We account for our oil and natural gas exploration and development activities using the full cost method of accounting prescribed by the SEC. Accordingly, all productive and non-productive costs incurred in connection with the acquisition, exploration and development of our oil, NGLs, and natural gas reserves, including directly related overhead costs and related asset retirement costs, are capitalized and amortized on a units-of-production method based on proved oil and natural gas reserves. Directly related overhead costs of $21.5 million, $17.6 million, and $15.6 million were capitalized in 2013, 2012, and 2011, respectively. Independent petroleum engineers annually audit our internal evaluation of our reserves. The average rates used for depreciation, depletion, and amortization (DD&A) were $13.32, $14.70, and $15.06 per Boe in 2013, 2012, and 2011, respectively. The calculation of DD&A includes estimated future expenditures to be incurred in developing proved reserves and estimated dismantlement and abandonment costs, net of estimated salvage values. Our unproved properties totaling $545.6 million are excluded from the DD&A calculation.
No gains or losses are recognized on the sale, conveyance or other disposition of oil and natural gas properties unless a significant reserve amount to our total reserves is involved.
Revenue from the sale of oil and natural gas is recognized when title passes, net of royalties.
Under the full cost rules, at the end of each quarter, we review the carrying value of our oil and natural gas properties. The full cost ceiling is based principally on the estimated future discounted net cash flows from our oil and natural gas properties discounted at 10%. We use the unweighted arithmetic average of the commodity prices existing on the first day of each of the 12 months before the end of the reporting period to calculate discounted future revenues, unless prices were otherwise determined under contractual arrangements. In the event the unamortized cost of oil and natural gas properties being amortized exceeds the full cost ceiling, as defined by the SEC, the excess is charged to expense in the period during which such excess occurs. Once incurred, a write-down of oil and natural gas properties is not reversible.
For the quarter ended June 30, 2012, the 12-month average commodity prices, including the discounted value of our cash flow hedges, decreased significantly, resulting in a non-cash ceiling test write down of $115.9 million pre-tax ($72.1 million, net of tax). Our qualifying cash flow hedges used in the ceiling test determination at June 30, 2012, consisted of swaps and collars, covering production of 2.9 MMBoe in 2012 and 4.5 MMBoe in 2013. The effect of those hedges on the June 30, 2012 ceiling test was a $32.5 million pre-tax increase in the discounted net cash flows of our oil and natural gas properties.
For the quarter ended December 31, 2012, the 12-month average commodity prices, including the discounted value of our cash flow hedges, decreased further, resulting in an additional non-cash ceiling test write down of $167.7 million pre-tax ($104.4 million, net of tax). Our qualifying cash flow hedges used in the ceiling test determination at December 31, 2012, consisted of swaps and collars covering 6.9 MMBoe in 2013. The effect of those hedges on the December 31, 2012 ceiling test was a $29.8 million pre-tax increase in the discounted net cash flows of our oil and natural gas properties. Our oil and natural gas hedging is discussed in Note 13 of the Notes to our Consolidated Financial Statements.
At December 31, 2013, using the existing 12-month average commodity prices, we were not required to record a ceiling test write-down. All cash flow hedges expired at December 31, 2013 and did not effect the ceiling test determination.
If there are declines in the 12-month average prices, we may be required to record a write-down in future periods.
Our contract drilling segment provides drilling services for our exploration and production segment. Depending on their timing some of the drilling services performed on our properties are also deemed to be associated with the acquisition of an ownership interest in the property. Revenues and expenses for such services are eliminated in our income statement, with any profit recognized as a reduction in our investment in our oil and natural gas properties. The contracts for these services are issued under the same conditions and rates as the contracts entered into with unrelated third parties. We eliminated revenue of $64.3 million, $49.6 million, and $52.2 million for 2013, 2012, and 2011, respectively from our contract drilling segment and eliminated the associated operating expense of $46.9 million, $34.1 million, and $32.6 million during 2013, 2012, and 2011, respectively, yielding $17.4 million, $15.5 million, and $19.6 million during 2013, 2012, and 2011, respectively, as a reduction to the carrying value of our oil and natural gas properties.
