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Share-Based Compensation (Tables)
9 Months Ended
Sep. 30, 2021
Share-based Payment Arrangement [Abstract]  
Quantitative information regarding the Stock Options and Stock Grants:

Quantitative information regarding the Stock Options and Stock Grants:

 

 

 

 

 

 

 

 

 

 

Nine Months Ended
September 30,

 

 

 

2021

 

 

2020

 

Stock options granted

 

 

10,000

 

 

 

535,000

 

Stock options exercised

 

 

367,000

 

 

 

78,277

 

Proceeds to Nanophase from exercises

 

$

152

 

 

$

23

 

Stock options forfeited

 

 

34,500

 

 

 

202,134

 

Stock option expirations

 

 

220,800

 

 

 

460,640

 

Stock options outstanding

 

 

2,833,650

 

 

 

3,507,073

 

Weighted average exercise price per share

 

$

0.55

 

 

$

0.58

 

The following table illustrates the various assumptions used to calculate the Black-Scholes option pricing model for stock options granted during the three-month and nine-month periods presented:

The following table illustrates the various assumptions used to calculate the Black-Scholes option pricing model for stock options granted during the three-month and nine-month periods presented:

 

For the three months ended

 

September 30,
2021

 

 

September 30,
2020

 

Weighted-average risk-free interest rates

 

 

1.0

%

 

 

n/a

 

Dividend yield

 

 

0.00

%

 

 

n/a

 

Weighted-average expected life of the option

 

 

7 years

 

 

 

n/a

 

Weighted-average expected stock price volatility

 

 

65

%

 

 

n/a

 

Weighted-average fair value of the options granted

 

$

2.45

 

 

 

n/a

 

 

For the nine months ended

 

September 30,
2021

 

 

September 30,
2020

 

Weighted-average risk-free interest rates

 

 

1.0

%

 

 

0.5

%

Dividend yield

 

 

0.00

%

 

 

0.00

%

Weighted-average expected life of the option

 

 

7 years

 

 

 

7 years

 

Weighted-average expected stock price volatility

 

 

65

%

 

 

94

%

Weighted-average fair value of the options granted

 

$

2.45

 

 

$

0.36