
    EASTERN MINERALS INTERNATIONAL, INC., et al., Plaintiffs, v. UNITED STATES of America, Defendant.
    No. 94-1098 L.
    United States Court of Federal Claims.
    Nov. 25, 1997.
    
      Raymond D. Battocchi and John R. Powell, McLean, VA, for plaintiffs.
    Marc A Smith, United States Department of Justice, Washington, DC, for defendant.
   OPINION & ORDER

HODGES, Judge.

This case involves a taking by the United States of plaintiffs’ right to mine coal in Tennessee. After plaintiffs made substantial investments in a mineral lease and in preparing the land, the Government destroyed the fruits of those investments by purposely delaying action on plaintiffs’ application until after their lease expired. The United States took plaintiffs’ right to mine coal and their right to renew the mining lease.

We dismissed the claims of plaintiffs Milton Bernos Sr., Van Burén Minerals, Mary Ann Wyatt, Nancy Wyatt Zorn, and Wilson W. Wyatt, Jr. See Eastern Minerals International, Inc. v. United States, 36 Fed.CI. 541 (1996). Van Buren’s claim is not ripe for adjudication, so the value of the coal seams on the Colten property is not included in our damages valuation. Id. at 548. We enter judgment for plaintiffs Wilson W. Wyatt, Sr., Anne D. Wyatt, and Eastern Minerals International, Inc.

Facts

Cane Tennessee, Inc. bought the property at issue from Wilson W. Wyatt, Sr., and Anne D. Wyatt in 1979. The Wyatts retained a 3.5% mineral royalty interest. Cane leased the property in 1979 to Eastern Minerals International, Inc., a company formed by Milton Bernos, Jr. Eastern had the exclusive right to mine coal on the property. The lease was to expire in February 1991, but Eastern had the right to extend the lease for four additional ten-year terms. The right to extend the lease expired in August 1990.

The Tennessee Department of Conservation, Division of Surface Mining, granted Eastern two one-year permits in 1980 and 1981 to disturb 33 acres of the Cane property to mine the Sewanee seam. Eastern excavated a box cut on the property and constructed a sediment pond, a backfill area, and roads to and from the box cut.

Eastern applied for a third permit in 1982, and Tennessee denied the permit in May 1984. Pursuant to a consent order before the Tennessee Board of Reclamation Review, Eastern withdrew its application. The United States Office of Surface Mining (OSM) assumed federal enforcement of Tennessee’s program in late 1984. Eastern then submitted its permit application to OSM rather than to the state agency.

OSM’s standard practice was to respond promptly when it received a permit application. The first step in the application review process was to determine whether the applications were administratively complete. Most applications contained errors, so OSM dealt with deficiencies on a regular basis. Despite this practice, OSM required six months to determine that Eastern’s application was administratively complete.

OSM sent two technical deficiency letters to Eastern in 1985. In response, Eastern applied to OSM for monetary assistance in obtaining the required information. The application for assistance was placed on hold because OSM was planning to deny the permit.

OSM denied Eastern’s permit in July 1986, ostensibly because the noise of the mine could have an adverse impact on a nearby state park. This was Tennessee’s concern, not OSM’s. Eastern appealed the permit denial. The administrative law judge who heard the appeal in June 1987 was not impressed by OSM’s noise allegations. OSM raised hydrological concerns in the permit denial letter, but lacked data to support them. Because the judge did not want to resolve the case “piecemeal,” he asked OSM to make findings concerning the alleged hydrological impacts. He directed OSM to inform plaintiffs promptly what hydrological information it needed. OSM consumed four years pursuing that information.

Eastern’s right to extend its lease expired on August 31, 1990. It did not extend the lease because it believed that OSM would never grant the permit. In fact, OSM never would have granted the permit. The Government would not have approved the coal mine because Tennessee did not want it near a state park.

Unreasonable Delay in Denial

The Tennessee Wildlife Resources Agency expressed opposition to the Eastern Minerals permit in 1984. The State felt that the mine would have adverse impacts on Fall Creek Falls State Park and on the recreation, hunting, and fishing experiences of visitors to the park. Because the State had joint reviewing authority for the permit under the applicable regulations, Eastern’s permit would not be granted if the State objected.

Eastern sought aid from OSM in obtaining the information that the agency was requiring. The Small Operator Assistance Program (SOAP) was available to provide such assistance. Before the SOAP program could begin studies to provide the necessary hydrological information, the SOAP application was placed on hold and then denied when OSM denied Eastern’s permit in 1986. The permit was denied before SOAP studies could be commissioned to provide information. OSM’s standard practice was to make a technical decision only after it had received all the information it needed.

An internal OSM memorandum dated July 1985 states that because OSM did not have a strong defense to points raised by Eastern in its response to a technical deficiency letter, OSM “would have to hang [its] hat[ ] elsewhere.” OSM denied Eastern’s application in 1986, for adverse noise impact on Fall Creek Falls State Park. An administrative law judge ruled that the 1986 denial of the permit was premature because OSM did not have all the information necessary regarding the hydrological impact question. OSM requested additional information from Eastern to supplement the hydrological impact information.

After appeal of the permit denial, the SOAP process began again. In May 1988, an OSM attorney placed the SOAP application on hold because of an outstanding reclamation order on the Eastern box cut. This reclamation order and an accompanying cessation order had been issued in 1986 when the permit was denied by OSM. Despite the appeal before the Office of Hearings and Appeals, OSM used the reclamation order as a reason for delaying the SOAP application. In September 1988, the SOAP study was placed on hold, this time to determine if the study would be worth the expense. The SOAP study was placed on hold yet again in May 1989 due to another outstanding reclamation order. The issues were resolved and the SOAP process resumed.

SOAP personnel and OSM permitting personnel collaborated to determine what studies were necessary to satisfy the hydrological impact question. Despite close coordination between the two, the Permitting Division said that it was not satisfied with SOAP’s report. In late summer 1990, OSM rejected the SOAP report and laid out a new multiphase approach to the collection of SOAP data.

OSM concluded that further studies should be undertaken because the first SOAP study had not been conclusive as to hydrological impact. An internal memorandum outlined plans for further testing: “If, after collection of Phase II and Phase III data, no impact to the hydrologic balance can be documented, additional [testing] wells should be installed ____” OSM’s policy was to stop Eastern’s development without taking a final action that plaintiff could appeal. OSM abandoned the original approach in favor of an eight-step approach outlined in the internal memorandum cited above. Before any steps could be taken to implement the new approach, still another approach was developed requiring a lineament study. OSM requested further studies and created further delays. These requests continued until the permit was finally denied in 1994. By then, Eastern had lost its lease.

War of Attrition

The Government waged a war of attrition against Eastern. Eastern could not afford to retain an expensive leasehold when it knew that state and federal authorities would never renew its permit. The Fifth Amendment does not permit the Government to avoid liability for a taking merely because it has the resources to outlast a property owner. Equity is the compelling force driving just compensation under the Fifth Amendment. As defendant noted in its brief the search for fairness and justice guides regulatory takings.

The Constitution is “intended to preserve practical and substantial rights, not to maintain theories.” U.S. v. Dickinson, 331 U.S. 745, 748, 67 S.Ct. 1382, 1384, 91 L.Ed. 1789 (1947) (citing Davis v. Mills, 194 U.S. 451, 457, 24 S.Ct. 692, 695, 48 L.Ed. 1067 (1904)). The Fifth Amendment “expresses a principle of fairness and not a technical rule of procedure.... ” Pleasant Country Ltd. v. United States, 37 Fed.Cl. 321, 328 (1997) (citing United States v. Dickinson, 331 U.S. 745, 748, 67 S.Ct. 1382, 1384-85, 91 L.Ed. 1789 (1947)). “The constitutional requirement of just compensation derives as much content from the basic equitable principles of fairness * * * as * * * [it] does from technical concepts of property law.” Georgia-Pacific Corporation v. United States, 226 Ct.Cl. 95, 640 F.2d 328, 336 (1980) (citing United States v. Fuller, 409 U.S. 488, 490, 93 S.Ct. 801, 803, 35 L.Ed.2d 16 (1973)). “The word ‘just’ in the Fifth Amendment evokes ideas of ‘fairness’ and ‘equity,’.... ” United States v. Commodities Trading Corp. 339 U.S. 121, 124, 70 S.Ct. 547, 549-50, 94 L.Ed. 707 (1950).

At trial it was clear that OSM, based in large part on Tennessee’s opposition, had no intention of allowing mining next to the park. The testing conducted after the administrative law judge’s decision was not going to satisfy the Tennessee Wildlife Resources Agency that the mine was not a danger to the scenic and ecological resources of the park. When the Permitting Division requested even more testing and proposed a new multi-phased approach, the delay became unreasonable. The Permitting Division knew that Tennessee opposed the mine, and further delay in making the decision was unnecessary and unjustifiable.

The Government requisitioned Eastern’s right to mine the Cane property and its right to renew the lease. Both are property interests for which Eastern is entitled to just compensation.

Just Compensation

The Government denied Eastern’s permit because of the State’s concerns that the proposed activities would have adverse effects on a public park. Plaintiffs are not required to bear the burden of this public benefit.

The standard measure of just compensation in a permanent taking situation is the value of the property on the date of the taking. First English Evangelical Lutheran Church v. Los Angeles, 482 U.S. 304, 320,107 S.Ct. 2378, 2388-89, 96 L.Ed.2d 250 (1987). Courts should not “reduce the concept of ‘just compensation’ to a formula,” or “make a fetish even of market value, since it may not be the best measure of value in some cases.” United States v. Cors, 337 U.S. 325, 332, 69 S.Ct. 1086, 1090, 93 L.Ed. 1392 (1949). “Both fairness and equity must be considered in awarding compensation----” Yaist v. United States, 17 Cl.Ct. 246,257 (1989).

The loss of a contractual right to renew a lease is considered to be a taking of property for Fifth Amendment purposes. United States v. Petty Motor Co., 327 U.S. 372, 66 S.Ct. 596, 90 L.Ed. 729 (1946). In a World War II condemnation action, the Supreme Court stated that the value of a tenant’s leasehold interest included a contractual right to renew the lease. Id. at 381, 66 S.Ct. at 601. The Government condemned the building in 1942 for a three year period, with the option to terminate possession in June 1943 and June 1945. Id. at 374, 66 S.Ct. at 598. Plaintiff Petty Motors Company’s lease expired in October 1943, with an option to extend for an additional year. Id. at 375, 66 S.Ct. at 598-99. The Court did not require the plaintiff to exercise the option in the hopes that the Government would terminate possession before 1945. Instead, it stated that Petty Motors’ damages would be the term of the original lease plus the one year renewal term. Id. at 381, 66 S.Ct. at 601.

The Government prevented Eastern both from obtaining the benefit of its leasehold interest and from renewing its lease. If a permit had been granted before August 1990, Eastern would have extended the lease for as long as necessary to mine all the merchantable coal in the ground.

The traditional method of determining just compensation is to use comparable sales to arrive at fair market value. Whitney Benefits v. United States, 18 Cl.Ct. 394,408 (1989). When comparable sales data are unavailable, a cash flow analysis is an acceptable alternative. Id. The Claims Court in Whitney noted that the value of coal reserves “can only be measured by their ability to produce income.” Id. at 409. Both parties’ experts agree that a discounted cash flow analysis is the best approximation of the value of the property. This method produces a value for property based on the income stream the property will produce. A discount rate is applied to the income stream in order to produce a present value for the property as of the date of the taking. The discount rate represents the rate of return an investor would require in order to risk capital on the project. The rate is a combination of the time value of money and the risk involved in the transaction.

Expert Reports

Experts for plaintiffs and defendant presented their evaluations of the value of the Cane leasehold held by Eastern, and the royalty interest retained by the Wyatts. Plaintiffs’ experts produced a fair market value for the Eastern-Cane lease in 1990 of $31,359,822. The fair market value of the Wyatts’ 3.5% royalty interest was $5,887,-611. The Government’s experts concluded that the underground minable coal on the Cane property was worth negative $9.7 million, and the surface minable coal as negative $945,000. They valued the Wyatt’s royalty interest at $0.

The Government’s experts were not persuasive for the most part. The testimony and conclusions of one expert clearly were designed to mesh with the Government’s legal theories. His refusal to acknowledge input from counsel in reaching his conclusions was not credible. An expert should not be an advocate. The Government’s other expert estimated capital costs based on a purchase of real estate at three times the current fair market value. Plaintiffs’ expert testimony generally was more credible.

Coal Reserves

Plaintiffs’ experts estimated the minable coal reserves in the Sewanee seam on the Cane property to be 16,673,629 tons. The Government’s experts estimated 20,693,000 tons. Although the two approaches differed a great deal in methodology, the results were fairly consistent. The isopach method used by plaintiffs’ experts traces and recognizes trends in the coal seam by providing a weighted average of thickness. This method is accepted in the field for coal reserve evaluations.

The Government’s experts also analyzed the reserves according to the isopach method. They prepared an isopach map of the Sewanee seam, but it was destroyed before trial. That map would have been favorable to plaintiffs’ ease.

The government expert switched to the unweighted average method for use at trial. This method estimated greater resources than the isopach method, but it assumed a greater variability in the thickness of the coal seam. This led defendant to the conclusion that huge quantities of rock would have had to be mined to recover an adequate amount of coal. This would have meant higher production costs and loss of efficiency by the mining teams. The plaintiffs’ estimation of coal reserves and the variability in the Se-wanee seam was more credible, especially in light of defendant’s actions regarding the destroyed map.

Extraction Rate

The Cane-Eastern Minerals lease requires that, “in connection with any mining activity of Tenant [Eastern], other than strip-mining, Tenant shall take all action necessary to support the surface of the land.” Eastern therefore had a duty to prevent subsidence of the Cane property through its operations. Both parties’ experts agree that a 50% removal rate would prevent subsidence. For all areas except those under Cane Creek, we employed a 50% removal rate. The experts do not agree that Eastern could have mined under Cane Creek. Defendant’s expert projected no mining at all under and within 100 feet of the creek because he expected to encounter poor roof conditions and water problems. Plaintiffs assumed a 45% recovery rate for the reserves located under Cane Creek. The 45% recovery rate is consistent with both experts’ opinions of surface integrity. We used the 45% rate for areas under and within 100 feet of Cane Creek.

The 50% recovery rate is applied to a total available reserve of 15,916,461, producing 7,958,230 recoverable tons. The 45% recovery rate applies to a total reserve of 757,168, producing 340,724 tons of raw coal. This results in 8,298,954 recoverable tons from the Cane property. We did not include the Se-wanee seam coal located near Brock Ridge because plaintiffs indicated that such reserves were inferred. Inferred reserves means that the geologist has a low level of confidence in finding the reserves as marked on the isopaeh map. This low level of confidence, combined with the lack of a mine plan for that area led us to exclude those reserves from plaintiffs’ estimate.

The profitability of the operation and the life of the mine depend on the price set for coal, the discount rate to be applied, the productivity of the miners, and the capital costs. These factors are addressed below.

Coal Price

The experts presented an approximation of the price for coal over the life of the mine. Plaintiffs used the average spot price of coal at the Widow’s Creek power plant for the years 1989 and 1990 to reach an estimate over the life of the mine. Their expert testified that the spot price was more susceptible to changes in supply and demand than were long-term contract prices. However, he felt that the spot prices for 1990 were a better indicator of coal price than the long-term contract prices. The average long-term contract price would contain prices from contracts entered long before 1990 and therefore would not be as indicative of coal value in 1990.

A government expert performed a historical and geographic analysis of coal prices in the United States as well as in Tennessee. He compared prices of the various available consumers of Eastern’s coal. Based on the quality of the coal, he assumed that 90% of Eastern’s production would be lower-price utility coal and 10% would be higher price stoker coal. His long-term sales contract estimate for utility coal was $31.00 per ton free on board (FOB) shipping point. Long-term contracts for higher-quality stoker coal would bring $34.00 per ton FOB shipping point, according to defendant.

Plaintiffs’ experts were more persuasive on this point. The best estimate of the value of the coal in 1990 is the average spot price in 1990. Plaintiffs utilized that price across the life of the mine, in essence transforming it into a long-term price for the coal. Plaintiffs’ converted long-term contract price for 1990 was $35.19 per ton FOB shipping point. This price provides a better estimate of coal prices in 1990.

Discount Rate

In preparing a cash flow analysis, a discount rate is employed to take account of risk and to convert the future income stream to present value. Plaintiffs used a 10% discount rate based in part on a Bureau of Land Management (BLM) circular published in 1986 for the appraisal of federal coal property. The BLM publication advises that the 10% discount rate assumes a normal debt-equity mix in the capital required for the project. The publication advises against adjusting the discount rate to account for risk because the selection of a risk premium for this purpose is highly subjective. Instead, it provides four alternatives to account for the uncertainty: (1) probability weighted scenarios; (2) sensitivity analysis of input; (3) discount value based on subjective criteria linked to likelihood of property development; (4) timing development variation.

Plaintiffs’ expert did not utilize any of these methods to account for uncertainties in property development. He testified that a basis for his ten percent figure was a report in another case before this court, Whitney Benefits v. United States, 18 Cl.Ct. 394 (1989). That report incorporated a sensitivity analysis that imposed an additional risk factor on the cash flow. He did not perform such a risk analysis for this case. The risk analysis in Whitney Benefits was used to account for the risk inherent in that project because the project required the plaintiff to change the course of a river.

Plaintiffs’ ten percent rate is consistent with the BLM standard. There are two problems with this figure, however. While they claimed to have taken account of risk in applying the ten percent rate, neither the expert’s report nor his testimony give any indication of the manner in which the ten percent discount rate approximates the risk of an undeveloped property. He stated that he uses the ten percent rate in 89% of his eases, but did not explain the circumstances under which he normally applies that rate.

Defendant’s expert chose a fifteen percent discount rate for his cash flow analysis. He stated that applying a fifteen to twenty percent rate to undeveloped properties is standard in the field. He also stated that ten percent would be appropriate for a developed property. Because the Cane property was essentially undeveloped, the higher discount rate would apply. His rate took into account extensive exploration of the property, nearby productive mines in the same seam, and quality of the Sewanee coal. This figure is supported by adequate explanation and will be used in discounting the income stream of the Cane property.

We could not determine how the Government arrived at the discount factors listed at the bottom of Table III of its expert report. We applied the formula for present value:

PV= Cash Flow

(1 + discount rate)time

This formula did not reproduce the Government’s figures. A standard annuity table using a 15% rate of return matched the figures reached with the above formula. We substituted the annuity table figures for the discount factors in defendant’s report.

Production

The productivity of the mine and the amount of clean coal produced affect the income stream. Both experts presented rates of productivity of clean, marketable coal. Plaintiffs’ expert had experience in assessing coal properties along the Appalachian corridor. Defendant’s expert also had experience in Appalachian coal. We accepted plaintiffs’ estimation of the productivity of the coal mining sections and the estimation of the capital resources (shuttle cars, continuous miners, roof bolters, and belt feeders) necessary to achieve that level of production because his explanation for the estimates was more credible.

The Government’s plan called for building a washing facility prior to the start of production. This plan created a two-year delay in the start of mining and required huge capital expenditures prior to revenue production. The Government’s expert included in this portion of the plan the purchase of property for the washing plant at three times the fair market value.

Plaintiffs’ expert assumed that Eastern would wash its coal at the nearby Tennessee Consolidated coal-washing plant. We determined that Tennessee Consolidated had excess capacity at its washing plant, and that plaintiffs’ assumptions were entirely reasonable. The Government’s experts created delay and unnecessary capital expenditures by planning for the construction of a new coal-washing plant. Even if coal-washing at Tennessee Consolidated were to become impractical at some point during the life of the mine, the delay and capital required would be spread over a period when the mine was already in production. Plaintiffs’ estimates of clean coal production from the washing facility was more reasonable and credible.

The construction of a coal-washing plant would cause a two-year delay in coal production. In a discounted cash flow analysis, the income stream in the first few years is worth more than in later years. This is because money earned in the future is worth less than money earned in the present or immediate future. The discount rate accounts for risk but also for the time value of money, so that a dollar earned in the first year of the mine has a higher present value than a dollar earned in the eighth year of the mine. In defendant’s plan, the most profitable years in the analysis are consumed by large capital outlays and no revenue income. Plaintiffs proposed to use an existing, nearby coal-washing facility. This was a reasonable assumption that allowed them to move into production in the first year of the mine.

Capital Costs

The parties’ experts did not agree on how to treat the capital required to mine the Sewanee seam. Plaintiffs amortized the capital over the life of the mine. The Government expensed capital costs in the year incurred, greatly reducing the cash flow in the initial years when 1990 dollars were worth the most.

The Department of the Interior circular that plaintiffs relied upon expensed capital costs in the year they are incurred. The Claims Court in the Whitney Benefits ease, relying on the same circular, also expensed capital costs in the year they were incurred. Whitney Benefits, 18 Cl.Ct. at 417. Plaintiffs relied on both the circular and Whitney Benefits in its cash flow analysis. Because plaintiffs provided no rational explanation for its departure from the method used in these two sources, we expensed capital costs in the year incurred.

Plaintiffs’ expert provided an annual breakdown of capital costs, but did not use the breakdown because it had amortized the capital expenses over the life of the mine. The Government expert did expense capital costs in the year incurred, so we will utilize that breakdown in estimating capital costs and in expensing capital costs in the year incurred. The figures in defendant’s tables are adjusted to avoid the need for a coal-washing plant and related equipment.

Wyatts’ Royalty Interest

The Wyatts’ royalty interest is described in the Cane lease as three and one-half percent of gross sales price. The lease defines gross sales price as “an amount equal to the total gross proceeds payable to Grantee ... from the sale of coal mined and removed ... FOB railroad car ... and FOB truck.” As noted above, we accept plaintiffs’ long term price for the Sewanee coal as of 1990. We also accept plaintiffs’ price per ton of $31.91 in their revised Table 3 for calculation of the Wyatts’ interest.

Defendant argued both at trial and for reconsideration that the Wyatt’s royalty income in this analysis should be reduced by the applicable tax rate. The lump sum payment to the Wyatts is in lieu of the income stream the mine would have generated. This lump sum will be taxed as a capital gain.

The Government makes the new argument from a new expert on reconsideration that the Wyatts can roll these proceeds into similar investment property within two years and avoid the capital gains tax. We noted two problems with the new expert’s declaration. First, a rollover merely postpones the Wyatts tax liability; it does not reheve them of the obligation to pay the tax. Deferral of this tax may provide a benefit to the Wyatts, but that is not a sufficient reason essentially to tax them twice on the same award. Second, the fact that Mr. Hufendick located a method by which the Wyatts could avoid this tax liability does not mean that the Wyatts would choose such an option.

Conclusion

We accept plaintiffs’ estimations of coal reserves, productivity, and projected capital expenditures. We find that expensing the capital required for the project in the year incurred is the appropriate method. We adopt defendant’s suggested discount rate. Discount factors for a 15% rate are taken from the annuity tables. The rate of recovery of coal reserves is adjusted to 50% for most of the reserves and 45% for the reserves under or within 100 feet of Cane Creek. The reduction in the recovery rate reduces the life of the mine to nine years. We concluded that plaintiffs’ mine plan provided for production in Year One of 387,507 clean tons. The mine produced 778,216 clean tons per year in Years Two through Eight. In Year Nine, 714,292 clean tons of coal would be recovered prior to the depletion of the estimated reserves.

The present discounted value of Eastern Minerals’ leasehold and renewal right is $15,-866,311. The present discounted value of the Wyatts’ royalty interest is $3,743,766.

The Clerk will enter judgment for Eastern Minerals International, Inc. for the sum of $15,866,311 and for Wilson W. Wyatt, Sr., and Anne D. Wyatt in the amount of $3,743,766 plus compound interest at the tax overpayment rate. We noted in the April 21, 1997 opinion that no costs should be awarded. We referred to costs as taxed by the Clerk of Court pursuant to RCFC 77.4. We did not intend to limit plaintiffs’ rights to obtain costs pursuant to other statutory authority. See 42 U.S.C.A. § 4254(c). 
      
      . "Because the [Department of Conservation] is concerned with maintaining the aesthetic and environmental integrity of the Park ... we would recommend that mining regulatory authorities (DSM or OSM) deny any request to mine this site.”; See also Defendant’s Exhibit 194 ("Our [Tennessee's] position remains that the permit be denied.”)
     
      
      . The State’s opposition continued throughout the permit application process. The Commissioner of the Tennessee Department of Conservation wrote Mr. Bemos in 1989, pointing out that the department had opposed Eastern’s permit in writing five separate times. Despite the studies being conducted, the Commissioner concluded by stating that "the department must continue its stated opposition to any proposed mining in this area.”
     
      
      . In other words, in order to stop this project, OSM would have to find another basis for denying the permit.
     
      
      . The lineament study was designed to produce a map and report detailing linear surface features on the Colten property in order to estimate underground formations and groundwater conduits. The study was completed in 1991.
     
      
      . Discount rates normally include a factor for inflation. Both experts used constant dollars in their analysis, so no inflation factor is included in our discount rate.
     
      
      . Plaintiffs’ valuation has been reduced because of a stipulated interpretation of the Cane-Eastern lease. Eastern Minerals is responsible for paying the Wyatt’s royalty interest under the stipulation, reducing the fair market value of the lease to $26,346,299. The Wyatt’s interest remains at $5,887,611.
     
      
      . The Government moved to reconsider these conclusions because (it argued) they are not supported by the record. A trial court has broad discretion to assess credibility because testimony may be judged on demeanor and bearing of witnesses during trial; such determinations and inferences often are not conveyed by words in a transcript.
     
      
      . Defendant notes in its motion for reconsideration that the court accepted the Government’s expert testimony concerning discount rate and other factors. It asserts that we must believe all of a government expert's testimony if we accept any of it. We are not aware of any principle that requires such a result.
     
      
      . CHARLES H. GUSHEE, ed„ FINANCIAL COMPOUND INTEREST AND ANNUITY TABLES 734 (5th ed.1972). The discount figures for the nine year life of the mine are as follows:
      Year 1 — .869
      Year 2 — .756
      Year 3 — .657
      Year 4 — .571
      Year 5 — .497
      Year 6 — .432
      Year 7 — .375
      Year 8 — .326
      Year 9 — .284
     
      
      . We found at trial that plaintiffs were reasonable in assuming that coal could be washed at the Tennessee Consolidated facility. Plaintiffs’ estimates of necessary equipment were more reasonable than the Government’s. Defendant and plaintiffs included the excavation and use of a second box cut to reach the mine face later in the life of the mine. Plaintiffs’ cost estimate for the second project was not reasonable. We included defendant’s estimated capital costs for the second box cut. We removed from defendant’s breakdown of capital costs (Appendix 3, Micon Report) the following capital required for the preparation plant and for the belt feeders that we found not to be necessary:
      1989: 1) land acquisition ($50,000)
      1990: 1) land acquisition ($150,000)
      2) coarse refuse site ($181,000)
      3) fine refuse slurry dam ($475,000)
      4) prep plant site grading ($72,000)
      5) prep plant construction ($2,400,000)
      6) plant sub station ($75,000)
      7) plant office ($35,000)
      8) refuse conveyor ($125,000)
      9) belt feeder ($150,000)
      1991: 1) plant feed dozer ($265,000)
      2) D7H for refuse ($260,000)
      3) belt feeder ($150,000)
      1997: 1) belt feeder ($150,00)
      1998: 1) belt feeder ($150,000)
      We also made adjustments to Appendix 3 to defendant's expert report to reflect the investment required for continuous miners and roof bolters under plaintiffs’ mine plan. The following amounts were substituted in the years indicated as the capital requirements for underground equipment:
      1990: Continuous miners (2) — $1,850,000 Shuttle cars (4) — $651,000 Roof bolters (4) — $651,000
      1991: Continuous miners, roof bolters, and shuttle cars should be $0 because all initial equipment was purchased in 1990.
      1997: Continuous miners (2) — $1,850,000 Shuttle cars (4) — $651,000 Roof bolters (4) — $651,000
      We adjusted defendant’s capital layout in Appendix 3 to account for the reduced life of the mine. With the available resources, the mine will operate for only nine years. Defendant’s mine plan did not begin production until 1991 and the reduced life of the mine would end at 1999 under defendant’s schedule. Therefore, the capital expenses included in defendant’s report after 1999 are disregarded. We also adjusted the layout to account for plaintiffs' assumption that mining will begin in the first year of the mine. All 1989 and 1990 capital expenditures in defendant’s tables are moved to 1991.
     
      
      . For each of the nine years of the mine, we reduced the gross profit by the capital expenditures incurred in that year. We also reduced the profit by the appropriate depletion allowance of 10% of gross income (exclusive of rents and royalties) not to exceed 50% of taxable income pursuant to 26 U.S.C.A. § 613 (1997 Supp.). We applied an effective corporate tax rate of 38% to arrive at net profit. We added the depletion allowance to the net profit to arrive at a cash flow that was discounted by the appropriate discount factor. We added all the discounted cash flow figures to arrive at the net present value of Eastern Minerals leasehold and renewal interest.
     
      
      . We used the clean tons produced each year and the $31.91 per ton figure discussed supra to arrive at the gross revenue figure for the Wyatts' royalty interest. We then calculated 3.5% of each year’s gross revenues. We discounted the royalty figure by the appropriate discount factor for a 15% discount rate. The Wyatts’ royalty interest is subject to the same risk and lime value of money concerns to which Eastern's interest is subject. Therefore, we chose the same discount rate as that applied to the Eastern cash flow.
     
      
      . Plaintiffs requested on reconsideration that we award interest on the judgment. We agree that plaintiffs are entitled to compound interest at the tax overpayment rate. Defendant argues that plaintiffs are entitled only to simple interest at the rate specified in the Declaration of Takings Act. 40 U.S.C.A. § 258A, et seq. The Declaration of Takings Act on which defendant relies for application of the 52-week T-bill rate calls for compound interest. Compound interest is appropriate because (1) the case involves commercial property for which plaintiffs expected a good return on their investment; and (2) plaintiffs have suffered a long period of delay between the taking and judgment. See Whitney Benefits, Inc. v. U.S., 30 Fed.Cl. 411 (1994).
      Interest at the tax overpayment rate is appropriate. This rate has been approved by the Federal Circuit. Hughes Aircraft v. U.S., 86 F.3d 1566 (Fed.Cir.1996), vacated and remanded on other grounds,-U.S.-, 117 S.Ct. 1466, 137 L.Ed.2d 680 (1997).
     