing model with the following assumptions:


	Nine Months Ended July 31,
	2019		2018
Risk-free interest rate	2.86	%	1.87	%
Dividend yield	0.98	%	3.28	%
Expected life of the option	5.90	years	4.54	years
Volatility factor	55.42	%	46.83	%

Expected volatilities are based on historical volatility of the Company’s stock price and other factors. The Company used the historical method to calculate the expected life of the 2019 and 2018 option grants. The expected life represents the period of time that options granted are expected to be outstanding. The risk-free rate is based on the U.S. Treasury rate with a maturity date corresponding to the options’ expected life. The dividend yield is based upon the historical dividend yield.

Company stock option plans

Descriptions of the Company’s stock option plans are included in Note 9 of the Company’s Annual Report on Form 10‑K for the year ended October 31, 2018. A summary of the status of the options granted under the Company’s stock option plans as of July 31, 2019 and the changes in options outstanding during the nine months then ended is presented in the table that follows:


		Weighted
		Average
	Shares	Exercise Price
Outstanding at November 1, 2018	942,366	$	3.09
Options granted	124,097	$	8.16
Options exercised	(99,150)	$	4.17
Options canceled or expired	(5,250)	$	6.82
Options outstanding at July 31, 2019	962,063	$	3.61
Options exercisable at July 31, 2019	671,897	$	3.27
Options vested and expected to vest at July 31, 2019	961,004	$	3.61

Weighted average remaining contractual life of options outstanding as of July 31, 2019: 4.13 years

Weighted average remaining contractual life of options exercisable as of July 31, 2019: 2.73 years

Weighted average remaining contractual life of options vested and expected to vest as of July 31, 2019: 4.11 years

Aggregate intrinsic value of options outstanding at July 31, 2019: $3,721,000

Aggregate intrinsic value of options exercisable at July 31, 2019: $2,792,000

Aggregate intrinsic value of options vested and expected to vest at July 31, 2019: $3,706,000

As of July 31, 2019, $492,000 of expense with respect to nonvested share-based arrangements has yet to be recognized but is expected to be recognized over a weighted average period of 5.35 years.

Non-employee directors receive a compensation package of $50,000 annually, which is paid one-half in cash and one-half through the grant of non-qualified stock options to purchase shares of the Company’s common stock. During the quarter ended January 31, 2019, the Company granted each of its five non-employee directors 7,203 non-qualified stock options. The options have an exercise price of $8.07 per share. The number of stock options granted to each director was determined by dividing $25,000 by the fair value of a stock option grant using the Black-Scholes model ($3.471 per share). These options vest ratably over fiscal year 2019 and expire five years from the date of grant. Effective November 1, 2018, in addition to the compensation received for serving on the Board of Directors, the Chairman of each committee of the Board will receive $15,000 per year in cash for services rendered as Chairman. On June 7, 2019, a new director joined the Board. The Company granted the new director 3,082 non-qualified stock options with an exercise price of $7.50 per share. The number of stock options granted to this director was determined by dividing $10,000 of compensation (prorated for the period as an active director) by the fair value of a stock option grant using the Black-Scholes model ($3.245 per share). These options vest ratably over fiscal year 2019 and expire five years from the date of grant. No other non-qualified stock options were granted during the three and nine months ended July 31, 2019.

Stock option expense

During the nine months ended July 31, 2019 and 2018, stock-based compensation expense totaled $260,000 and $189,000, respectively, and was classified in selling and general expenses. During the three months ended July 31, 2019 and 2018, stock-based compensation expense totaled $68,000 and $57,000, respectively, and was classified in selling and general expenses.