UNITED AIR LINES, INC., Plaintiff-Appellee, Cross-Appellant,
v.
REGIONAL AIRPORTS IMPROVEMENT CORPORATION and UMB Bank, N.A., Defendants-Appellants, Cross-Appellees.

*875 Mark F. Hebbeln, Foley & Lardner, LLP, Chicago, IL, Amy D. Caton, Kramer, Jeffrey S. Trachtman (argued), Levin, Naftalis & Frankel, LLP, New York, NY, for Defendants-Appellants, Cross-Appellees.

Alexander L. Karan (argued), Kirkland & Ellis LLP, Chicago, IL, for Plaintiff-Appellee, Cross-Appellant.

David A. Golin (argued), Arnstein & Lehr LLP, Chicago, IL, for Appellant.

Harold L. Kaplan, Foley & Lardner, LLP, Chicago, IL, for Trustee.

Micah E. Marcus Kirkland & Ellis LLP, Chicago, IL, for Debtor.

Before EASTERBROOK, Chief Judge, and BAUER and MANION, Circuit Judges.

EASTERBROOK, Chief Judge.

When United Air Lines left bankruptcy, its plan of reorganization marked some issues for later resolution. One was how much United owes to lenders that put up the money for improvements at several air terminals. We concluded that the transaction supplying the funds used to improve United's space at Los Angeles International Airport should be treated as a secured loan rather than as a lease. United Air Lines, Inc. v. U.S. Bank N.A., 447 F.3d 504 (7th Cir.2006), applying the approach of United Airlines, Inc. v. HSBC Bank USA, N.A., 416 F.3d 609 (7th Cir.2005). As a result, United must pay the lenders the full value of the assets that serve as security; any excess is unsecured debt. 11 U.S.C. §§ 506(a), 1129(b)(2)(A). United's plan of reorganization provides that the valuation decision may be made after confirmation, and that United then will pay accordingly.

Valuation would be straightforward if there were a market for improved space at airports. An asset's value depends on the price that could be agreed by willing buyers and sellers negotiating for a replacement. See Associates Commercial Corp. v. Rash, 520 U.S. 953, 117 S. Ct. 1879, 138 L. Ed. 2d 148 (1997). But there is no liquid market for this asset. Every airport has different forces of supply and demand, and United leases rather than owns space at airports. Although some carriers may sublease space to others, the record does not contain evidence of the prices at which these transactions occur. So the bankruptcy court decided to value the collateral by a discounted-cash-flow analysis. It determined that 345,167 square feet of improved space are subject to the security agreement and set an annual value of $17 per square foot for that space as of 2004. The court projected increases in these rents at a rate reflecting experience in the business, added up the imputed rentals through 2021 (when the loan comes due), and discounted the result at 10% per annum. That produced a present value of roughly $35 million for the lenders' security. United owes the lenders roughly $60 million, so $25 million was treated as unsecured debt and written down according to the plan of reorganization. The district judge affirmed. 2008 WL 2566927, 2008 U.S. Dist. LEXIS 48738 (N.D. Ill. June 25, 2008).

Both the lender (the Regional Airports Improvement Corp. or RAIC) and *876 the Trustee (UMB Bank) for the investors who put up RAIC's money, challenge every step of the bankruptcy court's procedure. (We refer to RAIC and the Trustee collectively as "the Lenders.") The Lenders also contend that they did not receive appropriate "adequate protection" payments under 11 U.S.C. § 363 to compensate for the diminution in the collateral's value while the litigation continued. That argument is a nonstarter, because it conflicts with the confirmed plan of reorganization. Whatever rights the Lenders may have had under § 363 had to be liquidated as part of the plan. All that matters now is whether the bankruptcy court has implemented the plan correctly. We can be similarly brief in dealing with the Lenders' contention that the collateral includes all of Terminals 7 and 8, which United uses. The bankruptcy court's negative finding is not clearly erroneous.

Two questions remain: what is the annual rental rate, and what is the appropriate discount rate? The bankruptcy court used as the rental rate the price that Los Angeles Airport charges United (and other airlines) for space in the terminals. It derived a discount rate by adding the Lenders' proposed rate to United's proposed rate, and dividing by two. Neither of these decisions is sound. We start with the implicit annual rental per square foot.

United contends, and the bankruptcy judge found, that $17 per square foot per year is the market rate for terminal space in Los Angeles because that is what a willing seller (the airport) charges to willing buyers (the airlines). The Lenders respond that this is not a "market" rate but reflects a discount that the airport extended in the years before the 1984 Olympics to persuade air carriers to make investments, and that the airport promised to continue over the long term by tying rentals to its costs rather than permitting them to rise with demand for air travel and terminal space. As the Lenders see things, Los Angeles International Airport could charge much more than $17 per square foot because the demand for air travel (and thus for gates) has gone up, while the airport has been unable to expand. This is a seller's market—or could be, if the airport were allowed by its contracts to take advantage of the air carriers' demand—and the Lenders say that they, as secured creditors, are entitled to a higher price even if the airport authority has disabled itself from increasing rents to market levels.

A bankruptcy judge might have accepted the Lenders' argument on this score, but this judge did not commit clear error (or abuse his discretion) in preferring the evidence of actual transaction prices over an argument based on beliefs about what prices could have been. Real transactions are a vital anchor in litigation. There is no "just price" for any asset, and a court is entitled to reject an effort to show that willing buyers and sellers are "wrong" in valuing a particular asset.

Still, it is essential to understand what the price of $17 per square foot represents. It is a price for unimproved terminal space. Air carriers build out terminals and gates to their own specifications. The airport promised in the leases not to increase rent to reflect the value of the improvements made by the air carriers. (No tenant is willing to pay twice for the same improvements—once to have them built, and a second time to the landlord through rent reflecting the value of the improved space.) So the annual rent reflects the value of basic space in the Los Angeles terminals. Yet the Lenders' security is in the improved space. A price for unimproved space does not measure the value of the collateral. If the Lender foreclosed and took over the space, it could *877 rent the gates to United or some other airline at more than $17 a square foot—at perhaps four times that much, to go by prices at the airport's one terminal that leases fully built-out gates. (More on this below.)

If United had leased bare ground and built a terminal there from scratch, no one would say that the terminal's value is measured by the rental price for the underlying land. That, however, is fundamentally what the bankruptcy court did here. The Lenders have been told that their collateral is worth no more than if United had not made the improvements. If the terminal were unimproved, it would have a capital value of $35 million (on the bankruptcy court's methodology); after United borrowed $75 million to make improvements, the improved space was still valued at $35 million. (The original loan was $75 million; United repaid about $15 million before the bankruptcy began.) But, if United was rational, it would not have put in $75 million of improvements unless it increased the space's value by at least that much—making it worth $110 million or more. Any valuation method that treats improvements as worthless can't be appropriate.

United has two responses. One is that the improvements were made more than a decade ago, and that like other capital investments they wear down. That's true enough; the improved terminal may be worth less than $110 million today. But the improvements surely have not depreciated to a value of zero. United's second response is that it pays $17 a square foot not only for the space subject to the Lenders' security interest, but also for other space that United occupies at the airport. This must mean that the $17 is the value of improved space. That understanding assumes, however, that the other space was built out at the airport's expense rather than United's. As we read the record, however, United improved all of the space it occupies—not all with the money furnished by these Lenders, to be sure, but the improvements were at United's expense. Other air carriers, too, have paid for improvements. If this is so, then the $17 rent per square foot in 2004 is for unimproved space, as the leases promised carriers. (United has not argued that the airport is violating its contractual commitment to set rents based on the value of bare rather than improved terminals.)

One telling bit of evidence that the $17 rental reflects basic rather than improved space is the price charged by a consortium of airlines that operates the airport's Terminal 2, which the parties call LAX2. The consortium's members use some of the terminal's 11 gates and rent others at a price that in 2004 was $63 per square foot per year. The bankruptcy judge and district judge thought that the Trustee, were it to take over United's gates and rent them out, could not get as much. They gave this explanation:

[The Trustee's] expert concluded that the market rental established by LAX2 was $63 per square foot. The Bankruptcy Court did not accept the expert's conclusion, and found that "it was inappropriate to use the net revenues as a measure of market rent" and that there was no evidence submitted of what internal rate of return a hypothetical LAX2 operator would require. The Court also found that there were significant gaps identifying projected revenues and expenses which would make a square footage rental determination highly speculative. While the Court agrees with the Bankruptcy Court on these criticisms, the Court finds that the most persuasive reason for discounting the LAX2 model as a comparable is scaling: the [collateral] facilities include *878 at most 7 gates out of the 20 gates in United's terminal facilities (United claims it is only 4 gates). The ratio of costs to revenue in operating a few gates in a terminal would not be the same as the ratio in operating an entire terminal as is the case with LAX2. Would a bidder on the ... facilities upon which are located either 4 gates out of 20 (United) or 7 out of 20 ([the Lenders]) pay the same amount as a bidder who would acquire 20 gates if the entire United leasehold was for sale? The answer is obviously no.

2008 WL 2566927 at *3, 2008 U.S. Dist. LEXIS 48738 at *9-*10. Neither the bankruptcy judge nor the district judge explained why "the ratio of costs to revenue" or an owner's target internal rate of return affects an asset's market price. An operator (airline or Trustee) would not charge less than avoidable cost; it could do better by giving the space back to the airport authority. But how much more it can get depends not on some ratio but on the demand for the space and on the price that its competitors charge. If, as the Lenders contend, all gates at Los Angeles are in use and building more is a protracted endeavor, then the price depends entirely on what airlines will pay: current owners will receive an economic rent. (An economic rent is the portion of the price, in excess of the seller's cost, that a good fetches because its supply is inelastic, a good description of gates at Los Angeles International Airport.) A potential to command an economic rent is part of the value of the Lenders' collateral.

Now it may be that it would be more costly for the Trustee (after foreclosure) to manage four, or seven, gates in United's terminals than it is for the consortium to manage all 11 gates at LAX2. If so, even though the price that air carriers would pay is apt to be in the same range, the net realized by the owner might be smaller. This possibility, however, does not justify disregarding the fact that air carriers willingly pay $63 per square foot for space at Los Angeles International Airport, the only estimate in the record of improved space's going price. That the Trustee's net may be somewhat less than the LAX2 consortium's hardly justifies using the price for unimproved space instead. Nor can the $63 figure be thrown out the window because the LAX2 consortium provides some services to its customers that the Trustee, as operator of United's space, might not provide. The bankruptcy court did not attempt to determine how much of the $63 is attributable to these services, and it is most unlikely that they account for half of the price.

It does not matter whether the Trustee could lease United's gates for $63 a foot or only $40. Any potential rental price higher than $30 would make the collateral worth at least $60 million, and thus make the loan fully secured, even with the 10% discount rate that the bankruptcy court selected. The data from LAX2 show that United's space could be leased to other air carriers for at least $30 a foot. The Lenders therefore are entitled to collect 100¢ on the dollar, plus interest.

What is more, we conclude that the 10% discount rate is too high. The Lenders' expert chose 8% because it is the rate of return that Los Angeles International Airport itself pays on general revenue bonds, which are unsecured. United's expert chose 12% as the rate of return that debt investors in the air transportation business would demand, given the risks of that business, which is volatile. The bankruptcy judge added the two estimates and divided by two. An arbitrator might choose such a method, and perhaps a jury would do so behind closed doors, but a judge should choose the right discount rate *879 rather than split the difference between the parties. What if United's estimate had been 20%, or the Lenders' estimate 3%?

The risks of the air terminal business depend in part on the fate of air carriers. When Eastern Airlines failed, two entire terminals at Hartsfield Airport in Atlanta were shuttered, and the airport did not return to full operations for almost a generation. But for a long time Los Angeles International Airport has had less capacity than the airlines prefer. Gates are fully used; takeoff and landing slots are limited. As far as this record shows, no gates at the airport are idle today—despite the fluctuating fortunes of air carriers—and none has been idle for a long time. Airlines have been clamoring for gates. The airport is building a new 10-gate terminal, the first addition since the early 1980s, that is projected to be ready in 2012. That implies that being the proprietor of terminal space in this airport is not particularly risky, and that secured debt investors in United's space would not demand more than 8%. Real prices are much more informative than lawyers' talk. It would be good to know what investors were willing to accept in 2004 (or today) on secured loans to Los Angeles International Airport, or its air carriers borrowing to improve their space, but it is unnecessary to track down that detail. The fact that the airport is operating at capacity, and can raise money at 8% without giving security, is all we need to know to conclude that the discount rate cannot exceed 8%.

In a discounted-cash-flow analysis, the discount rate has a powerful effect on the present value. See International Federation of Accountants, Project Appraisal Using Discounted Cash Flow (2007); Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (1996). A lump sum of $146 million, payable in 2021, is worth $35 million in 2006 when discounted to present value at 10% per annum. (The bankruptcy court's actual calculation is more complex, because the collateral would have been rented over time rather than sold for a lump sum, but we simplify.) The same $146 million in 2021 would have a present value of $46 million in 2006 at an 8% discount rate, and $27 million at 12%. Thus simply changing the discount rate from 10% to 8% would mean that an extra $11 million of the loan is secured, even holding the rental rate at $17 per square foot. With the discount rate at 8%, a rental of roughly $23 per square foot is enough to make the Lenders fully secured. Because improved space in Terminal 2 fetches almost three times the price needed to make these loans against space at Terminals 7 and 8 fully secured, the Lenders are entitled to a full recovery.

The judgment is reversed, and the case is remanded for further proceedings consistent with this opinion.