## Table 0 ##
ITEM 7.
MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS The following discussion should be read in conjunction with our audited consolidated financial statements and the notes thereto, included elsewhere herein.
This discussion may contain forward-looking statements that anticipate results based on management’s plans that are subject to uncertainty.
We discuss in more detail various factors that could cause actual results to differ from expectations in Item 1A.
Risk Factors.
Overview We are the second largest provider of services in the domestic non-hazardous solid waste industry, as measured by revenue.
We provide non-hazardous solid waste collection services for commercial, industrial, municipal and residential customers through 348 collection companies in 40 states and Puerto Rico.
We own or operate 204 transfer stations, 193 active solid waste landfills and 76 recycling facilities.
We also operate 73 landfill gas and renewable energy projects.
We completed our acquisition of Allied Waste Industries, Inc.  (Allied) in December 2008.
We believe that this acquisition creates a strong operating platform that will allow us to continue to provide quality service to our customers and superior returns to our stockholders.
Despite the challenging economic environment, our business has performed well during 2010 due in large part to the indispensable nature of our services and the scalability of our business.
Revenue for the year ended December 31, 2010 decreased by 1.1% or $92.5 million to $8,106.6 million as compared to $8,199.1 million during the comparable period in 2009.
Due to the Allied acquisition, the DOJ required us to divest of certain assets and related liabilities.
The resulting divestitures, as well as other divestitures in the normal course of business, decreased revenue by 1.1% for the year ended December 31, 2010 from the year ended December 31, 2009.
Excluding divested revenue, core revenue for the year ended December 31, 2010 was unchanged, consisting of a 1.6% increase in core price, 1.4% increase in commodity price and a 0.5% increase in fuel charges, offset by a decrease of 3.5% in core volume due to the continued weak economy.
The core price increase, together with operating efficiencies arising from the acquisition and cost control measures taken by our operations management to scale the business down for lower volumes, served to moderate profit margin declines.
During 2010, we completed the integration of Allied operations resulting in approximately $190 million of annual run-rate synergy savings, of which $161 million relates to operating synergies and $29 million relates to financing synergies, exceeding our original estimate of approximately $150 million by 26.7%.
Since the acquisition in 2008, we have repaid $1.3 billion of net borrowings through December 31, 2010 and have refinanced $1.5 billion of senior notes and $677.4 million of tax-exempt financings at lower interest rates.
Free cash flow generated from operations allowed us to increase our regular quarterly dividend 5% in the third quarter of 2010 and in November 2010, our board of directors approved a share repurchase program pursuant to which we may repurchase up to $400.0 million of our outstanding shares of common stock.
REPUBLIC SERVICES, INC.  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS—(Continued) the Plan to reflect the Allied acquisition.
The 2006 Plan, as amended and restated, provides for the grant of nonqualified stock options, incentive stock options, shares of restricted stock, shares of phantom stock, stock bonuses, restricted stock units, stock appreciation rights, performance awards, dividend equivalents, cash awards, or other stock-based awards.
Awards granted under the 2006 Plan prior to December 5, 2008 became fully vested and nonforfeitable upon the closing of the acquisition.
Awards may be granted under the 2006 Plan, as amended and restated, after December 5, 2008 only to employees and consultants of Allied and its subsidiaries who were not employed by Republic prior to such date.
As of December 31, 2013, there were approximately 15.6 million shares of common stock reserved for future grants under the 2006 Plan.
Stock Options We use a lattice binomial option-pricing model to value our stock option grants.
We recognize compensation expense on a straight-line basis over the requisite service period for each separately vesting portion of the award, or to the employee’s retirement eligible date, if earlier.
Expected volatility is based on the weighted average of the most recent one year volatility and a historical rolling average volatility of our stock over the expected life of the option.
The risk-free interest rate is based on Federal Reserve rates in effect for bonds with maturity dates equal to the expected term of the option.
We use historical data to estimate future option exercises, forfeitures (at 3.0% for each of the periods presented) and expected life of the options.
When appropriate, separate groups of employees that have similar historical exercise behavior are considered separately for valuation purposes.
The weighted-average estimated fair values of stock options granted during the years ended December 31, 2013, 2012 and 2011 were $5.27, $4.77 and $5.35 per option, respectively, which were calculated using the following weighted-average assumptions:
## Table 1 ##
Cost of goods sold relates to rebates paid for volumes delivered to our recycling facilities.
Cost of goods sold in aggregate dollars and as a percentage of revenue decreased $32.2 million and 0.4%, respectively, primarily due to a decline in the market value of recycled commodities, offset by an increase in the volume of commodities processed.  ?
Risk management expenses increased, primarily due to lower favorable actuarial development compared to the prior year.  ?
We recorded environmental remediation charges at our closed Bridgeton Landfill in Missouri of $74.1 million during 2012 to manage the remediation area and monitor the site.
Depreciation, Amortization and Depletion of Property and Equipment The following table summarizes depreciation, amortization and depletion of property and equipment for the years ended December 31, 2013, 2012 and 2011 (in millions of dollars and as a percentage of revenue):
## Table 2 ##
Depreciation, Amortization and Depletion of Property and Equipment - 2013 compared to 2012 Depreciation and amortization of property and equipment in aggregate dollars increased $24.0 million, primarily due to higher costs of residential side loaders for automating our residential collection routes and an increased number of CNG vehicles, which are more expensive to purchase than diesel vehicles.
In addition, we made increased investments in new and upgraded recycling infrastructure projects that became operational over the past several quarters.
Depreciation and amortization of property and equipment as a percentage of revenue remained relatively consistent at 6.5% for 2013 and 6.4% for 2012.
Landfill depletion and amortization expense in aggregate dollars increased $4.3 million, primarily due to increased landfill disposal volumes, as well as an overall increase in our average depletion rate.
Offsetting these increases were favorable amortization adjustments of $0.3 million that were recognized in 2013 relative to asset retirement obligations, compared to net unfavorable adjustments of $4.9 million in 2012.
Landfill depletion and amortization as a percentage of revenue remained relatively consistent at 3.1% for 2013 and 3.2% for 2012.
Depreciation, Amortization and Depletion of Property and Equipment - 2012 compared to 2011 Depreciation and amortization of property and equipment increased $9.4 million for 2012, primarily due to higher costs of residential side loaders and an increased number of CNG vehicles.
In addition, we made increased investments in new and upgraded recycling infrastructure projects that became operational in 2012.
Landfill depletion and amortization expense increased $2.1 million, primarily due to unfavorable adjustments to landfill depletion and amortization expense for asset retirement obligations of $4.9 million recorded during 2012 compared to favorable adjustments of $9.6 million recorded during 2011.
Offsetting the increase in costs relative to asset retirement obligations was an overall decline in landfill depletion due to lower disposal volumes.
Amortization of Other Intangible Assets and Other Assets Expenses for amortization of intangible and other assets were $70.7 million, $70.1 million and $76.7 million for 2013, 2012 and 2011, respectively, or, as a percentage of revenue, 0.8% for 2013 and 0.9% for 2012 and 2011.
Our other intangible assets and other assets primarily relate to customer lists, franchise agreements, municipal
contracts, trade names (now fully amortized in 2013), favorable lease assets and, to a lesser extent, non-compete agreements.
Amortization of intangible assets in aggregate dollars decreased during 2012 as compared to 2011 primarily due to municipal agreement intangibles acquired from Allied that are now fully amortized.
Accretion Expense Accretion expenses were $76.6 million, $78.4 million and $78.0 million, or, as a percentage of revenue, 0.9%, 1.0% and 0.9% for 2013, 2012 and 2011, respectively.
Accretion expenses have remained relatively unchanged as our asset retirement obligations remained relatively consistent period over period.
Selling, General and Administrative Expenses Selling, general and administrative expenses include salaries, health and welfare benefits and incentive compensation for corporate and field general management, field support functions, sales force, accounting and finance, legal, management information systems, and clerical and administrative departments.
Other expenses include rent and office costs, fees for professional services provided by third parties, legal settlements, marketing, investor and community relations services, directors’ and officers’ insurance, general employee relocation, travel, entertainment and bank charges.
Restructuring charges are excluded from selling, general and administrative expenses and are discussed separately below.
The following table provides the components of our selling, general and administrative expenses for the three years ended December 31, 2013, 2012 and 2011 (in millions of dollars and as a percentage of revenue):

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="5">Year Ended December 31,</td></tr><tr><td></td><td>2010</td><td>2009</td><td>2008</td><td>2007</td><td>2006</td></tr><tr><td> Other Operating Data:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cash flows from operating activities</td><td>$1,433.7</td><td>$1,396.5</td><td>$512.2</td><td>$661.3</td><td>$511.2</td></tr><tr><td>Capital expenditures</td><td>794.7</td><td>826.3</td><td>386.9</td><td>292.5</td><td>326.7</td></tr><tr><td>Proceeds from sales of property and equipment</td><td>37.4</td><td>31.8</td><td>8.2</td><td>6.1</td><td>18.5</td></tr><tr><td> Balance Sheet Data:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cash and cash equivalents</td><td>$88.3</td><td>$48.0</td><td>$68.7</td><td>$21.8</td><td>$29.1</td></tr><tr><td>Restricted cash and marketable securities</td><td>172.8</td><td>240.5</td><td>281.9</td><td>165.0</td><td>153.3</td></tr><tr><td>Total assets</td><td>19,461.9</td><td>19,540.3</td><td>19,921.4</td><td>4,467.8</td><td>4,429.4</td></tr><tr><td>Total debt</td><td>6,743.6</td><td>6,962.6</td><td>7,702.5</td><td>1,567.8</td><td>1,547.2</td></tr><tr><td>Total stockholders’ equity</td><td>7,848.9</td><td>7,567.1</td><td>7,282.5</td><td>1,303.8</td><td>1,422.1</td></tr></table>
<table><tr><td></td><td>2013</td><td>2012</td><td>2011</td></tr><tr><td>Expected volatility</td><td>28.9%</td><td>27.8%</td><td>27.3%</td></tr><tr><td>Risk-free interest rate</td><td>0.7%</td><td>0.8%</td><td>1.7%</td></tr><tr><td>Dividend yield</td><td>3.2%</td><td>3.2%</td><td>2.7%</td></tr><tr><td>Expected life (in years)</td><td>4.5</td><td>4.5</td><td>4.4</td></tr><tr><td>Contractual life (in years)</td><td>7.0</td><td>7.0</td><td>7.0</td></tr></table>
<table><tr><td></td><td colspan="2">2013</td><td colspan="2">2012</td><td colspan="2">2011</td></tr><tr><td>Depreciation and amortization of propertyand equipment</td><td>$544.8</td><td>6.5%</td><td>$520.8</td><td>6.4%</td><td>$511.4</td><td>6.3%</td></tr><tr><td>Landfill depletion and amortization</td><td>261.9</td><td>3.1</td><td>257.6</td><td>3.2</td><td>255.5</td><td>3.1</td></tr><tr><td>Depreciation, amortization and depletionexpense</td><td>$806.7</td><td>9.6%</td><td>$778.4</td><td>9.6%</td><td>$766.9</td><td>9.4%</td></tr></table>

Question: what was the growth of the weighted-average estimated fair values of stock options granted from 2012 to 2013
Answer: 0.10482
Reasoning program: subtract(5.27,4.77), divide(#0,4.77)