FIDELITY NATIONAL INFORMATION SERVICES, INC.  AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (Continued) (a) Intrinsic value is based on a closing stock price as of December 31, 2016 of $75.64.
The weighted average fair value of options granted during the years ended December 31, 2016, 2015 and 2014 was estimated to be $9.35, $10.67 and $9.15, respectively, using the Black-Scholes option pricing model with the assumptions below:
## Table 0 ##
The Company estimates future forfeitures at the time of grant and revises those estimates in subsequent periods if actual forfeitures differ from those estimates.
The Company bases the risk-free interest rate that is used in the stock option valuation model onn U. S.  Treasury securities issued with maturities similar to the expected term of the options.
The expected stock volatility factor is determined using historical daily price changes of the Company's common stock over the most recent period commensurate with the expected term of the option and the impact of any expected trends.
The dividend yield assumption is based on the current dividend yield at tthe grant date or management's forecasted expectations.
The expected life assumption is determined by calculating the average term from the t Company's historical stock option activity and considering the impact of expected future trends.
The Company granted a total of 1 million restricted stock shares at prices ranging from $56.44 to $79.41 on various dates in 2016.
The Company granted a total of 1 million restricted stock shares at prices ranging from $61.33 to $69.33 on various dates in 20 t 15.
The Company granted a total of 1 million restricted stock shares at prices ranging from $52.85 to $64.04 on various dates in 2014.
These shares were granted at the closing market price on the date of grant and vest annually over three years.
As of December 31, 2016 and 2015, we have approximately 3 million and 4 million unvested restricted shares remaining.
The December 31, 2016 balance includes those RSU's converted in connection with the SunGard acquisition as noted above.
The Company has provided for total stock compensation expense of $137 million, $98 million and $56 million for the years ended December 31, 2016, 2015 and 2014, respectively, which is included in selling, general, and administrative expense in the Consolidated Statements of Earnings, unless the expense is attributable to a discontinued operation.
Of the total stock compensation expense, $2 million for 2014 relates to liability based awards that will not be credited to additional paidd in capital until issued.
Total compensation expense for 2016 and 2015 did not include amounts relating to liability based awards.
As of December 31, 2016 and 2015, the total unrecognized compensation cost related to non-vested stock awards is $141 million and $206 million, respectively, which is expected to be recognized in pre-tax income over a weighted average period of 1.4 years and 1.6 years, respectively.
German Pension Plans Our German operations have unfunded, defined benefit plan obligations.
These obligations relate to benefits to be paid to Germaan employees upon retirement.
The accumulated benefit obligation as of December 31, 2016 and 2015, was $49 million and $48 million, respectively, and the projected benefit obligation was $50 million and $49 million, respectively.
The plan remains unfunded as of December 31, 2016.
(15)Divestitures and Discontinued Operations On December 7, 2016, the Company entered into a definitive agreement to sell the SunGard Public Sector and Education ("PS&E") businesses for $850 million.
The transaction included all PS&E solutions, which provide a comprehensive set of technology solutions to address public safety and public administrationn needs of government entities as well as the needs of K-12 school districts.
The divestiture is consistent with our strategy to serve the financial services markets.
We received cash proceeds, net of taxes and transaction-related expenses of approximately $500 million.
Net cash proceeds are expected to be used to reduce outstanding debt (see Note 10).
The PS&E businesses are included in the Corporate and Other segment.
The transaction closed on February 1, 2017, resulting in an expected pre-tax gain ranging from $85 million to $90 million that will
## Table 1 ##
The risk-free interest rate is based on the zero-coupon U. S.  Treasury yield curve in effect at the time of grant.
The expected life computation is derived from historical exercise patterns and anticipated future patterns.
Expected volatilities are based on historical volatility of the Company’s stock.
Expected dividend yields have historically been 0% since prior to the November 13, 2013 acquisition of NYSE Euronext, the Company has not contemplated paying dividends.
The Company's new dividend policy will impact the expected dividend yield on all stock options granted post-acquisition.
Restricted Stock Plans Restricted stock grants are granted at the discretion of the compensation committee of the board of directors.
Excluding the Company restricted stock issued in connection with the NYSE Euronext acquisition, discussed below, the Company granted a maximum of 874,018, 948,625 and 744,145 time-based and performance-based restricted stock units during the years ended December 31, 2013, 2012 and 2011, respectively, including 249,670, 295,615 and 285,655 time-based restricted stock units during the years ended December 31, 2013, 2012 and 2011, respectively.
The grant date fair value of each award is based on the closing stock price at the date of grant.
The fair value of the time-based restricted stock units on the date of grant is recognized as expense ratably over the vesting period, which is typically three years, net of forfeitures.
Granted but unvested shares would be forfeited upon termination of employment.
When restricted stock is forfeited, compensation costs previously recognized for unvested shares are reversed.
Until the shares vest and are issued, the participants have no voting or dividend rights and the shares may not be sold, assigned, transferred, pledged or otherwise encumbered.
Following the NYSE Euronext acquisition and in connection with the Company's new dividend declaration policy, unvested restricted stock is now subject to earn dividend equivalents which are paid in cash on the vest date.
The Company recognizes compensation costs, net of forfeitures, using an accelerated attribution method over the vesting period for awards with performance conditions.
Compensation costs for such awards are recognized only if it is probable that the condition will be satisfied.
If the Company initially determines that it is not probable that the performance condition will be satisfied and later determines that it is probable that the performance condition will be satisfied, or vice versa, the effect of the change in estimate is accounted for in the period of change by recording a cumulative catch-up adjustment to retroactively apply the new estimate.
The Company would recognize the remaining compensation costs over the remaining vesting period.
The Company’s compensation committee, pursuant to the terms of the ICE Plans and the authority delegated to it by the Company’s board of directors, can make equitable adjustments to the performance condition in recognition of unusual or non-recurring events.
During the fourth quarter of 2013, the Company reserved a maximum of 154,912 restricted shares for potential issuance as performance-based restricted shares for certain Company employees.
The number of shares granted under the performance awards will be based on the Company’s actual financial performance as compared to financial performance targets set by the Company’s board of directors and compensation committee for the three years ending December 31, 2016.
The grant dates were the dates on which the Company and the employees reached a mutual understanding of award terms and are the same as the service inception dates when the requisite service period began.
The maximum compensation expense to be recognized under these performance-based restricted shares is $31 million if the maximum financial performance target is met and 154,912 shares vest.
The compensation expense to be recognized under these performance-based restricted shares will be $30 million if the target financial performance is met and 147,535 shares vest.
The Company will recognize expense on a straight-line basis over the three-year vesting period based on the Company’s quarterly assessment of the probable three-year actual financial performance as compared to the financial performance targets.
In January 2013, the Company reserved a maximum of 449,420 restricted shares for potential issuance as performance-based restricted shares for certain Company employees.
These restricted shares were subject to a market condition that could have reduced the number of shares that were granted if the 2013 Company total shareholder return fell below that of the 2013 return of the S&P 500 Index and if the Company achieved a “target” financial performance level or above threshold.
The Company’s total shareholder return for the year ended December 31, 2013 was higher than the 2013 return of the S&P 500 Index and the Company achieved below a “target” financial performance level based on its actual 2013 financial performance compared to the financial performance level thresholds.
Therefore, no additional share reduction was taken.
Based on the Company’s actual 2013 financial performance as compared to the 2013 financial performance targets, 173,776 restricted shares were granted, which resulted in $22 million in compensation expenses that will be expensed over the three-year accelerated vesting period, including $14 million that was expensed
## Table 2 ##
(1) We acquired several companies during the periods presented and have included the financial results of these companies in our consolidated financial statements effective from the respective acquisition dates.
Refer to note 3 to our consolidated financial statements and related notes, which are included elsewhere in this Annual Report, for more information on some of these acquisitions, including the acquisitions of Interactive Data on December 14, 2015 and NYSE on November 13, 2013.
(2) Our transaction and clearing fees are presented net of rebates paid to our customers.
We also report transaction-based expenses relating to Section 31 fees and payments made for routing services and to certain U. S.  equities liquidity providers.
For a
Depreciation and Amortization Expenses Depreciation and amortization expense results from depreciation of long-lived assets such as buildings, leasehold improvements, planes, furniture, fixtures and equipment over their estimated useful lives.
This expense includes amortization of intangible assets obtained in our acquisitions of businesses, as well as on various licensing agreements, over their estimated useful lives.
Intangible assets subject to amortization consist primarily of customer relationships, trading products with finite lives and technology.
This expense also includes amortization of internally developed and purchased software over their estimated useful lives.
We recorded amortization expenses on the intangible assets acquired as part of our acquisitions, as well as on the other intangible assets, of $356 million, $160 million and $151 million for the years ended December 31, 2016, 2015 and 2014, respectively.
We recognized $182 million and $8 million in amortization expenses on the Interactive Data, Trayport, Securities Evaluations and Credit Market Analysis intangible assets during the years ended December 31, 2016 and 2015, respectively.
We recorded an impairment of the Creditex customer relationship intangible asset of $33 million during the year ended December 31, 2016, which was recorded as amortization expense.
See “- Recent Developments - Creditex Customer Relationship Intangible Asset Impairment” above.
The increases in amortization expenses for the year ended December 31, 2016 discussed above were partially offset by a reduction in amortization expenses recorded on intangible assets which became fully amortized during 2016, primarily related to certain of the NYSE intangible assets.
We recorded depreciation expenses on our fixed assets of $254 million, $213 million and $182 million for the years ended December 31, 2016, 2015 and 2014, respectively.
We recognized $42 million and $2 million in depreciation expenses on the Interactive Data, Trayport, Securities Evaluations and Credit Market Analysis during the years ended December 31, 2016 and 2015, respectively.
In addition to the impact of the acquisitions, depreciation expenses increased for the year ended December 31, 2015 primarily due to additional fixed asset additions and capitalized internally developed software, including additions relating to the NYSE integration and real estate expenditures during the last several years relating primarily to the Atlanta, New York and London headquarters.
Non-Operating Income (Expenses) Income and expenses incurred through activities outside of our core operations are considered non-operating.
The following tables present our non-operating income (expenses) (dollars in millions):

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td>2016</td><td>2015</td><td>2014</td></tr><tr><td>Risk free interest rate</td><td>1.2%</td><td>1.4%</td><td>1.4%</td></tr><tr><td>Volatility</td><td>20.4%</td><td>21.7%</td><td>21.2%</td></tr><tr><td>Dividend yield</td><td>1.6%</td><td>1.6%</td><td>1.6%</td></tr><tr><td>Weighted average expected life (years)</td><td>4.2</td><td>4.2</td><td>4.2</td></tr></table>
<table><tr><td></td><td colspan="3">Year Ended December 31,</td></tr><tr><td>Assumptions</td><td>2013</td><td>2012</td><td>2011</td></tr><tr><td>Risk-free interest rate</td><td>0.53%</td><td>0.57%</td><td>1.46%</td></tr><tr><td>Expected life in years</td><td>4.0</td><td>4.0</td><td>4.0</td></tr><tr><td>Expected volatility</td><td>37%</td><td>42%</td><td>72%</td></tr><tr><td>Expected dividend yield</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Estimated weighted-average fair value of options granted per share</td><td>$38.41</td><td>$36.96</td><td>$60.97</td></tr></table>
<table><tr><td rowspan="3"></td><td colspan="5">Year Ended December 31,</td></tr><tr><td>2016</td><td>2015</td><td>2014</td><td>2013</td><td>2012</td></tr><tr><td colspan="5">(In millions, except for per share data)</td></tr><tr><td>Consolidated Statement of Income Data<sup>-1</sup></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Revenues:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Transaction and clearing, net<sup>-2</sup></td><td>$3,384</td><td>$3,228</td><td>$3,144</td><td>$1,393</td><td>$1,185</td></tr><tr><td>Data services</td><td>1,978</td><td>871</td><td>691</td><td>246</td><td>161</td></tr><tr><td>Listings</td><td>419</td><td>405</td><td>367</td><td>33</td><td>—</td></tr><tr><td>Other revenues</td><td>177</td><td>178</td><td>150</td><td>58</td><td>17</td></tr><tr><td>Total revenues</td><td>5,958</td><td>4,682</td><td>4,352</td><td>1,730</td><td>1,363</td></tr><tr><td>Transaction-based expenses<sup>-2</sup></td><td>1,459</td><td>1,344</td><td>1,260</td><td>132</td><td>—</td></tr><tr><td>Total revenues, less transaction-based expenses</td><td>4,499</td><td>3,338</td><td>3,092</td><td>1,598</td><td>1,363</td></tr><tr><td>Operating expenses:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Compensation and benefits</td><td>945</td><td>611</td><td>592</td><td>302</td><td>251</td></tr><tr><td>Professional services</td><td>137</td><td>139</td><td>181</td><td>54</td><td>33</td></tr><tr><td>Acquisition-related transaction and integration costs<sup>-3</sup></td><td>80</td><td>88</td><td>129</td><td>143</td><td>19</td></tr><tr><td>Technology and communication</td><td>374</td><td>203</td><td>188</td><td>63</td><td>46</td></tr><tr><td>Rent and occupancy</td><td>70</td><td>57</td><td>78</td><td>39</td><td>19</td></tr><tr><td>Selling, general and administrative</td><td>116</td><td>116</td><td>143</td><td>51</td><td>37</td></tr><tr><td>Depreciation and amortization</td><td>610</td><td>374</td><td>333</td><td>156</td><td>131</td></tr><tr><td>Total operating expenses</td><td>2,332</td><td>1,588</td><td>1,644</td><td>808</td><td>536</td></tr><tr><td>Operating income</td><td>2,167</td><td>1,750</td><td>1,448</td><td>790</td><td>827</td></tr><tr><td>Other expense, net<sup>-4</sup></td><td>138</td><td>97</td><td>41</td><td>286</td><td>37</td></tr><tr><td>Income from continuing operations before income tax expense</td><td>2,029</td><td>1,653</td><td>1,407</td><td>504</td><td>790</td></tr><tr><td>Income tax expense</td><td>580</td><td>358</td><td>402</td><td>184</td><td>228</td></tr><tr><td>Income from continuing operations</td><td>1,449</td><td>1,295</td><td>1,005</td><td>320</td><td>562</td></tr><tr><td>Income (loss) from discontinued operations, net of tax<sup>(5)</sup></td><td>—</td><td>—</td><td>11</td><td>-50</td><td>—</td></tr><tr><td>Net income</td><td>$1,449</td><td>$1,295</td><td>$1,016</td><td>$270</td><td>$562</td></tr><tr><td>Net income attributable to non-controlling interest</td><td>-27</td><td>-21</td><td>-35</td><td>-16</td><td>-10</td></tr><tr><td>Net income attributable to ICE<sup>-6</sup></td><td>$1,422</td><td>$1,274</td><td>$981</td><td>$254</td><td>$552</td></tr><tr><td>Basic earnings (loss) per share attributable to ICE common shareholders<sup>(7)</sup>:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Continuing operations<sup>-6</sup></td><td>$2.39</td><td>$2.29</td><td>$1.70</td><td>$0.78</td><td>$1.52</td></tr><tr><td>Discontinued operations<sup>-5</sup></td><td>—</td><td>—</td><td>0.02</td><td>-0.13</td><td>—</td></tr><tr><td>Basic earnings per share</td><td>$2.39</td><td>$2.29</td><td>$1.72</td><td>$0.65</td><td>$1.52</td></tr><tr><td>Basic weighted average common shares outstanding<sup>-8</sup></td><td>595</td><td>556</td><td>570</td><td>392</td><td>364</td></tr><tr><td>Diluted earnings (loss) per share attributable to ICE common shareholders<sup>(7)</sup>:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Continuing operations<sup>-6</sup></td><td>$2.37</td><td>$2.28</td><td>$1.69</td><td>$0.77</td><td>$1.50</td></tr><tr><td>Discontinued operations<sup>-5</sup></td><td>—</td><td>—</td><td>0.02</td><td>-0.13</td><td>—</td></tr><tr><td>Diluted earnings per share</td><td>$2.37</td><td>$2.28</td><td>$1.71</td><td>$0.64</td><td>$1.50</td></tr><tr><td>Diluted weighted average common shares outstanding<sup>-8</sup></td><td>599</td><td>559</td><td>573</td><td>396</td><td>367</td></tr><tr><td>Dividend per share<sup>-7</sup></td><td>$0.68</td><td>$0.58</td><td>$0.52</td><td>$0.13</td><td>$—</td></tr></table>

Question: In the year with largest amount of Data services, what's the increasing rate of Total operating expenses?
Answer: 0.31904
Reasoning program: subtract(2332,1588), divide(#0,2332)