With the Employee Retirement Income Security Act of 1974 came a form of pension insurance. On the termination of a pension plan whose assets are insufficient to pay all vested benefits, the Pension Benefit Guaranty Corporation covers some or all of the unfunded remainder. This gives pension funds an opportunity, and hence an incentive, to "put" unfunded promises to the PBGC. Because the PBGC can recover from the plans' sponsors, the opportunity to back out is not attractive to solvent corporations managing their own pension plans. In some industries, however, many employers participate in industry-wide plans. Withdrawal from underfunded multi-employer plans does not precipitate assessments by the PBGC, which need not assume the fund's liabilities so long as it continues to meet its obligations. But a series of withdrawals, much like a bank run, can leave the fund unable to pay off vested obligations.

Congress amended ERISA in 1980 to provide for piecemeal assessments of unfunded liability. Instead of waiting until the last period, when the PBGC may be unable to find or collect from the employers responsible, the fund itself assesses any withdrawing employer a portion of the shortfall. The Multiemployer Pension Plan Amendments Act (familiarly if tongue-trippingly called the MPPAA) requires a withdrawing firm to pay on the fund's demand, with arbitration in the event of disagreement. See Connolly v. PBGC, 475 U.S. 211, 106 S. Ct. 1018, 89 L. Ed. 2d 166 (1986); PBGC v. R.A. Gray & Co., 467 U.S. 717, 104 S. Ct. 2709, 81 L. Ed. 2d 601 (1984); Chicago Truck Drivers Pension Fund v. Central Transport, Inc., 935 F.2d 114 (7th Cir.1991). Anyone dissatisfied with the arbitrator's decision is entitled to judicial review--de novo on questions of law, deferential on conclusions of fact. Trustees of Iron Workers Local 473 Pension Trust v. Allied Products Corp., 872 F.2d 208, 211 (7th Cir.1989).

If the original version of ERISA prompted employers to desert multi-employer funds, the MPPAA may induce them to stay too long. For it permits the trust to determine the degree of funding shortfall "on the basis of any reasonable actuarial method of valuation". 29 U.S.C. § 1082(c)(2)(A). Valuation of benefits due in the future depends on assumptions about future rates of interest and growth in wages. When reducing future cash flows to present value, a change of even a few percent in the interest rate can double or halve the resulting valuation. See Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523, 533-47, 103 S. Ct. 2541, 2548-55, 76 L. Ed. 2d 768 (1983); Metlyn Realty Corp. v. Esmark, Inc., 763 F.2d 826, 834-38 (7th Cir.1985); O'Shea v. Riverway Towing Co., 677 F.2d 1194, 1199-1201 (7th Cir.1982); Lucian Arye Bebchuk & Marcel Kahan, Fairness Opinions: How Fair Are They and What Can Be Done About It?, 1989 Duke L.J. 27, 35. Because precognition is so rare (and not a good source of evidence in court), there will be legitimate debate about tomorrow's interest rates and a correspondingly wide range of "reasonableness." Funds seeking to improve their solvency will make generous assumptions about these rates--generous, that is, from the standpoint of a creditor seeking to collect as much as possible. Employers grouse about "staggering" and "unanticipated" assessments, but those who wrote and supported the MPPAA over the violent opposition of the employers in these industries understood trusts' incentives and the likely effects of combining discretion in the trustees with arbitration (and the correspondingly confined judicial role).

* Muskegon Paper Box Company closed its doors in August 1986, thus withdrawing from the Paper Industry Union-Management Pension Fund to which it had contributed. At the end of 1985 (the relevant date for these purposes) the Fund had assets with a market value of $355,272,400. The Fund sent Artistic Carton Company, Muskegon's parent corporation, a notice stating that the value of the Fund's vested obligations was $336,458,900, a substantial surplus. Nonetheless the Fund sought to recover more than $450,000 as Artistic Carton's share of the plan's "underfunding." Baffled, Artistic Carton asked for an explanation. Eventually it received two. (More, actually, but only two matter. We disregard the others, and disregard as well the fact that Artistic Carton as a corporate group did not withdraw fully from the Fund. None of these complications matters.)

First, the Fund asserted that its positive net worth is irrelevant because it determines funding employee-by-employee, and the contribution history of Muskegon's work force was insufficient to pay their vested benefits. Second, the Fund maintained that, despite what its notice said, it was indeed underfunded. In coming to a present value of $336 million for benefits that had vested, the Fund used an interest rate assumption derived from a blend of short- and long-term rates. It used this same rate in determining the present value of the vested benefits attributable to Muskegon's workers. For other purposes, however, the Fund uses an interest rate based on long-term rates. Applying this rate generated a present value of $388,675,500, and a funding shortfall of $33,403,100. The Fund sent Artistic Carton the form it had prepared for the Internal Revenue Service showing its financial condition on January 1, 1986. Schedule B of this Form 5500 recites a valuation of $389 million for vested benefits.

Artistic Carton demanded arbitration. Arbitrator Dreyer sided with the Fund, concluding that the $389 million reflected a "reasonable actuarial method of valuation" and that the Fund had computed Artistic Carton's liability properly under the Fund's organic documents. The Fund uses the statutory "attributable method", 29 U.S.C. § 1391(c)(4), matching contributions on account of each employee against the costs of that employee's vested benefits. In calculating both contributions and benefits, the Fund included each employee's entire working history, including time with other employers. Artistic Carton, which bought the assets of Muskegon Paper Box from Cosco Industries in 1980, contended that the Fund could not count any of the time its workers had been employed by Cosco. The arbitrator rejected this contention and ordered Artistic Carton to pay the full sum the Fund specified, approximately $485,000. The district court enforced this decision on Artistic Carton's petition for review under 29 U.S.C. § 1401(b)(2). 1990 U.S. Dist. LEXIS 16744, 1991 U.S. Dist. LEXIS 2195.

Section 4201 of the MPPAA makes a withdrawing employer responsible for "the allocable amount of unfunded vested benefits". 29 U.S.C. § 1381(b)(1). Artistic Carton insists that the Paper Industry Fund had no unfunded vested benefits--the Fund's own notice said so--and that it therefore owes nothing.

In 1983 the PBGC issued an opinion letter (No. 83-19) concluding that a pension fund need not have net unfunded benefits for a particular employer to have an "allocable amount of" unfunded benefits. Section 4211, 29 U.S.C. § 1391, gives funds several ways to define each employer's responsibility. One way to understand § 4211 is to say that "allocable ... unfunded vested benefits" means the amounts produced by application of the statutory formulae. One of these is direct allocation. If some employers have chipped in more than the amount necessary to pay for their employees' vested benefits, while others have paid less, the latter group may have "allocable" unfunded benefits even though the pension trust as a whole is solvent. Pension funds that allow firm-by-firm negotiation of benefits may find that this is a common situation. The Paper Industry Fund allows the employer and union to negotiate over both contribution and benefit levels. So although the Fund spans many employers and protects workers against transitory or insolvent businesses, there is not a common contribution rate or benefit level for the entire industry. Some employers may be contributing too little to pay for benefits they agreed to provide, while others are over-funding their promises.

Allowing withdrawals without collecting employer-specific shortfalls acts as a tax on the payments by other employers. It also creates a discontinuity. Suppose a method prescribed by § 4211 requires a given employer to pay $500,000. If the pension fund's net worth is a penny less than the present value of vested benefits, it may collect the whole half million; if its net worth is two cents greater, it collects nothing. Such considerations led one court of appeals to agree with the PBGC's opinion. Ben Hur Construction Co. v. Goodwin, 784 F.2d 876 (8th Cir.1986).

Although the PBGC persuaded the eighth circuit, the eighth circuit did not persuade the PBGC. After reading Ben Hur, the agency did an about-face and concluded that an amount is "allocable" only if the plan as a whole has "unfunded vested benefits." Notice of Interpretation, 51 Fed.Reg. 47342 (Dec. 31, 1986). If the plan is solvent, there is less risk of "runs" by employers seeking to avoid future obligations and no need to regulate private activity in order to reduce risk to the insurance pool. Plans get their choice of actuarial assumptions; if they cannot find even one set of assumptions that causes the value of benefits to exceed current assets, they must be secure indeed. Just as there are anomalies in saying that the fund may not assess employers with sums computed under § 4211, so there are anomalies in allowing collection while the fund as a whole is above water. When a plan is terminated, no employer pays anything extra so long as the fund has the assets to meet vested obligations. 29 U.S.C. § 1399(c)(8). As withdrawal is termination at retail rather than wholesale, it is hard to justify different treatment. Moreover, 29 U.S.C. § 1381(b)(1)(A) cuts down a withdrawing employer's liability via the "de minimis reduction applicable under" 29 U.S.C. § 1389, an amount determined by reference to the shortfall in the fund as a whole. Considerations of this kind persuaded the first circuit that the eighth circuit was wrong, and that the PBGC had grasped the brass ring on the second try. Berkshire Hathaway, Inc. v. Textile Workers Pension Fund, 874 F.2d 53 (1st Cir.1989).

What the first circuit found persuasive, the fourth circuit found illiteral. Wise v. Ruffin, 914 F.2d 570 (4th Cir.1990). Wise reminded the agency that § 4201 refers to § 4211: the "withdrawal liability of an employer ... is the amount determined under section 1391 of this title [§ 4211 of MPPAA] to be the allocable amount of unfunded vested benefits". 29 U.S.C. § 1381(b)(1). Funds' net valuation fluctuates with the interest rate. If employers that have contributed less than the value of vested benefits enjoyed by their workers can get out free of charge when the fund's ink is black, the deficit will be all the greater when a future change in interest rates turns the balance sheet red. After reading Wise, the PBGC concluded once again that it should switch sides. Notice of Interpretation, 56 Fed.Reg. 12288 (Mar. 22, 1991). At least for the moment, then, the PBGC believes that pension trusts may collect from withdrawing employers whose own accounts show a shortfall, even though assets of the fund exceed the value of all vested benefits. Artistic Carton wants us to embrace Berkshire Hathaway and scorn the agency's latest gyration.

Unless the Paper Industry Fund had assets sufficient to cover vested benefits when Artistic Carton withdrew, the difference between the PBGC's current views and its former ones is a sideshow. A pension trust may select a "reasonable actuarial method of valuation". 29 U.S.C. § 1082(c)(2)(A). The method the Fund used in reporting to the IRS implied a shortfall exceeding $33 million. Arbitrator Dreyer found that the Fund came by this number using a "reasonable actuarial method of valuation". Reasonableness is a zone, not a point. Just as jurors assess reasonableness in tort cases with minimal appellate review, so an arbitrator's assessment of reasonableness under the MPPAA is subject to minimal judicial review. Cf. Mars Steel Corp. v. Continental Bank N.A., 880 F.2d 928 (7th Cir.1989) (in banc). Artistic Carton does not seriously contend that in preparing Form 5500 the Fund used an "unreasonable" method. It is the same method the Fund uses when determining contributions and calculating benefits, indeed the same method the PBGC uses when determining the amount it must contribute to underfunded plans. Unless the arbitrator committed a legal error, we must respect his decision that the Paper Industry plan was underfunded.

Does ERISA require a pension trust to use the same actuarial method in determining aggregate funding as it uses in assessing withdrawal liability? Artistic Carton does not identify any such requirement in the statute. And a plan may have good reasons to use multiple methods. Consider how a defined-benefit plan (which the Paper Industry Fund is) would go about assessing the present value of its vested obligations. Workers' benefits may be stated as a percentage of their highest average incomes (a three-year average is the norm), multiplied by the number of years of covered employment. Although the right to some pension vests after five years, the amount of the pension will depend on future events, including inflation, which determine the level of wages preceding retirement. Interest rates on long-term investments (such as 30-year high-grade bonds) reflect the best current estimates of future inflation and real productivity. A pension fund uses these long-term rates to determine the present value of its obligations, on the assumption that it is a going concern.

When a firm withdraws, however, the fund has been terminated in part--and the employment histories of its workers (at least the portion reflected in service credited to the fund) may come to a close. In determining the value of vested benefits, the trust has less (and perhaps no) need to take account of uncertain future growth in average wages. It can determine the payments to these workers with greater certainty than it can determine the value of all vested benefits. So the fund makes two computations, only one of which projects an increase in vested obligations with the rate of interest. That is exactly what the Paper Industry Fund did here. Nothing in the statute forbids this approach--which works in withdrawing employers' favor by reducing the value of the vested benefits attributed to their former workers, and so reducing the amount of withdrawal liability. If we were to compel pension trusts to use only one valuation rule for all purposes, they would be inclined to choose the rule that magnified the estimated cost of vested benefits. Employers (that is, investors) would suffer. The resulting discouragement of mobility and corresponding

disincentive to join a multi-employer pension fund might injure everyone in the long run.

When determining withdrawal liability, the Paper Industry Fund constructs an account for each worker. (These are not real accounts, for the Fund operates a defined-benefit rather than a defined-contribution plan.) It compares vested benefits attributable to that person's years of service with the withdrawing employer against the employer's contributions on account of that worker. Some of these virtual accounts may have deficits and others surpluses; the Fund offsets these and presents the employer with a bill for any net shortfall. Congress explicitly authorized this method in § 4211(c)(4)(B), 29 U.S.C. § 1391(c)(4)(B), but the statutory language also sets up the parties' dispute. For the statute speaks of "benefits under the plan which are attributable to participants' service with such employer (determined under plan rules not inconsistent with regulations of the [PBGC]".

To what does this parenthetical apply? Does it allow plans to attribute service with one employer to another? Article 13, § 6(h) of the Fund's Agreement and Declaration of Trust provides:

(1) Service with an Employer shall include all service ... credited to the Employees ... for whom it was the last contributing Employer prior to the relevant date [of withdrawal].

(2) Service with a predecessor shall be taken into account as service with a withdrawing Employer, and contributions by and withdrawal liability assessed against such predecessor shall be treated as contributions of the withdrawing Employer for purposes of this Article ....... The predecessors taken into account for this purpose may include any Employer that was treated as not withdrawing by reason of a transaction described in Section 4204 or 4218 of ERISA.

When Artistic Carton withdrew, the Fund treated Muskegon Paper Box as a single employer, not distinguishing the years Artistic Carton owned the assets from the years Cosco did so. It gave Artistic Carton credit for all of Cosco's contributions. But because there was a net deficit during the Cosco years, the result of treating Muskegon Paper Box as a single employer was withdrawal liability exceeding the amount that Artistic Carton would have owed had the Fund limited its calculations to the years 1980 to 1986.

Cosco sold the plant to Artistic Carton after the effective date of the MPPAA, and it did not obtain a statutory exception. Cf. Central States Pension Fund v. Lady Baltimore Foods, Inc., 960 F.2d 1339 (7th Cir.1992). The deficit in its employees' virtual accounts could have been assessed against Cosco in 1980. That did not happen. The Fund asserts that it did not learn until recently that Artistic Carton bought the assets of the business in 1980. Artistic Carton insists that the Fund's reason for failing to pursue Cosco is irrelevant. It bought the assets, not the stock of the corporation. New owners of assets are not liable for the old owner's debts; to make this doubly clear, Cosco and Artistic Carton agreed that the latter would bear no responsibility for the former's withdrawal liability. Artistic Carton views the shortfall in the accounts at the instant it took over as Cosco's debt. A creditor that neglects its remedies against a debtor has only itself to blame. Congress removed all doubt, Artistic Carton submits, in § 4204, 29 U.S.C. § 1384.

Section 4204 gives withdrawing employers a way to avoid making up their shares of a pension plan's shortfall. Roughly, the statute prevents an underfunded plan from assessing an employer that procures a substitute--a successor that not only promises to contribute for five years but also promises to pay the predecessor's withdrawal liability if it withdraws earlier (and backs up that promise with a bond). Far from promising to pay Cosco's withdrawal liability if it vamoosed during the five years, Artistic Carton disclaimed any responsibility. Because it was not liable under § 4204, Artistic Carton concludes, it is not liable, period. Any other conclusion would unsettle many transactions, its brief tells us: "For years, attorneys and other advisers have been counseling companies involved in acquiring businesses that purchasers will not be subject to withdrawal liability if they structure their deals as sales of assets and do not intentionally assume that liability pursuant to section 4204." See Ronald A. Kladder, Asset Sales After MPPAA--An Analysis of ERISA Section 4204, 39 Bus.Law. 101, 116 (1983).

Conspicuously absent from Artistic Carton's argument is the language of § 4204 itself. The text begins: "A complete or partial withdrawal of an employer ... does not occur solely because ...". The rest of the section continues in that vein. It identifies conditions under which "withdrawal" does not occur, and under which the trust therefore may not assess withdrawal liability against the old owner. It creates an immunity for sellers that meet its conditions. It does not create any immunity for buyers under any circumstances. Artistic Carton believes that the MPPAA carries a negative implication: by setting out in § 4204 one way in which buyers could be responsible, Congress implied that responsibility was otherwise impossible. Nothing in § 4204 or any other part of the MPPAA says so, and collection from buyers under provisions such as § 6(h) does not undermine any statutory objective. To the contrary, the prospect of liability ensures that new owners will notify pension trusts of the change, the better to ensure that they pursue the departing owners for withdrawal liability. Artistic Carton could have protected itself by telling the Fund about the shift and obtaining Cosco's promise to pay up, fortified by a standby letter of credit. Artistic Carton could have negotiated for indemnity should the Fund try to collect from it. By making the switch in silence (or with at best verbal notification), and permitting Cosco to slink into the night, Artistic Carton increased the Fund's risks and should not be surprised that the trust sought to lump the owners together.

Instead of forbidding clauses such as § 6(h), ERISA gives pension funds the power to attribute service to particular employers. Arbitrator Dreyer tells us that such approaches are "common to attributable rule plans". Perhaps Artistic Carton is right to say that one parenthetical phrase in § 4211(c)(4)(B) is a slight foundation for so muscular a provision, but the Fund does not depend on ERISA for its authority. The MPPAA establishes mandatory liability, overriding contracts that allowed firms to withdraw with an effective transfer of unfunded liability to the federal Treasury. It does not forbid employers from agreeing to pay extra money to a pension trust--as Artistic Carton did. The Agreement and Declaration of Trust is a contract, and Artistic Carton agreed to be bound by its provisions. When it took over Muskegon's plant in 1980, Artistic Carton signed an agreement to participate in the Fund. Another signed in 1983 states that the employer "agrees to become a party to the Agreement and Declaration of Trust establishing the said Fund ... [and] to be bound by all the terms and provisions of said Agreement (including all amendments thereto, whether adopted before or after the date of this Agreement)." Article 13, containing § 6(h), was added to the Agreement and Declaration of Trust in 1984. Arbitrator Dreyer concluded that these agreements permitted the Fund to apply § 6(h) to Artistic Carton.

Artistic Carton tells us that the participation agreements expired with the collective bargaining agreements whose provisions they enforced. The 1983 participation agreement went with a 1983-85 collective bargaining agreement; when it signed a new collective bargaining agreement in 1985, Artistic Carton did not sign a corresponding participation agreement. Thus, it concludes, when it closed the plant in 1986 it was not bound by § 6(h). Yet the participation agreements lack terminal dates. True, each says that "[t]he termination date of the Employer's obligation to contribute to the Fund shall be the same as the termination date of the said Collective Bargaining Agreement unless otherwise specified." Spelling out the final date for contributions does not mean that the participation agreements themselves lapse. Many things happen after contributions cease. The employees may become entitled to pensions, or the employer may be exposed to withdrawal liability. Disregard for the moment the gap between the expiration of the collective bargaining agreement in 1985 and the abandonment of the plant in 1986, and suppose Artistic Carton had closed the plant the day after the expiration of the agreement. Would the withdrawing employer be entirely unfettered by the participation agreement--even to the extent it was called on to make withdrawal payments for the years it owned the plant--just because it had stopped paying its workers? It is to avoid such absurdities that the participation agreement speaks of the "termination date of the Employer's obligation to contribute to the Fund" and not the termination date of the participation agreement itself. Another part of the trust agreement, Art. 12 § 1, makes this explicit in providing that any employer accepts responsibility for sums due on withdrawal. Because the agreement "to be bound by all the terms and provisions of said [trust] Agreement" has no terminal date, the right question is what the trust agreement provides should occur on withdrawal.

If this is so, Artistic Carton believes, then the Fund is not using the method of attribution established by § 4211(c)(4) but has made up a different one. It may, but only with the PBGC's approval: "The corporation shall prescribe by regulation a procedure by which a plan may ... adopt any other alternative method for determining an employer's allocable share of unfunded vested benefits under this section, subject to the approval of the corporation based on its determination that adoption of the method by the plan would not significantly increase the risk of loss to plan participants and beneficiaries or to the corporation." Section 4211(c)(5)(A), 29 U.S.C. § 1391(c)(5)(A). The Fund did not obtain the PBGC's approval for § 6(h). It is a nice question whether § 6(h) is an "alternative method" for which the PBGC's approval is required, or just a rule elaborating the method prescribed by § 4211(c)(4)(B), which under the parenthetical expression takes effect unless the PBGC objects. The PBGC apparently puts such rules in the "elaboration" zone. See Opinion Letter 89-8 (concluding that employers may waive limitations on their withdrawal liability under the direct allocation method without approval as an alternative method under § 4211(c)(5)(A)). We need not decide where within the penumbra between elaboration and novation--for there is no line, only shadings--a rule such as § 6(h) belongs, because Artistic Carton did not make this argument to the arbitrator or the district court.

So, too, Artistic Carton neglected to ask the arbitrator to exclude from the computation 12 persons who retired from Muskegon Paper Box before the transfer of ownership in 1980. Although Artistic Carton argues forcefully that it was not the "last contributing Employer" for these 12 within the meaning of § 6(h), this is not the sort of argument that may be stored up for judicial review. Sifting participant-by-participant who worked for whom, and when, is exactly what Congress thought arbitrators are supposed to do.

We appreciate that permitting pension funds to impose withdrawal liability attributable to deficits during a predecessor's operations could have untoward effects when the predecessor is bankrupt. So long as both buyer and seller are solvent, allocation of liability is a matter of fixing the price of the sale, provided the legal rules are understood. But if the seller is bankrupt and can write off the debt for withdrawal liability, it may be hard to transfer the assets. Suppose a firm has operated a paper mill for 30 years, has a deficit of $5 million in its workers' pension accounts, and liquidates under Chapter 7 of the Bankruptcy Code without provision for withdrawal liability. If the plant is worth $6 million as a going concern, a solvent buyer would pay no more than $1 million--the difference being set up as a reserve for withdrawal liability. If the plant is worth $4 million, no one would buy it, for it would come attached to a $5 million liability. Discouraging the transfer of assets that have continuing productive value, and turning the employees out of work, would frustrate the Bankruptcy Code and ERISA simultaneously.

A successor could avoid withdrawal liability by removing its work force from the pension plan as soon as ownership changes hands--tossing the liability to the PBGC and ceasing the accumulation of pension credits for workers. We do not suppose, however, that this was the course Congress preferred when it enacted the MPPAA. Perhaps a potential successor could insist that the bankruptcy court obtain a release from the pension trust (or a contribution from the PBGC) as part of the transaction by which the debtor sells the assets. Or perhaps a would-be successor could negotiate a deal with the multi-employer fund, under which unsatisfied obligations of bankrupt predecessors are treated, for purposes of clauses such as § 6(h)(2), the same as paid-up withdrawal liability. To most contractual conundrums there are contractual solutions. They may not be cheap, and avoiding the costs of complex contracting is one important objective of the legal system, but we cannot forget that despite ERISA and the MPPAA pensions remain fundamentally contractual arrangements. No governmental official crammed § 6(h) down the throats of unwilling businesses. What unions and employers agreed to, they may revise. Until they do, courts will enforce the prevailing rules.

AFFIRMED.