## Table 0 ##
* Long-term AUM became a debt covenant measure as part a prior credit facility agreement and was discontinued as a financial covenant measure in a later agreement.
Long-term AUM was not required to be restated as part of the agreement and therefore amounts have not been adjusted from what was previously reported.
The December 31, 2011, coverage ratio calculations are as follows:
## Table 1 ##
* Adjustments for unrealized gains and losses from investments, as defined in our credit facility, include non-cash gains and losses on investments to the extent that they do not represent anticipated future cash receipts or expenditures.
** EBITDA and Adjusted debt are non-GAAPfinancial measures; however management does not use these measures for anything other than these debt covenant calculations.
The calculation of EBITDA above (a reconciliation from net income attributable to common shareholders) is defined by our credit agreement, and therefore net income attributable to common shareholders is the most appropriate GAAP measure from which to reconcile to EBITDA.
The calculation of adjusted debt is defined in our credit facility and equals total debt of $1,284.7 million plus $20.0 million in letters of credit.
We have received credit ratings of A3/Stable and A-/Stable from Moody's and Standard and Poor's credit rating agencies, respectively, as of the date of this Annual Report on Form 10-K.  Disclosure of these ratings is not a recommendation to buy, sell or hold our debt.
These credit ratings may be subject to revision or withdrawal at anytime by Moody's or Standard & Poor's.
Each rating should be evaluated independently.
See also Part I, Item 1A - "Risk Factors," for more detailed discussion on reliance on credit ratings.
The discussion that follows identifies risks associated with the company's liquidity and capital resources.
The Executive Overview of this Management's Discussion and Analysis of Financial Condition and Results of Operations contains a broader discussion of the company's overall approach to risk management.
Credit and Liquidity Risk Capital management involves the management of the company's liquidity and cash flows.
The company manages its capital by reviewing annual and projected cash flow forecasts and by monitoring credit, liquidity and market risks, such as interest rate and foreign currency risks (as discussed in Item 7A, “Quantitative and Qualitative Disclosures About Market Risk”), through measurement and analysis.
The company is primarily exposed to credit risk through its cash and cash equivalent deposits, which are held by external firms.
The company invests its cash balances in its own institutional money market products, as well as with
exception of net income attributable to common shareholders, basic earnings per share, and diluted earnings per share.
Prior period amounts have been reclassified to conform with this presentation.
(2) Net revenues is a non-GAAP financial measure.
See Item 7, “Summary Operating Information,” footnote 2, for the definition of this measure and the related reconciliation reference.
(3) Adjusted operating income and adjusted operating margin are non-GAAP financial measures.
See Item 7, “Summary Operating Information,” footnote 3, for the definition of these measures and the related reconciliation reference.
(4) Adjusted net income attributable to common shareholders and adjusted diluted EPS are non-GAAP financial measures.
See Item 7, “Summary Operating Information,” footnote 4, for the definition of these measures and the related reconciliation reference.
Item 7.
Management's Discussion and Analysis of Financial Condition and Results of Operations Executive Overview The following executive overview summarizes the significant trends affecting our results of operations and financial condition for the periods presented.
This overview and the remainder of this management's discussion and analysis supplements and should be read in conjunction with the Consolidated Financial Statements of Invesco Ltd.  and its subsidiaries (collectively, the “company” or “Invesco”) and the notes thereto contained elsewhere in this Annual Report on Form 10-K.
Global financial markets in 2014 were characterized by two distinct periods.
The first half of 2014 saw the continuation of the equity market strength seen in 2013.
Returns for most equity markets across the globe were positive, if not strong, driven in part by supportive conditions from global central banks.
The second half of 2014 saw the return of volatility and sell-off of risk assets, especially in Europe and emerging markets.
A number of factors contributed to the souring of investor sentiment including geopolitical risks in Russia and Greece and a genuine deterioration of macro-economic data in Continental Europe.
As a result, most European and emerging markets declined in 2014 as seen by the FTSE 100, which was down 2.7% , and the MSCI Emerging Markets index, which declined 4.6% .
The U. S.  market fell from its highs in mid-2014, but still managed an impressive S&P 500 return of 11.4% .
Japan was also positive in 2014, with the Nikkei 225 up 7.1% , which was driven by the fiscal and monetary policy actions taken by the Japanese government and central bank, respectively.
The sell-off of risk assets benefited the US Treasury market as investors sought the safety of US government bonds.
Yields on the 10- year and 30- year Treasury reached historic lows benefiting returns of government bond indices.
The Barclays US Aggregate Bond index returned 6.0% for the year.
The table below summarizes the year ended December 31 returns based on price appreciation/(depreciation) of several major market indices for 2014 , 2013 , and 2012 :
## Table 2 ##
Throughout 2014, we continued to execute our long-term strategy, which further improved our ability to serve clients, strengthened our investment performance, and helped to deliver competitive levels of operating income and margins.
We also took advantage of opportunities in the market and invested in our products and capabilities, our brand, our global platform and our people in ways that strengthened our business and competitive position for long-term success.
As a global investment management firm dedicated to delivering investment excellence to our clients, Invesco is committed to further strengthening and enhancing our risk management approach.
We believe a key factor in Invesco's ability to manage through the economic uncertainty of recent years was our integrated approach to risk management.
Invesco's enterprise risk management approach is embedded in its management processes across the organization.
Broadly, our approach includes two governance structures - one for investments and another for business risk.
LKQ CORPORATION AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (Continued) Note 5.
Long-Term Obligations (Continued) As part of the consideration for business acquisitions completed during 2007, 2006 and 2005, we issued promissory notes totaling approximately $1.7 million, $7.2 million and $6.4 million, respectively.
The notes bear interest at annual rates of 3.0% to 6.0%, and interest is payable at maturity or in monthly installments.
We also assumed certain liabilities in connection with a business acquisition during the second quarter of 2005, including a promissory note with a remaining principle balance of approximately $0.2 million.
The annual interest rate on the note, which was retired during 2006, was 5.1%.
Note 6.
Commitments and Contingencies Operating Leases We are obligated under noncancelable operating leases for corporate office space, warehouse and distribution facilities, trucks and certain equipment.
The future minimum lease commitments under these leases at December 31, 2007 are as follows (in thousands):
## Table 3 ##
Rental expense for operating leases was approximately $27.4 million, $18.6 million and $12.2 million during the years ended December 31, 2007, 2006 and 2005, respectively.
We guaranty the residual values of the majority of our truck and equipment operating leases.
The residual values decline over the lease terms to a defined percentage of original cost.
In the event the lessor does not realize the residual value when a piece of equipment is sold, we would be responsible for a portion of the shortfall.
Similarly, if the lessor realizes more than the residual value when a piece of equipment is sold, we would be paid the amount realized over the residual value.
Had we terminated all of our operating leases subject to these guaranties at December 31, 2007, the guarantied residual value would have totaled approximately $24.0 million.
Litigation and Related Contingencies On December 2, 2005, Ford Global Technologies, LLC (‘‘Ford’’) filed a complaint with the United States International Trade Commission (‘‘USITC’’) against Keystone and five other named Respondents, including four Taiwan-based manufacturers.
On December 12, 2005, Ford filed an Amended Complaint.
Both the Complaint and the Amended Complaint contended that Keystone and the other Respondents infringed 14 design patents that Ford alleges cover eight parts on the 2004-2005

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="4">2009</td></tr><tr><td></td><td>Q1</td><td>Q2</td><td>Q3</td><td>Q4</td></tr><tr><td>Leverage Ratio</td><td>1.48</td><td>1.63</td><td>1.77</td><td>1.11</td></tr><tr><td>Interest Coverage Ratio</td><td>11.31</td><td>9.64</td><td>9.12</td><td>11.01</td></tr><tr><td>Long-term AUM</td><td>N/A*</td><td>299.0</td><td>329.7</td><td>343.6</td></tr></table>
<table><tr><td>$ millions</td><td>Total</td><td>Q4 2011</td><td>Q3 2011</td><td>Q2 2011</td><td>Q1 2011</td></tr><tr><td>Net income attributable to common shareholders</td><td>729.7</td><td>202.3</td><td>166.9</td><td>183.0</td><td>177.5</td></tr><tr><td>Net income attributable to Consolidated Investment Products</td><td>-20.2</td><td>-1.9</td><td>-3.5</td><td>-5.2</td><td>-9.6</td></tr><tr><td>Tax expense</td><td>286.1</td><td>76.0</td><td>59.1</td><td>75.4</td><td>75.6</td></tr><tr><td>Amortization/depreciation</td><td>117.4</td><td>22.1</td><td>35.3</td><td>32.1</td><td>27.9</td></tr><tr><td>Interest expense</td><td>61.8</td><td>14.3</td><td>15.3</td><td>16.0</td><td>16.2</td></tr><tr><td>Share-based compensation expense</td><td>115.1</td><td>29.1</td><td>29.2</td><td>30.5</td><td>26.3</td></tr><tr><td>Unrealized gains and losses from investments, net*</td><td>3.6</td><td>-3.8</td><td>11.4</td><td>-1.9</td><td>-2.1</td></tr><tr><td>EBITDA**</td><td>1,293.5</td><td>338.1</td><td>313.7</td><td>329.9</td><td>311.8</td></tr><tr><td>Adjusted debt**</td><td>$1,304.7</td><td></td><td></td><td></td><td></td></tr><tr><td>Leverage ratio (Debt/EBITDA - maximum 3.25:1.00)</td><td>1.01</td><td></td><td></td><td></td><td></td></tr><tr><td>Interest coverage (EBITDA/Interest Expense - minimum 4.00:1.00)</td><td>20.93</td><td></td><td></td><td></td><td></td></tr></table>
<table><tr><td></td><td colspan="3">Year ended December 31,</td></tr><tr><td>Equity Index</td><td>2014</td><td>2013</td><td>2012</td></tr><tr><td>S&P 500</td><td>11.4%</td><td>29.6%</td><td>13.4%</td></tr><tr><td>FTSE 100</td><td>-2.7%</td><td>14.4%</td><td>5.8%</td></tr><tr><td>Nikkei 225</td><td>7.1%</td><td>56.7%</td><td>22.9%</td></tr><tr><td>MSCI Emerging Markets</td><td>-4.6%</td><td>-5.0%</td><td>15.2%</td></tr><tr><td>Bond Index</td><td></td><td></td><td></td></tr><tr><td>Barclays U.S. Aggregate Bond</td><td>6.0%</td><td>-2.0%</td><td>4.2%</td></tr></table>
<table><tr><td>2008</td><td>$42,335</td></tr><tr><td>2009</td><td>33,249</td></tr><tr><td>2010</td><td>25,149</td></tr><tr><td>2011</td><td>17,425</td></tr><tr><td>2012</td><td>11,750</td></tr><tr><td>Thereafter</td><td>28,581</td></tr><tr><td>Future Minimum Lease Payments</td><td>$158,489</td></tr></table>

Question: what was the percentage change in rental expense from 2005 to 2006?
Answer: 0.52459
Reasoning program: subtract(18.6,12.2), divide(#0,12.2)