<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>113 - Disclosure - Deferred Financing Costs</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>eol_PE10315---1310-Q0011_STD_181_20130630_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001069308</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>opxa_DeferredChargesDisclosureTextBlock</ElementName><ElementPrefix>opxa_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="eol_PE10315---1310-Q0011_STD_181_20130630_0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt"&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold"&gt;
Note 5.&amp;#xA0;&amp;#xA0;Deferred Financing Costs&lt;/font&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="TEXT-INDENT: 18pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt"&gt;Deferred
financing costs at June 30, 2013 consist of costs incurred from
third parties in conjunction with the July 2012
Notes.&amp;#xA0;&amp;#xA0;The costs in connection with the debt financing
were capitalized and are amortized to interest expense over the
term of the related debt. As of June 30, 2013, the unamortized
deferred financing costs totaling $112,515 are reported as deferred
financing costs in the consolidated balance sheets. During the six
months ended June 30, 2013, Opexa amortized $98,964 of deferred
financing costs as interest expense.&lt;/font&gt;&lt;/div&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>Deferred Charges Disclosure.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Deferred Financing Costs</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Deferred Financing Costs</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.opexatherapeutics.com/taxonomy/role/NotesToFinancialStatementsDeferredChargesDisclosureTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>1</NumberOfRows></InstanceReport>
