Results of Operations The operating results of Ansoft and Fluent have been included in the results of operations since the acquisition dates of July 31, 2008 and May 1, 2006, respectively.
For purposes of the following discussion and analysis, the table below sets forth certain consolidated financial data for the years 2008, 2007 and 2006.
## Table 0 ##
Year Ended December 31, 2008 Compared to Year Ended December 31, 2007 Revenue:
## Table 1 ##
The increase in software license revenue was the result of overall growth in both lease and perpetual license sales, as well as the addition of Ansoft-related license revenue of $21.1 million for the period from the acquisition (July 31, 2008) through December 31, 2008.
The increase in maintenance revenue was primarily the result of annual maintenance subscriptions sold in connection with new perpetual license sales in recent quarters and Ansoft-related maintenance revenue of $8.4 million for the period from the acquisition (July 31, 2008) through December 31, 2008.
$900,000 as compared to the year ended December 31, 2007.
Partially offsetting the increases in selling, general, and administrative costs were decreases in tax compliance costs of $1.8 million and incentive compensation of $1.7 million.
The Company anticipates that it will make investments throughout 2009 in its global sales and marketing organization and its global business infrastructure to enhance major account sales activities and to support both its worldwide sales distribution and marketing strategies and the growth of the business in general.
Research and Development: Ansoft-related research and development costs were $7.4 million for the period from the acquisition (July 31, 2008) through December 31, 2008.
Non-Ansoft related expenses increased by $7.7 million during the year ended December 31, 2008 which included increased salary costs of $4.1 million.
In addition, stock-based compensation expense and consulting fees increased by $900,000 and $800,000, respectively as compared to the year ended December 31, 2007.
The Company has traditionally invested significant resources in research and development activities and intends to continue to make significant investments in this area, particularly as it relates to ongoing integration and evolution of its portfolio of software technologies.
Amortization: Ansoft-related amortization expense was $2.1 million for the period from the acquisition (July 31, 2008) through December 31, 2008.
Interest Expense: The Company’s long-term debt incurred interest expense, including the amortization of debt financing costs, of $9.3 million during the year ended December 31, 2008, as compared to $6.5 million during the year ended December 31, 2007.
The interest expense on the term loans and amortization related to debt financing costs were as follows:
## Table 2 ##
The increased interest costs shown above for the 2008 period are primarily a result of a higher average outstanding debt balance, partially offset by a lower weighted-average effective interest rate of 4.72% as compared to 5.85% in the 2007 period.
The increased amortization costs shown above for 2008 are primarily a result of the early prepayment of the 2006 term loan as well as the additional amortization related to the 2008 term loan.
Interest Income (Expense), net: Interest income for the year ended December 31, 2008 was $5.6 million as compared to $4.9 million for the year ended December 31, 2007.
Interest income increased as a result of additional funds invested in the 2008 period as compared to the 2007 period.
Other Income (Expense), net: The Company recorded other income of $727,000 during the year ended December 31, 2008 as compared to other expense of $600,000 for the year ended December 31, 2007.
The net change was primarily the result of changes in foreign currency transaction gains and losses.
As the Company’s presence in foreign locations continues to expand, the Company, for the foreseeable future, will have increased exposure to volatility of foreign exchange rates.
Income Tax Provision: The Company recorded income tax expense of $55.0 million and had income before income taxes of $166.7 million for the year ended December 31, 2008.
This represents an effective tax rate of 33.0%.
During the year ended December 31, 2007, the Company recorded income tax expense of $41.9 million and had income before income taxes of $124.3 million.
The Company’s effective tax rate was 33.7% for the year ended December 31, 2007.
Total stock-based compensation expense, recognized for the years ended December 31, 2008, 2007 and 2006 is as follows:
## Table 3 ##
The net impact of stock-based compensation expense reduced 2008 basic and diluted earnings per share by $0.11 and $0.10, respectively, reduced 2007 basic and diluted earnings per share each by $0.09 and reduced 2006 basic and diluted earnings per share each by $0.06.
The Company recorded stock-based compensation expense of $1.9 million, $1.3 million and $913,000 during 2008, 2007 and 2006, respectively, related to stock-based awards granted during each respective year.
FAIR VALUE OF FINANCIAL INSTRUMENTS: The carrying values of cash, cash equivalents, accounts receivable, accounts payable, accrued expenses, other accrued liabilities and short-term obligations are deemed to be reasonable estimates of their fair values because of their short-term nature.
The fair values of investments are based on quoted market prices for those or similar investments.
The carrying value of long-term debt is considered a reasonable estimate of fair value due to the variable interest rate underlying the Company’s credit facility.
The Company’s interest rate swap agreement is recorded at fair value, utilizing the value of a hypothetical derivative with the same characteristics as the swap agreement.
DERIVATIVE FINANCIAL INSTRUMENTS: The Company holds a derivative financial instrument to manage interest rate risk.
The Company accounts for this instrument as a cash flow hedge in accordance with FASB Statement No.133, “Accounting for Derivative Instruments and Hedging Activities” (“Statement No.133”), which requires that every derivative instrument be recorded on the balance sheet as either an asset or liability measured at its fair value as of the reporting date.
Statement No.133 also requires that changes in the Company’s derivative fair value be recognized in earnings, unless specific hedge accounting and documentation criteria are met (i. e.  the instrument is accounted for as a hedge).
The Company records the effective portion of its derivative financial instrument in accumulated other comprehensive income on the consolidated balance sheets.
Any ineffective portion or excluded portion of the designated cash flow hedge would be recognized in earnings.
The Company’s current cash flow hedge does not have an ineffective or excluded portion.
The Company utilizes the hypothetical derivative method to ensure the hedge is effective in offsetting variability in interest expense associated with its credit facility.
The Company uses the dollar offset method for calculating ineffectiveness by comparing the cumulative fair value of the swap to the cumulative fair value of the hypothetical derivative.
OTHER RECENTLY ISSUED ACCOUNTING PRONOUNCEMENTS: In July 2006, the FASB issued Interpretation No.48, “Accounting for Uncertainty in Income Taxes” (“FIN 48”).
This interpretation clarifies the accounting for uncertainty in income taxes recognized in a company’s financial statements in accordance with FASB Statement No.109, “Accounting for Income Taxes.
” This interpretation prescribes a recognition threshold and measurement attribute for the financial statement recognition and measurement of a tax position taken or expected to be taken in a tax return.
This interpretation also provides guidance on derecognition, classification,
Under the terms of the ANSYS, Inc.
Long-Term Incentive Plan, in the first quarter of 2013, 2012 and 2011, the Company granted 94,300, 100,000 and 92,500 performance-based restricted stock units, respectively.
Vesting of the full award or a portion thereof is based on the Company’s performance as measured by total shareholder return relative to the median percentage appreciation of the NASDAQ Composite Index over a specified measurement period, subject to each participant’s continued employment with the Company through the conclusion of the measurement period.
The measurement period for the restricted stock units granted pursuant to the Long-Term Incentive Plan is a three-year period beginning January 1 of the year of the grant.
Each restricted stock unit relates to one share of the Company’s common stock.
The weighted average fair value of each restricted stock unit granted in 2013, 2012 and 2011 was estimated on the grant date to be $50.05, $33.16 and $32.05, respectively.
The fair value of the restricted stock units was estimated using a Monte Carlo simulation model.
The determination of the fair value of the awards was affected by the grant date and a number of variables, each of which has been identified in the chart below.
Stock-based compensation expense based on the fair value of the award is being recorded from the grant date through the conclusion of the three-year measurement period.
On December 31, 2013, employees earned 92,500 restricted stock units, which will be issued in the first quarter of 2014.
Total compensation expense associated with the awards recorded for the years ended December 31, 2013, 2012 and 2011 was $3.6 million, $2.6 million and $1.6 million, respectively.
Total compensation expense associated with granted awards for the years ending December 31, 2014 and 2015 is expected to be $2.8 million and $1.7 million, respectively.
## Table 4 ##
In addition, the Company grants deferred stock units to non-affiliate Independent Directors, which are rights to receive shares of common stock upon termination of service as a Director.
The deferred stock units are issued in arrears and vest immediately.
As of December 31, 2013, 115,842 deferred stock units have been earned with the underlying shares remaining unissued until the service termination of the respective Director owners.
Of this amount, 26,215 units were earned during the year ended December 31, 2013.
In accordance with the Apache merger agreement, the Company granted performance-based restricted stock units to key members of Apache management and employees, with a maximum of $13.0 million to be earned over a three-fiscal-year period beginning January 1, 2012.
Vesting of the full award or a portion thereof is determined discretely for each of the three fiscal years based on the achievement of certain revenue and operating income targets by the Apache subsidiary, and the recipient's continued employment through the measurement period.
The value of each restricted stock unit on the August 1, 2011 grant date was $50.30, the closing price of ANSYS stock as of that date.
Total compensation expense associated with the awards recorded for the years ended December 31, 2013 and 2012, was $3.8 million and $3.9 million, respectively.
For the year ended December 31, 2013, employees earned 75,477 units, which will be issued in the first quarter of 2014.
To the extent the Company changes the terms of its stock-based compensation programs, experiences market volatility in the pricing of its common stock that increases the implied volatility assumption used in the Black-Scholes model, refines different assumptions in future periods such as forfeiture rates that differ from current estimates, or assumes stock awards from acquired companies that are different in nature than the Company's stock award arrangements, among other potential impacts, the stockbased compensation expense recorded in future periods and the related tax benefits may differ significantly from what was recorded in previous reporting periods.
Estimates of stock-based compensation expense are significant to the Company’s financial statements, but this expense is based on the aforementioned option valuation models and will never result in the payment of cash by the Company.
For this reason, and because the Company does not view stock-based compensation as related to its operational performance, the Board of Directors and management exclude estimated stock-based compensation expense when evaluating the Company’s underlying business performance.
Recent Accounting Guidance For information regarding recent accounting guidance and the impact of this guidance on the Company’s consolidated financial statements, see Note 2 to the consolidated financial statements in Part IV, Item 15 of this Annual Report on Form 10-K.
REPUBLIC SERVICES, INC.  AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED The following table summarizes the activity in our gross unrecognized tax benefits for the years ended December 31:
## Table 5 ##
New accounting guidance for business combinations is effective for our 2009 financial statements.
This new guidance significantly changes the treatment of acquired uncertain tax liabilities.
Under previous guidance, changes in acquired uncertain tax liabilities were recognized through goodwill.
Under this new guidance, subsequent changes in acquired unrecognized tax liabilities are recognized through the income tax provision.
As of December 31, 2009, $211.9 million of the $242.2 million of unrecognized tax benefits related to tax positions taken by Allied prior to the merger.
Included in the balance at December 31, 2009 are approximately $217.6 million of unrecognized tax benefits (net of the federal benefit on state issues) that, if recognized, would affect the effective income tax rate in future periods.
During 2009, we settled our outstanding tax dispute related to Allied’s risk management companies (see — Risk Management Companies) with both the DOJ and the IRS.
This settlement reduced our gross unrecognized tax benefits by approximately $299.6 million.
During 2009, we also settled with the IRS, through an accounting method change, our outstanding tax dispute related to intercompany insurance premiums paid to Allied’s captive insurance company.
This settlement reduced our gross unrecognized tax benefits by approxi- mately $62.6 million.
In addition to these federal matters, we also resolved various state matters that, in the aggregate, reduced our gross unrecognized tax benefits during 2009 by approximately $5.8 million.
We recognize interest and penalties as incurred within the provision for income taxes in our consolidated statements of income.
Related to the unrecognized tax benefits previously noted, we accrued interest of $24.5 million during 2009 and, in total as of December 31, 2009, have recognized a liability for penalties of $1.5 million and interest of $92.3 million.
During 2008, we accrued penalties of $0.2 million and interest of $5.2 million and, in total at December 31, 2008, had recognized a liability for penalties of $88.1 million and interest of $180.0 million.
During 2007, we accrued interest of $0.9 million and, in total at December 31, 2007, had recognized a liability for penalties and interest of $5.5 million.
The decrease in accrued interest and penalties between 2009 and 2008 was driven mainly by the settlements discussed previously.
However, the current year interest expense increased due to the accrual of a full twelve months of interest expense on Allied’s acquired uncertain tax positions versus only one month of accrued interest expense recorded in 2008.
Gross unrecognized tax benefits that we expect to settle in the following twelve months are in the range of $10.0 million to $20.0 million.
It is reasonably possible that the amount of unrecognized tax benefits will increase or decrease in the next twelve months.

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="3">Year Ended December 31,</td></tr><tr><td>  <i>(in thousands)</i> </td><td>2008</td><td>2007</td><td>2006</td></tr><tr><td>Revenue:</td><td></td><td></td><td></td></tr><tr><td>Software licenses</td><td>$318,154</td><td>$253,287</td><td>$156,960</td></tr><tr><td>Maintenance and service</td><td>160,185</td><td>132,053</td><td>106,680</td></tr><tr><td>Total revenue</td><td>478,339</td><td>385,340</td><td>263,640</td></tr><tr><td>Cost of sales:</td><td></td><td></td><td></td></tr><tr><td>Software licenses</td><td>9,766</td><td>9,113</td><td>7,306</td></tr><tr><td>Amortization</td><td>27,803</td><td>21,532</td><td>14,909</td></tr><tr><td>Maintenance and service</td><td>53,845</td><td>47,402</td><td>34,512</td></tr><tr><td>Total cost of sales</td><td>91,414</td><td>78,047</td><td>56,727</td></tr><tr><td>Gross profit</td><td>386,925</td><td>307,293</td><td>206,913</td></tr><tr><td>Operating expenses:</td><td></td><td></td><td></td></tr><tr><td>Selling, general and administrative</td><td>134,887</td><td>115,108</td><td>86,901</td></tr><tr><td>Research and development</td><td>71,594</td><td>56,481</td><td>49,406</td></tr><tr><td>Amortization</td><td>10,713</td><td>8,935</td><td>6,350</td></tr><tr><td>In-process research and development</td><td>—</td><td>—</td><td>28,100</td></tr><tr><td>Total operating expenses</td><td>217,194</td><td>180,524</td><td>170,757</td></tr><tr><td>Operating income</td><td>169,731</td><td>126,769</td><td>36,156</td></tr><tr><td>Interest expense</td><td>-9,342</td><td>-6,822</td><td>-7,779</td></tr><tr><td>Interest income</td><td>5,575</td><td>4,916</td><td>4,766</td></tr><tr><td>Other income (expense), net</td><td>727</td><td>-600</td><td>-82</td></tr><tr><td>Income before income tax provision</td><td>166,691</td><td>124,263</td><td>33,061</td></tr><tr><td>Income tax provision</td><td>55,020</td><td>41,871</td><td>18,905</td></tr><tr><td>Net income</td><td>$111,671</td><td>$82,392</td><td>$14,156</td></tr></table>
<table><tr><td></td><td colspan="2"> Year Ended December 31,</td><td colspan="2">Change</td></tr><tr><td>  <i>(in thousands, except percentages)</i> </td><td> 2008</td><td> 2007</td><td>Amount%</td><td></td></tr><tr><td>Revenue:</td><td></td><td></td><td></td><td></td></tr><tr><td>Lease licenses</td><td>$177,427</td><td>$150,554</td><td>$26,873</td><td>17.8</td></tr><tr><td>Perpetual licenses</td><td>140,727</td><td>102,733</td><td>37,994</td><td>37.0</td></tr><tr><td>Software licenses</td><td>318,154</td><td>253,287</td><td>64,867</td><td>25.6</td></tr><tr><td>Maintenance</td><td>135,773</td><td>104,939</td><td>30,834</td><td>29.4</td></tr><tr><td>Service</td><td>24,412</td><td>27,114</td><td>-2,702</td><td>-10.0</td></tr><tr><td>Maintenance and service</td><td>160,185</td><td>132,053</td><td>28,132</td><td>21.3</td></tr><tr><td>Total revenue</td><td>$478,339</td><td>$385,340</td><td>$92,999</td><td>24.1</td></tr></table>
<table><tr><td></td><td colspan="2"> December 31, 2008</td><td colspan="2"> December 31, 2007</td></tr><tr><td>  <i>(in thousands)</i> </td><td> Interest Expense</td><td> Amortization</td><td> Interest Expense</td><td> Amortization</td></tr><tr><td>May 1, 2006 term loan</td><td>$1,219</td><td>$952</td><td>$6,023</td><td>$504</td></tr><tr><td>July 31, 2008 term loan</td><td>6,524</td><td>573</td><td>—</td><td>—</td></tr><tr><td>Total</td><td>$7,743</td><td>$1,525</td><td>$6,023</td><td>$504</td></tr></table>
<table><tr><td>  <i>(in thousands)</i> </td><td>Year Ended December 31, 2008</td><td>Year Ended December 31, 2007</td><td>Year Ended December 31, 2006</td></tr><tr><td>Cost of sales:</td><td></td><td></td><td></td></tr><tr><td>Software licenses</td><td>$72</td><td>$52</td><td>$42</td></tr><tr><td>Maintenance and service</td><td>783</td><td>518</td><td>212</td></tr><tr><td>Operating expenses:</td><td></td><td></td><td></td></tr><tr><td>Selling, general and administrative</td><td>8,022</td><td>6,299</td><td>3,990</td></tr><tr><td>Research and development</td><td>2,902</td><td>2,049</td><td>1,382</td></tr><tr><td>Stock-based compensation expense before taxes</td><td>11,779</td><td>8,918</td><td>5,626</td></tr><tr><td>Related income tax benefits</td><td>-2,833</td><td>-1,566</td><td>-965</td></tr><tr><td>Stock-based compensation expense, net of taxes</td><td>$8,946</td><td>$7,352</td><td>$4,661</td></tr></table>
<table><tr><td></td><td colspan="3">Year Ended December 31,</td></tr><tr><td>Assumption used in Monte Carlo lattice pricing model</td><td>2013</td><td>2012</td><td>2011</td></tr><tr><td>Risk-free interest rate</td><td>0.35%</td><td>0.16%</td><td>1.35%</td></tr><tr><td>Expected dividend yield</td><td>—%</td><td>—%</td><td>—%</td></tr><tr><td>Expected volatility—ANSYS Stock Price</td><td>25%</td><td>28%</td><td>40%</td></tr><tr><td>Expected volatility—NASDAQ Composite Index</td><td>20%</td><td>20%</td><td>25%</td></tr><tr><td>Expected term</td><td>2.8 years</td><td>2.8 years</td><td>2.9 years</td></tr><tr><td>Correlation factor</td><td>0.70</td><td>0.75</td><td>0.70</td></tr></table>
<table><tr><td></td><td>2009</td><td>2008</td><td>2007</td></tr><tr><td>Balance at beginning of year</td><td>$611.9</td><td>$23.2</td><td>$56.4</td></tr><tr><td>Additions due to the acquisition of Allied</td><td>13.3</td><td>582.9</td><td>-</td></tr><tr><td>Additions based on tax positions related to current year</td><td>3.9</td><td>10.6</td><td>16.3</td></tr><tr><td>Reductions for tax positions related to the current year</td><td>-</td><td>-5.1</td><td>-17.2</td></tr><tr><td>Additions for tax positions of prior years</td><td>5.6</td><td>2.0</td><td>2.0</td></tr><tr><td>Reductions for tax positions of prior years</td><td>-24.1</td><td>-1.3</td><td>-12.3</td></tr><tr><td>Reductions for tax positions resulting from lapse of statute of limitations</td><td>-0.5</td><td>-0.4</td><td>-0.4</td></tr><tr><td>Settlements</td><td>-367.9</td><td>-</td><td>-21.6</td></tr><tr><td>Balance at end of year</td><td>$242.2</td><td>$611.9</td><td>$23.2</td></tr></table>

Question: as of december 31 , 2009 , what was the percent unrecognized tax benefits related to tax positions taken by allied prior to the merger .
Answer: 0.8749
Reasoning program: divide(211.9,242.2)