Contractual Obligations In 2011, we issued $1,200 million of senior notes and entered into the Credit Facility with third-party lenders in the amount of $1,225 million.
As of December 31, 2011, total outstanding long-term debt was $1,859 million, consisting of these senior notes and the Credit Facility, in addition to $105 million of third party debt that remained outstanding subsequent to the spin-off.
In connection with the spin-off, we entered into a Transition Services Agreement with Northrop Grumman, under which Northrop Grumman or certain of its subsidiaries provides us with certain services to help ensure an orderly transition following the distribution.
Under the Transition Services Agreement, Northrop Grumman provides, for up to 12 months following the spin-off, certain enterprise shared services (including information technology, resource planning, financial, procurement and human resource services), benefits support services and other specified services.
The original term of the Transition Services Agreement ends on March 31, 2012, although we have the right to and have cancelled certain services as we transition to new third-party providers.
The services provided by Northrop Grumman are charged to us at cost, and a limited number of these services may be extended for a period of approximately six months to allow full information systems transition.
See Note 20: Related Party Transactions and Former Parent Company Equity in Item 8.
In connection with the spin-off, we entered into a Tax Matters Agreement with Northrop Grumman (the “Tax Matters Agreement”) that governs the respective rights, responsibilities and obligations of Northrop Grumman and us after the spin-off with respect to tax liabilities and benefits, tax attributes, tax contests and other tax sharing regarding U. S.  federal, state, local and foreign income taxes, other taxes and related tax returns.
We have several liabilities with Northrop Grumman to the IRS for the consolidated U. S.  federal income taxes of the Northrop Grumman consolidated group relating to the taxable periods in which we were part of that group.
However, the Tax Matters Agreement specifies the portion of this tax liability for which we will bear responsibility, and Northrop Grumman has agreed to indemnify us against any amounts for which we are not responsible.
The Tax Matters Agreement also provides special rules for allocating tax liabilities in the event that the spin-off, together with certain related transactions, is not tax-free.
See Note 20: Related Party Transactions and Former Parent Company Equity in Item 8.
We do not expect either the Transition Services Agreement or the Tax Matters Agreement to have a significant impact on our financial condition and results of operations.
The following table presents our contractual obligations as of December 31, 2011, and the related estimated timing of future cash payments:
## Table 0 ##
(1) Interest payments include interest on $554 million of variable interest rate debt calculated based on interest rates at December 31, 2011.
(2) A “purchase obligation” is defined as an agreement to purchase goods or services that is enforceable and legally binding on us and that specifies all significant terms, including: fixed or minimum quantities to be purchased; fixed, minimum, or variable price provisions; and the approximate timing of the transaction.
These amounts are primarily comprised of open purchase order commitments to vendors and subcontractors pertaining to funded contracts.
(3) Other long-term liabilities primarily consist of total accrued workers’ compensation reserves, deferred compensation, and other miscellaneous liabilities, of which $201 million is the current portion of workers’ compensation liabilities.
It excludes obligations for uncertain tax positions of $9 million, as the timing of the payments, if any, cannot be reasonably estimated.
The above table excludes retirement related contributions.
In 2012, we expect to make minimum and discretionary contributions to our qualified pension plans of approximately $153 million and $65 million, respectively, exclusive of any U. S.  Government recoveries.
We will continue to periodically evaluate whether to make additional discretionary contributions.
In 2012, we expect to make $35 million in contributions for our other postretirement plans, exclusive of any
The main categories of revenues, and the dollar and percentage change between the periods, are as follows:
## Table 1 ##
Investment Management Fees Investment management fees are derived from providing professional services to manage client accounts and include fees earned from retail mutual funds, unit trusts, investment companies with variable capital (ICVCs), exchange-traded funds, investment trusts and institutional and private wealth management advisory contracts.
Investment management fees for products offered in the retail distribution channel are generally calculated as a percentage of the daily average asset balances and therefore vary as the levels of AUM change resulting from inflows, outflows and market movements.
Investment management fees for products offered in the institutional and private wealth management distribution channels are calculated in accordance with the underlying investment management contracts and also vary in relation to the level of client assets managed.
Investment management fees decreased 19.0% in 2009 to $2,120.2 million (2008: $2,617.8 million) due to decreases in average AUM during the year, changes in the mix of AUM between various asset classes, and foreign exchange rate movements.
Average AUM for the year ended December 31, 2009, were $388.7 billion (2008: $440.6 billion), a decrease of 11.8%.
Average long-term AUM, which generally earn higher fee rates than institutional money market AUM, for the year ended December 31, 2009, were $301.7 billion, a decrease of 16.4% from $360.8 billion for the year ended December 31, 2008, while average institutional money market AUM increased 9.0% to $87.0 billion at December 31, 2009, from $79.8 billion for the year ended December 31, 2008.
Service and Distribution Fees Service fees are generated through fees charged to cover several types of expenses, including fund accounting fees and other maintenance costs for mutual funds, unit trusts and ICVCs, and administrative fees earned from closed-ended funds.
Service fees also include transfer agent fees, which are fees charged to cover the expense of processing client share purchases and redemptions, call center support and client reporting.
U. S.  distribution fees can include 12b-1 fees earned from certain mutual funds to cover allowable sales and marketing expenses for those funds and also include asset-based sales charges paid by certain mutual funds for a period of time after the sale of those funds.
Distribution fees typically vary in relation to the amount of client assets managed.
Generally, retail products offered outside of the U. S.  do not generate a separate distribution fee, as the quoted management fee rate is inclusive of these services.
In 2009, service and distribution fees decreased 19.5% to $412.6 million (2008: $512.5 million) primarily due to decreases in average AUM during the year.
Included in the decline in service and distribution fees in the three months ended December 31, 2009, was a reduction of $5.4 million reflecting the full-year impact of a reduction in transfer agency and administrative revenues in Canada, as certain fund expense recovery limits were reached.
Performance Fees Performance fee revenues are generated on certain management contracts when performance hurdles are achieved.
Such fee revenues are recorded in operating revenues as of the performance measurement date, when the contractual performance criteria have been met and when the outcome of the transaction can be measured reliably in accordance with Method 1 of ASC Topic 605-20-S99, “Revenue Recognition – Services – SEC Materials.
” Cash receipt of earned performance fees occurs after the measurement date.
The performance measurement date is defined in each contract in which incentive and performance fee revenue agreements are in effect, and therefore we have performance fee arrangements that include monthly, quarterly and annual measurement dates.
Given the uniqueness of each transaction, performance fee contracts are evaluated on an individual basis to determine if revenues can and should be recognized.
Performance fees are not recorded if there are any future performance contingencies.
If performance
The following table presents the carrying value of the plan assets, including major security type for equity and debt securities, which are measured at fair value as of December 31, 2014:
## Table 2 ##
The following is a description of the valuation methodologies used for each major category of plan assets measured at fair value.
Information about the valuation hierarchy levels used to measure fair value is detailed in Note 2, “Fair Value of Assets and Liabilities.
” Cash and cash equivalents Cash equivalents include cash investments in money market funds and time deposits.
Cash investments in money market funds are valued under the market approach through the use of quoted market prices in an active market, which is the net asset value of the underlying funds, and are classified within level 1 of the valuation hierarchy.
Cash investments in time deposits of $5.2 million held at December 31, 2015 (December 31, 2014: $3.8 million) are not included in the table above, as they are not measured at fair value on a recurring basis.
Time deposits are valued at cost plus accrued interest, which approximates fair value.
Fund investments These plan assets are primarily invested in affiliated funds and are classified within level 1 of the valuation hierarchy.
They are valued at the net asset value of shares held by the plan at year end.
Equity securities, corporate debt securities and other investments These plan assets are classified within level 1 of the valuation hierarchy and are valued at the closing price reported on the active market on which the individual securities are traded.
Government debt securities Government debt securities that have a readily available market price are classified within level 1 of the valuation hierarchy.
These securities are valued at the closing price reported on the active market on which the individual securities are traded.
Government debt securities that include index-linked bonds are classified within level 2 of the valuation hierarchy.
Prices for these bonds are calculated using the relevant index ratio.
Guaranteed investment contracts These plan assets are classified within level 3 of the valuation hierarchy and are valued through use of unobservable inputs by discounting the related cash flows based on current yields of similar instruments with comparable durations considering the creditworthiness of the issuer.
The following table shows a reconciliation of the beginning and ending fair value measurement for level 3 assets, which is comprised solely of the guaranteed investment contracts, using significant unobservable inputs:
## Table 3 ##
Repurchases of Equity Securities The following table shows share repurchase activity during the three months ended December 31, 2015:
## Table 4 ##
(1) An aggregate of 164,730 shares were surrendered to us by Invesco employees to satisfy tax withholding obligations in connection with the vesting of equity awards during the three months ended December 31, 2015.
(2) In October 2013, our board of directors authorized a $1.5 billion share repurchase program of our common shares with no stated expiration date.
As of December 31, 2015, $678.0 million remained authorized under this plan.
Item 6.
Selected Financial Data The following tables present selected consolidated financial information for the company as of and for each of the five fiscal years in the period ended December 31, 2015.
Except as otherwise noted below, the consolidated financial information has been prepared in accordance with U. S.  generally accepted accounting principles.

Tables referenced above, in order (Table 0 first):
<table><tr><td>($ in millions)</td><td>Total</td><td>2012</td><td>2013 - 2014</td><td>2015 - 2016</td><td>2017 and beyond</td></tr><tr><td>Long-term debt</td><td>$1,859</td><td>$29</td><td>$129</td><td>$396</td><td>$1,305</td></tr><tr><td>Interest payments on long-term debt -1</td><td>854</td><td>112</td><td>219</td><td>202</td><td>321</td></tr><tr><td>Operating leases</td><td>124</td><td>21</td><td>32</td><td>23</td><td>48</td></tr><tr><td>Purchase obligations -2</td><td>2,425</td><td>1,409</td><td>763</td><td>209</td><td>44</td></tr><tr><td>Other long-term liabilities -3</td><td>587</td><td>66</td><td>96</td><td>67</td><td>358</td></tr><tr><td>Total contractual obligations</td><td>$5,849</td><td>$1,637</td><td>$1,239</td><td>$897</td><td>$2,076</td></tr></table>
<table><tr><td> $ in millions</td><td> 2009</td><td> 2008</td><td> $ Change</td><td> %Change</td></tr><tr><td>Investment management fees</td><td>2,120.2</td><td>2,617.8</td><td>-497.6</td><td>-19.0%</td></tr><tr><td>Service and distribution fees</td><td>412.6</td><td>512.5</td><td>-99.9</td><td>-19.5%</td></tr><tr><td>Performance fees</td><td>30.0</td><td>75.1</td><td>-45.1</td><td>-60.1%</td></tr><tr><td>Other</td><td>64.5</td><td>102.2</td><td>-37.7</td><td>-36.9%</td></tr><tr><td>Total operating revenues</td><td>2,627.3</td><td>3,307.6</td><td>-680.3</td><td>-20.6%</td></tr><tr><td>Third-party distribution, service and advisory expenses</td><td>-693.4</td><td>-875.5</td><td>182.1</td><td>-20.8%</td></tr><tr><td>Proportional share of revenues, net of third-partydistribution expenses, from joint venture investments</td><td>44.8</td><td>57.3</td><td>-12.5</td><td>-21.8%</td></tr><tr><td>Net revenues</td><td>1,978.7</td><td>2,489.4</td><td>-510.7</td><td>-20.5%</td></tr></table>
<table><tr><td></td><td colspan="4">As of December 31, 2014</td></tr><tr><td>$ in millions</td><td>Fair Value Measurements</td><td>Quoted Prices in Active Markets for Identical Assets (Level 1)</td><td>Significant Other Observable Inputs (Level 2)</td><td>Significant Unobservable Inputs (Level 3)</td></tr><tr><td>Cash and cash equivalents</td><td>7.2</td><td>7.2</td><td>—</td><td>—</td></tr><tr><td>Fund investments</td><td>197.5</td><td>197.5</td><td>—</td><td>—</td></tr><tr><td>Equity securities</td><td>124.8</td><td>124.8</td><td>—</td><td>—</td></tr><tr><td>Government debt securities</td><td>76.5</td><td>15.2</td><td>61.3</td><td>—</td></tr><tr><td>Other assets</td><td>4.9</td><td>4.9</td><td>—</td><td>—</td></tr><tr><td>Guaranteed investment contracts</td><td>13.1</td><td>—</td><td>—</td><td>13.1</td></tr><tr><td>Total</td><td>424.0</td><td>349.6</td><td>61.3</td><td>13.1</td></tr></table>
<table><tr><td>$ in millions</td><td>Year ended December 31, 2015</td><td>Year ended December 31, 2014</td></tr><tr><td>Balance, beginning of year</td><td>13.1</td><td>15.2</td></tr><tr><td>Unrealized gains/(losses) relating to the instrument still held at the reporting date</td><td>0.1</td><td>1.0</td></tr><tr><td>Purchases, sales, issuances and settlements (net)</td><td>-1.5</td><td>-3.1</td></tr><tr><td>Balance, end of year</td><td>11.7</td><td>13.1</td></tr></table>
<table><tr><td>Month</td><td>Total Numberof SharesPurchased<sup>-1</sup></td><td>Average Price Paid Per Share</td><td>Total Number of SharesPurchased as Part ofPublicly Announced Plans or Programs<sup>-2</sup></td><td>Approximate DollarValue of Shares thatMay Yet Be PurchasedUnder the Plansor Programs<sup>-2</sup>(millions)</td></tr><tr><td>October 1 - 31, 2015</td><td>55,742</td><td>$31.51</td><td>—</td><td>$892.8</td></tr><tr><td>November 1 - 30, 2015</td><td>4,948,388</td><td>$33.15</td><td>4,941,924</td><td>$729.0</td></tr><tr><td>December 1 - 31, 2015</td><td>1,647,187</td><td>$32.92</td><td>1,544,663</td><td>$678.0</td></tr><tr><td></td><td>6,651,317</td><td></td><td>6,486,587</td><td></td></tr></table>

Question: In the section with lowest amount of Approximate DollarValue of Shares thatMay Yet Be PurchasedUnder the Plansor Programs-, what's the increasing rate of Average Price Paid Per Share? (in %)
Answer: -0.00694
Reasoning program: subtract(32.92,33.15), divide(#0,33.15)