<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>006180 - Disclosure - New Accounting Pronouncements</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>9/1/2010 - 2/28/2011
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>c00053</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000104207</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2010-09-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-02-28T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>u000</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>u003</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>pure</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>u001</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>u002</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="6 Months Ended" /><Label Id="2" Label="Feb. 28, 2011" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>wag_NotesToFinancialStatementsAbstract</ElementName><ElementPrefix>wag</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Notes to Financial Statements [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>wag_DescriptionOfNewAccountingPronouncementsNotYetAdoptedTextBlock</ElementName><ElementPrefix>wag</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>For a new accounting pronouncement that has been issued but not yet adopted, an entity's disclosure should (1) describe the...</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="DISPLAY: block; MARGIN-LEFT: 0pt; TEXT-INDENT: 0pt; MARGIN-RIGHT: 0pt" align="left"&gt;&lt;font style="DISPLAY: inline; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman"&gt;&amp;#160;(18)&amp;#160;&amp;#160;In August 2010, the Financial Accounting Standards Board (FASB) issued an exposure draft on lease accounting that would require entities to recognize assets and liabilities arising from lease contracts on the balance sheet.&amp;#160;&amp;#160;The proposed exposure draft states that lessees and lessors should apply a &amp;#8220;right-of-use model&amp;#8221; in accounting for all leases.&amp;#160;&amp;#160;Under the proposed model, lessees would recognize an asset for the right to use the leased asset, and a liability for the obligation to make rental payments over the lease term.&amp;#160;&amp;#160;The lease term is defined as the longest possible term that is &amp;#8220;more likely than not&amp;#8221; to occur.&amp;#160;&amp;#160;The accounting by a lessor would reflect its retained exposure to the risks or benefits of the underlying leased asset.&amp;#160;&amp;#160;A lessor would recognize an asset representing its right to receive lease payments based on the expected term of the lease.&amp;#160;&amp;#160;The final standard is expected to be issued in calendar 2011.&amp;#160;&amp;#160;The proposed standard, as currently drafted, will have a material impact on the Company&amp;#8217;s reported results of operations and financial position.&amp;#160;&amp;#160;This exposure draft is non-cash in nature and will not impact the Company&amp;#8217;s cash position.&lt;/font&gt;&lt;/div&gt;</NonNumbericText><NonNumericTextHeader>&amp;#160;(18)&amp;#160;&amp;#160;In August 2010, the Financial Accounting Standards Board (FASB) issued an exposure draft on lease accounting that would require entities</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>For a new accounting pronouncement that has been issued but not yet adopted, an entity's disclosure should (1) describe the new pronouncement, the date that adoption is required and the date that the entity plans to adopt, if earlier; (2) discuss the methods of adoption allowed by the pronouncement and the method expected to be utilized by the entity, if determined; (3) discuss the impact that adoption of the pronouncement is expected to have on the financial statements of the entity, unless such impact is not known or reasonably estimable (in which case, a statement to that effect should be made) and; (4) disclose the potential impact of other significant matters that the entity believes might result from the adoption of the pronouncement (for example, technical violations of debt covenant agreements and planned or intended changes in business practices.)</ElementDefenition><ElementReferences>No authoritative reference available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>New Accounting Pronouncement</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>New Accounting Pronouncements</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
