Task: Table-QA (source dataset: FinQA)

Task: 
You are given a table containing structured data and a natural language question referring to the table. Your goal is to analyze the table and provide an accurate and concise answer based on the given data.

Instructions:
1. Understand the Table: Examine the structure, headers, and data in the table. Identify relevant columns and rows related to the question.
2. Interpret the Question: Determine whether the question requires direct retrieval, aggregation, comparison, sorting, filtering, or inference.
3. Extract the Answer: Use logical reasoning and numerical operations (if necessary) to derive the correct response from the table.
4. Format the Answer: No explanation, return the answer in a structured JSON format: {"answer": <answer>}. If the question cannot be answered due to missing or ambiguous data, return a JSON response with {"answer": null}.

Table:
| Unnamed: 0                        | 2005             | 2006             | 2007             |
|:----------------------------------|:-----------------|:-----------------|:-----------------|
| risk-free interest rate           | 3.87% ( 3.87 % ) | 4.14% ( 4.14 % ) | 4.97% ( 4.97 % ) |
| expected option life ( in years ) | 7.5              | 7.3              | 6.25             |
| expected volatility               | 84% ( 84 % )     | 73% ( 73 % )     | 65% ( 65 % )     |

Question:
what is the average expected volatility used in the black scholes formula?


pre_text: abiomed , inc .
and subsidiaries notes to consolidated financial statements 2014 ( continued ) note 11 .
stock award plans and stock based compensation ( continued ) the 2000 stock incentive plan , ( the 201c2000 plan 201d ) , as amended , was adopted by the company in august 2000 .
the 2000 plan provides for grants of options to key employees , directors , advisors and consultants to the company or its subsidiaries as either incentive or nonqualified stock options as determined by the company 2019s board of directors .
up to 4900000 shares of common stock may be awarded under the 2000 plan and are exercisable at such times and subject to such terms as the board of directors may specify at the time of each stock option grant .
options outstanding under the 2000 plan generally vest 4 years from the date of grant and options awarded expire ten years from the date of grant .
the company has a nonqualified stock option plan for non-employee directors ( the 201cdirectors 2019 plan 201d ) .
the directors 2019 plan , as amended , was adopted in july 1989 and provides for grants of options to purchase shares of the company 2019s common stock to non-employee directors of the company .
up to 400000 shares of common stock may be awarded under the directors 2019 plan .
options outstanding under the director 2019s plan have vesting periods of 1 to 5 years from the date of grant and options expire ten years from the date of grant grant-date fair value the company estimates the fair value of each stock option granted at the grant date using the black-scholes option valuation model , consistent with the provisions of sfas no .
123 ( r ) , sec sab no .
107 share-based payment and the company 2019s prior period pro forma disclosure of net loss , including stock-based compensation ( determined under a fair value method as prescribed by sfas no .
123 ) .
the fair value of options granted during the fiscal years 2005 , 2006 and 2007 were calculated using the following weighted average assumptions: .
post_text: the risk-free interest rate is based on the united states treasury yield curve in effect at the time of grant for a term consistent with the expected life of the stock options .
volatility assumptions are calculated based on a combination of the historical volatility of our stock and adjustments for factors not reflected in historical volatility that are more indicative of future volatility .
by using this combination , the company is taking into consideration estimates of future volatility that the company believes will differ from historical volatility as a result of product diversification and the company 2019s acquisition of impella .
the average expected life was estimated using the simplified method for determining the expected term as prescribed by the sec 2019s staff accounting bulletin no .
107 .
the calculation of the fair value of the options is net of estimated forfeitures .
forfeitures are estimated based on an analysis of actual option forfeitures , adjusted to the extent historic forfeitures may not be indicative of forfeitures in the future .
in addition , an expected dividend yield of zero is used in the option valuation model , because the company does not pay cash dividends and does not expect to pay any cash dividends in the foreseeable future .
the weighted average grant-date fair value for options granted during fiscal years 2005 , 2006 , and 2007 was $ 8.05 , $ 6.91 , and $ 8.75 per share , respectively .
the application of sfas no .
123 ( r ) resulted in expense of $ 5.8 million , or $ 0.21 per share for the 2007 fiscal year which is recorded within the applicable operating expense where the company reports the option holders 2019 compensation cost in the consolidated statements of operations .
the remaining unrecognized stock-based compensation expense for unvested stock option awards at march 31 , 2007 was approximately $ 9.0 million , net of forfeitures , and the weighted average time over which this cost will be recognized is 1.9 years .
sfas no .
123 ( r ) also requires the benefits of tax deductions in excess of recognized compensation cost to be reported as a financing cash flow , rather than as an operating cash flow .
because the company does not recognize the benefit of tax deductions in excess of recognized compensation cost due to its net operating loss position , this change had no impact on the company 2019s consolidated statement of cash flows for the twelve months ended march 31 , 2007 .
accounting prior to adoption of sfas no .
123 ( r ) prior to april 1 , 2006 , the company accounted for stock-based compensation in accordance with the provisions of apb no .
25 .
the company elected to follow the disclosure-only alternative requirements of sfas no .
123 , accounting for stock-based compensation .
accordingly , the company did not recognize the compensation expense for the issuance of options with fixed exercise prices at least equal to .
label: 0.74
qa: answer: 74
ann_table_rows: 3
steps: op: average1-1
arg1: expected volatility
arg2: none
res: 74
program: table_average(expected volatility, none)
gold_inds: table_3: the expected volatility of 2005 is 84% ( 84 % ) ; the expected volatility of 2006 is 73% ( 73 % ) ; the expected volatility of 2007 is 65% ( 65 % ) ;
exe_ans: 0.74
tfidftopn: text_15: volatility assumptions are calculated based on a combination of the historical volatility of our stock and adjustments for factors not reflected in historical volatility that are more indicative of future volatility .
text_17: the average expected life was estimated using the simplified method for determining the expected term as prescribed by the sec 2019s staff accounting bulletin no .
program_re: table_average(expected volatility, none)
model_input: text_13
the fair value of options granted during the fiscal years 2005 , 2006 and 2007 were calculated using the following weighted average assumptions: .
table_3
the expected volatility of 2005 is 84% ( 84 % ) ; the expected volatility of 2006 is 73% ( 73 % ) ; the expected volatility of 2007 is 65% ( 65 % ) ;
text_17
the average expected life was estimated using the simplified method for determining the expected term as prescribed by the sec 2019s staff accounting bulletin no .