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7. Shareholders' Equity (Tables) | 12 Months Ended
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Dec. 31, 2018
Equity [Abstract] |
Schedule of stock purchases | The table below describes the purchase of our common stock for the twelve-month periods ended December 31, 2018 and 2017:
|  | Twelve Months Ended |
|  | December 31, 2018 |  |  | December 31, 2017 |
|  | Shares |  |  | Avg. Price |  |  | Shares |  |  | Avg. Price |
Open market purchases |  |  | 1,258,797 |  |  | $ | 3.77 |  |  |  | 2,693,562 |  |  | $ | 4.48 |
Shares redeemed upon net exercise of stock options |  |  | 33,604 |  |  |  | 4.37 |  |  |  | 51,931 |  |  |  | 4.50 |
Other |  |  | 90,000 |  |  |  | 4.13 |  |  |  | – |  |  |  | – |
Total stock purchases |  |  | 1,382,401 |  |  | $ | 3.81 |  |  |  | 2,745,493 |  |  | $ | 4.49 |
Schedule of assumptions for stock options | The dividend yield is estimated to be zero based on our intention not to issue dividends for the foreseeable future.
|  | Year Ended December 31, |
|  | 2018 |  |  | 2017 |  |  | 2016 |
Expected life (years) |  |  | 3.99 |  |  |  | 4.02 |  |  |  | 4.04 |
Risk-free interest rate |  |  | 2.74 | % |  |  | 1.59 | % |  |  | 1.09 | %
Volatility |  |  | 34 | % |  |  | 36 | % |  |  | 51 | %
Expected dividend yield |  |  | – |  |  |  | – |  |  |  | – |
Schedule of option activity | Stock option activity for the year ended December 31, 2018 for stock options under the 2006 and 1997 plans is as follows:
|  |  |  |  |  |  |  | Weighted
|  | Number of |  |  | Weighted |  |  | Average
|  | Shares |  |  | Average |  |  | Remaining
|  | (in thousands) |  |  | Exercise Price |  |  | Contractual Term
Options outstanding at the beginning of period |  |  | 13,135 |  |  | $ | 4.66 |  |  | N/A
Granted |  |  | 1,720 |  |  |  | 3.49 |  |  | N/A
Exercised |  |  | (315 | ) |  |  | 1.53 |  |  | N/A
Forfeited/Expired |  |  | (119 | ) |  |  | 7.20 |  |  | N/A
Options outstanding at the end of period |  |  | 14,421 |  |  | $ | 4.57 |  |  | 3.91 years
Options exercisable at the end of period |  |  | 8,789 |  |  | $ | 4.76 |  |  | 3.42 years

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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of stock options, including, but not limited to: (a) expected term of share options and similar instruments, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2) -URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901 + Details
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