Citrus Valley Estates v. Commissioner

Citrus Valley Estates, Inc., et al., 1 Petitioners v. Commissioner of Internal Revenue, Respondent Citrus Valley Estates v. Commissioner Docket Nos. 12900-89, 22599-89, 6505-90, 13406-90, 13407-90, 13449-90, 19117-90, 19654-90, 19716-90, 24352-90, 177-91, 15473-91 United States Tax Court 99 T.C. 379; 1992 U.S. Tax Ct. LEXIS 75; 99 T.C. No. 21; 15 Employee Benefits Cas. (BNA) 2521; September 29, 1992, Filed Decisions will be entered for petitioners in docket Nos. 12900-89, 22599-89, 6505-90, 13406-90, 13407-90, 19117-90, 24352-90, and 177-91. Decisions will be entered under Rule 155 in docket Nos. 13449-90, 19654-90, 19716-90, and 15473-91. Ps are small businesses engaged in a variety of activities. Ps each adopted small defined benefit plans for one or two key employees. Each plan created a trust to provide for the investment and administration of plan assets. For the taxable years at issue, all contributions to the plans were made within the time required by sec. 401(a)(1) and (6), and each of the plans and related trusts was qualified under sec. 401(a) and was exempt from taxation under sec. 501(a). The appropriate Forms 5500 and Schedules B were filed with the Service. R challenged various funding assumptions made by the plans' enrolled actuaries in determining the amount of tax-deductible contributions for each plan for the plan years at issue. R also determined that the certifying actuaries for the plans using the unit credit funding method did not fund within allowable limits and did not make reasonable allocations of costs. In addition, *76 R concluded that certain formal requirements relating to plan amendments and terms were not met. Finally, R determined that certain excise taxes and additions to tax were due. 1. Held, all of the challenged actuarial assumptions for each of the plans at issue were reasonable. Held, further: The certifying actuaries for the plans using the unit credit funding method funded within allowable limits and made reasonable allocations of costs, and the enrolled actuary for the Fox plan made reasonable allocations of costs. Accordingly, the actuarial assumptions and methods used for the plans are reasonable in the aggregate. A fortiori, these assumptions are not substantially unreasonable so as to permit retroactive changes of assumptions for years prior to the year in which the audit was made. The actuarial assumptions and methods certified by the three enrolled actuaries in combination offer the actuaries' best estimates of anticipated experience under the plans. 2. Held, further, the timing of the amendments of two of the plans at issue was irrelevant, the proper election was made for the amendment of one plan to have retroactive effect, and the first amendment of one plan*77 was at issue and was not adopted timely. Held, further, one P failed to file the proper notice for automatic approval for a change in valuation date, and three plan participants completed 1,000 hours of service for each year of service claimed, as required by their plans. 3. Held, further, one P is liable for the sec. 4972 excise tax on nondeductible contributions, but is not liable for additions to tax under sec. 6651(a) for failure to file excise tax returns. Held, further, six Ps are not liable for sec. 6659A additions to tax, and two are liable for sec. 6659A additions to tax if the overstated liabilities are 150 percent or more of the correct liabilities. Gregory A. Robinson, Neil H. Hiller, Brad S. Ostroff, and John F. Daniels, for petitioners. * Anne W. Durning, Susan T. Mathew, James S. Stanis, and Andrew J. Gottlieb, for respondent. Clapp, Judge. Hamblen, Chabot, Parker, Cohen, Swift, Jacobs, Gerber, Wright, Parr, Wells, Whalen, Colvin, Halpern, and Beghe, JJ., agree with the majority*78 opinion. Ruwe, J., dissenting. CLAPP *380 TABLE OF CONTENTS Page Factual Background [383] Law [397] Certifying Actuaries [406] Experts [407] Interest Rate Background [409] Petitioners' Expert [413] Long-Term Rates of Return [413] Adjustments for Plan Size [415] Pre-retirement Adjustments [416] Post-retirement Adjustments [417] Comparison to Actuarial Experience [418] Regulatory and Legal Guidance [419] Conclusion [420] Respondent's Actuarial Expert [420] Discussion [421] Retirement Age General Background and Retirement Trends [428] Segregation Provisions [430] Davis [431] Lear [432] Stephan [433] Fox [435] Brody Enterprises [436] Mortality Assumptions Citrus Valley [437] Fox [438] Brody Enterprises [439] Post-retirement Expense Load Assumptions Brody Enterprises [440] Unit Credit Funding Method [441] Timing of Plan Amendments Citrus Valley [453] Davis [454] Lear [455] Fox [457] Change in Valuation Date Boren Steel [458] Hours of Service Citrus Valley [460] Old Frontier [460] Boren Steel [461] Section 4972 Excise Tax [461] Section 6651 Failure to File Addition to Tax [462] Section 6659A Additions to Tax [463] Conclusions [465] *79 *381 OPINION Clapp, Judge: Respondent determined the following deficiencies in and additions to petitioners' Federal income tax: Additions to tax Year Sec. Sec. Petitioner Docket No. ended Deficiency 6651(a)(1) 6659A Citrus Valley Estates, Inc. et al. 12900-89 12/31/82 $ 6,182.00 --- --- 12/31/83 5,737.00 --- --- 12/31/85 22,462.00 --- --- 24352-90 12/31/88 4,265.00 --- $ 1,280.00 Robert J. & Janice A. Davis 22599-89 12/31/85 57,246.00 --- --- 12/31/86 173,975.00 --- 52,193.00 Old Frontier Investment, Inc., of Arizona 6505-90 12/31/83 7,869.00 --- 2,361.00 12/31/84 7,183.00 --- 2,155.00 12/31/85 6,302.00 --- 1,891.00 12/31/86 909.00 --- --- Lear Eye Clinic, Ltd. 13406-90 09/30/86 69,136.00 --- --- 19117-90 09/30/87 62,055.00 --- 14,567.00 Robert Stephan, Jr., P.C. 13407-90 07/31/87 1 89,807.00 --- 26,942.00 Boren Steel Consultants, Inc. 13449-90 03/31/87 26,561.00 --- 5,303.00 12/31/87 2,647.00 --- --- 12/31/88 1,802.00 --- --- 15473-91 12/31/87 8,105.00 $ 2,026.25 --- 12/31/88 10,806.00 2,701.50 --- Arizona Orthopedic Institute of Traumatic and Reconstructive Surgery, P.C. 19654-90 04/30/87 139,909.00 --- 32,699.00 12/31/87 45,507.00 --- 2,623.00 Jonathan R. and Renee K. Fox 19716-90 12/31/86 13,750.00 --- 4,125.00 Brody Enterprises, Inc. 177-91 01/31/86 64,054.78 --- 19,216.50 01/31/87 32,334.00 --- 9,700.20 *80 *382 Respondent also determined a 10-percent excise tax under section 4972 in Boren Steel Consultants, Inc. (docket No. 15473-91), for the years 1987 and 1988. The issues for decision are: (1) Whether the actuarial assumptions used by the certifying actuaries for petitioners' small defined benefit pension plans (plans) were reasonable in the aggregate and represented the actuaries' best estimates of anticipated experience under the plans as required by section 412(c)(3), specifically: (a) Whether the 5-percent pre- and post-retirement interest rate assumptions used in all of the plans were reasonable, (b) whether the age 55 retirement assumption used in some of the plans was reasonable, (c) whether the mortality assumptions for some of the plans were reasonable, and (d) whether the post-retirement expense load used in one of the plans was reasonable; (2) whether the certifying actuaries, for the plans using the unit credit funding method, funded within allowable limits and made reasonable allocations of costs; *383 (3) whether certain formal *81 requirements relating to plan amendments and terms were met, specifically: (a) Whether plan amendments for some of the plans were timely adopted, and whether the proper elections were made for them to have retroactive effect, (b) alternatively, whether the timing of the plan amendments was relevant, (c) whether proper notice was filed for automatic approval of a change in valuation date for one plan, and (d) whether three of the plan participants completed 1,000 hours of service for each year of service claimed as required by the plans; and (4) whether certain additions to tax and excise taxes are applicable, specifically: (a) Whether one petitioner is liable for the excise tax on nondeductible pension plan contributions prescribed by section 4972, (b) whether that petitioner is liable for additions to tax under section 6651(a)(1) for failure to file excise tax returns, and (c) whether all petitioners are liable for additions to tax for overstatement of pension liabilities under section 6659A. All section references are to the Internal Revenue Code in effect for the years in issue, and all Rule references are to the Tax Court Rules of Practice and Procedure, unless otherwise specified. *82 Factual Background We incorporate by reference the stipulation of facts and attached exhibits. Citrus Valley Estates, Inc./Citrus Valley Estates, Inc., An Arizona Corporation (Citrus Valley) Citrus Valley was incorporated in 1977 under the laws of the State of Arizona. Citrus Valley was in the business of acquiring and developing real estate in the Phoenix metropolitan area and selling the lots to developers and individuals. Citrus Valley timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for its taxable years 1982 through 1988. Citrus Valley's taxable year for Federal income tax purposes was a calendar year, and it employed the accrual method of accounting. Everett L. King (King) was the president and sole employee of Citrus Valley during the years in issue, and he *384 owned 1 percent of the stock of Citrus Valley. During the years 1977 through 1984, King received no salary from Citrus Valley. King's salary, on the accrual basis, from Citrus Valley for the years 1985 through 1988 was $ 67,400, $ 80,000, $ 87,200, and zero, respectively. In 1985, Citrus Valley adopted a defined benefit pension plan. King was the only participant in the plan*83 during the years 1985 through 1988. On May 9, 1986, Citrus Valley received a favorable determination letter from respondent qualifying the plan under section 401(a). Citrus Valley's plan was amended twice. The enrolled actuary for the plan was John W. Lawrence, Jr. (Lawrence). In making the annual actuarial computations of funding requirements and funding limits for the plan years 1985 through 1988, Lawrence used the following actuarial assumptions: Plan year ending 12/31/85 12/31/86 12/31/87 12/31/88 Pre-retirement interest 5% 5% 5% 5% Post-retirement interest [1] 5% 5% 5% Retirement age [3] Salary scale 8% -0- -0- -0- Benefit form [4] Pre-retirement mortality -0- -0- -0- -0- Post-retirement mortality [7] Expense load $ 360 $ 360 $ 360 -0- Turnover -0- -0- -0- -0- *84 For purposes of these calculations, Lawrence used the individual aggregate actuarial cost method of funding and the following data for King: *385 Date of birth 12/13/25 Date of spouse's birth --- Date of hire 7/1/77 Date of entry into the plan 1/1/85 For the plan years 1985 through 1988, Citrus Valley contributed $ 225,360, $ 190,864, $ 59,257, and $ 62,590, respectively. Lawrence prepared and signed the Internal Revenue Service (the Service) Schedules B of the Forms 5500 2 with respect to the plan for each of the plan years 1985 through 1988. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of the anticipated experience under the plan. *85 In 1986, Citrus Valley timely filed a Form 1139, Corporation Application for Tentative Refund, and received tentative refunds of income tax for 1982 and 1983 in the amounts of $ 6,182 and $ 5,737, respectively. On March 13, 1989, respondent timely mailed Citrus Valley a notice of deficiency determining deficiencies in tax for 1982, 1983, and 1985. On August 8, 1990, respondent timely mailed Citrus Valley a notice of deficiency determining a deficiency in tax for 1988 and an addition to tax under section 6659A. Robert J. and Janice A. Davis (Davis) The Davises were husband and wife who resided in Paradise Valley, Arizona, when the petition in this case was filed. The Davises timely filed their joint Federal income tax returns for the years ending December 31, 1985, and December 31, 1986, with the Ogden, Utah, service center. Hereinafter, Davis in the singular will refer to Robert J. Davis. Davis was the sole proprietor and registered representative of GRH Securities involved in direct participation programs during the years in issue. Effective January 1, 1984, Davis adopted the Robert J. Davis Defined Benefit Plan (the plan). During the years at issue, Davis was the only*86 participant in the plan. On March 20, 1986, Davis received a favorable *386 determination letter from respondent qualifying the plan under section 401(a). Davis' plan was amended twice. The enrolled actuary for the plan was Steven Matthews (Matthews) of Matthews, Malone & Associates. In making the annual actuarial computations of the funding requirements and funding limits for the plan years ending December 31, 1984, 1985, and 1986, Matthews used $ 200,000 as the annual compensation for Davis. Matthews also used the following actuarial assumptions: Plan year ending 12/31/84 12/31/85 12/31/86 Retirement age [55] Pre-retirement interest 5% 5% 5% Post-retirement interest 5% 5% 5% Salary scale -0- -0- -0- Pre-retirement turnover -0- -0- -0- Mortality (males) 1971 IAM-2 1971 IAM-2 1971 IAM-2 Mortality (females) 1971 IAM-8 1971 IAM-8 1971 IAM-8 Form of benefit [1] For purposes of these calculations, Matthews used the following data for Davis: Date of birth 5/7/34 Date of spouse's birth 2/12/34 Date of hire 1/1/70 Date of entry into the plan 1/1/84 The following is an*87 annual benefit accrual schedule for the Davis plan: Annual Total benefit Total accrued accrual at accrued Sec. 415 benefit 10% of benefit limit if no used by Compen- compen- before further plan's Year sation sation sec. 415 service 1 actuary [1984] $ 200,000 $ 20,000 $ 20,000 $ 75,000 $ 20,000 [1985] 200,000 20,000 40,000 75,000 40,000 [1986] 200,000 20,000 60,000 75,000 60,000 *387 For the plan years ending December 31, 1985, and December 31, 1986, Davis contributed $ 308,613 and $ 308,613, respectively. Matthews prepared and signed the Schedules B with respect to the plan for each of the plan years in issue. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of the anticipated experience under the plan. On July 31, 1989, respondent timely mailed the Davises a notice of deficiency determining deficiencies in income tax for 1985 and 1986 and *88 an addition to tax for 1986 under section 6659A. Old Frontier Investment, Inc., of Arizona (Old Frontier) Old Frontier was incorporated in 1962 under the laws of the State of Arizona. During the years in issue, Old Frontier received revenues from various sources. Old Frontier operated an insurance adjusting school, provided claims adjusting services to various insurance companies, sold baseball cards and other baseball memorabilia, and owned and leased real estate in Phoenix, Arizona. Old Frontier timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for the years at issue. Old Frontier's taxable year for Federal income tax purposes was a calendar year, and it employed the cash method of accounting. William J. Rocke (Rocke) was the president of Old Frontier during the years 1983 through 1987. During these years, Rocke's salary from Old Frontier was $ 12,000, $ 12,000, $ 15,600, $ 90,000, and $ 24,000, respectively. In June 1971, Old Frontier adopted a prototype pension plan known as the Equitable Prototype Noncontributory Combination Pension Plan and Trust. On December 17, 1986, Old Frontier amended and restated this previously existing pension plan, effective*89 January 1, 1984. On July 11, 1987, Old Frontier received a favorable determination letter from respondent qualifying the plan under section 401(a). The plan's enrolled actuary for the plan years 1985 through 1987 was Matthews. In making the annual actuarial computations of funding requirements and funding limits for *388 the plan years 1985 through 1987, Matthews used the following actuarial assumptions: Plan year ending 12/31/85 12/31/86 12/31/87 Pre-retirement interest 5% 5% 5% Post-retirement interest 5% 5% 5% Retirement age [65] Salary scale -0- -0- -0- Benefit form [1] Pre-retirement mortality -0- -0- -0- Post-retirement mortality [2] Expense load -0- -0- -0- Turnover -0- -0- -0- For purposes of these calculations, Matthews used the following data for Rocke: Date of birth 7/23/24 Date of spouse's birth assumed to be 3 years younger Date of hire 7/1/65 Date of entry into the plan 6/28/71 The funding method used by Matthews was the individual aggregate method. Rocke was the *90 only participant in the plan during 1986, and for funding purposes, Matthews considered his compensation in 1986 to be $ 73,952. For the plan years 1985 and 1986, Old Frontier contributed $ 12,000 and $ 225,000 to the plan, respectively. Matthews prepared and signed the Schedules B with respect to the plan for plan years 1985 and 1986. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On April 30, 1987, Old Frontier timely filed a Form 1139, Corporation Application for Tentative Refund, and received tentative refunds of income tax for 1983, 1984, and 1985 in the amounts of $ 7,869, $ 7,183, and $ 6,302, respectively. On February 6, 1990, respondent timely mailed Old Frontier a notice of deficiency determining deficiencies in income tax for *389 the taxable years 1983 through 1986 and additions to tax for the taxable years 1983 through 1985 under section 6659A. Lear Eye Clinic, Ltd. (Lear) Lear was incorporated in 1979 under the laws of the State of Arizona. Lear timely filed its Forms*91 1120, U.S. Corporation Income Tax Returns, for the years at issue. Lear's taxable year for Federal income tax purposes was a fiscal year ending September 30, and it employed the cash method of accounting. Samuel L. Pallin (Pallin), a practicing ophthalmologist, was the president and sole shareholder of Lear during the years at issue. Effective October 1, 1984, Lear adopted a defined benefit plan. On September 4, 1986, Lear received a favorable determination letter from respondent qualifying the plan under section 401(a). The plan's enrolled actuary for the plan years ending September 30, 1986, and September 30, 1987, was Matthews. In making the annual actuarial computations of funding requirements and funding limits for the plan years 1986 and 1987, Matthews used the following actuarial assumptions: Plan year ending 9/30/86 9/30/87 Retirement age [55] Pre-retirement interest 5% 5% Post-retirement interest 5% 5% Salary scale -0- -0- Pre-retirement turnover -0- -0- Mortality (males) 1971 IAM-1 1971 IAM-1 Mortality (females) 1971 IAM-7 1971 IAM-7 Form of benefit [1] For purposes of these calculations, *92 Matthews used the following for Pallin: Date of birth 5/8/41 Date of spouse's birth 4/2/46 Date of hire 1 10/1/79 Date of entry into the plan 10/1/84 *390 Pallin was the only participant in the plan for the years at issue. For funding purposes, Matthews considered his compensation for each of these years to be $ 200,000. The following is an annual benefit accrual schedule for the Lear plan: Annual Total benefit Total accrued accrual at accrued Sec. 415 benefit 16.22% of benefit limit if no used by Compen- compen- before further plan's Year sation sation sec. 415 service 1 actuary [1986] $ 200,000 $ 32,440 2 $ 68,440 $ 75,000 $ 32,440 For the plan years 1986 and 1987, Lear contributed $ 340,092 and zero, respectively. Matthews prepared and signed the Schedules B with respect to the plan for plan years 1986*93 and 1987. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On May 25, 1990, respondent timely mailed Lear a notice of deficiency determining a deficiency in income tax for the taxable year ending September 30, 1986. On August 20, 1990, respondent timely mailed Lear a notice of deficiency determining a deficiency in income tax for the taxable year ending September 30, 1987, and an addition to tax under section 6659A. Robert Stephan, Jr., P.C. (Stephan) Stephan was incorporated in 1980 under the laws of the State of Arizona. Stephan timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for the taxable years ending July 31, 1986, and July 31, 1987. Stephan's taxable year for Federal income tax purposes was a fiscal year ending July 31, and Stephan employed the cash method of accounting. Robert Stephan, Jr. (Robert Stephan), an attorney specializing in plaintiff's personal injury cases, was the sole shareholder and president of Stephan. On August 1, 1980, *391 Robert Stephan*94 became an employee and an officer of Stephan. Effective August 8, 1980, Stephan adopted the Robert Stephan, Jr., P.C. Defined Benefit Pension Plan and Retirement Trust (the plan). On December 21, 1981, and July 19, 1985, Stephan received favorable determination letters from respondent qualifying the plan under section 401(a). During the year at issue, the plan had two participants, Robert Stephan and his secretary, Diane Morris (Morris). The plan's enrolled actuary for the plan years 1986 and 1987 was David Goodell (Goodell) of the Wyatt Co. (Wyatt). In making the annual actuarial computations of funding requirements and funding limits for the plan years 1986 and 1987, Goodell used the following actuarial assumptions: Plan year ending 7/31/86 7/31/87 Retirement age [55] Pre-retirement interest 5% 5% Post-retirement interest 5% 5% Salary scale -0- -0- Pre-retirement turnover -0- -0- Benefit form [1] Pre-retirement mortality -0- -0- Post-retirement mortality [2] Expense load -0- -0- For purposes of these calculations, *95 Goodell used the following data for Robert Stephan: Date of birth 8/17/47 Date of spouse's birth 6/26/51 Date of hire 8/1/77 Date of entry into the plan 8/1/80 Goodell used the following data for Morris: Date of birth 3/1/54 Date of spouse's birth --- Date of hire 12/15/81 Date of entry into the plan 8/1/82 *392 For funding purposes, Goodell assumed the compensation of Robert Stephan to be zero and $ 200,000 for 1986 and 1987, respectively. For Morris, he assumed the compensation to be $ 34,000 and $ 70,000 for 1986 and 1987, respectively. The following is an annual benefit accrual schedule for the Stephan plan: Annual Total benefit Total accrued accrual at accrued Sec. 415 benefit 3.9% of benefit limit if no used by Compen- compen- before further plan's Year sation sation sec. 415 service 1 actuary [1981] $ 50,000 $ 1,950.00 $ 1,950.00 $ 30,000 $ 1,950.00 [1982] 35,150 1,370.85 3,320.85 37,500 3,320.85 [1983] 262,000 10,218.00 13,538.85 45,000 13,538.85 [1984] 370,000 14,430.00 27,968.85 52,500 27,968.85 [1985] --- --- 27,968.85 60,000 27,968.85 [1986] --- --- 27,968.85 67,500 27,968.85 [1987] 200,000 20,000.00 47,968.85 75,000 47,968.85 *96 For the plan years 1986 and 1987, Stephan contributed $ 7,999 and $ 196,293 to the plan, respectively. Goodell prepared and signed the Schedules B with respect to the plan for the plan years 1986 and 1987. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On March 29, 1990, respondent timely mailed Stephan a notice of deficiency determining a deficiency in income tax and an addition to tax under section 6659A for the taxable year ending July 31, 1987. Boren Steel Consultants, Inc. (Boren Steel) Boren Steel was incorporated in 1986 under the laws of the State of Arizona. During the years at issue, Boren Steel provided consulting services to clients in the reinforcement steel production business. Boren Steel timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for the years at issue. Petitioner employed the cash method of accounting. William R. Boren (Boren) *97 was the president of Boren Steel. Boren and his wife were the sole shareholders of Boren Steel under Arizona community property laws. *393 Effective April 22, 1986, Boren Steel adopted the Boren Steel Consultants, Inc. Defined Benefit Plan (the plan). The plan year for the plan is a fiscal year ending March 31. On July 29, 1987, Boren Steel received a favorable determination letter from respondent qualifying the plan under section 401(a). The plan's enrolled actuary for the plan years 1987 and 1988 was Matthews. In making the annual actuarial computations of funding requirements and funding limits for the plan years 1987 and 1988, Matthews used the following actuarial assumptions: Plan year ended 3/31/87 3/31/88 Retirement age [63] Pre-retirement interest 5% 5% Post-retirement interest 5% 5% Form of benefit [1] Salary scale 2% -0- Pre-retirement turnover -0- -0- Mortality (males) 1983 IAM (-2) 1951 GA Mortality (females) 1983 IAM (-8) 1951 GA (-6) For purposes of these calculations, Matthews used the following data for Boren: Date of birth 3/26/27 Date of spouse's birth assumed to be 3 years younger Date of hire 1 4/22/86 Date of entry into the plan 4/22/86 *98 The funding method used by Matthews was the individual aggregate actuarial cost method. Boren was the only participant in the plan during the years at issue, and for funding purposes, Matthews considered his compensation for plan years ended 1987, 1988, and 1989 to be $ 52,000, $ 52,000, and $ 70,000, respectively. Matthews prepared and signed the Schedules B with respect to the plan for plan years 1987 and 1988. He certified on the Schedules B that the assumptions used in the aggregate *394 were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On June 7, 1990, and April 11, 1991, respondent timely mailed Boren Steel notices of deficiency determining deficiencies in income tax for the years ending March 31, 1987, December 31, 1987, and December 31, 1988, an excise tax under section 4972, and additions to tax under sections 6651(a)(1) and 6659A. Jonathan R. Fox (Jonathan Fox) and Renee K. Fox (Renee Fox); Arizona Orthopedic Institute of Traumatic and Reconstructive Surgery,*99 P.C. (Arizona Orthopedic) Arizona Orthopedic was incorporated in 1986 under the laws of the State of Arizona. Arizona Orthopedic timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for the years at issue. Arizona Orthopedic employed a modified cash basis method of accounting. Jonathan Fox and Renee Fox (the Foxes) were married and resided in Phoenix, Arizona, at the time the petition in this case was filed. They timely filed their Form 1040, Individual Income Tax Return, for the year at issue. Jonathan Fox was a practicing orthopedic surgeon and the sole shareholder and president of Arizona Orthopedic during the years at issue. Prior to the incorporation of Arizona Orthopedic, he operated his medical practice as a sole proprietorship. Effective January 1, 1986, Jonathan Fox adopted the Jonathan R. Fox, M.D. Defined Benefit Pension Plan (the plan). The plan was subsequently adopted by the successor employer, Arizona Orthopedic. The plan year was a fiscal year ending October 31. On November 4, 1987, Arizona Orthopedic received a favorable determination letter qualifying the plan under section 401(a). The plan's enrolled actuary for the plan years ending October*100 31, 1986, and October 31, 1987, was Matthews. For the plan year ending October 31, 1986, Jonathan Fox was the only participant in the plan. For the plan year ending October 31, 1987, Jonathan and Renee Fox were plan participants. In making the annual actuarial computations of funding *395 requirements and funding limits for the plan years at issue, Matthews used the following actuarial assumptions: Plan year ending 10/31/86 10/31/87 Retirement age [55] Pre-retirement interest 5% 5% Post-retirement interest 5% 5% Salary scale 4% -0- Pre-retirement turnover -0- -0- Mortality (males) 1983 IAM-4 1983 IAM-4 Mortality (females) 1983 IAM-10 1983 IAM-10 Form of benefit [1] For purposes of these calculations, Matthews used the following data for the Foxes: Jonathan Fox Renee Fox Date of birth 2/2/53 2/20/52 Date of spouse's birth [2] Date of hire 6/1/85 5/1/86 Date of entry into the plan 11/1/85 11/1/86 For funding purposes, Matthews assumed Jonathan Fox's compensation to be *101 $ 30,000 and $ 100,000 for plan years ending 1986 and 1987, respectively. For plan year ending 1987, Matthews assumed Renee Fox's compensation to be $ 20,000. The contributions for the plan years ending October 31, 1986, and October 31, 1987, were $ 47,146 and $ 259,254, respectively. Matthews prepared and signed the Schedules B with respect to the plan for plan years 1986, 1987, and 1988. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On July 11, 1990, respondent timely mailed Arizona Orthopedic a notice of deficiency determining deficiencies in income tax and additions to tax under section 6659A for the taxable years ending April 30, 1987, and December 31, 1987. *396 On July 11, 1990, respondent timely mailed the Foxes a notice of deficiency determining a deficiency in tax and an addition to tax under section 6659A for the tax year ending December 31, 1986. (As Arizona Orthopedic was a successor to Jonathan Fox's individual medical practice, hereinafter we will refer to them jointly *102 as Fox.) Brody Enterprises, Inc. (Brody Enterprises) Brody Enterprises was originally incorporated in 1983 as Marvin D. Brody, P.C., under the laws of the State of Arizona. Marvin D. Brody (Brody), a practicing attorney specializing in Federal tax law and employee benefit plans, was the sole shareholder and president of Brody Enterprises during the years at issue. Brody Enterprises timely filed its Forms 1120, U.S. Corporation Income Tax Returns, for the years at issue. Brody Enterprises' taxable year for Federal income tax purposes was a fiscal year ending January 31, and Brody Enterprises employed the cash method of accounting. On June 13, 1983, Brody Enterprises adopted the Marvin D. Brody, P.C. Defined Benefit Pension Plan (the plan), effective February 1, 1983. The plan year was a fiscal year ending May 31. On December 8, 1986, Brody Enterprises received a favorable determination letter from respondent, qualifying the plan under section 401(a). The plan's enrolled actuary for the plan years ending May 31, 1986, and May 31, 1987, was Lawrence. In making the annual actuarial computations of funding requirements and funding limits for the plan years 1986 and 1987, Lawrence*103 used the following actuarial assumptions: Plan year ended 5/31/86 5/31/87 Retirement age [55] Pre-retirement interest 5% 5% Post-retirement interest 5% 5% Salary scale -0- -0- Benefit form [1] Turnover -0- -0- Pre-retirement mortality -0- -0- Post-retirement mortality [3] Expense load 6% 4.5% *397 The following is an annual benefit accrual schedule for the Brody plan: Annual benefit Total Total accrual at accrued Sec. 415 accrued 9.65% of benefit limit if no benefit used Compen- compen- before further by plan's Year sation sation sec. 415 service 1 actuary [1984] $ 265,000 $ 25,572.48 $ 25,572.48 $ 75,000 $ 25,572.48 [1985] 197,998 19,106.76 44,579.24 75,000 44,579.24 [1986] 200,000 19,300.00 63,979.24 75,000 63,979.24 [1987] 200,000 19,300.00 83,279.24 75,000 75,000.00 For the plan years 1986 and 1987, Brody Enterprises*104 contributed $ 170,396 and $ 114,000, respectively. Lawrence prepared and signed the Schedules B with respect to the plan for plan years 1986 and 1987. He certified on the Schedules B that the assumptions used in the aggregate were reasonably related to the experience of the plan and to reasonable expectations and represented his best estimate of anticipated experience under the plan. On October 4, 1990, respondent timely mailed Brody Enterprises a notice of deficiency determining deficiencies in income tax and additions to tax under section 6659A for taxable years ending January 31, 1986, and January 31, 1987. Law Each of petitioners' plans was a small defined benefit pension plan. A defined benefit plan provides a participant at retirement with the benefit stated in the plan. The costs of benefits payable from such plans are funded incrementally on an annual basis over the pre-retirement period. Secs. 404, 412. Contributions made to the plans, within certain limits, *398 are deductible. Sec. 404(a)(1). Earnings on the contributions are not taxed as they accumulate. Sec. 501(a). Plan assets are taxed to participants only as they are paid out as benefits. Sec. *105 402(a)(1). The amount estimated to fund a defined benefit plan is calculated by the plan's actuary and is determined based upon actuarial assumptions about a number of future events, such as rates of return on investments, the benefit commencement date, future earnings, and participant mortality, among other things. Section 404(a)(1)(A) provides that the amount deductible by a taxpayer in any year shall be determined using the actuarial assumptions and methods that meet the requirements of section 412. At issue in these cases is whether the assumptions and methods made by each plan's actuary, in determining the amount of deductible contributions for each plan for the years at issue, were reasonable in the aggregate and represented the actuary's best estimate of anticipated experience under the plans, as required by section 412(c)(3). Section 412(c)(3) is part of a statutory scheme designed to regulate pension plans, and provided as follows: (3) Actuarial assumptions must be reasonable. -- For purposes of this section, all costs, liabilities, rates of interest, and other factors under the plan shall be determined on the basis of actuarial assumptions and methods which, in the aggregate, *106 are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan. Section 6059 requires that the administrator of a pension plan to which section 412 applies must enlist the services of an enrolled actuary to file an actuarial report for the plan's first year and every third year thereafter. This actuarial report shall contain, inter alia, the actuary's funding methods and assumptions deemed necessary to fund the plan's costs and the actuary's certification that to the best of his knowledge the report is complete and accurate and that he has complied with the requirements of section 412(c). Sec. 6059(b). Section 7701(a)(35) defines an enrolled actuary as a person who is enrolled by the Joint Board for the Enrollment of Actuaries (Joint Board) established under the Employee Retirement Income Security Act of 1974 (ERISA), Pub. L. 93-406, 88 Stat. 829. *399 Sections 412(c)(3), 6059, and 7701(a)(35) were added to the Internal Revenue Code by ERISA sections 1013(a), 1033(a), and 3043, 88 Stat. 914, 947, 1003, to apply for plan years beginning after December*107 31, 1975. ERISA had a significant impact on pension plans, and one of its objectives was to place reliance upon enrolled actuaries to assist plan fiduciaries in ensuring that pension plans would be able to provide earned benefits to participants when due. ERISA was enacted, in part, because the growth and development of the private pension system in the United States had been substantial since the forties. The legislative history of ERISA states: In 1940, an estimated four million employees were covered by private pension plans; in 1950, the figure had increased to almost 10 million and in 1960 over 21 million were covered. Currently, over 30 million employees or almost one half of the private non-farm work force are covered by these plans. This phenomenal expansion of coverage has been matched by an even more startling accumulation of assets to back the benefit structure. Today, in excess of $ 150 billion in assets are held in reserve to pay benefits credited to private plan participants. [H. Rept. 93-533 (1973), 1974-3 C.B. 210, 212.] However, regulation of the private pension system's scope and operation had been minimal. Although there have *108 been significant legislative changes since the present basic framework of the tax laws relating to pensions was first adopted -- principally in allowing self-employed people to establish retirement plans for themselves and their employees and in requiring the disclosure of information regarding welfare and pension plans -- it has been more than 30 years since these basic pension provisions were first adopted. It is time for new legislation to conform the pension provisions to the present day situation and to provide remedial action for the various problems that have arisen in the retirement plan area during the past three decades. [H. Rept. 93-807 (1974), 1974-3 C.B. (Supp.) 236, 249.] The enactment of ERISA was a legislative attempt to assure equitable and fair administration of pension plans and to remedy problems that had arisen which prevented many of those plans from achieving their full potential as a source for retirement income. One of the most important matters of public policy facing the nation today is how to assure that individuals who have spent their careers in useful and socially productive work will have adequate incomes to meet their needs*109 when they retire. This legislation is concerned with improving *400 the fairness and effectiveness of qualified retirement plans in their vital role of providing retirement income. In broad outline, the objective is to increase the number of individuals participating in employer-financed plans; to make sure to the greatest extent possible that those who do participate in such plans actually receive benefits and do not lose their benefits as a result of unduly restrictive forfeiture provisions or failure of the pension plan to accumulate and retain sufficient funds to meet its obligations; and to make the tax laws relating to qualified retirement plans fairer by providing greater equality of treatment under such plans for the different taxpayer groups concerned. [H. Rept. 93-807 (1974), 1974-3 C.B. (Supp.) 243.] The enactment of ERISA mandated a cooperative effort whereby the Department of Labor (Labor) and the Department of the Treasury (Treasury) would jointly oversee the participation in and vesting and funding of pension plans and the reporting and disclosure requirements for pension plans, fiduciary standards, and plan termination insurance. *110 In enacting ERISA, Congress was well aware that actuaries would play a major role in ensuring that retirement plans would be sufficiently able to provide retirement income when due. Throughout the reports of the Senate Finance Committee and the House Ways and Means Committee, Congress recognized the importance of the assumptions and methods chosen by actuaries in determining plan funding amounts. Congress also explicitly noted that such determinations by actuaries would involve making predictions and would be a matter of judgment involving many factors and producing a range of results. In estimating pension costs, actuaries must make assumptions ("actuarial assumptions") about a number of future events, such as the rate of return on investments ("interest"), employees' future earnings, and employee mortality and turnover. Actuaries also must choose from a number of methods to calculate future plan liabilities. The amounts required to fund any given pension plan can vary significantly according to the mix of these actuarial assumptions and methods. As a result, the assumptions and methods used by actuaries are basic to the application of minimum funding standards for defined*111 benefit pension plans. [S. Rept. 93-383 (1973), 1974-3 C.B. (Supp.) 80, 147.] See also H. Rept. 93-807 (1974), 1974-3 C.B. (Supp.) 262. Congress realized that making predictions and forecasts to determine plan funding costs was the professional duty and function of actuaries. *401 [The House Ways and Means] committee recognizes that the amount required to fund a pension plan is in large part determined by actuaries' estimates of future plan costs, which in turn are based on the actuarial methods and assumptions used for each plan. Consequently, the determination of the amount of contributions that must be made to a plan to adequately fund the plan benefits is significantly affected by the professional decisions of the plan's actuary. * * * [H. Rept. 93-807 (1974), 1974-3 C.B. (Supp.) 309.] Accordingly, Congress decided that accepting a range of reasonableness for funding amounts for retirement plans would be more desirable and more effective than imposing an inflexible legislative standard on actuaries and, therefore, rejected imposing mandatory funding assumptions and methods. Congress*112 acknowledged that actuaries are not charged with the responsibility of determining a "correct" set of assumptions, but with the responsibility of determining assumptions that fall within a range of reasonableness. Conceivably an attempt might be made to secure uniform application of the minimum funding standards by authorizing the Secretary of the Treasury or some other authority to establish the specific actuarial assumptions and methods that could be used by pension plans. This would involve, for example, setting a specific rate of interest that could be used by certain pension plans or by specifying certain turnover rates for specified types of firms. However, the committee does not believe that this would be an appropriate procedure, since the proper actuarial assumptions may differ substantially between industries, among firms, geographically, and over time. Further, in estimating plan costs each actuarial assumption may be reasonable over a significant range and it would appear that the proper test would be whether all actuarial assumptions used together are reasonable. These considerations strongly indicate that any attempt to specify actuarial assumptions and funding *113 methods for pension plans would in effect place these plans in a straitjacket so far as estimating costs is concerned, and would be likely to result in cost estimates that are not reasonable. [Id., 1974-3 C.B. (Supp.) 262.] By deferring to the professional judgment of actuaries in the area of plan funding, Congress expressed its intent that actuaries be afforded a range of latitude in establishing a mix of reasonable assumptions, and that only if such assumptions are "substantially unreasonable" should they be challenged and changed retroactively. Since the actuarial assumptions used must be reasonable in the aggregate, it is anticipated that, on audit, the Internal Revenue Service will (as presently) require a change of assumptions where they do not meet this standard. However, unless the assumptions used are substantially *402 unreasonable, it is contemplated that generally the Service will not require a change of assumptions to be made effective for years prior to the year in which the audit is made. [Id., 1974-3 C.B. (Supp.) 330.] The language of the conference report adopted the rules relating to actuarial *114 assumptions of the House Ways and Means bill, as amended by the Senate amendment, and the result was as follows: The conference substitute combines the rules relating to actuarial assumptions of the House bill and of the Senate amendment and requires that, for purposes of the minimum funding standard, all plan costs, liabilities, rates of interest, and other factors under the plan are to be determined on the basis of actuarial assumptions and methods which, in the aggregate, are reasonable. Actuarial assumptions are to take into account the experience of the plan and reasonable expectations. These assumptions are expected to take into consideration past experience as well as other relevant factors. In addition, under the conference substitute, the actuarial assumptions in combination are to offer the actuary's best estimate of anticipated experience under the plan. * * * [H. Conf. Rept. 93-1280 (1974), 1974-3 C.B. 415, 445-446.] The conference report expresses the intent of Congress to place with enrolled actuaries the responsibility for arriving at reasonable assumptions regarding plan funding costs. These assumptions are to be based, inter alia, *115 on a plan's objective experience and on the subjective professional judgment of an enrolled actuary regarding potential future plan experience. The actuary's assumptions should not be challenged and changed retroactively unless substantially unreasonable. We note that the requirement that assumptions used to determine plan funding costs be reasonable predates ERISA. The regulations accompanying section 404 state: In no event shall costs for the purpose of section 404(a)(1) exceed costs based on assumptions and methods which are reasonable in view of the provisions and coverage of the plan, the funding medium, reasonable expectations as to the effects of mortality and interest, reasonable and adequate regard for other factors such as withdrawal and deferred retirement (whether or not discounted) which can be expected to reduce costs materially, reasonable expenses of operation, and all other relevant conditions and circumstances. * * * [Sec. 1.404(a)-3(b), Income Tax Regs.] Also, Rev. Rul. 63-11, 1963-1 C.B. 94, states the Service's position with respect to various methods of valuing assets *403 and the proper interest rate to be *116 used in valuing liabilities for computing costs in determining the limitations on deductions for employer contributions to pension plans under section 404. Respondent stated in the revenue ruling: However, it should be emphasized that, for the purpose of determining deductible limits, it is not essential that each individual assumption used be reasonable. It is merely required that the combination of all assumptions produces reasonable results. * * * [Rev. Rul. 63-11, 1963-1 C.B. 94, 95.] Although the legislative history of ERISA evidences congressional intent to rely exclusively on actuarial assumptions regarding plan funding costs -- such assumptions will be accepted if reasonable in the aggregate -- Congress did not permit actuaries unfettered liberty. To do so might invite the unprofessional selling of expertise to achieve tax-desired results rather than prudent plan funding. However, instead of imposing uniform and specific assumptions for pension plans, Congress decided to impose uniform standards for the qualification of actuaries. Congress recognized that there was no existing government regulation of the actuarial profession *117 as there was for other professions such as the medical, legal, and accounting professions. The Committee [on Labor and Public Welfare] is unaware of any significant licensing procedures for actuaries at either the state [or] federal level and this may, to some extent, explain inadequate funding procedures which have been found to exist. * * * [S. Rept. 93-127 (1973), 1974-3 C.B. (Supp.) 17.] Accordingly, Congress directed the Secretaries of Labor and of the Treasury to establish a Joint Board which would create and administer standards for enrollment of actuaries; enroll actuaries to practice before Labor and the Service; administer standards for disenrollment of actuaries; and write the appropriate regulations. See H. Conf. Rept. 93-1280 (1974), 1974-3 C.B. 523. By creating a system of actuarial certification, Congress could be satisfied that actuaries who performed services for qualified pension plans would meet an appropriate level of competence in choosing their funding methods and assumptions. The Joint Board is composed of three members appointed by the Secretary of the Treasury and two appointed by the *404 *118 Secretary of Labor. 20 C.F.R. sec. 900.3 (1991). ERISA section 3042(a), 88 Stat. 1002, provides that individuals performing actuarial services and applying for enrollment before the Joint Board on or after January 1, 1976, must satisfy the following standards and qualifications: (1) education and training in actuarial mathematics and methodology, as evidenced by -- (A) a degree in actuarial mathematics or its equivalent from an5 accredited college or university, (B) successful completion of an examination in actuarial mathematics and methodology to be given by the Joint Board, or (C) successful completion of other actuarial examinations deemed adequate by the Joint Board, and (2) an appropriate period of responsible actuarial experience. * * * The Federal regulations governing the performance of actuarial services under ERISA prescribe rules for renewal of enrollment. Those regulations provide that as a condition for renewal, an individual enrolled to perform actuarial services under ERISA must periodically complete a minimum number of hours of continuing education courses. The content of such courses must be "designed to enhance the knowledge of an enrolled actuary with respect*119 to matters directly related to the performance of pension actuarial services under ERISA or the Internal Revenue Code." 20 C.F.R. sec. 901.11(f) (1991). Examples of the subject matter of such courses are: Actuarial cost methods under ERISA, requirements with respect to the valuation of plan assets, requirements for qualification of pension plans, excise taxes related to the funding of qualified pension plans, economics, computer programs, pension accounting, investment and finance, and business and general tax law. Id. ERISA section 3042(b), 88 Stat. 1003, provides that the Joint Board may, after notice and an opportunity for a hearing, suspend or terminate the enrollment of an individual who fails to discharge his duties or does not satisfy the requirements for enrollment. Only persons who have satisfied the standards and qualifications for becoming an enrolled actuary may determine plan funding methods and assumptions under ERISA. ERISA requires that the administrator of a defined benefit plan retain on behalf of all plan participants an enrolled actuary to prepare an actuarial statement to be filed annually with *405 the Secretary of Labor. ERISA sec. 103(a)(4)(A), *120 88 Stat. 842 (current version at 29 U.S.C. sec. 1023(a)(4)(A) (1988)). This actuarial statement is to contain, among other things, information pertaining to the plan year such as the normal costs, accrued liabilities, actuarial assumptions and methods used to determine costs, and the value of assets accumulated in the plan. The enrolled actuary also is required to make an actuarial valuation of the plan for every third plan year, or more frequently if deemed necessary. ERISA sec. 103(d), 88 Stat. 845, 846 (current version at 29 U.S.C. sec. 1023(d) (1988)). Section 6059(b), as added by ERISA section 1033, 88 Stat. 947, requires each defined benefit plan to which section 412 applies to file, for the first plan year and for each third plan year thereafter (or more frequently if the Secretary of the Treasury determines), a report prepared and signed by an enrolled actuary. Those reports shall contain: (1) a description of the funding method and actuarial assumptions used to determine costs under the plan, (2) a certification of the contribution necessary to reduce the accumulated funding deficiency (as defined*121 in section 412(a)) to zero, (3) a statement -- (A) that to the best of his knowledge the report is complete and accurate, and (B) the requirements of section 412(c) (relating to reasonable actuarial assumptions) have been complied with, (4) such other information as may be necessary to fully and fairly disclose the actuarial position of the plan, and (5) such other information regarding the plan as the Secretary may by regulations require. In summary, the statutory scheme for satisfying the provisions of section 412(c)(3) requires that an administrator of a pension plan engage the services of an enrolled actuary who determines the methods and assumptions necessary to fund costs under the plan and certifies that to the best of his knowledge such methods and assumptions are reasonable in the aggregate and represent his best estimate of anticipated experience under the plan. Upon audit by respondent, these actuarial assumptions may be determined to be unreasonable in the aggregate, and petitioners have the burden of proving that the assumptions are reasonable in the aggregate. However, these actuarial assumptions will not be changed retroactively *406 unless they are found*122 to be substantially unreasonable. Accordingly, we shall now examine the various challenged assumptions. Certifying Actuaries Steven Matthews, B.S., M.S., M.A.A.A., 3 A.S.A., 4*123 E.A., 5 was the certifying actuary for Davis, Old Frontier, Lear, Boren Steel, and Fox. Matthews is an actuary for the actuarial firm of Matthews, Malone & Associates. He began performing actuarial services for both small and large pension plans in 1974 as an actuarial assistant. In 1979, he became an enrolled actuary, and the following year he formed his own firm. Matthews has performed services for more than 500 small plans and 50-75 large plans. He is a member of the American Society of Pension Actuaries. John W. Lawrence, Jr., B.S., M.S., F.S.A., 6 E.A., was the certifying actuary for Citrus Valley and Brody Enterprises. Lawrence has been working as an actuary for pension plans since the early sixties when he began designing pension plans at American United Life Insurance Co. (American United Life). After 15 years at American United Life, he joined Howard E. Nyhard Co. as vice president in charge of the firm's actuarial activities. Lawrence later worked for the Actuarial Administrative Services prior*124 to forming his own firm. He has been involved in designing and implementing both large and small plans and has performed services for more than 1,000 small plans. David Goodell, B.S., A.S.A., E.A., was the certifying actuary for Stephan. Goodell is the manager of the Phoenix office *407 of Wyatt and previously was employed by Wyatt's Dallas office. He began performing services for pension plans in 1976, when he started working with large plans. In 1986, Goodell certified approximately 250 plans, which were mostly small plans. Experts The following experts, whose reports and testimony will be discussed later in this opinion, appeared on behalf of petitioners: Kenneth D. Klingler (Klingler), B.S., F.S.A., M.A.A.A., E.A., is a consulting actuary with Wyatt, a position he has held since 1982. Wyatt is one of the world's largest actuarial consulting*125 firms, with annual revenues in excess of $ 400 million. Klingler served as an actuary for more than 100 small (fewer than 10 participants) defined benefit pension plans. He also served as actuary for several large (more than 500 participants) defined benefit plans. Klingler testified as to the reasonableness of each of the actuarial assumptions. Arthur W. Anderson (Anderson), B.S., A.S.A., M.A.A.A., E.A., has been a pension actuary for nearly 30 years. He is a fellow of the Conference of Actuaries in Public Practice and served on that organization's board between 1987 and 1990. Anderson worked at many of the country's largest actuarial consulting firms, including William M. Mercer, Inc., Johnson & Higgins, and Wyatt. He is the author of the standard textbook on pension mathematics, Pension Mathematics for Actuaries, and has published several articles in scholarly journals. Anderson has made numerous professional appearances and is a frequent lecturer and panelist at continuing education programs. He testified as an expert only with respect to the use of the unit credit funding method in the Davis, Lear, Stephan, Fox, and Brody Enterprises plans. The following experts, whose*126 reports and testimony will be discussed later in this opinion, appeared on behalf of respondent: J. Ruben Rigel (Rigel), B.A., J.D., F.S.A., F.C.A., 7 M.A.A.A., E.A., has been a consulting pension actuary for the *408 past 17 years and has worked in the actuarial field for nearly 30 years. He is a senior vice president with W.F. Corroon, formerly C&B Consulting Group. Rigel's firm generally provides consulting services to midsized (100 to 500 participants) and large (more than 500 participants) pension plans. Rigel has served only occasionally as consultant to small (which he defines as fewer than 100 participants) plans. Rigel testified with respect to each of the actuarial assumptions and to the use of the unit credit funding method. Roger Ibbotson (Ibbotson), *127 B.S., M.S., M.B.A., Ph.D., is president and chief executive officer of Ibbotson & Associates, Inc., which sells financial software and data and provides consulting services to investment management firms. Ibbotson has been a member of the faculty at Yale University since 1984. He has published several books and articles in scholarly journals, in addition to the annual publication of the Stocks, Bonds, Bills, and Inflation Yearbook. He is qualified as an expert only with respect to the interest rate assumption. William S. Borden (Borden), B.A., Ph.D., is senior program analyst at Mathematica Policy Research (Mathematica), a position he has held since 1979. Mathematica conducts statistical evaluations of the effectiveness of Federal and State programs. In 1984, Borden was retained by Labor to create a research database of Form 5500 data from the original filings. Since that date, nearly all of his professional time has been devoted to evaluating Form 5500 data. Borden was qualified by the Court as an expert in the analysis of Form 5500 data with respect to petitioners' interest rate and retirement age assumptions. Borden submitted expert testimony evaluating petitioners' interest*128 rate and retirement age assumptions on the basis of analysis of Form 5500 data obtained from Labor. James E. Holland, Jr. (Holland), B.A., A.S.A., E.A., provided an expert report on behalf of respondent but did not testify at trial. Holland is chief of the Pension Actuarial Branch of the Service and has been employed as an actuary by the Service since 1977. He has lectured to numerous professional meetings and is an adjunct professor at the George Washington University National Law Center, where he teaches a course in pensions. *409 Interest RateBackground The three certifying actuaries for petitioners' plans established interest rate assumptions of 5 percent for both the pre- and post-retirement periods and used that rate to calculate the contributions for the years at issue. Respondent challenged those 5-percent assumptions as unreasonable and determined that an 8-percent pre- and post-retirement interest rate assumption should be used for petitioners' plans for the years at issue. As with all the actuarial assumptions, there is no single formula or set of criteria used by actuaries to establish interest rate assumptions. Actuaries consider the facts and circumstances*129 of each plan and use their experience and subjective judgment, based on actuarial criteria, in establishing this and all of the actuarial assumptions. The phrase "interest rate" assumption is more accurately described as an "investment rate" assumption as it represents the expected aggregate earnings, gains, and losses on all investment vehicles held in trust for the plan during its existence. As a matter of convention, however, this aggregate return concept usually is referred to in the actuarial and pension community as an "interest rate" assumption, and we will refer to it here as such. In general, a defined benefit pension plan is established and maintained by an employer (plan sponsor) who systematically funds a pension plan trust from which a trustee (plan administrator) will make payments of definitely determinable benefits to participating employees (participants) over a period of years, usually for life. The definitely determinable benefits usually take the form of an annuity commencing at retirement and payable over the life of the participant or the joint lives of the participant and his or her spouse. For each participant, these definitely determinable benefits are*130 measured by, and based on, factors such as years of service with the plan sponsor, compensation level, and other factors, all of which are incorporated into a benefit formula. The benefit formula determines what the plan's ultimate benefit obligation will be. However, since many, if not all, benefit formula factors are unknown at the plan's inception, *410 and some are unknown until benefit payout ceases under the plan, the amount of the benefit obligation is indeterminate and will be so until it is satisfied. Thus, the plan's ultimate benefit obligation is an estimate. The pension trust from which benefits will be paid accumulates assets from two sources: contributions from the plan sponsor during the pre-retirement period and earnings on the trust assets during both pre- and post-retirement periods. The interest rate assumption serves to predict the rate at which the trust will self-generate growth as opposed to increasing due to the sponsor's annual contributions. As noted above, earnings on the trust assets will accumulate tax free. Secs. 401(a), 501(a). The interest rate assumption is used by the actuary to predict the annual rate of return on assets in the trust*131 over the life of the plan. This assumption is then used along with all of the other actuarial assumptions to calculate the required contributions. The actuarial assumptions do not affect the ultimate pension benefits paid under the plan or actual aggregate cost of those benefits. Rather, the assumptions affect the pattern of asset buildup in the pension trust because they affect the timing and amount of the sponsor's contributions. Actuarial assumptions can be either conservative or optimistic. Conservative assumptions about future events affecting funding, such as lower estimated fund earnings and earlier retirement, tend to create higher required contributions. Optimistic assumptions tend to create lower required contributions. Sponsors of qualified defined benefit pension plans must make timely contributions sufficient to assure that the plans' estimated benefit obligations are satisfied ultimately in accordance with the plans. Sec. 412. The size of the annual contribution will vary under a defined benefit plan depending on the actuarial cost method chosen and the actuarial assumptions made, but is always actuarially calculated with the objective of having the pension trust*132 attain a funding level sufficient to satisfy the pension obligations as they come due. The enrolled actuary also attempts to choose an actuarial method and assumptions that will provide for a smooth funding pattern over the life of a plan. The actuary's primary duty to plan participants under the statutory scheme established by Congress is to establish a realistic contribution pattern over the long term so that the *411 plan sponsor will provide adequate funding for the ultimate pension obligation. Thus, in selecting actuarial assumptions, prudent actuaries maintain a long-term conservative view that will ensure benefit security for plan participants. All of the actuaries who testified at trial confirmed this basic characteristic of actuarial science. Once a plan has established "credible experience", selecting actuarial assumptions becomes a less worrisome task in this regard; the actuary can take comfort that this actual experience has established a reliable trend, and such experience is then useful in predicting future plan experience. Actuaries generally agree that a plan should sustain at least 3 years, and as much as 5 years, of plan experience before such experience*133 can be considered "credible experience" for purposes of significantly affecting the establishment of actuarial assumptions for the plan. See Rev. Rul. 63-11, 1963-1 C.B. 94, 96 (reasonableness of the originally established actuarial assumptions should be reassessed after a plan has been in effect for a period of about 5 years); cf. Jerome Mirza & Associates, Ltd. v. United States,692 F. Supp. 918 (C.D. Ill. 1988), affd. 882 F.2d 229 (7th Cir. 1989) (reasonableness of actuarial assumptions reviewed where 73 percent of pension benefit obligation was funded in first year of plan). Conversely, where the plan is new or lacks such credible experience, the actuary must be cautious in selecting actuarial assumptions that reflect only recent economic or plan experience. Also, general or even specific participant statements of intended investment strategy, or even an expressed intention to obtain a specific investment, does not provide a reliable basis on which an actuary can base the choice of interest rate assumption. Such intentions often fail to be carried out, and the choice of investment*134 vehicles as well as economic conditions can vary widely in the short run. Experience under the plan should be sustained before it becomes a primary basis for selecting assumptions. This fact is recognized by the Interim Actuarial Standards Board of the American Academy of Actuaries, which recommends as follows: The actuarial assumptions in combination should reflect the actuary's best judgment of future events affecting the related pension obligations. The actuary should consider the actual experience of the covered group but should emphasize expected long-term future trends rather than give undue weight to recent past experience. * * * [Actuarial Standard of Practice No. *412 4, Recommendations for Measuring Pension Obligations, sec. 7.1 (Interim Actuarial Standards Board 1990 reprint).] In addition, selecting actuarial assumptions that are too optimistic in a new or relatively young plan adversely affects the ability of the plan to "self-correct" without significantly increasing the required contributions. A plan will actuarially self-correct in a mathematical sense through the annual actuarial contribution calculation: the contribution in a subsequent plan year will*135 be higher or lower than originally anticipated for that year to correct for prior years' actual experience under the plan. When the assumptions are too optimistic, future contributions will have to be higher than originally planned. This disrupts not only the desirable smooth funding pattern, but burdens the plan sponsor to provide higher than anticipated contributions. If the assumptions are too conservative, then the plan sponsor will decrease contributions accordingly -- an easier task than finding resources that were not budgeted. Use of overly optimistic assumptions therefore increases the chances that the sponsor may ultimately fail to fully fund the plan. It is common knowledge that many pension funds have fallen prey to just such a fate with the Pension Benefit Guarantee Corp. (PBGC), a Federal agency which insures the pension benefit obligations of certain ERISA-qualified pension plans, having to cover the resulting losses. 8 *136 Moreover, if the assumptions remain consistently too optimistic, even for a relatively brief number of years, asset accumulation suffers further because investment income fails to accrue on contributions that, in hindsight, should have been made earlier. This loss of compounded earnings can be a significant factor especially in tax-exempt trusts. In addition, the impact of and the risk associated with failing to earn the anticipated rate of return is magnified in small plans where actuarial losses cannot be spread among many participants. The Interim Actuarial Standards Board of the American Academy of Actuaries recognizes this fact in guiding actuaries in establishing assumptions for small plans: *413 In a plan where much of the obligation is associated with a small number of participants, special attention should be paid to potential fluctuations and the aggregate effect of the assumptions. * * * [Actuarial Standard of Practice No. 4, Recommendations for Measuring Pension Obligations, sec. 7.3 (Interim Actuarial Standards Board 1990 reprint).] If actual experience for an assumption, or assumptions, varies significantly from the predicted results so that a consistent*137 pattern of gains or losses emerges, the enrolled actuary will adjust the actuarial assumptions accordingly. 9 Also, any actuarial gains are amortized over time with a corresponding reduction in contributions. Sec. 412(b)(3)(B)(ii). Two actuarial experts testified at trial. Each had his own experiences from which to draw, but based on commonalities in their testimony, there are certain factors which all actuaries apparently consider in establishing an interest rate assumption: (1) Long-term historical economic trends and investment rates of return; (2) the economic components inherent in interest rates; (3) the current rates on long-term investments; and (4) actuarial and plan-specific factors for which benchmark rates or ranges of rates are adjusted. Petitioners' Expert Klingler testified for petitioners and concluded that*138 5-per-cent pre- and post-retirement interest rate assumptions were within the range of reasonableness. His analysis was divided into three sections: (1) Definition of a range of reasonable long-term rates of return on various investments; (2) adjustment of these rates downward for certain pre- and post-retirement contingencies unique to small plans in general and to petitioners' plans in specific; and (3) comparison of the adjusted ranges with his own personal experience as an enrolled actuary, the general consensus in the actuarial community, and available regulatory and legal guidance on interest rate assumptions. Long-Term Rates of Return To establish a range of reasonable long-term rates of return, Klingler first discussed interest rate component theory, which seeks to explain investment returns as a combination *414 of three components: (1) The risk-free real interest rate (e.g., the yield on long-term Treasury bonds minus inflation); (2) an inflation factor; and (3) a risk premium for lower grade or illiquid investments. Based on a study conducted by the American Society of Actuaries, Klingler found the 25- and 62-year real rates of return on Treasury bonds to be*139 2.43 percent and 1.88 percent, respectively, and the 25- and 62-year rates of inflation to be 5.44 percent and 3.1 percent, respectively. Combining these figures, he concluded that a reasonable range of riskless interest rates was between 4.98 percent and 7.87 percent. Klingler opined that the unadjusted yield of a 30-year Treasury bond is an inappropriate benchmark for a small defined pension plan's interest rate assumption. According to Klingler, the liquidity needs of a small plan generally require that 30-year bonds purchased by a plan not be held to maturity. If interest rates increase after a bond is acquired, the bond's market value declines. A forced disposition to meet pension obligations means that the plan suffers a commensurate capital loss. To illustrate, Klingler estimated that a 1-percentage point rise in bond yields from 8 percent to 9 percent would cause a 17.33-percent loss in market value for an 8-percent bond. Klingler thus concluded that an appropriate interest rate assumption for a small defined plan should be somewhat more conservative than current long-term bond yields. Klingler also noted that the concept of "reinvestment risk", the risk that a plan's*140 investment earnings will be reinvested at yields lower than those current, cuts against the use of the current 30-year Treasury bond yield as an effective interest rate assumption. For example, Klingler stated that if a plan with a 30-year bond yielding 7.8 percent is able to reinvest interest payments at 7.8 percent for 10 years, but for the next 20 years can only reinvest in instruments yielding 6 percent, the ultimate compounded annual return achieved by the plan is only 6.93 percent. This reinvestment risk is exacerbated by the possibility that future plan contributions will be invested in Treasury bonds with yields lower than those current, a notion Klingler referred to as the "future investment options risk". The President's Council of Economic Advisors (CEA) in 1985, 1986, and 1987 predicted that yields on 10-year Treasury *415 bonds would fall to between 4.5 percent and 5.5 percent within 5 years. Klingler used the CEA predictions to calculate a reinvestment risk of roughly 1.7 percent and a future investment options risk of between 0.8 percent and 1.2 percent, depending on how much of the pension benefit obligation still remains to be funded. In 1985, 1986, and*141 1987, 10-year Treasury bonds yielded 10.8 percent, 7.7 percent, and 8.0 percent, respectively. Calculating reinvestment risk and future investment options, Klingler determined a range of reasonable interest rate assumptions between 5.1 percent and 6.4 percent. Adjustments for Plan Size Klingler then adjusted his reasonable range downward to account for contingencies unique to small plans like petitioners'. First, he concluded that use of a risk premium is inappropriate in calculating a small plan's interest rate assumption, given that such a plan is unable to attain the level of diversification of a larger plan with greater resources. Second, he noted that small plans, unlike larger plans, typically do not employ professional investment advisers. Third, transaction costs as a percentage of total investments are higher for a small plan as compared to a large plan. These factors led Klingler to conclude that a small plan's sponsor might seek a "pooled investment source", normally a bank trust department. A survey conducted by Klingler of the three largest bank trust departments in Arizona showed that fees for managing small funds ($ 500,000 or less) ran about 0.5 percent *142 higher than the fees for managing larger funds ($ 10 million or more), meaning that plans such as petitioners' would have a lower return than a large plan receiving the same advice. Klingler added that, because petitioners' plans have only one or two participants and thus a fixed funding period, sufficient funding must occur by the time the participant retires. Small plans such as petitioners' do not have the cushion larger plans enjoy -- the ability to spread any experience and actuarial losses among many participants. Klingler therefore recommended an additional measure of conservatism, a set-aside of 0.3 percent, to account for this contingency. Adjusting his reasonable range for investment fees and the fixed funding period factor, Klingler concluded that *416 the range of reasonable interest rate assumptions for any of petitioners' plans ran between 4.3 percent and 5.6 percent for a new plan and 5.1 percent and 6.8 percent for a mature plan. Pre-retirement Adjustments Klingler also adjusted his range of reasonable assumed interest rates downward on the basis of certain pre-retirement contingencies in petitioners' plans. Klingler noted that the annual contributions*143 for a given year could be made as much as 8-1/2 months after the end of the plan year and be deemed to have been made on the last day of the plan year. Sec. 412(c)(10)(A); sec. 11.412(c)-12(b)(1), Temporary Income Tax Regs., 41 Fed. Reg. 46597 (Oct. 21, 1976). Thus, contributed funds may not earn interest for as long a period as possible, warranting a more conservative interest rate assumption for the plans' funds overall. In Klingler's opinion, any assumed interest rate should take into account the effect of contribution timing. He recommended a downward adjustment of between 0.4 percent and 1.07 percent, depending on plan maturity and the unadjusted assumed interest rate. Klingler also noted that many of the plans use a 5-percent interest rate for the purposes of actuarial equivalence in the calculation of a pre-retirement lump-sum benefit pursuant to section 415(b)(2)(E)(i), but make no assumptions for preretirement severance of service (voluntary or involuntary). He argued that implicit turnover and mortality assumptions must be made by the certifying actuaries to ensure that the full benefit is available in the event of a pre-retirement contingency*144 which requires payment of a lump sum. To illustrate, Klingler assumed an individual plan with the following characteristics: (1) An 8-percent interest rate assumption; (2) a lump sum of $ 500,000 available at normal retirement date; (3) 15 years to normal retirement date; (4) a 25-percent chance of severance of service within 5 years; (5) a 25-percent chance of severance of service within 10 years; (6) a 50-percent chance that the plan will continue to normal retirement; and (7) a 5-percent discount rate for the purposes of actuarial equivalence. Klingler contended that it was reasonable for such a plan to have adjusted downward its interest rate assumption by 0.8 percent to take account of the fact that, *417 were the plan to terminate prior to normal retirement, a lump sum based on the 5-percent actuarially equivalent rate would have to be paid to a participant or a participant's survivor(s). For instance, if a participant in Klingler's hypothetical plan were to die with 15 years of service remaining, his or her survivors would be due a death benefit of $ 240,509, based on the actuarially equivalent rate of 5 percent specified in the plan, but, at the assumed 8-percent*145 interest rate, the present value of the lump-sum benefit would be only $ 157,621. For petitioners' plans, Klingler posited that a 0.2-percent to 0.4-percent downward adjustment in interest rate assumptions would be an actuarially reasonable manner in which to account for the possibility of preretirement plan termination, depending on plan maturity and the unadjusted interest rate assumption. If the assumed interest rate and the actuarially equivalent discount rate were the same, no downward adjustment would be necessary. Post-retirement Adjustments Klingler opined that certain downward adjustments to post-retirement interest assumptions also would be reasonable. First, he stated that if no explicit expense load assumption were made to cover trust and investment fees, some adjustment would be warranted to fund these costs. In Klingler's opinion, such an implicit load would require a 0.2-percent to 0.5-percent downward adjustment in assumed interest rate. In addition, because several of petitioners' plans provided a lump-sum payment option (as opposed to an annuity) at retirement based on an actuarially equivalent 5-percent post-retirement discount rate, the assumed interest*146 rate should be adjusted to ensure that funding is available to make this lump-sum payment. For instance, to provide a $ 75,000 annual pension beginning at age 55, funds on hand would have to be $ 959,055 assuming 6-percent interest post-retirement, but would have to be $ 1,060,669 assuming 5-percent interest post-retirement. Klingler concluded that it would be reasonable for the actuary for a plan with a lump-sum cashout provision to adjust downward the interest rate assumption to ensure that necessary funds would be available if the participant elected to avail himself of that option. *418 Klingler thus arrived at a range of reasonable pre-retirement interest rate assumptions between 3.8 percent and 6.4 percent and a range of reasonable post-retirement interest rate assumptions between 3.8 percent and 6.6 percent. A 5-percent assumption is within both of these ranges. Comparison to Actuarial Experience Klingler next compared petitioners' 5-percent interest rate assumptions to his own experience as a small plan actuary, as well as to the collective experience of the actuarial community. Klingler first found that the actual rates of return of 609 separate small (10 or*147 fewer participants) plans prepared by Wyatt's Phoenix office (where he is employed as consulting actuary) averaged 4.98 percent. The average annual rate of return calculated on the basis of each of the separate 2,449 plan years represented in his sample of 609 plans was 5.6095 percent. Using this data as representative of his own personal experience, Klingler concluded that his proposed range of interest rate assumptions, and in particular 5 percent, was reasonable. Moreover, Klingler found that 5 percent conformed with the judgment of his peers in the actuarial community. He first drew on two separate studies of Form 5500 data -- the first conducted by the national actuarial firm of Wolper Ross & Co. (Wolper Ross) and the second by Wyatt, Klingler's own firm. The Wolper Ross study found that 70 percent of plans with 100 or fewer participants used an interest rate assumption of 5 percent to 6 percent. The Wyatt study found that plans with fewer than five participants earned a median rate of return of 5.0 percent, while plans with more than 25 participants earned median rates of return in excess of 8 percent. Klingler concluded on the basis of this data that not only did many*148 members of the actuarial community consider 5 percent a reasonable interest rate assumption, but empirical evidence of actual rates of return shows that small plans earn less than large plans. To determine the standards of the actuarial community, Klingler also drew on evidence provided by the Federal Government's Civil Service Retirement and Disability Fund (the Civil Service plan), which covers respondent's employees. *419 A study conducted by Wolper Ross of the Civil Service plan found: (1) That it used interest rate assumptions between 6.0 percent and 7.0 percent for the years 1979 to 1988; (2) that the assumptions used were consistently 250 to 500 basis points less than actual rates of return; and (3) that assumptions were adjusted not more often than once every 4 years. To buttress his conclusion that conventional actuarial wisdom found 5 percent a reasonable interest rate assumption in 1986 and 1987, Klingler looked finally to statistics provided by the PBGC. The PBGC surveys insurance company deferred annuity premiums each month, and, based on its findings, publishes a set of recommended interest rate assumptions for those plans it insures. Klingler found that during*149 1986 and 1987 these PBGC-recommended rates ranged between 5.7 percent and 7.75 percent, depending on the length of the funding period. As these recommended rates apply only to large PBGC-insured plans, Klingler stated that they should be adjusted downward for small plans such as petitioners', bringing a 5-percent interest rate assumption within the range of reasonableness. Regulatory and Legal Guidance Klingler concluded his discussion of interest rates by stating that a certifying actuary should take any pronouncements by regulatory and legal authorities into account when making assumptions. He noted that no governmental agency or court had issued any restrictions on the interest rate assumptions. He did, however, find certain rulings and other guidance issued by the Service itself which, when considered in the context in which these plans' actuaries were making their assumptions, would indicate that 5 percent was generally considered to be reasonable. Klingler cited various revenue rulings and technical advice memoranda (TAM's), as well as a 1986 speech made by Ira Cohen (Cohen), thendirector of the Actuarial and Technical Division of the Service. Cohen told a large gathering*150 of enrolled actuaries that a 4-percent corridor on either side of the prevailing long-term bond yield defined the range of reasonable interest rate assumptions. Klingler noted that in 1986, long-term bonds were yielding an average of 7.8 percent, which, using Cohen's method, would indicate an interest rate assumption as low as *420 3.8 percent to be reasonable. Klingler also relied on section 415(b)(2)(E), which establishes 5 percent as the lower limit for interest rate assumptions in connection with lump-sum cashouts under section 415 as further evidence that a 5-percent interest rate assumption was reasonable. The only judicial guidance found by Klingler was Jerome Mirza & Associates, Ltd. v. United States,692 F. Supp. 918 (C.D. Ill. 1988), affd. 882 F.2d 229 (7th Cir. 1989), in which the court ruled that a 5-percent interest rate was not reasonable. Klingler, however, distinguished that case from the instant cases on the grounds that the facts were extreme; certificates of deposit were purchased by the Mirza plan with yields of 11 percent to 13 percent guaranteed for the first 3 years of a 12-year funding *151 period. In addition, that case was decided in 1989 and thus provided no guidance to an actuary who was making funding assumptions in 1986. Klingler also noted that, as long-term bonds were yielding 11.3 percent in 1980 (the plan year at issue), the Mirza decision could be seen as being "in harmony with" Cohen's 4-percent corridor. Conclusion Klingler applied the above concepts regarding interest rate assumptions to each of the eight plans in the instant cases. Factors affecting his calculations included: (1) Plan maturity; (2) whether or not the plan provides the option of a lump-sum benefit at retirement; (3) the life expectancy of participant and survivor; (4) the discount rate used for actuarial equivalence; and (5) whether or not a post-retirement expense load factor was included in the plan provisions. Through the application of those factors and the principles he articulated regarding long-term rates of return, Klingler found interest rate assumption reasonable ranges from 3.4 percent to 6.8 percent. Therefore, 5 percent was within each of the eight plans' reasonable ranges. Respondent's Actuarial Expert In comparison to the well-reasoned approach of Klingler, *152 the methodology of respondent's actuarial expert Rigel was less complete and did not account for all of the factors affecting the choice of an interest rate assumption. Rigel's expert opinion consisted of an examination of the funding period at *421 issue in each of petitioners' plans using the then-current Treasury bond yields with a similar maturity as a benchmark for a riskless interest rate. He then reduced this benchmark by an unspecified factor to arrive at a "reasonable" interest rate assumption. For example, in his examination of the Stephan plan, Rigel found that the funding period anticipated in the plan was 10 to 20 years. For the valuation dates in question, August 1, 1985, and August 1, 1986, Rigel found that 10- to 20-year Treasury bonds were yielding 10 percent and 8 percent, respectively. Based on this information, Rigel concluded that the Stephan plan would be able to achieve at least a 7.5-percent rate of return over its 10- to 20-year anticipated funding period. If the yield on Treasury bond obligations were to drop below 7.5 percent, Rigel stated, Stephan could buy corporate debt or another instrument with a higher rate of return to make up the difference. *153 An integral part of Rigel's analysis in this respect was the contention, supported by a chart of long-term interest rates from the year 1800 to present, that yields on Treasury bonds were in a lasting upward trend. He added that he has "not assumed that investment returns will dramatically decline" from his recommended 7.5-percent assumption. As additional support for his contention that a 5-percent interest rate assumption was unreasonable, Rigel asserted that it was implausible that a group of investors as sophisticated as petitioners would be willing to settle for investment performance as lackluster as 5 percent. He also noted various comments of pension actuaries at national meetings in 1985 and 1986 questioning the use of a 5-percent assumption. Discussion While Rigel and Klingler differed in their ultimate conclusions about the reasonableness of the 5-percent interest rate assumption in question here, they agreed on several basic tenets regarding actuarial assumptions. They agreed that actuarial interest rate assumptions are long-range predictions that become increasingly speculative with the length of the prediction, and that an element of conservatism is appropriate*154 in the selection of actuarial assumptions. They also recognized that the existing experience of new, *422 immature plans without "credible experience" should not guide the actuary in the selection of assumptions and that the actuary's choice of assumptions is guided by his or her professional experience as well as actuarial analysis. They both employed an analytical approach that involved selecting a suitable starting point derived either from historical economic data or a current economic benchmark, and then adjusted it for various established actuarial factors as well as for those plan-specific factors that, in that actuary's judgment, produced the appropriate actuarially reasonable range. We found petitioners' expert Klingler to be thorough and persuasive. Klingler's analysis presents an appropriate approach to the task of selecting an actuarial interest rate assumption, and we accept his conclusions. In contrast, we found Rigel's methodology simplistic and unconvincing. He simply stated that he found 7.5 percent to be a reasonable pre-retirement assumption and 7.0 percent to be a reasonable post-retirement assumption, while providing little indication of how he arrived*155 at those numbers. For example, at trial Rigel suggested that 1 percent was an appropriate factor by which to reduce the yield of a Treasury bond with a maturity equal to a plan's remaining funding period. If that were in fact Rigel's professional opinion, however, then he would be willing to give his imprimatur to an interest rate assumption as low as 5.33 percent, 10 little different from petitioners' assumption of 5 percent. In addition, to state that a plan can simply trade down to lower quality corporate obligations if the yields on Treasury bonds fall below 7.5 percent oversimplifies the nature of investment risk. Moreover, such an assertion cuts against his contention that interest rates are in a lasting upward trend. *156 Respondent took issue with several aspects of Klingler's testimony and report. First, respondent challenged Klingler's use of CEA interest rate projections as a predictor of future rates of return, claiming that CEA projections are political documents and not intended as forecasts of future economic conditions. Klingler noted that many economists in the mideighties believed that interest rates would decline. *423 Klingler stated, for example, in June 1988, Edward Yardeni, the then-chief economist of Prudential Bache, predicted a decline in interest rates to 5 percent. The CEA projections were a part of the data upon which an actuary might have drawn in making an interest rate assumption. It was appropriate for Klingler to use the CEA projections in his calculations of a reasonable interest rate assumption. Respondent also questioned Klingler's notions of reinvestment risk and future investment options risk, stating that he did not take into account the fact that interest rates might rise, giving petitioners an opportunity to enhance rates of return, or fall, giving petitioners a chance to realize capital gains on the sale of bonds. One of the premises of Klingler's argument*157 was that interest rates in the early eighties were high and appeared to be due for retrenchment. He buttresses this contention with use of the CEA projections. In addition, the capital gains that could be earned from the sale of bonds in 1 year of a plan, the lifetime of which could be 30 years or more, do not seem sufficient to make up for the future funding shortfalls that would result from lower interest rates. Reinvestment risk and future investment options risk are valid concerns of an actuary establishing an interest rate assumption. Respondent criticized Klingler's contention that a risk premium is inappropriate for a small plan. Respondent stated that "[Klingler] assumes that all small investors act irrationally and will receive less than the risk-free rate. He did not appear to consider the fact that Davis was an investment broker * * * [and that] all of the plan trustees/participants in these cases are educated, intelligent, and relatively sophisticated individuals." Klingler's point, however, was not to question petitioners' investment acumen but rather to state that risk premiums are only appropriate for larger pension plans which can effectively self-insure by spreading*158 losses among participants and properly diversifying their investment portfolios. In this regard, we note that investment broker Davis, sophisticated though he may be, testified that he was unable to retire at his normal retirement age due to investment losses. Respondent took issue with Klingler's 0.5-percent downward adjustment for investment fees, stating that none of petitioners used the investment services of Phoenix area *424 banks. Klingler used those rates only as an example of investment fees Phoenix area residents might have expected to pay. Respondent also challenged Klingler's contribution timing argument, stating that Klingler assumes that level annual contributions would be made for each plan for a 10-year period. Klingler only used a uniform 10-year funding scenario as an illustration and made separate adjustments to each plan's interest assumption ranging from 0.1 percent to 1.7 percent, and averaging 0.52 percent, based on each plan's individual maturity and funding profile. We also note that in each case Klingler only made these adjustments to the low end of his reasonable range of assumptions; his purpose was simply to illustrate a different funding scenario. *159 In that context, Klingler's use of contribution timing adjustments was appropriate and a factor which a certifying actuary should take into account. Respondent questioned Klingler's use of implicit pre-retirement mortality and turnover assumptions, stating that the possibility of a participant's pre-retirement death in any one of petitioners' plans was too remote to be accounted for actuarially. Respondent also stated that Klingler provided no authority for his assertion that there was only a 50-percent chance that a participant in his hypothetical plan would reach normal retirement age before receiving a benefit. While we agree with respondent that the probability of pre-retirement death of one of the participants may be low, this was not the only reason why a plan participant would receive a lump-sum payout prior to normal retirement. For instance, a participant might terminate his employment with the plan sponsor, or the plan sponsor might go out of business. While we do not necessarily endorse Klingler's use of the 50-percent figure, we do believe that, in the case of a plan using 5 percent for the purposes of actuarial equivalence and a higher-than-5-percent interest rate*160 assumption, some implicit adjustment for the risk of the payout of a pre-retirement benefit is reasonable. Respondent criticized Klingler's use of a post-retirement load factor in his calculation of post-retirement interest rate assumptions, but conceded that such an allowance was necessary if a participant elected to take payment as an annuity rather than a lump-sum payment. Respondent acknowledged *425 that the discount rate inherent in an actuarial equivalence is the appropriate post-retirement interest rate assumption in the event a lump-sum payout, as opposed to an annuity, is assumed by the certifying actuary. Respondent argued that Klingler improperly used a post-retirement load factor and a lump-sum payment factor in conjunction with one another. We agree that these two factors are in conflict with one another, but, in practice, the use of either adjustment produces a post-retirement interest rate assumption of 5 percent or less, making any conflict insignificant. In each of petitioners' eight plans, Klingler used a post-retirement load factor between 0.3 percent and 0.5 percent (0 percent for Brody Enterprises, the one plan with an explicit load), in each instance*161 lowering the range of reasonable assumptions below 5 percent. In the event a participant elected to receive a lump-sum payment upon retirement, a post-retirement interest rate assumption of 5 percent is, by respondent's admission, reasonable in accordance with the 5-percent discount rate used for the purposes of an actuarial equivalence. Thus in both instances, the assumption of a 5-percent post-retirement interest rate is reasonable. Respondent criticized the methodology in Klingler's survey of plans certified by Wyatt's Phoenix office. Respondent's expert Borden analyzed Klingler's data and recalculated his conclusions, arriving at an average rate of return for five-participant plans of 9.89 percent. Borden, however, assumed that contributions were made at yearend, rather than in the middle of the year, and removed rates of return for all years after 1986. Both of these adjustments are inappropriate. Klingler assumed that plan contributions were made mid-year; this is a reasonable compromise and is consistent with the formula required by Form 5500 for the computation of investment return. Borden removed post-1986 rates of return from his calculations in order to remove unusually*162 low rates of return for 1987 and 1988 plan years, which reflected the October 1987 stock market crash. By this method, respondent managed to take advantage of the inflated equity prices of the early eighties but discounted entirely the ensuing market correction. This would have been a part of petitioners' plans' experience and should have been included in any calculation of return. *426 Borden also testified that the Wyatt study, cited by Klingler as evidence that small plans earn only 5 percent and larger plans earn in excess of 8 percent, was flawed. Borden stated that Wyatt's methodology tended to skew the results in favor of petitioners' desired outcome. It is significant, however, that even though Borden questioned the results of the Wyatt study, he still found that small plans in general earned less than large plans. Finally, respondent stated that the revenue rulings cited by Klingler were misconstrued, and that TAM's cited by Klingler cannot be used as precedent. Respondent further argued that the Cohen speech, as the words of one Service employee, cannot be considered to "create a safe harbor where none otherwise exists." Klingler does not, however, rely solely*163 on the Cohen speech, the revenue rulings, or the TAM's to support his assertions that a 5-percent assumption is reasonable. These items were used by Klingler to illustrate the prevailing wisdom in the actuarial community at the time the plans' funding assumptions were made. In combination with the evidence concerning the Civil Service plan and the PBGC data, we find Klingler's argument regarding the prevailing consensus among actuaries persuasive. The interest rate assumption is a long-term estimate that must accommodate diverse and erratic market conditions. Since the actuary's paramount duty is to create a realistic pattern of contributions over the life of the plan which ensures that the plan sponsor will be able to provide adequate funding of the ultimate pension obligation, funding assumptions must have viability in the long term. Against this background, we find the following factors discussed above particularly important in determining the reasonableness of the 5-percent actuarial interest rate assumption: (1) The nature of the responsibility Congress entrusted to enrolled actuaries in the statutory scheme enacted for defined benefit pension plans; (2) the conservative nature*164 of the actuarial assumption selection process; (3) the fact that petitioners' plans were long term in nature with funding to occur over a period of 30 or more years; (4) the fact that petitioners' plans were self-directed; (5) the fact that petitioners' plans lacked "credible experience" with respect to earnings, investment strategies and otherwise for most if not all of the years at issue; (6) the risk of losing *427 compounded earnings in a tax-exempt trust associated with using overly optimistic assumptions, and the resulting requirement for unanticipated higher contributions in later years; and (7) the fact that most actuaries used interest rate assumptions close to 5 percent for the years at issue. The combination of these factors weighs heavily in favor of concluding that 5 percent was reasonable. Respondent also proffered the testimony of Ibbotson, a nonactuary financial expert. Ibbotson testified regarding econometric forecasting techniques and the market's expected rates of return, concluding that a 5-percent return was an unreasonably low forecast of expected earnings for assets invested during the period at issue. We received Ibbotson's testimony and expert report*165 with the caveat that he was not an actuary and, as such, conclusions he drew would have limited application in the determination of the reasonableness of actuarial assumptions. Ibbotson has never established any actuarial assumptions, and he has not studied actuarial science or its underlying principles. Ibbotson chose the long-term Treasury bond yield as a means of determining the long-term riskless rate of return. He stated that this bond yield is an effective indicator of long-term rates of return because it incorporates the collective knowledge of the marketplace. He added that any other type of investment (e.g., equities or lower grade debt) should yield at least this rate of return plus a premium for the risk which the investor is willing to assume. Ibbotson's probabalistic economic forecasting technique, however, is different from and contrary to actuarial principles in several material respects. For example, Ibbotson's analysis does not take into account that each of petitioners' self-directed plans may not represent the market, but only one small investor. The law of averages cannot be made to apply to an individual; given the fluctuating nature of markets, many small*166 investors are likely to be buying and selling at the wrong time. Thus, the total return for those investors may be substantially less than yields predicted for the broader market, regardless of how well that market performs. A principal distinction between the viewpoint of a financial analyst projecting future investment returns and an enrolled actuary establishing an interest rate actuarial assumption is *428 that the latter projection is made with the objective of assuring that the plan has adequate assets to meet the pension benefit obligations as they come due. If a financial analyst's predicted rate of return is higher than the actual rate earned, the investor simply earns less than he supposed he would earn. If an actuary makes the same mistake, there is a significant risk that the plan will become underfunded and the pensioners' full benefits will be unpaid. With all due respect to Ibbotson, while we have considered the information he presented regarding financial and equity markets, we cannot accept his conclusions. The analysis propounded fails to account for certain concerns and contingencies that an actuary for a self-directed small defined benefit plan must *167 take into account. Such contingencies include the need for liquidity, the high cost of transactions, the difficulty in diversification, the plan's fixed funding period, and the often whimsical investment strategies of a small-plan administrator. Congress did not entrust the Nation's tax-advantaged retirement savings system to hypothetical returns that the markets "should" bear. That task was left to enrolled actuaries whose background, training, orientation, and philosophy are well suited to the task. As practitioners specifically enrolled under the scheme established by Congress to create a smooth funding pattern assuring that benefit obligations will be met, they necessarily have a different perspective. The selection of an interest rate assumption is an actuarial judgment made in accordance with actuarial principles materially different from financial market performance forecasting. In sum, after considering all of the evidence presented, we conclude that the 5-percent pre- and post-retirement interest rate actuarial assumption used to calculate the contributions for petitioners' plans was reasonable for the years at issue. Retirement Age General Background and Retirement*168 Trends The certifying actuaries established a retirement age assumption of age 55 for Davis, Lear, Stephan, Fox, and Brody Enterprises. The terms of all of those plans except Davis' provided for a "normal retirement age" of the later of age 55 or 10 years of plan participation. The terms of the *429 Davis plan, as amended, provided for a "normal retirement age of the later of age 55 or the tenth anniversary of employment with the employer." Each plan participant could begin receiving full benefits under the plan at the "normal retirement date". That date was defined in the plan as the first day of the month coinciding with, or next following, the participant's normal retirement age. Respondent's expert Rigel did not agree with the retirement age assumptions used by the certifying actuaries and stated in his reports relating to the Davis, Lear, and Brody Enterprises plans that "it is unlikely that [the plan participant] will retire from work at age 55 and commence annuity payments", and in his reports relating to the Stephan and Fox plans that "the retirement assumption is unreasonable." Petitioners' expert Klingler noted in his report that employees in the United States*169 are retiring at earlier ages than in the past and that private pension plans are providing opportunities for employees to retire at earlier ages. He explained in his report that among the most significant factors influencing one's decision to retire are an individual's ability to provide adequate income for retirement, an individual's health, an individual's attitude toward the job, and the physical and emotional demands of the job. Klingler cited various reports by the General Accounting Office (GAO) to demonstrate a clear trend toward earlier retirement in the general population, including a July 15, 1985, GAO report which indicated that the median retirement age in the private sector for those workers with pensions was age 62. For further support of a trend toward earlier retirement, Klingler referred to the Civil Service plan, under which a participant can collect an unreduced retirement benefit after 30 years of service and attainment of age 55. In 1982, 33.5 percent of those reaching age 55 with 30 years of service retired at age 55. In 1987, that figure increased to 40.7 percent. Klingler also determined that due to the inapplicability of the law-of-averages principle*170 in a one-participant pension plan, an actuary generally should assume for funding purposes a retirement age that is the same as the normal retirement age stated in the plan. Moreover, Klingler noted that for each petitioner there were specific facts which made an age 55 retirement assumption reasonable. *430 Segregation Provisions The Davis, Lear, and Brody Enterprises plans contained provisions which permitted the participant to segregate his accrued benefits at the normal retirement date even if he chose to continue working beyond such date. At the date of segregation, the defined benefit obligation would be satisfied and future earnings questions and retirement questions would become immaterial to the funding of the plans. Actual earnings and losses would be credited to this segregated account and distributions would begin upon actual retirement. Both Rigel and Klingler agreed that the inclusion of this "segregated account" provision in the plans rendered the date of a participant's actual retirement irrelevant. Both Rigel and Klingler assumed that a participant would elect to segregate his lump-sum accrued benefits at age 55, the normal retirement date stated *171 in the plan, as this form of payout would be the most valuable at such date. Klingler provided the following chart which demonstrates the advantage of segregation. The chart assumes 5-percent growth after segregation: Expected value of fund at at- tained age as- Maximum Maximum suming assets Retirement annual lump-sum Attained segregated at age benefit value age age 55 [55] $ 75,000 $ 1,060,670 [55] $ 1,060,670 [56] 75,000 1,043,130 [56] 1,113,704 [57] 75,000 1,025,045 [57] 1,169,389 [58] 75,000 1,006,384 [58] 1,227,858 [59] 75,000 987,119 [59] 1,289,251 [60] 78,125 1,007,539 [60] 1,353,714 [61] 83,807 1,057,923 [61] 1,421,399 [62] 90,000 1,110,815 [62] 1,492,469 [63] 90,000 1,084,887 [63] 1,567,093 [64] 90,000 1,058,383 [64] 1,645,447 [65] 90,000 1,031,376 [65] 1,727,720 As the chart reveals, the section 415 maximum benefit limits cause the value of the lump-sum payout to trend downward at each benefit level. However, because the section 415 limits do not apply once the accrued benefits have been segregated, the value of the segregated fund will continually increase. *431 Since segregation would result*172 in the receipt of the most valuable benefit, the experts concluded that the appropriate assumed retirement age was the normal retirement date specified in the plan as that was the date on which a participant would commence benefits. If the participant retired at any time after the normal retirement date stated in the plan, the present value of his or her payout, whenever it occurred, would be approximately equivalent to the present value of the lump-sum payout at age 55. Accordingly, the experts concluded that it was not necessary to predict, or for an actuary to assume, precisely when a participant would retire. The normal retirement date specified in a plan generally is the date at which a participant is entitled to commence benefits. The retirement age assumption arrived at by a plan's actuary affects the amount of contributions that a participant must make to the plan and reflects the date at which the plan should be fully funded so that a participant can commence benefits. This assumption is based on, among other things, a participant's objectives, general retirement trends, and retirement trends within a specific occupational group, as well as the provisions of the plan. *173 We agree with the experts that in these particular cases, the normal retirement dates stated in the participants' plans are the dates at which the participants will elect to segregate their accrued benefits; therefore, the normal retirement date and the assumed retirement age are the same. Davis Although the segregation provision in the Davis plan justified the finding that the age 55 retirement assumption was reasonable, Davis' testimony provided additional support for finding that the assumed retirement age of 55 was reasonable. During the years in issue, Davis was an investment broker specializing in raising equity capital to finance the purchase of hotels. Davis testified that, when he adopted the plan in 1984, he expressed to his actuary, Matthews, that he wished to retire at age 55. At that time, Davis had been successful in his personal investments and he felt that the next 4 or 5 years would be the most financially rewarding of his working career; he had been in the brokerage business for 2 decades and felt that was long enough; he felt that his *432 pension fund would adequately finance his retirement; and he was interested in pursuing other interests, in*174 particular, a professional golfing career. He testified that at the time of trial in 1992, he was 57 years of age and had not yet retired. He stated that this was because he had made several bad real estate investments -- some of which resulted in the institution of bankruptcy proceedings -- and that his income had dropped substantially. Upon review of all the evidence, we find that the actuary's retirement age assumption of 55 used to calculate the contributions for Davis' plan was reasonable for the years at issue. Lear Although the segregation provision in the Lear plan justified the finding that the age 55 retirement assumption was reasonable, Pallin's testimony provided additional support for that assumption. Pallin was an ophthalmic surgeon who graduated from medical school in 1968 and had been in practice in Arizona since 1975. He testified that when he decided to adopt a defined benefit plan in 1985, he advised Matthews that his goal was to retire at the earliest possible age because he believed that he could not maintain for very long the physical skills necessary for his profession. Pallin testified that 2 to 3 days a week he performed cataract surgery and lens*175 implants. A typical day might involve surgery on 16 to 21 patients. On these days he would typically spend 8 hours "hunched over a microscope" looking into a patient's eye. He testified that it required a great deal of manual dexterity as it was "very precise work and you have to have a steady hand and two steady feet. We have three foot pedals and both hands are occupied the entire time." The depth of the area in which he performed surgery -- the anterior chamber of the eye -- was four-tenths of a centimeter deep, and he was required to remain very focused throughout surgery. After a typical day of surgery, he found it difficult to be in an environment with lots of bright light, and he had to be driven home from work because he was unable to stay awake at the wheel. He testified that he was always worried about the day when something might arise which would affect the steadiness of his hands and make it impossible for *433 him to continue to operate. He testified that he was 50 years old and was concerned about the possibility of arthritis, failing eyesight, or some other disability which could affect his ability to operate. The evidence shows that in 1985, the time*176 of adoption of Pallin's plan, Pallin was earning a substantial salary; he had become concerned about the physically taxing nature of his profession and whether he could continue to perform surgery in the later years of his life; he had expressed his desire to retire at an early age; and the terms of his plan provided for a full benefit at age 55. Upon review of all the evidence, we find that the actuary's retirement age assumption of 55 used to calculate the contributions for Pallin's plan was reasonable for the years at issue. Stephan Because the Stephan plan did not contain a segregation provision, respondent's expert Rigel concluded that the retirement age assumption used by Goodell was unreasonable. Rigel stated in his report: (1) Because Robert Stephan had a successful, lucrative legal practice, it seemed unlikely that there was a 100-percent probability that he would retire at age 55; (2) retirement statistics for the general population suggested that retirement is often deferred to ages 60-70 and that retirement at early ages is unusual; and (3) the provisions of Stephan's plan required that he terminate service before commencing plan benefits. Rigel noted that discovery*177 materials he reviewed indicated that Robert Stephan had "a certain intention to retire at age 55" and that the plan benefits to be provided were generous and offered "some encouragement for early retirement". However, he concluded "that an age 60 retirement is a reasonable accommodation of all the competing factors present in this case." During the years in issue, Robert Stephan was a practicing attorney. He graduated from Arizona State University Law School in 1972, and since about 1978 had been a sole practitioner specializing in personal injury and medical malpractice cases on behalf of plaintiffs. He testified that his income had always fluctuated. Robert Stephan testified that he was a member of the Church of Jesus Christ of Latter-Day Saints (Mormons). He *434 joined the church when he was 30 years old and, therefore, missed the opportunity to serve the 2-year mission that usually is performed by young Mormons. He testified that in adopting his plan, he had expressed his desire to retire at age "50 or thereabouts" so that he could serve as a missionary of the church; however, he was informed that age 55 was the earliest that he could prepare for under the plan. *178 Robert Stephan testified that at age 55 he would have practiced law for 30 years, and it was his hope to terminate the practice or to cut down significantly before such time. Upon review of all the evidence, in particular Robert Stephan's testimony, we find that at the time of adoption of the Stephan plan, he desired to commence benefits at an age earlier than 55. Although there was no 100-percent probability that Robert Stephan would actually retire at that age, an actuary is charged with looking into the future and based upon, among other things, a participant's reasonable objectives, making a determination as to when benefits under the plan could begin. We find Robert Stephan's testimony that he wished to retire at or about age 50 to become a missionary of his church was sincere, credible, and reasonable. Also, under the terms of the plan, Robert Stephan was entitled to full benefits at age 55 or upon 10 years of plan participation. An actuary is not charged with "rubber stamping" the terms of a plan; the normal retirement age specified in the plan is, however, a factor to be considered by an actuary in arriving at a reasonable retirement age assumption, and when the terms reasonably*179 provide that a participant is entitled to full benefits at a particular age, a prudent actuary must arrive at assumptions which will ensure that the promised benefits will be available for the participant at the desired time. Further, the importance of using assumptions which will ensure that the promised benefits are available at a particular time is heightened in a one-participant plan, as the funding costs cannot be spread among many participants as with large plans. Accordingly, we find the retirement age assumption of age 55 used by the plan's certifying actuary to calculate the contributions for Stephan's plan was reasonable for the years at issue. *435 Fox Because the Fox plan did not contain a segregation provision, respondent's expert Rigel concluded that the retirement age assumption used by Matthews was unreasonable. Rigel stated in his report: (1) Because the Foxes had a successful, lucrative medical practice, it seemed unlikely that there was a 100-percent probability that they would retire at age 55; (2) retirement statistics for the general population suggested that retirement is often deferred to ages 60-70 and that retirement at early ages is unusual; *180 and (3) the provisions of the Fox plan required that they terminate service before commencing plan benefits. Rigel noted that the discovery materials he reviewed provided details of the Foxes' retirement goals. Although those materials revealed that the Foxes indicated an intention to retire at age 55, he concluded "that an age 60 retirement is a reasonable accommodation of all the competing factors present in this case." During the years in issue, Jonathan Fox was an orthopedic surgeon practicing in Tempe, Arizona. He had his own patients and also performed many emergency room operations. Renee Fox assisted him with the business aspects of the practice. She became a plan participant for the plan year ending October 31, 1987. Jonathan Fox testified that when he established the plan in 1986, he was 34 years old and he felt that age 55 would be an appropriate retirement age. He described many changes in the practice of medicine that had taken place over the years, such as the increase in the amount of paperwork required by Medicare and health insurance providers, the increased competition for patients, and the constant fear of contracting hepatitis and AIDS. He testified about*181 the constant fear of malpractice claims. He also testified about his family medical history which did not bode well as a precedent for his longevity: his father died of a massive heart attack at the age of 62 and his mother has diabetes and hypertension. He testified that he has arthritis in his right thumb, which, at some point, could make it more difficult for him to perform surgery or hold the necessary surgical instruments. Respondent argued that this testimony is merely self-serving and that there was no evidence that Jonathan Fox had explained these concerns to his actuary when establishing *436 the plan. Further, respondent argued that the post-retirement mortality assumptions used for determining plan funding costs assumed improvements in mortality, directly refuting Jonathan Fox's testimony about his fears of an untimely death. We find Jonathan Fox's testimony that he wished to retire at age 55 to be credible and reasonable. Although there was no 100-percent probability that Jonathan Fox would actually retire at that age, an actuary is charged with looking into the future and based upon, among other things, a participant's reasonable objectives, making a determination*182 as to when benefits under the plan could begin. Also, under the terms of the plan, Jonathan Fox was entitled to full benefits at retirement upon age 55 or upon 10 years of plan participation. As we noted above, an actuary is not charged with "rubber stamping" the terms of a plan; the normal retirement age specified in the plan is, however, a factor to be considered by an actuary in arriving at a reasonable retirement age assumption, and when the terms reasonably provide that a participant is entitled to full benefits at a particular age, a prudent actuary must arrive at assumptions which will ensure that the promised benefits will be available for the participant at the desired time. Further, the importance of using assumptions which will ensure that the promised benefits are available at a particular time is heightened in a one-participant plan, as the funding costs cannot be spread among many participants as with large plans. Accordingly, we find that the retirement age assumption of age 55 used by the plan's certifying actuary to calculate the contributions for the Fox plan was reasonable for the years at issue. Brody Enterprises Although the segregation provision in the*183 Brody Enterprises plan justified the finding that the age 55 retirement assumption was reasonable, Brody's testimony provided additional support for finding that the assumed retirement age of 55 was reasonable. During the years in issue, Brody was a practicing attorney. He graduated from law school in 1969, whereupon he went to work as an estate and gift tax examiner for the Service in Chicago and later for a law firm in *437 Chicago. In 1977, he joined a law firm in Arizona, and in 1983 he formed his own corporation for which he continues to work. Since 1974, Brody practiced law in the area of pensions. Upon adoption of his plan in 1983, Brody informed Lawrence that he "wished to accrue a benefit consistent with the law so that I would be able to retire at the earliest time without any cutback, and that was age 55 at that time." He testified also that he had a very successful career as a lawyer, that he was a member of various corporate boards, and that he had several business interests he wished to pursue upon retirement. Upon review of all the evidence, we find that the actuary's retirement age assumption of 55 used to calculate the contributions for Brody's plan was*184 reasonable for the years at issue. Mortality Assumptions Citrus Valley For the 1985 plan year, Lawrence used the Manulife OMS B74 Guaranteed Annuity female table (Manulife table) to establish the mortality assumption for the Citrus Valley plan. For the 1988 plan year, he used the 1983 Individual Annuity Mortality (IAM) female table. Since life expectancy had been improving and was expected to continue to do so, Lawrence used a 7-year "setback" (applied the rates as if King were 7 years younger than he was). The Manulife table is an annuity table which combines the mortality and interest components. The table used by Lawrence for 1985 used an interest rate of 3 1/4 percent and mortality data from 1949. Respondent argued that the use of the Manulife table was unreasonable because it used a 3 1/4-percent interest rate, and it was programmed into Lawrence's computer, so no individual analysis was done. Furthermore, respondent noted that "Klingler had no opinion on the reasonableness of this table." Lawrence testified that he understood the rates that were assumed by the table and determined that they were acceptable because the low interest rate offset the outdated mortality*185 data. We find Lawrence's explanation of his use of the Manulife table convincing. We hold that the use of the *438 Manulife table to determine the mortality assumption for the Citrus Valley 1985 plan year was reasonable. With regard to the 1988 plan year, respondent did not challenge the use of the 1983 IAM table. However, respondent argued that the use of the female table and the 7-year setback overestimated costs. Citrus Valley's expert Klingler stated: "Since the most recent published tables are based on 1983 mortality rates and life expectancy has been trending upward very regularly, it is very common to see adjustments to the published mortality tables." Klingler explained that using a setback is an appropriate means of making such adjustment. He noted that the mortality assumption used by Lawrence for the Citrus Valley 1988 plan year projected significant mortality improvement; however, he determined that there was still a 25-percent chance that the funds would be insufficient to pay out all of the promised benefits. Klingler concluded: "Based on the application of my general analysis, I cannot say that these Assumed Mortality Rates are clearly reasonable. However, *186 I do not believe that these rates are clearly unreasonable." We hold that although we are not entirely convinced that the mortality assumption for the Citrus Valley 1988 plan year is completely reasonable, it is not substantially unreasonable so as to justify a retroactive adjustment. Furthermore, any misgivings we have about this assumption are not sufficient to affect the reasonableness of the actuarial assumptions in the aggregate. Fox Matthews used the 1983 IAM table with a 4-year setback to establish the mortality assumption for the Fox plan. Respondent argued that the setback was unreasonable because "Dr. Fox testified that he wished to retire at age 55 because his family medical history suggested he was likely to die at an early age." Jonathan Fox's concerns about his family medical history do not affect his actuarial life expectancy, nor would they decrease the cost of providing an annuity for him. Since the purpose of the mortality assumption is to determine cost and not actual mortality, it was reasonable for Matthews to disregard *439 Jonathan Fox's concerns when establishing the mortality assumption. Klingler concluded that Matthews projected an appropriate*187 degree of mortality improvement for the Fox plan; therefore, the assumed mortality rate was reasonable. We accept Klingler's conclusion and hold that the mortality assumption for the Fox plan was reasonable. Brody Enterprises For the years in issue, Lawrence used the 1983 IAM female table to determine the mortality assumption for the Brody Enterprises plan. Since life expectancy had been improving and was expected to continue to do so, Lawrence used a 7-year setback to reflect future mortality improvement. Respondent again questioned the use of the 7-year setback and the use of the female table for a male participant. According to respondent, those factors led to an overstatement of costs because females live longer than males, and the 1983 IAM table had sufficient mortality improvement built into it. As with Citrus Valley, Klingler determined that a setback was an appropriate means of adjusting mortality improvement. He further noted that the Society of Actuaries recommended improvement factors for use with the 1983 IAM table which result in mortality improvements of about 5.7 percent for each 10 years of projection. Based on the Society of Actuaries' recommendation, Klingler*188 concluded that it would have been appropriate for Lawrence to take into account a 17.4-percent mortality improvement when he determined the mortality assumption. However, Klingler determined that the mortality rate assumed by Lawrence for the Brody Enterprises plan resulted in a 22-percent improvement when compared to the 1983 IAM table. He was unable to conclude that the mortality assumption was clearly reasonable, but he determined that the assumption was "not clearly unreasonable either." Klingler's conclusion raises some doubt as to the reasonableness of the mortality assumption for the Brody Enterprises plan, and we are not convinced that the assumption was completely reasonable. We find, however, as we did in Citrus Valley, that the assumption is not substantially *440 unreasonable so as to justify a retroactive adjustment. Furthermore, any misgivings we have about this assumption are not sufficient to affect the reasonableness of the actuarial assumptions in the aggregate. Post-retirement Expense Load Assumptions Brody Enterprises Lawrence included in his actuarial assumptions for the Brody Enterprises plan post-retirement expense loads of 6 percent and 4.5 *189 percent for plan years ending May 31, 1986, and May 31, 1987, respectively. Respondent challenged these expense load assumptions as unreasonable. Petitioners' expert Klingler stated that, in the case of a small pension plan, the retirement of the principal usually means that the plan sponsor stops paying actuarial, legal, and accounting fees. As a result, the plan must cover the cost of those services itself and, Klingler opined, it is therefore reasonable to include some provision, or "load", to fund these expenses. Klingler estimated that the administrative fees currently run between $ 1,500 and $ 2,000 per year, and that, assuming a 25-year post-retirement lifespan, a 6-percent actual interest rate, and a 3-percent annual increase in administrative costs, the amount needed at retirement to fund the post-retirement expenses would be between $ 26,376 and $ 35,168. To account for this funding, Klingler stated that it would be reasonable for a certifying actuary to adjust downward a plan's interest rate assumption by a factor of between 0.2 and 0.5 percent. None of petitioners' plans, except Brody Enterprises, used an explicit post-retirement expense load. Klingler thus made *190 this downward adjustment to each of the other plans' interest rates, but in the case of Brody Enterprises, he made no such downward adjustment. He did, however, state that, given the assumed retirement age of 55 and the joint and survivor annuity benefit, there was potential for a very long period of post-retirement plan administration. In addition, he attested to the reasonableness of the Brody Enterprises plan's actuarial assumptions in the aggregate. Lawrence testified that he included the expense load factors in his actuarial assumptions for the plan years ending in 1986 and 1987 because the plan was "getting rid of the *441 Manulife [table] rates" in order to use the 1983 IAM table for post-retirement assumptions. The addition of the expense load factors compensated for the loss of the expense load in the Manulife table. We held above that petitioners were reasonable in their use of both the Manulife table and the 1983 IAM table. Therefore, the addition of post-retirement expense load to compensate for the change in mortality tables from the Manulife table to the 1983 IAM table also was reasonable. Respondent offered a rather perfunctory rebuttal, stating simply that*191 Lawrence's addition of post-retirement expense load assumptions "would further increase the funding goal and the amount of the deductions." Inarguably, a post-retirement expense load factor will increase funding goals and, therefore, contributions and deductions as well. This is not, however, unreasonable per se, as respondent seems to believe. There are undoubtedly costs to administering a small defined benefit plan; those costs continue post-retirement and the plan must provide for them. A post-retirement expense load is a reasonable manner in which to fund the post-retirement administrative fees. Accordingly, we hold that Lawrence was reasonable in assuming post-retirement expense loads of 6 percent and 4.5 percent for the plan years ending in 1986 and 1987, respectively. Unit Credit Funding Method The unit credit funding method is an actuarial cost method which is also known as the accrued benefit cost method. This method produces an annual contribution sufficient to fund the benefits that accrue in a particular plan year. Since the parties have referred to this method as the unit credit funding method, we will refer to it as such here. Respondent determined that the*192 actuaries' use of the unit credit funding method in the Davis, Lear, Stephan, Fox, and Brody Enterprises plans failed to make reasonable allocations between normal costs and past service costs and, thus, was not a reasonable funding method under section 412(c)(3). Petitioners argued that the allocation was reasonable and that the contributions for the years at issue were properly deductible *442 under section 404(a)(1)(A)(iii). To decide this issue, we first review the relevant sections of the Code and the regulations. As previously discussed, section 412(c)(3) requires that the plans' enrolled actuary employ actuarial assumptions and methods that are reasonable in the aggregate. Section 412 also establishes minimum funding standards for qualified pension plans. To accomplish this, section 412(b) requires that each qualified plan maintain a "funding standard account". All activity affecting the costing of pension benefits, as well as the accumulation of assets to fund those benefits, must be reflected in this account on an annual basis. For each plan year, the account is charged with, inter alia, the "normal cost" of the plan for the plan year and amounts necessary, if*193 any, to amortize in equal annual installments certain amortizable bases, including unfunded past service liability. Sec. 412(b)(2). Credits to the funding standard account include "the amount considered contributed by the employer" for the plan year. Sec. 412(b)(3)(A). If charges to the funding standard account exceed credits in a given year, a funding deficiency for the year may exist. The minimum funding level is the amount necessary to balance the funding standard account, thereby satisfying the minimum funding standard for that year. Thus, the funding standard account is the mechanism by which the plan's annual minimum funding level is determined. Section 404 limits the deduction for contributions made by sponsors of qualified pension plans. There are three alternative calculations under section 404(a)(1)(A) to determine the maximum deductible contribution in any given year. The amount determined under the applicable method is also subject to the overall full funding limitation provided by section 412(c)(7), but there is no indication that the full funding limitation was reached in any of petitioners' plans. Section 404(a)(1)(A) limits the deduction of a defined benefit*194 pension plan annual contribution to an amount determined as follows: (i) the amount necessary to satisfy the minimum funding standard provided by section 412(a) for plan years ending within or with such taxable year (or for any prior plan year), if such amount is greater than the amount determined under clause (ii) or (iii) (whichever is applicable with respect to the plan), (ii) the amount necessary to provide with respect to all of the employees under the trust the remaining unfunded cost of their past *443 and current service credits distributed as a level amount, or a level percentage of compensation, over the remaining future service of each such employee, as determined under regulations prescribed by the Secretary * * * (iii) an amount equal to the normal cost of the plan, as determined under regulations prescribed by the Secretary, plus, if past service or other supplementary pension or annuity credits are provided by the plan, an amount necessary to amortize the unfunded costs attributable to such credits in equal annual payments (until fully amortized) over 10 years, as determined under regulations prescribed by the Secretary. In determining the amount deductible*195 in such year under the foregoing limitations the funding method and the actuarial assumptions used shall be those used for such year under section 412, and the maximum amount deductible for such year shall be an amount equal to the full funding limitation for such year determined under section 412. With its reference to the amount necessary to satisfy the minimum funding standard of section 412(a), section 404(a)(1)(A)(i) establishes a deductible "floor" -- the minimum contributed amount that is deductible under section 404(a)(1). The maximum deductible amount is calculated in clause (ii) or (iii), depending on the type of funding method employed by the plan. Clause (ii) applies to plans using a funding method which funds all remaining unfunded costs in a level amount, for example, the individual level premium method. Clause (iii) applies to a funding method that funds the present value of benefits accruing in that year by computing normal cost, e.g., the unit credit funding method. The parties agree that since petitioners' plans use the unit credit funding method, the deductible contribution limits are determined under clause (iii) for the years at issue. Section 404(j)(1)*196 further limits the deduction taken under section 404(a) as follows: (1) No deduction in excess of section 415 limitation. -- In computing the amount of any deduction allowable under paragraph (1) * * * of subsection (a) for any year -- (A) in the case of a defined benefit plan, there shall not be taken into account any benefits for any year in excess of any limitation on such benefits under section 415 for such year * * * Section 415(a) limits qualified plans from providing for payment of annual benefits in excess of an amount determined under subsection (b). Section 415(b)(1) establishes an annual benefit limitation as the lesser of a dollar amount ($ 75,000, as adjusted under section 415(b)(2), for the years at *444 issue) or 100 percent of the participant's average compensation for his 3 highest paid years with the plan sponsor. For the years at issue, section 415(b)(5) reduced the subsection (b)(1) dollar limitation as follows: 11 (5) Reduction for service less than 10 years. -- In the case of an employee who has less than 10 years of service with the employer, the limitation referred to in paragraph (1) * * * shall be the limitation determined under such paragraph*197 * * * multiplied by a fraction, the numerator of which is the number of years (or part thereof) of service with the employer and the denominator of which is 10. Thus, a qualified defined benefit pension plan may not provide for payment of benefits in excess of the dollar limitation of section 415(b)(1) as further limited by section 415(b)(5). Allowable actuarial cost methods (funding methods) were enumerated by ERISA. An actuarial cost method is: a recognized actuarial technique utilized for establishing the amount and incidents of the annual actuarial cost of pension plan benefits and expenses. Acceptable actuarial cost methods shall include the accrued benefit cost method (unit credit method), the entry age normal cost method, the individual level premium cost method, the aggregate cost method, *198 the attained age normal cost method, and the frozen initial liability cost method. * * * The Secretary of the Treasury shall issue regulations to further define acceptable actuarial cost methods. [ERISA sec. 3(31), 88 Stat. 837.] Such regulations were promulgated under section 412(c)(3) and were finalized in 1980. Section 1.412(c)(3)-1, Income Tax Regs., provides in pertinent part: (a) Introduction -- (1) In general. This section prescribes rules for determining whether or not, in the case of an ongoing plan, a funding method is reasonable for purposes of section 412(c)(3). A method is unreasonable only if it is found to be inconsistent with a rule prescribed in this section. The term "reasonable funding method" under this section has the same meaning as the term "acceptable actuarial cost method" under section 3(31) of the Employee Retirement Income Security Act of 1974 (ERISA). * * * (b) General rules for reasonable funding methods -- (1) Basic funding formula. At any time * * * the present value of future benefits under a reasonable funding method must equal the sum of the following amounts: *445 (i) The present value of normal costs * * * over *199 the future working lifetime of participants; (ii) The sum of the unamortized portions of amortizable bases, if any * * * and (iii) The plan assets, decreased by a credit balance (and increased by a debit balance) in the funding standard account under section 412(b). (2) Normal cost. Normal cost under a reasonable funding method must be expressed as -- (i) A level dollar amount, or a level percentage of pay, that is computed from year to year on either an individual basis or an aggregate basis; or (ii) An amount equal to the present value of benefits accruing under the method for a particular plan year. * * * (e) Special rules for certain funding methods -- (1) Applicability of special rules. Paragraph (e) of this section applies to a funding method that determines normal cost under paragraph (b)(2)(ii) of this section. * * * (3) Allocation of liabilities. In determining a plan's normal cost and accrued liability for a particular plan year, the projected benefits of the plan must be allocated between past years and future years. Except in the case of a career average pay plan, this allocation must be in proportion to the applicable rates of benefit accrual under*200 the plan. * * * In the case of a career average pay plan, an allocation between past and future service benefits must be reasonable. While the parties disagreed on the ultimate conclusion regarding the reasonableness of petitioners' funding method, they agreed generally on several aspects of petitioners' plans and the governing law. The parties acknowledged that the plans at issue were career average pay plans during the years at issue. They further agreed that section 404(a)(1)(A)(iii) was the applicable section for determining the limit on deductible contributions for petitioners' plans. The parties recognized that petitioners' plans may not provide for the payment of benefits in excess of the applicable section 415 limits. Finally, the parties agreed that under section 1.412(c)(3)-1(e)(3), Income Tax Regs., plan benefits must be allocated; however, they disputed what means were permissible to accomplish that allocation. Respondent asserted that, in making an allocation, the section 415 limits must be taken into account. Respondent apparently came to that conclusion by looking to section 404(j)(1) and its direct reference to section 415. See also Jerome Mirza & Associates, Ltd. v. United States,882 F.2d 229*446 (7th Cir. 1989),*201 discussed infra. The thrust of respondent's argument is that in allocating benefits: the impact of the limitations of section 415 is that no more than 10 percent of the maximum benefit may be allocated to a year for normal cost with the remainder of the projected benefit allocated to past or future years of service. There are two reasons why this follows. The first is that the terms of a qualified plan must limit the accrual of benefits to those permitted by section 415. This limit on accruals results in no more than 10 percent of the maximum benefit accruing for one year of service by the very terms of a qualified plan. The second reason is that a participant must have ten years of service in order to receive the maximum benefit permitted by section 415. Allocating the projected benefit to years of service results in no more than 10 percent of the maximum benefit being allocated to any year. In other words, according to respondent, but for their preparticipation past service with the plan sponsor, the participants would not have been able to accrue more than one-tenth of the maximum benefit under section 415 in any 1 year. Therefore, under respondent's argument, any*202 benefit granted by the plan in excess of that amount must be credited to and allocated to past years, even if the plan does not so provide. As a result, the plan would be underfunded for 10 years. Respondent's argument confuses the separate and distinct functions performed by sections 412 and 415 in determining deductibility under section 404. Each of these sections must be separately applied when determining whether a contribution is deductible. Section 404(a)(1)(A)(iii) limits deductible contributions to the normal cost plus the amortization of past service liability if any past service credit is provided for by the plan. Normal cost under a reasonable funding method is determined according to the principles set forth in section 1.412(c)(3)-1, Income Tax Regs.Section 404(j)(1) also limits deductible contributions to the limitation provided in section 415. Despite respondent's assertions to the contrary, there is no express or implied connection between the limitations of section 415 and any allocation under section 1.412(c)(3)-1(e)(3), Income Tax Regs. To determine whether petitioners properly deducted the contributions for the years in issue, we must decide: (1) Whether *203 deductible normal costs were properly computed under the section 412(c)(3) regulations; and (2) whether the *447 entire contribution was deductible under section 404(j)(1). We shall discuss the latter issue first. Anderson described the two ways that actuaries interpret the section 415 limits in the context of section 404(j)(1). Under the first approach, which he called the "liberal interpretation" of section 404(j)(1), accrued benefits for funding purposes are limited only by the section 415 limit that will apply at retirement. Under the second approach, which Anderson referred to as the "conservative interpretation" of section 404(j)(1), the section 415 limit applied by section 404(j)(1) is "the one which would apply assuming no further service by the employee in question"; that is, the one which would apply if the plan were to terminate immediately after the contribution was made. By using the section 415 limitations to define the amount of the benefit contribution, the conservative approach ensures that the contribution will never exceed those limitations. Moreover, under the conservative approach, the plan, at all times, would have the exact amount necessary to pay*204 the promised benefit. To calculate the section 415 limit under the liberal approach, the actuary assumes that the participant will work until the normal retirement age (or until the participant accumulates at least 10 years of service with the plan sponsor). As a result, if a plan funded under the liberal approach were terminated immediately after the contribution was made, it is possible that the plan would be overfunded. In our view, this is not the proper interpretation of section 404(j)(1) because such interpretation fails to effectuate the purpose of section 404(j)(1), i.e., to limit deductible contributions to benefits payable under section 415. By contrast, we find that the conservative approach reflects Congress' intent to balance the need to have the funds to pay promised benefits and the need to prevent the abuse of tax-advantaged overfunding. Under this interpretation of section 404(j)(1), deductible contributions are limited to exactly the amount of benefits payable under section 415 determined at the time of the contribution in question. The plan would have sufficient funds to pay the properly accrued benefits that it is legally required to pay. We hold that the*205 conservative approach is the correct interpretation of the operation of section 404(j)(1). *448 In all of the plans under consideration here except the Fox plan, the contributions made during the years at issue were to fund benefits that would have been payable immediately under section 415. Therefore, the contributions for those years do not violate section 404(j)(1), and we so hold. The Fox plan as amended in its second year, however, funded benefits that would not have been immediately payable under section 415. Hence, the contribution for that year would have failed the section 404(j)(1) test. However, as we decide below, the amendment to the Fox plan, which increased the rate of benefit accrual, was not timely filed and, as a result, was not effective for any of the years in issue. Therefore, until new actuarial computations are completed, we do not have sufficient information to determine whether the Fox plan violates section 404(j)(1). We leave those computations to the parties under Rule 155 and turn to the second issue, the proper computation of normal cost. Although it was a necessary separate step in determining the deductibility of contributions, respondent*206 never expressly claimed that petitioners' plans violated section 404(j)(1). Rather, respondent used section 404(j)(1) as support for the proposition that the section 415 limits directly affect the section 1.412(c)(3)-1(e)(3), Income Tax Regs., allocation. Respondent implied that because section 404(j)(1) requires the limitations in section 415 to be taken into account for the purposes of determining the section 404(a)(1) limitation on deductions, those same limitations must be taken into account for the purposes of making an appropriate allocation in determining normal costs under section 1.412(c)(3)-1(e)(3), Income Tax Regs. In this manner, respondent concluded that a plan could never accrue benefits under section 415, allocate to normal cost under section 1.412(c)(3)-1(e)(3), Income Tax Regs., and fund and deduct as normal cost under section 404(a)(1)(A)(iii) an amount in excess of one-tenth of the section 415 limits in any one year. We disagree with each of these conclusions. As noted above, a reasonable funding method within the meaning of section 412(c)(3) is determined under section 1.412(c)(3)-1, Income Tax Regs. In establishing the general rules for reasonable funding*207 methods, paragraph (b)(1)(i) and (ii) sets forth a basic funding formula which includes "the present value of normal costs * * * over the future working *449 lifetime of participants", as well as "the sum of the unamortized portions of amortizable bases, if any." Paragraph (b)(2)(ii) describes one of the two ways that normal cost must be expressed under a reasonable funding method as "An amount equal to the present value of benefits accruing under the method for a particular plan year." Paragraph (e)(3) applies specifically and exclusively to funding methods that determine normal cost under paragraph (b)(2)(ii). In such cases, to determine normal cost for "a particular plan year, the projected benefits of the plan must be allocated between past and future years." Sec. 1.412(c)(3)-1(e)(3), Income Tax Regs. The allocation must be reasonable. Id. Respondent asserted that section 415 restricts the section 1.412(c)(3)-1(e)(3), Income Tax Regs., allocation based on years of service; therefore, any accrual for the current plan year in excess of one-tenth of the maximum benefit must be attributed to prior years of service. Thus, respondent concluded that petitioners' allocation*208 was violative of paragraph (e)(3) and the funding method was therefore unreasonable. Respondent relied on Jerome Mirza & Associates, Ltd. v. United States,882 F.2d 229 (7th Cir. 1989), in reaching this conclusion.12 In Mirza, the taxpayer established and funded a defined benefit pension plan under which a participant accrued a benefit of approximately $ 81,000 in the first year of the plan. The participant had sufficient service with the plan sponsor so that the section 415(b)(1) and (5) limit was not exceeded. In concluding that even though the plan did not grant credit for past service, the actuary should have allocated part of the benefit cost to past service, the Seventh Circuit reasoned that a portion of the benefit must be attributable to such past service: by upholding the taxpayer's deduction we would effectively eliminate the last part of section 404(a)(1)(A)(iii) which provided for the amortization of the cost of past service credits. It is simply inconceivable that Congress would take pains to provide for the amortization of past service credits but *450 intended to allow taxpayers to circumvent this requirement by the device*209 of structuring their plans to accrue benefits in a single year. * * * [Jerome Mirza & Associates, Ltd. v. United States, supra at 232; fn. ref. omitted.] *210 Respectfully, we must disagree with the Seventh Circuit in this regard, as we must with respondent's determination in these cases. 13 We are compelled to this conclusion for three reasons: (1) The language of section 404(a)(1)(A)(iii) setting forth the limit on deductible contributions uses the conditional phrase "if * * * provided by the plan" when setting forth the treatment for past service cost; (2) no express or implied connection exists between section 415 and section 1.412(c)(3)-1(e)(3), Income Tax Regs.; and (3) the unit credit funding method used in connection with a career average pay plan inherently allocates benefits in a reasonable manner to the past and future years of service with respect to which benefits accrued and will accrue. *211 Congress' use of the words "if * * * provided by the plan" in section 404(a)(1)(A)(iii) cannot be ignored simply because large deductions might be produced if a career average pay plan funded under the unit credit funding method does not grant credit for past service with the plan sponsor. While *451 such a result would not be possible for plan years beginning after December 31, 1986, 14 it is clearly the result under pre-1987 law. Since section 404(a)(1)(A)(iii) contemplates that plans might not grant credit for past service, there is no reason to believe that the normal cost -- the present value of benefit accruing in a particular plan year -- is not deductible so long as those benefits are payable under section 415(b)(1) and (5). We have concluded that the benefits petitioners, other than Fox, accrued were so payable and therefore were properly deducted under section 404(j)(1). *212 In addition, since there is no direct or implied relationship between section 415 and section 1.412(c)(3)-1(e)(3), Income Tax Regs., there is no authority supporting respondent's proposed one-tenth allocation formula in determining the normal cost for a particular plan year under section 1.412(c)(3)-1(e)(3), Income Tax Regs. Moreover, the allocation made under a career average pay plan funded under the unit credit funding method like petitioners' plans is automatic. A career average pay plan grants benefit accruals based on a specified percentage of each year's compensation (whatever it may be), and the present value of those benefits therefore relates directly to the year in which the benefits were accrued. Thus, the allocation of the projected benefits occurs annually via each year's normal cost in direct proportion to the accrual of those benefits. Accordingly, we hold that the allocations of projected benefits to past and future years of petitioners' plans were reasonable. We note again that respondent's interpretation results in underfunding the plan to the extent that respondent attributes a portion of the benefit to past service when the plan grants no credit for past *213 service. This underfunding would continue in a declining amount for 10 years, with the result that if the participant left the employ of the plan sponsor *452 or the plan otherwise terminated, there would be insufficient funds to pay the benefits. Petitioners' interpretation assures that all accrued benefits are funded, a clearly more desirable result. We also note that this is just a matter of timing. Once the benefit payable under the plan is fully funded, there can be no more contributions. Congress placed no restrictions on "frontloading" of accruals -- the concern was with "backloading" of accruals to circumvent the vesting requirements. The legislative history of each of the three tests in section 411(b) limiting the backloading of accruals expressly stated that unlimited frontloading of accruals is permissible. Sec. 411(b); H. Conf. Rept. 93-1280 (1974), 1974-3 C.B. 415, 434-435. Respondent also argued that petitioners' interpretation of the allocation provision would violate section 411(a)(3), which prohibits forfeitures of accrued benefits. According to respondent, if "a participant accrues a benefit in excess of the ratable portion*214 of the maximum benefit, then there will be a prohibited forfeiture if the participant leaves the service of the employer at any time before the full amount of the accrued benefit is payable under the phase-in rule of section 415(b)(5)." This argument, however, relies on the proposition that section 415 limits accruals. In support of this contention, respondent refers us to section 1.415-1(d)(1), Income Tax Regs. That section requires that the plan provisions of a qualified plan: preclude the possibility that the limitations imposed by section 415 will be exceeded. For example, a plan may include provisions which automatically freeze or reduce the rate of benefit accrual * * * to a level necessary to prevent the limitations from being exceeded with respect to any participant. * * * Respondent concluded that this language indicates that Congress intended section 415 to limit the accrual of benefits. We disagree. There is nothing in section 415 indicating that Congress intended section 415 to limit the accrual of benefits, and the regulation respondent cited does not compel such a result. The regulation's suggestion on how to prevent the plan from paying benefits in excess *215 of the section 415 limits cannot create a limitation on the accrual of benefits that Congress did *453 not expressly enact. Furthermore, we held that all of the plans, except perhaps Fox, funded no more than an amount which would be payable if the plan terminated immediately; therefore, no forfeiture could occur. Accordingly, we hold that petitioners' plans, other than the Fox plan, were funded within allowable limits and made reasonable allocations of costs. Timing of Plan Amendments Citrus Valley The Citrus Valley plan was amended twice. The first amendment was a conforming amendment which did not alter any of the provisions related to the computation of benefits. Respondent conceded that the first amendment did not affect the deductible contribution. The second amendment changed the normal retirement age from 65 to 64. Neither of the amendments contained an effective date or a signature date, and King's testimony regarding the date he signed the amendments was inconsistent. Citrus Valley argued that the timing of the amendment changing the normal retirement age is irrelevant because the use of age 65 as the normal retirement age was merely a mistake in drafting, *216 and Lawrence had independent knowledge of King's desire to retire at age 64. Respondent asserted that there was no evidence that the use of age 65 as the normal retirement age was a mistake, and that the timing of the second amendment is significant because the change in the normal retirement age affected the contribution level. As support for these arguments, respondent pointed to Lawrence's use of age 65 for the retirement age assumption in 1987 and 1988. The normal retirement age sets the date at which the plan participant is entitled to receive benefits; it does not affect directly the calculation of the benefit contribution. The determination of the retirement age assumption, which does affect the calculation of the benefit contribution, is influenced by the normal retirement age set by the plan documents; however, the normal retirement age is not controlling. Instead, the actuary must consider a variety of factors, particularly his expectations of the plan's retirement experience. *454 Lawrence knew that King intended to retire at age 64, and that the age 65 normal retirement age was a mistake. He spoke with the plan's attorney to ensure that the plan would be amended*217 to correct the error and was informed that the amendment had been made. Therefore, it was reasonable for him to assume age 64 as the retirement age for 1985 (as he also did for 1986), and the timing of the amendment to change the normal retirement age had no effect on the determination of the benefit contribution. Lawrence's use of age 65 as the retirement age assumption in 1987 and 1988 may or may not be relevant to this inquiry, but we are satisfied that for 1985, the year before us, age 64 was a reasonable assumption. Accordingly, we hold that the timing of the second amendment is irrelevant because it does not affect the calculation of the funding level. Davis Davis adopted a second amendment to his plan which was to be effective for the plan year ending December 31, 1985. The amendment changed the normal retirement age from 65 to 55. Respondent contended that the amendment was not effective for the 1985 plan year because it was not adopted timely, that no election of retroactive application was filed, and that Matthews had relied improperly on the amendment in computing the benefit contribution level. Davis argued that the timing of the amendment was not relevant *218 because the purpose of the amendment was to correct a drafting error, and Matthews had independent knowledge of Davis' intention to retire at age 55. Respondent asserted that the timing of the amendment was relevant, and the purpose of the amendment was to increase Davis' deduction, not to correct a drafting error. Respondent pointed to Matthews' use of an age 65 retirement age assumption for the 1984 plan year. As we noted above, it is the retirement age assumption, and not the plan's normal retirement age, that is used to calculate the benefit contribution. We concluded above that Matthews' use of age 55 for the retirement age assumption for the Davis plan was reasonable because Matthews had sufficient facts from which to conclude that Davis was likely to retire at age 55. In light of Davis' clear and adamant *455 statements that he was going to retire at age 55, the fact that Matthews used age 65 for the first year of the plan merely indicates that he made a mistake that year, not that Davis was attempting to manipulate his plan in order to obtain a greater deduction. We, therefore, hold that the second amendment to the Davis plan was irrelevant for the purpose of determining*219 the amount of the benefit contribution. Lear On December 15, 1986, Lear adopted an amendment relating to the benefit accrual formula and to benefit distribution which was to be effective for the plan year ending September 30, 1986. Both parties agreed that the amendment was adopted within the 2 1/2-month limit for it to have retroactive effect. The issue is whether the plan administrator made the necessary filing for electing retroactive application of the amendment. Section 11.412(c)-7(b)(3), Temporary Income Tax Regs., 39 Fed. Reg. 44751 (Dec. 27, 1974), requires the plan administrator to make a statement of election which shall: (i) State the date of the close of the first plan year to which the amendment applies and the date on which the amendment was adopted; (ii) Contain a statement that the amendment does not reduce the accrued benefit of any participant determined as of the beginning of the plan year preceding the plan year in which the amendment is adopted; and (iii) Contain either -- (A) A statement that the amendment does not reduce the accrued benefit of any participant determined as of the time of adoption of such amendment, or (B) *220 A copy of the notice filed with the Secretary of Labor under section 412(c)(8) and a statement that either the Secretary of Labor has approved the amendment or he has failed to act within 90 days after notification of the amendment. Lear acknowledged that a separate statement regarding the election was not filed; however, Lear argued that a separate statement was not required because the necessary information was supplied on the Form 5500-C. Lear noted that the year to which the amendment was to apply was stated at the top of the form, the date of adoption of the amendment was indicated on line 8c, and the necessary statements regarding the accrued benefits also were included on the form. Lear asserted that the information on the Form *456 5500-C was sufficient for substantial compliance, and that "letter-perfect compliance with Respondent's requirements is not always required." Respondent argued that the filing of the Form 5500 was not a satisfactory means of electing retroactive application of the amendment. Respondent asserted: "The requirement of the regulation would have no meaning if Form 5500 contained or requested all the pertinent information." Respondent maintained*221 that the information on the Form 5500 did not indicate that the plan administrator was making any election, or that the amendment was to be taken into account retroactively. We agree with Lear that the plan administrator provided sufficient information on the Form 5500-C to indicate that the amendment was to be given retroactive effect. This case is analogous to Martin Fireproofing v. Commissioner,92 T.C. 1173 (1989). In Martin Fireproofing, the plan administrator for a defined contribution plan failed to file a return or an "optional trust statement" in lieu of a return to start the running of the statute of limitations. Respondent had established the specific form for the optional trust statement; however, we held that the Form 5500 contained all of the required information; and therefore, a separate statement was not necessary. We decided that the plan was not required to use the exact form specified by respondent, provided the information supplied satisfied respondent's requirements. In the instant case, as in Martin Fireproofing, Lear provided all of the information required by respondent. The Form 5500 stated the plan year to which*222 the amendment applied. It also showed the date of adoption of the amendment, which was after the end of the plan year, indicating that the plan was to be retroactively effective. Since the Form 5500 also indicated that the amendment did not reduce any accrued benefits, the purposes of respondent's requirements have been satisfied. We hold that Lear substantially complied with the requirements of section 11.412(c)-7(b)(3), Temporary Income Tax Regs., supra, and the amendment was effective for the plan year ending September 30, 1986. *457 Fox The Fox plan adopted a first amendment relating to the benefit accrual formula, which was to be effective November 1, 1986, and a second amendment relating to participant eligibility and vesting, which was to be effective November 1, 1987. In the July 1, 1991, letter from respondent to Fox's counsel ordered by the Court to clearly set forth all contested issues, respondent stated that the timing of the second amendment was at issue, and failed to indicate that the timing of the first amendment was disputed. Fox argued that, as a result of respondent's failure, the timing of the first amendment was not at issue. Respondent*223 contended that the July 1, 1991, issue letter mistakenly identified the second, rather than the first, amendment as the amendment at issue, and that the first amendment was, in fact, at issue. We agree with respondent that the first amendment is the amendment at issue. Fox failed to raise this problem except on brief, despite the fact that respondent's discovery requests were aimed at the first amendment and not the second, and the stipulation of facts indicated that the timing of the first amendment was disputed. In addition, at trial, Fox introduced a substantial amount of evidence related to the timing of the first amendment. Fox had the opportunity to address the timing of the first amendment and to present evidence on that issue. We find that the timing of the first amendment is at issue. Fox argued that, even if the first amendment is at issue, the evidence showed that the amendment was timely adopted. However, the record does not support Fox's argument. The testimony of Fox's witnesses regarding the date of adoption of the first amendment is conflicting. Matthews testified that the decision to adopt the amendment was made in October 1987, and the letter setting forth*224 the recommended language was sent to Robert Lane (Lane), the plan's attorney, on December 5, 1987. Fox testified that the decision to adopt the amendment was made before October 31, 1986, even though, in response to respondent's interrogatories, Fox stated that the first amendment was not proposed until April-June 1987. Lane testified that the amendment was not signed on November 1, 1986, as the document stated but may have been signed prior to April of 1988. *458 The documentary evidence regarding the timing of the first amendment is much less equivocal. In a letter dated December 5, 1987, the actuaries sent the recommended language for the amendment to Lane, and in a letter dated April 8, 1988, Lane sent "the original and two copies of the First Amendment to the Jonathan R. Fox, M.D. Defined Benefit Pension Plan, which has been prepared at the request of your actuary, to achieve the desired funding level." The letter requested that the Foxes sign and return the documents. Fox attempted to explain away these documents as additional steps that took place after the amendment was signed, but the evidence does not support that contention. We hold that the first amendment*225 to the Fox plan was not timely filed and, therefore, was not effective for the plan year ending October 31, 1987. Change in Valuation Date Boren Steel During the second plan year, the valuation date of the Boren Steel plan was changed from the last day of the plan year, March 31, to the first day of the plan year, April 1. Boren Steel did not attach a statement regarding the change to the Schedule B for the year of the change; however, April 1, 1987, was listed on the Schedule B as the valuation date. Section 412(c)(5) requires the Secretary's approval for any change in funding method to be effective. Rev. Proc. 85-29, 1985-1 C.B. 581, provides for automatic approval of changes in funding methods subject to certain requirements. Under the revenue procedure, to qualify for automatic approval, a statement must be filed with the Schedule B which includes: (1) A description of the new funding method that is sufficiently complete so that another enrolled actuary can reproduce the result of the valuation of the plan year of change and for later plan years based upon such description; (2) A description of each amortization base that is being*226 maintained for the funding standard account for the plan, including the original amount of the base, the outstanding balance of the base as of the valuation date for the plan year for which the change in funding method is made, the remaining amortization period of the base, and the amortization charge or credit with respect to the base. [Rev. Proc. 85-29, 1985-1 C.B. at 583.] *459 A change in the valuation date is a change in funding method to which this requirement applies. Sec. 1.412(c)(2)-1(b)(3), Income Tax Regs. Boren Steel argued that the requirements of Rev. Proc. 85-29, supra, were met through the filing of the Form 5500 and the Schedule B for the year of the change. Boren Steel asserted that the change in funding method was described sufficiently by the statement of the new valuation date on the Schedule B. Moreover, Boren Steel asserted that no amortization schedule was required because "the individual aggregate cost funding method employed for the Boren Plan has no amortization base." Finally, Boren Steel noted that the plan administrator had manifested his approval by signing*227 the Form 5500 with the Schedule B attached. Respondent argued that the steps taken by Boren Steel were not sufficient to satisfy the requirements of Rev. Proc. 85-29, supra. Respondent noted that no separate statement requesting approval or describing the change in funding method was attached to the Form 5500, and Boren Steel answered "no" to the question on the Schedule B asking whether a change in funding method had been made. Respondent argues: "If this were adequate disclosure, the requirements of Rev. Proc. 85-29 would be meaningless." When discussing the timing of the Lear plan amendment above, we noted that an election need not be in the exact form mandated by respondent. However, Boren Steel was required to provide sufficient information to enable respondent to determine that a change had occurred. The Form 5500 and the attached Schedule B filed by Boren Steel did not meet that requirement. Looking at the Form 5500 and Schedule B alone, respondent could not tell that any change had occurred. Boren Steel stated on the form that no change in funding method had occurred. The question*228 regarding change in funding method should have been answered in the affirmative. We hold that Boren Steel did not provide sufficient information to take advantage of the automatic approval provisions of Rev. Proc. 85-29, supra; therefore, the change in valuation date for the Boren Steel plan is invalid. *460 Hours of Service Three of the eight plans, Citrus Valley, Old Frontier, and Boren Steel, required participants to work 1,000 hours per year to accrue benefits. Respondent argued that participants in each of these plans, King, Rocke, and Boren, respectively, failed to prove that they completed the requisite 1,000 hours of service. The only evidence proffered by petitioners in support of their contention that the 1,000-hour requirement was fulfilled was testimony at trial from the three plan participants. Citrus Valley Citrus Valley was engaged in the business of real estate development. King's duties included driving between job sites to supervise the work crews and check the progress of the construction projects which he oversaw. He testified that he got to his office at 8 a.m. and often was not home before 10 *229 p.m. due to planning and zoning meetings he would have to attend. He also stated that he usually worked on Saturdays and Sundays. Respondent countered King's testimony by stating that at the time he was employed by Citrus Valley, he also was employed by King Investment Corp., which provided services to Citrus Valley, and of which King was sole shareholder. To achieve 1,000 hours of service annually, King needed only an average of 20 hours of work per week. His testimony indicates that substantially in excess of 20 hours per week were devoted to Citrus Valley, over and above any service to King Investment Corp. We find that King fulfilled his obligation to work 1,000 hours for Citrus Valley in each of the years at issue. Old Frontier Old Frontier was engaged in the business of dealing in baseball cards. It also owned a small insurance adjusting company and a building which it leased to a commercial tenant. Rocke testified that he spent at least 5 hours per week doing light maintenance work on the building. He estimated that he also spent on average of 5 hours per week engaged in the insurance adjusting business. Finally, he stated that he spent at least another 1,000*230 hours per year working for the baseball card business, for which his duties included the *461 purchasing, sorting, classification, valuation, storage, and remarketing of very large numbers of baseball cards nationwide. Rocke testified that Old Frontier had more than 1 million cards in inventory. Respondent countered this testimony with the fact that at the same time he was employed by Old Frontier, Rocke was president of two other national insurance adjusting firms. Rocke's work with Old Frontier and the other two firms was not mutually exclusive. We are satisfied that Rocke worked more than 1,000 hours with Old Frontier in each of the years at issue in addition to fulfilling his other responsibilities, and we so find. Boren Steel Boren consulted with construction contractors, subcontractors, and others regarding structural steel, steel tanks, reinforcing steel (for concrete), steel stairs, and miscellaneous steel fabrication. Boren testified that he worked between 50 and 60 hours per week for Boren Steel. Respondent countered that Boren Steel's main client was Arizona Rebar (Rebar), and that Boren spent at least 30 hours per week working on the premises of Rebar. *231 Rebar was 43 percent owned by Boren and also was Boren's former employer. Boren testified that the majority of Boren Steel's income came from contracts with Rebar, which would account for much of his time spent at Rebar. He also identified five other non-Rebar clients of Boren Steel. We find that Boren worked at least 1,000 hours annually for Boren Steel during each of the years at issue. Section 4972 Excise Tax Respondent imposed an excise tax under section 4972 for Boren Steel's December 31, 1987, and December 31, 1988, tax years. Section 4972 provides for a 10-percent tax on any portion of a contribution that is determined to be nondeductible. Boren Steel conceded that if this Court determines that it made nondeductible contributions during the years in question, the excise tax applies. Matthews admitted that he calculated the contribution for the plan year ending March 31, 1988, based on a greater benefit than was permitted. In addition, our holding above that the change in valuation date for that year was ineffective *462 will likely reduce the amount of the deductible contribution. Therefore, we hold that Boren Steel made a nondeductible contribution and some*232 excise tax is owed. In making their Rule 155 calculation, the parties will have to determine the amount of the nondeductible contribution and will have to apply the 10-percent excise tax against that amount. Section 6651 Failure to File Addition to Tax Since respondent determined that Boren Steel owed an excise tax under section 4972 and Boren Steel failed to file a Form 5330, Return of Excise Taxes Related to Employee Benefit Plans, as required by section 54.6011-1, Pension Excise Tax Regs., respondent imposed additions to tax under section 6651(a)(1) for failure to file the required return. Boren Steel argued that section 6651(a)(1) was not applicable to the excise tax because: According to the express language of the statute, the penalty applies only to income tax returns and estate and gift tax returns covered by I.R.C. Chapter 61 and the returns required for the excise taxes on liquor, tobacco and machine guns and other firearms covered by I.R.C. Chapters 51, 52 and 53, respectively. I.R.C. section 6651(a)(1); Treas. Reg. section 301.6651-1(a). The statute makes no reference to the I.R.C. section 4972 excise tax on nondeductible contributions to qualified plans, which*233 is imposed under Chapter 43. Boren Steel misinterpreted the language of section 6651(a)(1). The statute imposes a penalty for "failure to file any return required under authority of subchapter A of chapter 61" (emphasis added), not just for failure to file income tax and estate and gift tax returns. Included in subchapter A of chapter 61 is section 6011(a), which states: "When required by regulations prescribed by the Secretary any person made liable for any tax imposed by this title, or with respect to the collection thereof, shall make a return or statement according to the forms and regulations prescribed by the Secretary." The Form 5330 is required to be filed under the authority of that section. Accordingly, section 6651(a)(1) is applicable in the case of a failure to file a Form 5330. Boren Steel further argued that the section 6651(a)(1) addition to tax should not be imposed in its case because its failure to file was "due to reasonable cause and is not due to willful neglect." Boren Steel asserted that its failure to file *463 the excise tax return was for reasonable cause, noting: "Boren reasonably relied on its experienced and knowledgeable Consulting Actuary, *234 Steven Matthews, in the technical and complex area of private pension plans." Respondent determined that Boren Steel did not exercise reasonable care, claiming that Boren Steel was not entitled to rely blindly on Matthews. Respondent cited various errors made by Matthews to demonstrate that Boren Steel had not acted reasonably. Although we agree that a taxpayer cannot rely blindly on a tax professional and then claim reasonable care has been exercised, we do not find that such was the case here. Boren Steel provided Matthews with the information he needed to complete the actuarial computations and consulted with him regarding the contributions and deductions. Due to the complicated nature of the actuarial calculations, it was reasonable for Boren Steel to accept the accuracy of the contribution amount computed by Matthews without question. Few nonactuaries would be able to follow the calculations, and Congress recognized the need to leave this complicated matter in the hands of the actuaries. Accordingly, we hold that Boren Steel's failure to file the Form 5330 was due to reasonable reliance on its actuary and was not due to willful neglect; therefore, the section 6651(a)(1)*235 addition to tax does not apply. Section 6659A Additions to Tax Respondent imposed additions to tax under section 6659A on each petitioner for various years. Section 6659A(a) provides for an addition to tax when an underpayment of tax is "attributable to an overstatement of pension liabilities". There is an overstatement of pension liabilities "if the actuarial determination of the liabilities taken into account for purposes of computing the deduction under * * * section 404(a) exceeds the amount determined to be the correct amount of such liability." Sec. 6659A(c). The addition to tax is imposed only if the overstated liability is 150 percent or more of the correct liability. Sec. 6659A(b). Section 6659A(e) states: "The Secretary may waive all or any part of the addition to the tax provided by this section on a showing by the taxpayer that there was a reasonable basis for the valuation *464 claimed on the return and that such claim was made in good faith." In Citrus Valley, Davis, Old Frontier, Lear, Stephan, and Brody Enterprises, we find for petitioners. The entire amount of each of the pension liabilities was properly deducted, and there were no overstatements*236 of pension liabilities. Therefore, for those six cases, there are no section 6659A additions to tax. In the remaining two cases, Boren Steel and Fox, we find for respondent in part; therefore, additions to tax under section 6659A may result. However, we do not have sufficient information to determine the appropriate amounts of the deduction and cannot determine if any overstated liabilities are 150 percent or more of the correct deductions. We leave those calculations to the parties under Rule 155. Petitioners argued that even if section 6659A applies, the additions to tax should not be imposed because there was a reasonable basis for the valuation and petitioners acted in good faith. Section 6659A(e) does not provide for automatic waiver upon proof of reasonable basis and of good faith; it states "The Secretary may waive" (emphasis added) the additions upon a finding of reasonable basis and good faith. Such language gives the Secretary discretion to determine whether waiver is appropriate. Any determination in that regard should stand unless it was arbitrary and capricious. Mailman v. Commissioner,91 T.C. 1079, 1083-1084 (1988) (interpreting*237 similar language in section 6661). Petitioners asserted that it was an abuse of discretion for respondent to refuse to waive the additions to tax under section 6659A(e) but have failed to demonstrate that respondent acted arbitrarily and capriciously. In the two cases in which that section remains at issue, Fox and Boren Steel, there were some facts from which respondent could have determined that petitioners did not have a reasonable basis for the valuation and had not acted in good faith. Therefore, we hold that it was not an abuse of discretion for respondent to decline to waive the section 6659A additions to tax. *465 Conclusions We find that all of the challenged actuarial assumptions for each of the plans at issue were reasonable. In addition, we find that the certifying actuaries for the Davis, Lear, Stephan, and Brody Enterprises plans funded within allowable limits and made reasonable allocations of costs, and the certifying actuary for the Fox plan made reasonable allocations of costs. Accordingly, we find that the actuarial assumptions and funding methods used for the plans are reasonable in the aggregate. A fortiori, these assumptions and methods are not*238 substantially unreasonable so as to permit retroactive changes for years prior to the year in which the audit was made. We further find that the actuarial assumptions and methods certified by the three enrolled actuaries in combination offer the actuaries' best estimates of anticipated experience under the plans. We also find that the timing of the Citrus Valley and Davis amendments at issue were irrelevant, that the proper election was made for the Lear plan amendment to have retroactive effect, and that the first amendment to the Fox plan was at issue and was not timely adopted. In addition, we find that Boren Steel failed to file the proper notice for automatic approval for a change in valuation date, and King, Rocke, and Boren completed 1,000 hours of service for each year of service claimed, as required by their plans. Finally, we find that Boren Steel is liable for the section 4972 excise tax on nondeductible contributions, but is not liable for the additions to tax under section 6651(a)(1) for failure to file excise tax returns; Citrus Valley, Davis, Old Frontier, Lear, Stephan, and Brody Enterprises are not liable for section 6659A additions to tax; and Boren Steel and*239 Fox are liable for section 6659A additions to tax if the overstated liabilities are 150 percent or more of the correct liabilities. Decisions will be entered for petitioners in docket Nos. 12900-89, 22599-89, 6505-90, 13406-90, 13407-90, 19117-90, 24352-90, and 177-91. Decisions will be entered under Rule 155 in docket Nos. 13449-90, 19654-90, 19716-90, and 15473-91. *466 Hamblen, Chabot, Parker, Cohen, Swift, Jacobs, Gerber, Wright, Parr, Wells, Whalen, Colvin, Halpern, and Beghe, JJ., agree with the majority opinion. RUWE Ruwe, J., dissenting: I respectfully dissent for the reasons set forth in Jerome Mirza & Associates, Ltd., v. United States,882 F.2d 229 (7th Cir. 1989), affg. 692 F. Supp. 918 (C.D. Ill. 1988), and Rev. Rul. 85-131, 1985-2 C.B. 138. Footnotes 1. Cases of the following petitioners are consolidated herewith: Robert J. Davis and Janice A. Davis, docket No. 22599-89; Old Frontier Investment, Inc., of Arizona, docket No. 6505-90; Lear Eye Clinic, Ltd., docket No. 13406-90; Robert Stephan, Jr., P.C., docket No. 13407-90; Boren Steel Consultants, Inc., docket No. 13449-90; Lear Eye Clinic, Ltd., docket No. 19117-90; Arizona Orthopedic Institute of Traumatic and Reconstructive Surgery, P.C., docket No. 19654-90; Jonathan R. Fox and Renee K. Fox, 19716-90; Citrus Valley Estates, Inc., An Arizona Corporation, docket No. 24352-90; Brody Enterprises, Inc., docket No. 177-91; and Boren Steel Consultants, Inc., docket No. 15473-91.↩ *. Brief amicus curiae was filed by David R. Levin, C. Frederick Reish, and Bruce L. Ashton as attorneys for the American Society of Pension Actuaries.↩ 1. This figure includes a net operating loss carryover from 1986 which takes into account the 1986 pension plan deduction.↩ 1. Manulife OMS B74 guaranteed annuity rates, female table.↩ 2. 64 and 5 years (1985 and 1986).↩ 3. 65 and 6 years (1987 and 1988).↩ 4. Straight life annuity (all years).↩ 5. Manulife OMS B74 guaranteed annuity rates, female table (1958).↩ 6. 1983 IAM, female rates (-3) (1986).↩ 7. 1983 IAM, female rates (-7) (1987 and 1988).↩ 2. Form 5500 is a report filed with the Dept. of Labor, the Internal Revenue Service, and Pension Benefit Guaranty Corp. by all ERISA-qualified (i.e., tax-qualified) pension plans. Form 5500 contains information such as interest rate assumptions, actual rates of return, and plan funding status.↩ 1. Joint and 100 percent survivor annuity.↩ 1. This number was in fact higher due to cost of living and other adjustments made annually pursuant to sec. 415(b)(2)↩. 1. Straight life annuity (all years).↩ 2. 1971 individual annuity table for males with 6-year setback for females.↩ 1. Joint and 100 percent survivor annuity.↩ 1. However, the actuary included service with a predecessor employer from 1975.↩ 1. This number was in fact higher due to cost of living and other adjustments made annually pursuant to sec. 415(b)(2)↩. 2. This number includes $ 36,000 of benefits accrued under a different actuarial method.↩ 1. Joint and 100 percent survivor annuity.↩ 2. Unisex table developed from the 1983 IAM table projected to 2000 Scale G.↩ 1. This number was in fact higher due to cost of living and other adjustments made annually pursuant to sec. 415(b)(2)↩. 1. Joint and 100 percent survivor annuity.↩ 1. The enrolled actuary included service from 4/1/81, with a predecessor employer from 1981.↩ 1. Joint and 100 percent survivor annuity.↩ 1. Female spouse assumed to be 3 years younger.↩ 2. Male spouse assumed to be 3 years older.↩ 1. Joint and 100 percent survivor annuity.↩ 2. 1983 IAM for females (-7) (8605).↩ 3. 1983 IAM for females (-7) (8705).↩ 1. This number was in fact higher due to cost of living and other adjustments made annually pursuant to sec. 415(b)(2)↩. 3. M.A.A.A.: Member of the American Academy of Actuaries. The highest (and only) designation in that organization. The American Academy of Actuaries issues standards of practice and sets discipline procedure for the actuarial profession.↩ 4. A.S.A.: Associate of the Society of Actuaries. "Associate" is a society designation below that of "fellow". The society is a certification organization for actuaries which administers exams to demonstrate educational qualifications. The society also conducts and publishes studies concerning mortality and health risks.↩ 5. E.A.: Enrolled Actuary. Actuaries may be "enrolled" by the Joint Board for the Enrollment of Actuaries, a certifying organization composed of members appointed by the Secretaries of the Treasury and of Labor, which was established in 1974 pursuant to the Employee Retirement Income Security Act of 1974 (ERISA), Pub. L. 93-406, 88 Stat. 829, 1002. ERISA requires that defined benefit plans be audited annually on behalf of their participants by an actuary so enrolled. The actuary makes funding assumptions for the plans and certifies as to the reasonableness in the aggregate of those assumptions.↩ 6. F.S.A.: Fellow of the Society of Actuaries. "Fellow" is the society's highest designation; to be so designated, one must pass a full syllabus of examinations.↩ 7. F.C.A.: Fellow of the Conference of Consulting Actuaries. The highest designation in that organization. Fellowship requires 12 years of responsible actuarial work. All members are consultants, as distinguished from insurance company actuaries.↩ 8. LTV, Eastern Air Lines, and Pan American Airlines are among the well-known, underfunded defined benefit pension plans to terminate leaving the Pension Benefit Guaranty Corp. (PBGC) to cover the underfunded benefit obligation. A Nov. 25, 1991, PBGC news release reported that the 50 largest underfunded pension plans were underfunded by $ 14.2 billion in 1990, up 50 percent from 1989.↩ 9. Sec. 412(c)(3)↩ requires the actuarial assumptions to be reasonable in the aggregate "taking into account the experience of the plan" as well as reasonable expectations for the future. 10. Citrus Valley had a valuation date of January 1. On that date in 1987, Citrus Valley had 2 years remaining until the normal retirement date, and 2-year Treasury obligations were yielding 6.33 percent. Using Rigel's methodology, we thus arrive at a reasonable interest rate assumption of 5.33 percent.↩ 11. For plan years beginning after Dec. 31, 1986, sec. 415(b)(5) was amended to restrict the sec. 415(b)(1) dollar limitation for participants with less than 10 years of participation in the plan. See infra↩ note 14. 12. Respondent also cites Custom Builders, Inc. v. Commissioner,T.C. Memo. 1989-620, which follows Jerome Mirza & Associates, Ltd. v. United States,882 F.2d 229 (7th Cir. 1989), in this respect. Since that case was appealable to the Seventh Circuit and was decided after Mirza, we were bound to follow Mirza. Golsen v. Commissioner,54 T.C. 742 (1970), affd. 445 F.2d 985 (10th Cir. 1971). Respondent proffered the expert report of James E. Holland, Jr. (Holland), prepared in connection with Custom Builders↩. We have reviewed the report and its rationale and have found the arguments offered are substantially the same as those respondent presents here. For the reasons stated below, we disagree with the conclusions reached by Holland in the report. 13. Congress must have recognized that the law it was enacting afforded plan sponsors the opportunity to avoid a lengthy amortization of past service liability by not providing participants credit for past service. Nevertheless, Congress gave plan sponsors a choice: they could grant credit for past service and amortize the resulting past service liability or they could not grant credit for past service and annually fund benefits as they accrued each year. We believe that Congress was focusing on large corporate plans rather than small plans when it enacted these provisions. Large corporations could create substantial employee relations problems by adopting plans which did not give credit for past services. It would be a deterrent to adopting any plan at all if a corporation were required to fund immediately the past service liability created. Thus, Congress allowed plan sponsors to fund past service liabilities over a period of 10 to 30 years, thereby permitting such corporations to spread out the payments and ease the strains on their cashflows. Secs. 404(a)(1)(A)(iii), 412(b)(2)(B)(ii). If a participant in a large plan were to become entitled to benefits before the past service funding period had expired, there would be adequate funds to pay those benefits. The underfunding as to that particular participant could be made up later out of contributions to the plan on behalf of participants who did not become entitled to benefits until after the amortization period had expired. That this sort of averaging is available to large plans and not to small plans, is a factor known to all actuaries, and is a factor which we believe was taken into account by Congress. In a small plan, a sponsor may omit providing for benefits based upon past service and thus avoid the amortization for past service if it so desires and is ready, willing, and able to fund all accrued benefits. The rationale for large corporations granting participants credit for past service does not necessarily apply to small plan sponsors. Congress clearly gave small plan sponsors the option not to provide for benefits based upon past services, thus allowing small plans to be fully funded immediately, which is a more desirable result than amortizing past service liabilities and being partially unfunded during the amortization period. We do not find that "It is simply inconceivable that Congress would take pains to provide" various options for plan sponsors because large and small plans have different concerns. Jerome Mirza & Associates, Inc. v. United States, supra↩ at 232. 14. The Tax Reform Act of 1986, Pub. L. 99-514, sec. 1106, 100 Stat. 2085, 2424, amended sec. 415(b)(5) so that for plan years beginning after Dec. 31, 1986, the sec. 415(b)(1)↩ dollar limitation is phased in over the first 10 years of participation in the plan rather than 10 years of service with the plan sponsor. The legislative history regarding the impetus behind this change is clear: Congress was concerned that plan sponsors could time the establishment of plans to discriminate in favor of highly compensated employees. Both House and Senate committee reports express the desire to limit a highly compensated employee's ability to accumulate the maximum benefit in a short period of plan participation after other employees had retired. Thus, Congress recognized that pre-1987 law permitted plan sponsors to fund substantial benefits quickly. H. Rept. 99-426 (1985), 1986-3 C.B. (Vol. 2) 737, 740-741; S. Rept. 99-313 (1985), 1986-3 C.B. (Vol. 3) 620, 623.