Year Ended December 31, 2012 Compared to Year Ended December 31, 2011 Revenue:
## Table 0 ##
The Company’s revenue increased 15.4% in 2012 as compared to 2011, including increases in all major revenue categories.
The Company's revenue included Apache operations for the full year in 2012 of $62.0 million as compared to five months in 2011 of $14.5 million.
The growth was partially influenced by benefits from the Company’s continued investment in its global sales and marketing organization.
Revenue from lease licenses increased 28.1% as compared to the prior year due to an increase in Apache-related lease license revenue and growth in sales of other lease licenses.
Annual maintenance contracts that were sold with new perpetual licenses, along with maintenance contracts sold with new perpetual licenses in previous years, contributed to maintenance revenue growth of 11.7%.
Perpetual license revenue, which is derived entirely from new sales during the period, increased 7.1% as compared to the prior year.
Esterel-related revenue for the period from the acquisition date (August 1, 2012) through December 31, 2012 was $3.3 million.
Service revenue increased 8.6% as compared to the prior year, primarily from increased revenue associated with engineering consulting services.
With respect to revenue, on average for the year ended December 31, 2012, the U. S.  Dollar was 3.7% stronger, when measured against the Company’s primary foreign currencies, than for the year ended December 31, 2011.
The net overall strengthening of the U. S.  Dollar resulted in decreased revenue and operating income during 2012, as compared to 2011, of $15.4 million and $7.4 million, respectively.
A substantial portion of the Company’s license and maintenance revenue is derived from annual lease and maintenance contracts.
These contracts are generally renewed on an annual basis and typically have a high rate of customer renewal.
In addition to the recurring revenue base associated with these contracts, a majority of customers purchasing new perpetual licenses also purchase related annual maintenance contracts.
As a result of the significant recurring revenue base, the Company’s license and maintenance revenue growth rate in any period does not necessarily correlate to the growth rate of new license and maintenance contracts sold during that period.
To the extent the rate of customer renewal for lease and maintenance contracts is high, incremental lease contracts, and maintenance contracts sold with new perpetual licenses, will result in license and maintenance revenue growth.
Conversely, if the rate of renewal for these contracts is adversely affected by economic or other factors, the Company’s license and maintenance growth will be adversely affected over the term that the revenue for those contracts would have otherwise been recognized.
The Company had a backlog of $55.2 million and $56.3 million of orders received but not invoiced as of December 31, 2012 and 2011, respectively.
International and domestic revenues, as a percentage of total revenue, were 66.7% and 33.3%, respectively, during the year ended December 31, 2012, and 68.8% and 31.2%, respectively, during the year ended December 31, 2011.
The Company derived 26.0% and 26.4% of its total revenue through the indirect sales channel for the years ended December 31, 2012 and 2011, respectively.
In valuing deferred revenue on the Esterel and Apache balance sheets as of their respective acquisition dates, the Company applied the fair value provisions applicable to the accounting for business combinations resulting in lower amounts of revenue than Esterel and Apache would have recognized absent the acquisitions.
The impact on reported revenue for the year ended December 31, 2012 was $9.6 million.
during the period and the fair market value of the Company’s stock price on the exercise dates.
Each of these items is subject to significant uncertainty.
Additionally, a significant portion of the tax benefits related to disqualified incentive stock options is accounted for as an increase to equity (additional paid-in capital) rather than as a reduction in income tax expense.
Although all such benefits continue to be realized through the Company’s tax filings, this accounting treatment has the effect of increasing tax expense and reducing net income.
For example, the Company realized a tax benefit of $7.6 million during the year ended December 31, 2012 related to disqualified dispositions of incentive stock options; however, only $1.7 million of such amount was recorded as a reduction in income tax expense.
Under the terms of the ANSYS, Inc.
Long-Term Incentive Plan, in the first quarter of 2012, 2011 and 2010, the Company granted 100,000, 92,500 and 80,500 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 estimated grant-date value of each restricted stock unit granted in 2012, 2011 and 2010 was $33.16, $32.05 and $25.00, respectively.
The estimate of the grant-date value of the restricted stock units was made 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.
Share-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, 2012, employees earned 76,500 restricted stock units, which will be issued in the first quarter of 2013.
## Table 1 ##
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, 2012, 95,227 deferred stock units have been earned with the underlying shares remaining unissued until the service termination of the respective Director owners.
Of this amount, 28,523 units were earned during the year ended December 31, 2012.
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 annually over a three-fiscalyear 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.
On December 31, 2012, employees earned 76,658 restricted stock units, which will be issued in the first quarter of 2013.
If factors change and the Company employs different assumptions in the application of share-based payment accounting guidance in future periods, the compensation expense that the Company will record may differ significantly from what the Company has recorded in the current period.
Therefore, it is important for investors to be aware of the high degree of subjectivity involved when using option pricing models to estimate share-based compensation.
Option pricing models were developed for use in estimating the value of traded options that have no vesting or hedging restrictions, are fully transferable and do not cause dilution.
Because the Company’s share-based payments have characteristics significantly different from those of freely-traded options and because changes in the input assumptions can materially affect the Company’s estimates of fair values, in the Company’s opinion, existing valuation models may not provide reliable measures of the fair values of the Company’s share-based compensation.
Consequently, there is a risk that the Company’s estimates of the fair values of the Company’s share-based compensation awards on the grant dates may bear little resemblance to the actual values realized upon the exercise, expiration, early termination or forfeiture of those share-based payments in the future.
Certain share-based payments, such as employee stock options, may expire worthless or otherwise result in zero intrinsic value as compared to the fair values originally estimated on the grant date and reported in the Company’s financial statements.
Alternatively, value may be realized from these instruments that is significantly in excess of the fair values originally estimated on the grant date and
16.
Leases The Company's executive offices and those related to certain domestic product development, marketing, production and administration are located in a 107,000 square foot office facility in Canonsburg, Pennsylvania.
In May 2004, the Company entered into the first amendment to its existing lease agreement on this facility, effective January 1, 2004.
The lease was extended from its original period to a period through 2014.
The Company incurred lease rental expense related to this facility of $1.3 million in each of the years ended December 31, 2012, 2011 and 2010.
The future minimum lease payments are $1.4 million per annum from January 1, 2013 through December 31, 2014.
On September 14, 2012, the Company entered into a lease agreement for 186,000 square feet of rentable space to be located in a to-be-built office facility in Canonsburg, Pennsylvania, which will serve as the Company's new headquarters.
The lease was effective as of September 14, 2012, but because the leased premises are to-be-built, the Company will not be obligated to pay rent until the later of (i) three months following the date that the leased premises are delivered to ANSYS, which delivery, subject to certain limited exceptions, shall occur no later than October 1, 2014, or (ii) January 1, 2015 (such later date, the “Commencement Date”).
The term of the lease is 183 months, beginning on the Commencement Date.
Absent the exercise of options in the lease for additional rentable space or early lease termination, the Company's base rent will be $4.3 million per annum for the first five years of the lease term, $4.5 million per annum for years six through ten and $4.7 million for years eleven through fifteen.
As part of the acquisition of Apache on August 1, 2011, the Company acquired certain leased office property, including executive offices, which comprise a 52,000 square foot office facility in San Jose, California.
In June 2012, the Company entered into a new lease for this property, with the lease term commencing July 1, 2012 and ending June 30, 2022.
Total remaining minimum payments under the operating lease as of December 31, 2012 are $9.2 million, of which $0.9 million will be paid in 2013.
The Company has entered into various other noncancellable operating leases for office space.
Office space lease expense totaled $13.7 million, $12.8 million and $11.5 million for the years ended December 31, 2012, 2011 and 2010, respectively.
Future minimum lease payments under noncancellable operating leases for office space in effect at December 31, 2012 are $12.6 million in 2013, $10.7 million in 2014, $10.0 million in 2015, $8.2 million in 2016 and $7.4 million in 2017.17.
Royalty Agreements The Company has entered into various renewable, nonexclusive license agreements under which the Company has been granted access to the licensor’s technology and the right to sell the technology in the Company’s product line.
Royalties are payable to developers of the software at various rates and amounts, which generally are based upon unit sales or revenue.
Royalty fees are reported in cost of goods sold and were $9.3 million, $8.4 million and $6.8 million for the years ended December 31, 2012, 2011 and 2010, respectively.18.
Geographic Information Revenue to external customers is attributed to individual countries based upon the location of the customer.
Revenue by geographic area is as follows:
## Table 2 ##
Property and equipment by geographic area is as follows:

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="2">Year Ended December 31,</td><td colspan="2">Change</td></tr><tr><td>(in thousands, except percentages)</td><td>2012</td><td>2011</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>$279,283</td><td>$218,005</td><td>$61,278</td><td>28.1</td></tr><tr><td>Perpetual licenses</td><td>222,587</td><td>207,876</td><td>14,711</td><td>7.1</td></tr><tr><td>Software licenses</td><td>501,870</td><td>425,881</td><td>75,989</td><td>17.8</td></tr><tr><td>Maintenance</td><td>275,498</td><td>246,546</td><td>28,952</td><td>11.7</td></tr><tr><td>Service</td><td>20,650</td><td>19,022</td><td>1,628</td><td>8.6</td></tr><tr><td>Maintenance and service</td><td>296,148</td><td>265,568</td><td>30,580</td><td>11.5</td></tr><tr><td>Total revenue</td><td>$798,018</td><td>$691,449</td><td>$106,569</td><td>15.4</td></tr></table>
<table><tr><td></td><td colspan="2">Year Ended December 31,</td></tr><tr><td></td><td>2012</td><td>2011 and 2010</td></tr><tr><td>Risk-free interest rate</td><td>0.16%</td><td>1.35%</td></tr><tr><td>Expected dividend yield</td><td>0%</td><td>0%</td></tr><tr><td>Expected volatility—ANSYS Stock Price</td><td>28%</td><td>40%</td></tr><tr><td>Expected volatility—NASDAQ Composite Index</td><td>20%</td><td>25%</td></tr><tr><td>Expected term</td><td>2.8 years</td><td>2.9 years</td></tr><tr><td>Correlation factor</td><td>0.75</td><td>0.70</td></tr></table>
<table><tr><td></td><td>Year Ended December 31,</td></tr><tr><td>(in thousands)</td><td>2012</td><td>2011</td><td>2010</td></tr><tr><td>United States</td><td>$265,436</td><td>$215,924</td><td>$188,649</td></tr><tr><td>Japan</td><td>122,437</td><td>112,171</td><td>95,498</td></tr><tr><td>Germany</td><td>82,008</td><td>72,301</td><td>60,399</td></tr><tr><td>Canada</td><td>12,384</td><td>12,069</td><td>9,875</td></tr><tr><td>Other European</td><td>177,069</td><td>166,551</td><td>138,157</td></tr><tr><td>Other international</td><td>138,684</td><td>112,433</td><td>87,658</td></tr><tr><td>Total revenue</td><td>$798,018</td><td>$691,449</td><td>$580,236</td></tr></table>

Question: what was the percentage change in the royalty fees are reported in cost of goods sold from 2011 to 2012
Answer: 9.3
Reasoning program: subtract(9.3,8.4), add(#0,8.4)