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Retirement Programs | 12 Months Ended
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Dec. 31, 2023
Retirement Benefits [Abstract] |
Retirement Programs | RETIREMENT PROGRAMS Defined Benefit Pension Plans - U.S. The Linde retirement plans are non-contributory defined benefit plans covering eligible employees and its participating affiliates. Effective July 1, 2002, the Linde U.S. Pension Plan was amended to give participating employees a one-time irrevocable choice between a traditional benefit (the “Traditional Design”) and an account-based benefit (the “Account-Based Design”). The Traditional Design pays a monthly benefit based on years of service and average pay during the last years of the participant’s career with Linde. The Account-Based Design gives participants annual pay credits equal to 4% of eligible compensation, plus interest credits based on long-term treasury rates on the accumulated account balance. This new formula applies to all new employees hired after April 30, 2002 into businesses adopting this plan. The U.S. pension plan assets are comprised of a diversified mix of investments, including corporate equities, government securities and corporate debt securities. Linde has several plans that provide supplementary retirement benefits primarily to higher level employees that are unfunded and are nonqualified for federal tax purposes. Pension coverage for employees of certain of Linde’s non-U.S. subsidiaries generally is provided by those companies through separate plans. Obligations under such plans are primarily provided for through diversified investment portfolios, with some smaller plans provided for under insurance policies or by book reserves. Defined Benefit Pension Plans - Non-U.S. Linde has Non-U.S., defined benefit commitments primarily in Germany and the U.K that include pension plan assets comprised of a diversified mix of investments. The defined benefit commitments in Germany relate to old age pensions, invalidity pensions and surviving dependents pensions. These commitments also take into account vested rights for periods of service prior to January 1, 2002 based on earlier final-salary pension plan rules. In addition, there are direct commitments in respect of the salary conversion scheme for the form of cash balance plans. The resulting pension payments are calculated on the basis of an interest guarantee and the performance of the corresponding investment. There are no minimum funding requirements. The pension obligations in Germany are partly funded by a Contractual Trust Agreement (CTA). Defined benefit commitments in the U.K. prior to July 1, 2003 are earnings-related and dependent on the period of service. Such commitments relate to old age pensions, invalidity pensions and surviving dependents pensions. Beginning in April 1, 2011, the amount of future increases in inflation-linked pensions and of increases in pensionable emoluments was restricted. Multi-employer Pension Plans In the United States Linde participates in eight multi-employer defined benefit pension plans ("MEPs"), pursuant to the terms of collective bargaining agreements, that cover approximately 200 union-represented employees. The collective bargaining agreements expire on different dates through 2028. In connection with such agreements, the company is required to make periodic contributions to the MEPs in accordance with the terms of the respective collective bargaining agreements. Linde’s participation in these plans is not material either at the plan level or in the aggregate. For all MEPs, Linde’s contributions were significantly less than 1% of the total contributions to each plan for 2022 and 2021. Total 2023 contr ibutions were not yet available from the MEPs. Linde has obtained the most recently available Pension Protection Act ("PPA") annual funding notices from the Trustees of the MEPs. As of December 31, 2023, there were two Red Zone plans, deemed to be in "critical" or "critical and declining" status that have implemented financial improvement or rehabilitation plans. Linde does not currently anticipate significant future obligations due to the funding status of these plans and any such obligation would be immaterial. If Li nde determined it was probable that it would withdraw from an MEP, the company would record a liability for its portion of the MEP’s unfunded pension obligations, as calculated at that time. Historically, such withdrawal payments have not been significant. Defined Contribution Plans Linde’s U.S. employees are eligible to participate in defined contribution savings plans offered by their applicable business. Employee contribution percentages vary by plan and are subject to the maximum allowable by IRS regulations. The cost for these defined contribution plans was $59 million in 2023, $56 million in 2022 and $51 million in 2021 (these costs are not included in the tables that follow). The defined contribution plans include a non-leveraged employee stock ownership plan ("ESOP") which covers all employees participating in this plan. The collective number of shares of Linde ordinary shares in the ESOP totaled 1,660,694 at December 31, 2023. Certain non-U.S. subsidiaries of the company also sponsor defined contribution plans where contributions are determined under various formulas. The expense for these plans was $60 million in 2023, $80 million in 2022 and $101 million in 2021 (these expenses are not included in the tables that follow). Postretirement Benefits Other Than Pensions (OPEB) Linde provides health care and life insurance benefits to certain eligible retired employees. These benefits are provided through various insurance companies and healthcare providers. The company does not currently fund its postretirement benefits obligations. Linde’s retiree plans may be changed or terminated by Linde at any time for any reason with no liability to current or future retirees. Linde uses a measurement date of December 31 for its pension and other post-retirement benefit plans. Pension and Postretirement Benefit Costs The components of net pension and postretirement benefits other than pension ("OPEB") costs for 2023, 2022 and 2021 are shown in the table below:
(Millions of dollars) | Year Ended December 31,
2023 |  | 2022 |  | 2021
Amount recognized in Operating Profit |  |  |  |  |
Service cost | $ | 84 |  |  | $ | 127 |  |  | $ | 157 |
Amount recognized in Net pension and OPEB cost (benefit), excluding service cost |  |  |  |  |
Interest cost | 373 |  |  | 201 |  |  | 154 |
Expected return on plan assets | (523) |  |  | (518) |  |  | (521) |
Net amortization and deferral | (30) |  |  | 74 |  |  | 171 |
Settlement charges (a) | 16 |  |  | 6 |  |  | 4 |
| $ | (164) |  |  | $ | (237) |  |  | $ | (192) |
Net periodic benefit cost (benefit) | $ | (80) |  |  | $ | (110) |  |  | $ | (35) |
(a) Settlement charges were triggered by lump sum benefit payments. Funded Status Changes in the benefit obligation and plan assets for Linde’s pension and OPEB programs, including reconciliation of the funded status of the plans to amounts recorded in the consolidated balance sheet, as of December 31, 2023 and 2022 are shown below.
(Millions of dollars) | Year Ended December 31,
2023 |  | 2022
U.S. |  | Non-U.S. |  | U.S. |  | Non-U.S.
Change in Benefit Obligation ("PBO") |  |  |  |  |  |  |
Benefit obligation, January 1 | $ | 2,129 |  |  | $ | 5,586 |  |  | $ | 2,719 |  |  | $ | 9,398 |
Service cost | 25 |  |  | 59 |  |  | 34 |  |  | 93 |
Interest cost | 105 |  |  | 268 |  |  | 60 |  |  | 141 |
Participant contributions | 11 |  |  | 18 |  |  | 11 |  |  | 17 |
Actuarial loss (gain) | 100 |  |  | 532 |  |  | (528) |  |  | (2,972) |
Benefits paid | (162) |  |  | (324) |  |  | (158) |  |  | (296) |
Plan settlement | (21) |  |  | (14) |  |  | (9) |  |  | (8) |
Foreign currency translation and other changes | — |  |  | 260 |  |  | — |  |  | (787) |
Benefit obligation, December 31 | $ | 2,187 |  |  | $ | 6,385 |  |  | $ | 2,129 |  |  | $ | 5,586 |
Accumulated benefit obligation ("ABO") | $ | 2,037 |  |  | $ | 6,300 |  |  | $ | 1,982 |  |  | $ | 5,508 |
Change in Plan Assets |  |  |  |  |  |  |
Fair value of plan assets, January 1 | $ | 1,891 |  |  | $ | 5,794 |  |  | $ | 2,448 |  |  | $ | 7,968 |
Actual return on plan assets | 300 |  |  | 365 |  |  | (421) |  |  | (1,302) |
Company contributions | — |  |  | 46 |  |  | — |  |  | 51 |
Participant contributions | — |  |  | 18 |  |  | — |  |  | 17 |
Benefits paid from plan assets | (141) |  |  | (320) |  |  | (136) |  |  | (248) |
Foreign currency translation and other changes | — |  |  | 275 |  |  | — |  |  | (692) |
Fair value of plan assets, December 31 | $ | 2,050 |  |  | $ | 6,178 |  |  | $ | 1,891 |  |  | $ | 5,794 |
Funded Status, End of Year | $ | (137) |  |  | $ | (207) |  |  | $ | (238) |  |  | $ | 208 |
Recorded in the Balance Sheet (Note 7) |  |  |  |  |  |  |
Other long-term assets | $ | 19 |  |  | $ | 361 |  |  | $ | 13 |  |  | $ | 648 |
Other current liabilities | (17) |  |  | (14) |  |  | (38) |  |  | (13) |
Other long-term liabilities | (139) |  |  | (554) |  |  | (213) |  |  | (427) |
Net amount recognized, December 31 | $ | (137) |  |  | $ | (207) |  |  | $ | (238) |  |  | $ | 208 |
Amounts recognized in accumulated other comprehensive income (loss) consist of: |  |  |  |  |  |  |
Net actuarial loss (gain) | $ | 290 |  |  | $ | 219 |  |  | $ | 357 |  |  | $ | (343) |
Prior service cost (credit) | (10) |  |  | 1 |  |  | (12) |  |  | 4 |
Deferred tax obligation (benefit) (Note 7) | (67) |  |  | 7 |  |  | (85) |  |  | 139 |
Amount recognized in accumulated other comprehensive income (loss) (Note 7) | $ | 213 |  |  | $ | 227 |  |  | $ | 260 |  |  | $ | (200) |
Comparative funded status information as of December 31, 2023 and 2022 for select non-U.S. pension plans is presented in the table below as the benefit obligations of these plans are considered to be significant relative to the total benefit obligation:
| United Kingdom |  | Germany |  | Other Non-U.S. |  | Total Non-U.S.
(Millions of dollars) | 2023 |  | 2023 |  | 2023 |  | 2023
Benefit obligation, December 31 | $ | 3,616 |  |  | $ | 1,684 |  |  | $ | 1,085 |  |  | $ | 6,385 |
Fair value of plan assets, December 31 | 3,858 |  |  | 1,370 |  |  | 950 |  |  | 6,178 |
Funded Status, End of Year | $ | 242 |  |  | $ | (314) |  |  | $ | (135) |  |  | $ | (207) |
| United Kingdom |  | Germany |  | Other Non-U.S. |  | Total Non-U.S.
(Millions of dollars) | 2022 |  | 2022 |  | 2022 |  | 2022
Benefit obligation, December 31 | $ | 3,100 |  |  | $ | 1,485 |  |  | $ | 1,001 |  |  | $ | 5,586 |
Fair value of plan assets, December 31 | 3,625 |  |  | 1,285 |  |  | 884 |  |  | 5,794 |
Funded Status, End of Year | $ | 525 |  |  | $ | (200) |  |  | $ | (117) |  |  | $ | 208 |
The changes in plan assets and benefit obligations recognized in other comprehensive income in 2023 and 2022 are as follows:
| Pensions
(Millions of dollars) | 2023 |  | 2022
Current year net actuarial losses (gains)* | $ | 480 |  |  | $ | (1,259) |
Amortization of net actuarial gains (losses) | 29 |  |  | (75) |
Amortization of prior service credits (costs) | 1 |  |  | 1 |
Pension settlements | (16) |  |  | (6) |
Foreign currency translation and other changes | — |  |  | (90) |
Total recognized in other comprehensive income | $ | 494 |  |  | $ | (1,429) |
________________________ * Pension net actuarial losses in 2023 are largely driven by the decrease in the discount rate environment resulting in actuarial losses from a higher PBO, which is partially offset by favorable plan asset experience for non-U.S plans. The U.S. plan derived a benefit from the actual return on plan assets. In 2022, the actuarial gains were largely driven by the significant increase in the discount rate environment resulting in actuarial gains from a lower PBO, which is partially offset by unfavorable plan asset experience for both non-U.S. and U.S. plans. The following table provides information for pension plans where the accumulated benefit obligation exceeds the fair value of plan assets:
(Millions of dollars) Year Ended December 31, | Pensions
2023 |  | 2022
U.S. |  | Non-U.S. |  | U.S. |  | Non-U.S.
Accumulated benefit obligation ("ABO") | $ | 1,952 |  |  | $ | 1,880 |  |  | $ | 1,895 |  |  | $ | 1,848 |
Fair value of plan assets | $ | 1,945 |  |  | $ | 1,385 |  |  | $ | 1,791 |  |  | $ | 1,472 |
The following table provides information for pension plans where the projected benefit obligation exceeds the fair value of plan assets:
(Millions of dollars) Year Ended December 31, | Pensions
2023 |  | 2022
U.S. |  | Non-U.S. |  | U.S. |  | Non-U.S.
Projected benefit obligation ("PBO") | $ | 2,012 |  |  | $ | 1,932 |  |  | $ | 1,948 |  |  | $ | 1,901 |
Fair value of plan assets | $ | 1,945 |  |  | $ | 1,390 |  |  | $ | 1,791 |  |  | $ | 1,478 |
Assumptions The assumptions used to determine benefit obligations are as of the respective balance sheet dates and the assumptions used to determine net benefit cost are as of the previous year-end, as shown below:
| Pensions
| U.S. |  | Non-U.S.
| 2023 |  | 2022 |  | 2023 |  | 2022
Weighted average assumptions used to determine benefit obligations at December 31, |  |  |  |  |  |  |
Discount rate | 5.03 | % |  | 5.35 | % |  | 4.27 | % |  | 4.58 | %
Interest crediting rate | 4.03 | % |  | 4.02 | % |  | 1.70 | % |  | 2.13 | %
Rate of increase in compensation levels | 3.50 | % |  | 3.25 | % |  | 2.58 | % |  | 2.59 | %
Weighted average assumptions used to determine net periodic benefit cost for years ended December 31, |  |  |  |  |  |  |
Discount rate | 5.35 | % |  | 2.78 | % |  | 4.58 | % |  | 1.82 | %
Interest crediting rate | 4.02 | % |  | 2.06 | % |  | 2.13 | % |  | 1.03 | %
Rate of increase in compensation levels | 3.25 | % |  | 3.25 | % |  | 2.59 | % |  | 2.55 | %
Expected long-term rate of return on plan assets (1) | 7.00 | % |  | 7.00 | % |  | 5.64 | % |  | 5.60 | %
(1) The expected long term rate of return on the U.S. and non-U.S. plan assets is estimated based on the plans' investment strategy and asset allocation, historical capital market performance and, to a lesser extent, historical plan per formance. For the U.S. plans, the expected rate of return of 7.00% was derived based on the target asset allocation of 50%-70% equity securities (approximately 8.40% expected return), 20%-50% fixed income securities (approximately 4.80% expected return) and 2%-8% alternative investments (approximately 3.40% expected return). For the non-U.S. plans, the expected rate of return was derived based on the weighted average target asset allocation of 15%-25% equity securities (approximately 7.20% expected return), 30%-50% fixed income securities (approximately 5.90% expected return), and 30%-50% alternative investments (approximately 5.80% expected return). For the U.S. plan assets, the actual annualized total return for the most recent 10-year period ended December 31, 2023 was approximately 6.60%. For the non-U.S. plan assets, the actual annualized total return for the same period was approximately 4.90%. Changes to plan asset allocations and investment strategy over this time period limit the value of historical plan performance as a factor in estimating the expected long term rate of return. For 2024, the expected long-term rate of return on plan assets will be 7.00% for the U.S. plans and 5.83%. for non-U.S. plans. Pension Plan Assets The investments of the U.S. pension plan are managed to meet the future expected benefit liabilities of the plan over the long term by investing in diversified portfolios consistent with prudent diversification and historical and expected capital market returns. Investment strategies are reviewed by management and investment performance is tracked against appropriate benchmarks. There are no concentrations of risk as it relates to the assets within the plans. The non-U.S. pension plans are managed individually based on diversified investment portfolios, with different target asset allocations that vary for each plan. Weighted-average asset allocations at December 31, 2023 and 2022 for Linde’s U.S. and non-U.S. pension plans, as well as respective asset allocation ranges by major asset category, are generally as follows:
| U.S. |  | Non-U.S.
Asset Category | Target 2023 |  | Target 2022 |  | 2023 |  | 2022 |  | Target 2023 |  | Target 2022 |  | 2023 |  | 2022
Equity securities | 50% | - | 70% |  | 50% | - | 70% |  | 59% |  | 60% |  | 15% | - | 25% |  | 15% | - | 25% |  | 22% |  | 20%
Fixed income securities | 20% | - | 50% |  | 20% | - | 50% |  | 31% |  | 29% |  | 30% | - | 50% |  | 30% | - | 50% |  | 30% |  | 30%
Other | 2% | - | 8% |  | 2% | - | 8% |  | 10% |  | 11% |  | 30% | - | 50% |  | 30% | - | 50% |  | 48% |  | 50%
The following table summarizes pension assets measured at fair value by asset category at December 31, 2023 and 2022. Transfers of assets were not material for the year ended December 31, 2023 and 2022. See Note 13 for the definition of levels within the fair value hierarchy:
| Fair Value Measurements Using |  |  |  |
| Level 1 |  | Level 2 |  | Level 3 ** |  | Total
(Millions of dollars) | 2023 |  | 2022 |  | 2023 |  | 2022 |  | 2023 |  | 2022 |  | 2023 |  | 2022
Cash and cash equivalents | $ | 368 |  |  | $ | 313 |  |  | $ | — |  |  | $ | — |  |  | $ | — |  |  | $ | — |  |  | $ | 368 |  |  | $ | 313 |
Equity securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Global equities | 926 |  |  | 778 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 926 |  |  | 778 |
Mutual funds | 298 |  |  | 248 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 298 |  |  | 248 |
Fixed income securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Government bonds | — |  |  | — |  |  | 1,486 |  |  | 1,317 |  |  | — |  |  | — |  |  | 1,486 |  |  | 1,317 |
Emerging market debt | — |  |  | — |  |  | 283 |  |  | 245 |  |  | — |  |  | — |  |  | 283 |  |  | 245 |
Mutual funds | 119 |  |  | 101 |  |  | 60 |  |  | 55 |  |  | — |  |  | — |  |  | 179 |  |  | 156 |
Corporate bonds | — |  |  | — |  |  | 324 |  |  | 372 |  |  | — |  |  | — |  |  | 324 |  |  | 372 |
Bank loans | — |  |  | — |  |  | 27 |  |  | 18 |  |  | — |  |  | — |  |  | 27 |  |  | 18 |
Alternative investments: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Real estate funds | — |  |  | — |  |  | — |  |  | — |  |  | 324 |  |  | 353 |  |  | 324 |  |  | 353 |
Private debt | — |  |  | — |  |  | — |  |  | — |  |  | 1,345 |  |  | 1,360 |  |  | 1,345 |  |  | 1,360 |
Insurance contracts | — |  |  | — |  |  | — |  |  | — |  |  | 51 |  |  | 46 |  |  | 51 |  |  | 46 |
Liquid alternative | — |  |  | — |  |  | 1,022 |  |  | 982 |  |  | — |  |  | — |  |  | 1,022 |  |  | 982 |
Other investments | 1 |  |  | 1 |  |  | 22 |  |  | 39 |  |  | — |  |  | — |  |  | 23 |  |  | 40 |
Total plan assets at fair value, December 31, | $ | 1,712 |  |  | $ | 1,441 |  |  | $ | 3,224 |  |  | $ | 3,028 |  |  | $ | 1,720 |  |  | $ | 1,759 |  |  | $ | 6,656 |  |  | $ | 6,228 |
Pooled funds * |  |  |  |  |  |  |  |  |  |  |  |  | 1,572 |  |  | 1,457 |
Total fair value plan assets December 31, |  |  |  |  |  |  |  |  |  |  |  |  | $ | 8,228 |  |  | $ | 7,685 |
* Pooled funds are measured using the net asset value ("NAV") as a practical expedient for fair value as permissible under the accounting standard for fair value measurements and have not been categorized in the fair value hierarchy. ** The following table summarizes changes in fair value of the pension plan assets classified as level 3 for the periods ended December 31, 2023 and 2022:
(Millions of dollars) | Insurance Contracts |  | Real Estate Funds |  | Private Debt |  | Total
Balance, December 31, 2021 | $ | 12 |  |  | $ | 360 |  |  | $ | 1,368 |  |  | $ | 1,740 |
Gain/(Loss) for the period | — |  |  | 5 |  |  | 93 |  |  | 98 |
Purchases | 2 |  |  | 18 |  |  | 63 |  |  | 83 |
Sales | — |  |  | (22) |  |  | (34) |  |  | (56) |
Transfer into/ (out of) Level 3 | 33 |  |  | — |  |  | — |  |  | 33 |
Foreign currency translation | (1) |  |  | (8) |  |  | (130) |  |  | (139) |
Balance, December 31, 2022 | 46 |  |  | 353 |  |  | 1,360 |  |  | 1,759 |
Gain/(Loss) for the period | — |  |  | (27) |  |  | (38) |  |  | (65) |
Purchases | 1 |  |  | 3 |  |  | 1 |  |  | 5 |
Sales | — |  |  | (15) |  |  | (44) |  |  | (59) |
Transfer into / (out of) Level 3 | — |  |  | — |  |  | — |  |  | — |
Foreign currency translation | 4 |  |  | 10 |  |  | 66 |  |  | 80 |
Balance, December 31, 2023 | $ | 51 |  |  | $ | 324 |  |  | $ | 1,345 |  |  | $ | 1,720 |
The descriptions and fair value methodologies for the company's pension plan assets are as follows: Cash and Cash Equivalents – This category includes cash and short-term interest bearing investments with maturities of three months or less. Investments are valued at cost plus accrued interest. Cash and cash equivalents are classified within level 1 of the valuation hierarchy. Equity Securities – This category is comprised of shares of common stock in U.S. and non-U.S. companies from a diverse set of industries and size. Common stock is valued at the closing market price reported on a U.S. or non-U.S. exchange where the security is actively traded. Equity securities are classified within level 1 of the valuation hierarchy. Mutual Funds – These categories consist of publicly and privately managed funds that invest primarily in marketable equity and fixed income securities. The fair value of these investments is determined by reference to the net asset value of the underlying securities of the fund. Shares of publicly traded mutual funds are valued at the net asset value quoted on the exchange where the fund is traded and are primarily classified as level 1 within the valuation hierarchy. Emerging Market Debt - This category includes fixed income debt issued by countries with developing economies as well as by corporations within those nations. They typically have higher yields but lower credit ratings relative to developed country corporate and government bonds. The fair values for these investments are classified as level 2 within the valuation hierarchy. U.S. and Non-U.S. Government Bonds – This category includes U.S. treasuries, U.S. federal agency obligations and non-U.S. government debt. The majority of these investments do not have quoted market prices available for a specific government security and so the fair value is determined using quoted prices of similar securities in active markets and is classified as level 2 within the valuation hierarchy. Corporate Bonds – This category is comprised of corporate bonds of U.S. and non-U.S. companies from a diverse set of industries and size. The fair values for U.S. and non-U.S. corporate bonds are determined using quoted prices of similar securities in active markets and observable data or broker or dealer quotations. The fair values for these investments are classified as level 2 within the valuation hierarchy. Pooled Funds - Pooled fund NAVs are provided by the trustee and are determined by reference to the fair value of the underlying securities of the trust, less its liabilities, which are valued primarily through the use of directly or indirectly observable inputs. Depending on the pooled fund, underlying securities may include marketable equity securities or fixed income securities. Bank Loans - This category is comprised of traded syndicated loans of larger corporate borrowers. Such loans are issued by sub-investment grade rated companies both in the U.S. and internationally and are syndicated by investment banks to institutional investors. They are regularly traded in an active dealer market comprised of large investment banks, which supply bid and offer quotes and are therefore classified within level 2 of the valuation hierarchy. Liquid Alternative Investments - This category is comprised of investments in alternative mutual funds whose holdings include liquid securities, cash, and derivatives. Such funds focus on diversification and employ a variety of investing strategies including long/short equity, multi-strategy, and global macro. The fair value of these investments is determined by reference to the net asset value of the underlying holdings of the fund, which can be determined using observable data (e.g., indices, yield curves, quoted prices of similar securities), and is classified within level 2 of the valuation hierarchy. Insurance Contracts – This category is comprised of purchased annuity insurance contracts (annuity contract buy-ins) and is intended to mitigate the Company's exposure to certain risks, such as longevity risk. The fair value is calculated based on the cash surrender value of the purchased annuity insurance contract, which is determined based on such factors as the fair value of the underlying assets and discounted cash flows. These contracts are with highly rated insurance companies. Insurance contracts are classified within level 3 of the valuation hierarchy. Real Estate Funds – This category includes real estate properties, partnership equities and investments in operating companies. The fair value of the assets is determined using discounted cash flows by estimating an income stream for the property plus a reversion into a present value at a risk adjusted rate. Yield rates and growth assumptions utilized are derived from market transactions as well as other financial and industry data. The fair value for these investments are classified within level 3 of the valuation hierarchy. Private Debt - This category includes non-traded, privately-arranged loans between one or a small group of private debt investment managers and corporate borrowers, which are typically too small to access the syndicated market and have no credit rating. This category also includes similar loans to real estate companies or individual properties. Loans included in this category are valued at par value, are held to maturity or to call, and are classified within level 3 of the valuation hierarchy. Contributions At a minimum, Linde contributes to its pension plans to comply with local regulatory requirements (e.g., ERISA in the United States). Discretionary contributions in excess of the local minimum requirements are made based on many factors, including long-term projections of the plans' funded status, the economic environment, potential risk of overfunding, pension insurance costs and alternative uses of the cash. Changes to these factors can impact the timing of discretionary contributions from year to year. Pension contributions were $46 million in 2023, $51 million in 2022 and $42 million in 2021. Estimated required contributions for 2024 are currently expected to be in the range of $35 million to $45 million. Estimated Future Benefit Payments The following table presents estimated future benefit payments, net of participant contributions:
(Millions of dollars) | Pensions
Year Ended December 31, | U.S. |  | Non-U.S.
2024 | $ | 203 |  |  | $ | 355 |
2025 | 166 |  |  | 341 |
2026 | 163 |  |  | 353 |
2027 | 166 |  |  | 359 |
2028 | 165 |  |  | 373 |
2029-2033 | 824 |  |  | 1,974 |

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