The determination of fair value for our reporting units is primarily based on an income approach whereby we use discounted cash flows for each reporting unit. When available, and as appropriate, we use market approaches or other valuation techniques to corroborate discounted cash flow results. The discounted cash flow model used for each reporting unit is based on either income or distributable cash flow, depending on the reporting unit being valued.
Brasilprev Seguros e Previdencia S.A. On April 30, 2010, we signed definitive agreements with Banco, including the Shareholders Agreement governing the operations of our pension joint venture, Brasilprev. The agreements result in Brasilprev having, for 23 years, the exclusive right to distribute pension products within the Banco bank network and a reduction in our economic interest from 46% to 25%, which resulted in a $72.1 million after-tax net realized capital gain in the second quarter of 2010. Brasilprev continues to be jointly managed and reported as an equity method investment in our Principal International segment. Due to the reduction in our economic interest, we reflect a lower percentage of the earnings from the operation. However, we expect the operation to grow and offset the decline from the lower percentage.
Reclassifications have been made to prior period financial statements to conform to the December 31, 2011, presentation.
The cost of fixed maturities is adjusted for amortization of premiums and accrual of discounts, both computed using the interest method. The cost of fixed maturities and equity securities classified as available-for-sale is adjusted for declines in value that are other than temporary. Impairments in value deemed to be other than temporary are primarily reported in net income as a component of net realized capital gains (losses), with noncredit impairment losses for certain fixed maturities, available-for-sale reported in OCI. Interest income, as well as prepayment fees and the amortization of the related premium or discount, is reported in net income. For loan-backed and structured securities, we recognize income using a constant effective yield based on currently anticipated cash flows.
We enter into reinsurance agreements with other companies in the normal course of business. We may assume reinsurance from or cede reinsurance to other companies. Assets and liabilities related to reinsurance ceded are reported on a gross basis. Premiums and expenses are reported net of reinsurance ceded. The cost of reinsurance related to long-duration contracts is accounted for over the life of the underlying reinsured policies using assumptions consistent with those used to account for the underlying policies. We are contingently liable with respect to reinsurance ceded to other companies in the event the reinsurer is unable to meet the obligations it has assumed. At December 31, 2011 and 2010, our largest exposures to a single third-party reinsurer in our individual life insurance business was $25.3 billion and $23.3 billion of life insurance in force, representing 16% and 15% of total net individual life insurance in force, respectively. The reinsurance recoverable related to this single third party reinsurer recorded in our consolidated statements of financial position was $22.6 million and $27.5 million at December 31, 2011 and 2010, respectively.
The net unrealized gains and losses on investments in fixed maturities available-for-sale, equity securities available-for-sale and derivative instruments are reported as a separate component of stockholders' equity. The cumulative amount of net unrealized gains and losses on available-for-sale securities and derivative instruments net of adjustments related to DPAC, sales inducements, unearned revenue reserves, changes in policyholder liabilities and applicable income taxes was as follows:
We actively monitor and manage our commercial mortgage loan portfolio. All commercial mortgage loans are analyzed regularly and substantially all are internally rated, based on a proprietary risk rating cash flow model, in order to monitor the financial quality of these assets. The model stresses expected cash flows at various levels and at different points in time depending on the durability of the income stream, which includes our assessment of factors such as location (macro and micro markets), tenant quality and lease expirations. Our internal rating analysis presents expected losses in terms of an S&P bond equivalent rating. As the credit risk for commercial mortgage loans increases, we adjust our internal ratings downwards with loans in the category "B+ and below" having the highest risk for credit loss. Internal ratings on commercial mortgage loans are updated at least annually and potentially more often for certain loans with material changes in collateral value or occupancy and for loans on an internal "watch list".
Our residential mortgage loan portfolio is monitored based on performance of the loans. Monitoring on a residential mortgage loan increases when the loan is delinquent or earlier if there is an indication of impairment. We define non-performing residential mortgage loans as loans 90 days or greater delinquent or on non-accrual status.
derivative is bifurcated from the host instrument for measurement purposes. The embedded derivative, which is reported with the host instrument in the consolidated statements of financial position, is carried at fair value.
We also have invested in fixed maturities classified as available-for-sale that contain credit default swaps that do not require bifurcation and fixed maturities classified as trading that contain credit default swaps. These securities are subject to the credit risk of the issuer, normally a special purpose vehicle, which consists of the underlying credit default swaps
The accumulated benefit obligation for all defined benefit pension plans was $2,027.8 million and $1,811.7 million at December 31, 2011 and 2010, respectively.
We may discuss such litigation in one of three ways. We accrue a charge to income and disclose legal matters for which the chance of loss is probable and for which the amount of loss can be reasonably estimated. We may disclose contingencies for which the chance of loss is reasonably possible, and provide an estimate of the possible loss or range of loss or a statement that such an estimate cannot be made. Finally, we may voluntarily disclose loss contingencies for which the chance of loss is remote in order to provide information concerning matters that potentially expose us to possible losses.
The following represents payments due by period for operating lease obligations (in millions):
As of December 31, 2011, we had 13.0 million shares of preferred stock authorized, issued and outstanding under the two series described below. Preferred stockholders have dividend and liquidation priority over common stockholders.
On May 11, 2009, we issued 58.2 million shares of common stock at a price of $19.75 per share. Net proceeds from the issuance were $1,109.1 million. The proceeds from this offering were used for general corporate purposes.
If we are unable to price a fixed maturity security using prices from third party pricing vendors or other sources specific to the asset class, we may obtain a broker quote or utilize an internal pricing model specific to the asset utilizing relevant market information, to the extent available, which are reflected in Level 3 and can include fixed maturities across all asset classes. As of December 31, 2011, less than 1% of our fixed maturities were valued using internal pricing models, which were classified as Level 3 assets accordingly.
Other investments reported at fair value also include commercial mortgage loans of consolidated VIEs for which the fair value option was elected, which are reflected in Level 3. Fair value of these commercial mortgage loans is computed
Separate account liabilities are not measured at fair value on a recurring basis. Fair values of separate account liabilities, excluding insurance-related elements, are estimated based on market assumptions around what a potential acquirer would pay for the associated block of business, including both the separate account assets and liabilities. As the applicable separate account assets are already reflected at fair value, any adjustment to the fair value of the block is an assumed adjustment to the separate account liabilities. To compute fair value, the separate account liabilities are originally set to equal separate account assets because these are pass-through contracts. The separate account liabilities are reduced by the amount of future fees expected to be collected that are intended to offset upfront acquisition costs already incurred that a potential acquirer would not have to pay. The estimated future fees are adjusted by an adverse deviation discount and the amount is then discounted at a risk-free rate as measured by the yield on U.S. Treasury securities at maturities aligned with the estimated timing of fee collection.
The total intrinsic value of stock options exercised was $4.0 million, $1.9 million and zero during 2011, 2010, and 2009, respectively.
We issue restricted stock units under the 2010 Stock Incentive Plan, 2005 Directors Stock Plan, Stock Incentive Plan, and Directors Stock Plan. Restricted stock units are treated as an equity award. There is no maximum contractual term on these awards. Dividend equivalents are credited on restricted stock units outstanding as of the record date. These dividend equivalents are only paid on the shares released. In 2011, 2010 and 2009, 0.9 million, 1.2 million and 1.9 million restricted stock units were granted, respectively.