Court Opinion

ID: 4336057
Source: CourtListenerOpinion
Date Created: 2018-11-14 02:37:25.715332+00
Date Added: 2024-06-11T14:48:02.947929
License: Public Domain

FEDERAL HOME LOAN MORTGAGE CORPORATION, Petitioner v. COMMISSIONER OF INTERNAL REVENUE, RespondentFed. Home Loan Mortg. Corp. v. Comm'rNos. 3941-99, 15626-99 United States Tax CourtT.C. Memo 2006-153; 2006 Tax Ct. Memo LEXIS 155; 92 T.C.M. 59; July 25, 2006, Filed Fed. Home Loan Mortg. Corp. v. Comm'r, 125 T.C. 248">125 T.C. 248, 2005 U.S. Tax Ct. LEXIS 33">2005 U.S. Tax Ct. LEXIS 33 (2005)2006 Tax Ct. Memo LEXIS 155">*155  At the close of business on Dec. 31, 1984, P had 30 debt   instruments outstanding on which it paid effective contract   interest rates that were below current interest rates that P   would have incurred had it issued comparable debt instruments.   P's right to use the proceeds of these financing arrangements   with below-market interest rates constitutes an economic   benefit generally referred to as "favorable financing". In a   prior Opinion, we held that special legislative provisions   entitled P to use the fair market values of its intangible   assets on Jan. 1, 1985, as its bases for purposes of   amortization. Fed. Home Loan Mortgage Corp. v.   Commissioner, 121 T.C. 125">121 T.C. 125 (2003). In another prior Opinion,   we held that the benefit of below-market financing can, as a   matter of law, constitute an intangible asset which P may   amortize if it establishes a fair market value and a limited   useful life. Fed. Home Loan Mortg. Corp. v.   Comm'r, 121 T.C. 254 (2003).   P calculated the fair market value of its favorable financing   intangible assets to be $ 428,391,5512006 Tax Ct. Memo LEXIS 155">*156  using the market approach;   the market approach compared the adjusted issue prices of P's   debt instruments to their market prices on Jan. 1, 1985. P   calculated the limited useful lives of its 30 debt instruments   to be their average weighted lives. R argues that P's favorable   financing had no value and was not an asset. R also argues that   P did not properly adjust for the volatility of the market in   determining the useful lives.   Held: P may amortize its favorable financing intangible   assets because it reasonably estimated the fair market value of   its favorable financing to be $ 428,391,551 and reasonably   estimated the remaining limited useful lives.  Robert A. Rudnick, B. John Williams, Jr., James F. Warren, Alan J.J. Swirski, and Richard J. Gagnon, Jr., for petitioner.Gary D. Kallevang, John A. Guarnieri, Ruth M. Spadaro, and Charles E. Buxbaum, for respondent.  Ruwe, Robert P.Robert P. RuweCONTENTSMEMORANDUM FINDINGS OF FACT AND OPINIONFINDINGS OF FACTI. Favorable Financing Intangible Assets   A. Ginnie Mae Bonds   B. Notes Issued to2006 Tax Ct. Memo LEXIS 155">*157 Federal Home Loan Banks   C. Debenture   D. Note Payable to North Dakota Bank   E. Capital Debentures   F. Zero Coupon Bonds   G. Collateralized Mortgage Obligations (CMOs)   H. Guaranteed Mortgage Certificates (GMCs)II. Average Weighted Lives of the Debt InstrumentsIII. Tax ReturnsOPINIONI. The Values of Petitioner's Favorable Financing Intangible Assets   A. Petitioner's Valuation of Its Favorable Financing Intangible   Assets as of January 1, 1985   B. Respondent's Position That Favorable Financing Has No Value     1. Expectation of Income     2. Realization of Value     3. Contra-Liability Theory        a. Favorable Financing Is an Asset        b. Favorable Financing Can Be Assigned a Separate        Value        c. Double Counting the Value     4. Petitioner's Purchase of Its Debt Obligations Would     Result in Discharge of Indebtedness Income   C. Respondent's Argument That the Value of Petitioner's   Favorable Financing Is Limited2006 Tax Ct. Memo LEXIS 155">*158  to the Value of Petitioner's   Income Spread   D. Respondent's Argument That Taxes Reduce the Value of   Favorable FinancingII. Favorable Financing Intangible Assets Have a Reasonably EstimableUseful Life As of January 1, 1985III. ConclusionAPPENDIX: Investment Bank Bid PricesMEMORANDUM FINDINGS OF FACT AND OPINIONRUWE, Judge: In docket No. 3941-99, respondent determined deficiencies in petitioner's Federal income tax of $ 36,623,695 for 1985 and $ 40,111,127 for 1986. Petitioner claims overpayments of $ 9,604,085 for 1985 and $ 12,418,469 for 1986.In docket No. 15626-99, respondent determined deficiencies in petitioner's Federal income tax of $ 26,200,358 for 1987, $ 13,827,654 for 1988, $ 6,225,404 for 1989, and $ 23,466,338 for 1990. Petitioner claims overpayments of $ 57,775,538 for 1987, $ 28,434,990 for 1988, $ 32,577,346 for 1989, and $ 19,504,333 for 1990.When petitioner was chartered, it was exempt from Federal, State, and local taxation, except for real estate tax imposed by any State or local taxing authority. Pursuant to the Deficit Reduction Act of 1984 (DEFRA), Pub. L. 98-369, sec. 177, 98 Stat. 709, petitioner became2006 Tax Ct. Memo LEXIS 155">*159  subject to Federal income tax effective January 1, 1985. In a prior opinion, Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 129">121 T.C. 129, 121 T.C. 129">147 (2003), we held "that petitioner's adjusted basis for purposes of amortizing intangible assets under section 167(g)1 is the higher of regular adjusted cost basis or fair market value as of January 1, 1985." (Fn. ref. omitted.) 2006 Tax Ct. Memo LEXIS 155">*160 In another prior opinion, Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 254, 121 T.C. 254">272 (2003), we held that "The benefit of petitioner's below-market financing can, as a matter of law, constitute an intangible asset which could be amortized if petitioner establishes a fair market value and a limited useful life as of January 1, 1985." The benefit of below- market financing is generally referred to as "favorable financing". In this opinion, we decide whether petitioner has established that its favorable financing intangible assets have fair market values that may be reasonably estimated and have ascertainable limited useful lives as of January 1, 1985. 2FINDINGS OF FACTSome of the facts have been stipulated and are so found. The stipulations of facts and the attached exhibits are incorporated herein by this reference. At the time the petitions were filed, petitioner's principal office was in McLean, Virginia.Congress created petitioner in 1970 to promote access to mortgage credit throughout the United States by increasing the liquidity of mortgage investments and improving the distribution of investment capital for mortgage financing. Since its incorporation, petitioner has facilitated investment by the capital markets in single-family and multifamily residential mortgages in two ways. First, petitioner has acquired mortgages from originators and resold them in securitization transactions, principally by pooling the mortgages and issuing participation certificates2006 Tax Ct. Memo LEXIS 155">*161  (PCs). Second, petitioner bought mortgages from originators and held them until maturity in its retained mortgage portfolio, generally financing this activity by issuing various debt instruments. Petitioner financed approximately 10 percent of its mortgage purchases through the issuance of long-term debt. 3I. Favorable Financing Intangible AssetsAt the close of business on December 31, 1984, petitioner had outstanding long-term indebtedness on a number of debt instruments. The effective contract interest rates 4 on some of these outstanding long-term debt obligations were below the interest rates that petitioner would have incurred on January 1, 1985, had it issued comparable debt instruments in the market for the remaining term of the particular debt instrument. Petitioner's favorable financing intangible assets consisted of the benefits it derived from financing arrangements that required2006 Tax Ct. Memo LEXIS 155">*162  it to pay interest at rates below those prevailing in the financial markets as of January 1, 1985.As of January 1, 1985, petitioner had the following 30 outstanding long-term debt instruments, which had below-market interest rates and market prices that were lower than the adjusted issue prices.A. Ginnie Mae BondsGinnie Mae Bonds G-15, G-16, and G-17 were mortgage-backed bonds, which consisted of promissory notes secured by mortgage loans owned by petitioner. The underlying mortgages were held in trust by petitioner as trustee as security for payment of the bonds. These mortgage-backed bonds were guaranteed as to principal and interest by the Government National Mortgage Association, 2006 Tax Ct. Memo LEXIS 155">*163  a wholly owned corporation within the Department of Housing and Urban Development.B. Notes Issued to Federal Home Loan BanksNotes F-8, F-12, F-15, F-18, F-11, and F-13 were promissory notes payable to Federal Home Loan Banks (FHLB). These notes were passthroughs of the FHLBs' own obligations. Under the Federal Home Loan Mortgage Corporation Act, Pub. L. 91-351, sec. 303(a), 84 Stat. 452 (1970), petitioner was deemed to be a member of each FHLB and was entitled to borrow from those institutions subject to certain security requirements.C. DebentureDebenture D-2 was issued under section 306(a) of the Federal Home Loan Mortgage Corporation Act. This debenture was an unsecured general obligation of petitioner.D. Note Payable to North Dakota BankThe note bearing code ND was a fixed-rate loan that petitioner issued in a private transaction to the Bank of North Dakota.E. Capital DebenturesCD-1, CD-2, and CD-3 were capital debentures. These capital debentures were subordinated and junior in right of payment to all obligations and liabilities of petitioner.F. Zero Coupon BondsPetitioner issued zero coupon bonds Z-2 and Z-3, which were subordinated capital debentures junior2006 Tax Ct. Memo LEXIS 155">*164  in right of payment to all senior obligations of petitioner. Zero coupon bonds have no stated interest rate but are issued at a substantial discount to face value. At maturity, the holder is entitled to receive the face of amount of the bond.G. Collateralized Mortgage Obligations (CMOs)CMO A-2, CMO A-3, and CMO C-4 were debt instruments secured by mortgages which were outstanding on December 31, 1984. These CMOs were subject to put and call options; the call dates, put dates, and final maturity dates were as follows:   Debt       Call   Put       Final  Instrument      Date n.1      Date n.2    Maturity Date  __________      ____       ____     _____________  CMO A-2       N/A       N/A      12/15/95  CMO A-3      6/15/03     6/15/08      6/15/13  CMO C-4      1/31/04     1/31/04      1/31/09n.1 The call date is the earliest date on which petitioner, if it so chose, could repay the debt in full.n.2 The put date is the earliest date on which the holder had the right to require2006 Tax Ct. Memo LEXIS 155">*165  petitioner to pay any remaining unpaid principal balance plus accrued interest.Each series of CMOs was collateralized by pools of mortgages owned by petitioner and held by it as trustee. 5 Petitioner made principal payments to holders in the greater amount of (1) the minimum scheduled payments, or (2) monthly and other payments of principal petitioner received on the mortgages serving as collateral. Petitioner structured the CMOs to permit holders of certain classes to receive payment in full before other classes.The terms of each CMO required petitioner to apply all payments of principal and interest on the subject mortgages into a sinking fund for the benefit of the holders. Petitioner was required to make payments to the sinking fund semiannually. The balance of the sinking fund was then used to make semiannual principal payments on2006 Tax Ct. Memo LEXIS 155">*166  the senior class of bonds until they were fully retired. Thereafter, additional amounts of principal were paid semiannually to the holders of the class of bonds next in seniority until those bonds were fully paid, and then on the same basis to holders of the most junior classes. The holders received semiannual interest payments at the stated rate. 6 The holders of CMOs received payments of principal at a rate at least corresponding to the schedule of minimum payments set forth in the offering circular or prospectus. The holders received payments at a faster rate if the principal amount of the mortgages that served as collateral paid down faster than implied by the schedule of minimum payments. Petitioner never had to satisfy any minimum sinking fund obligation (i.e., cover a deficit between funds received from mortgages and minimum payments of principal to CMO holders).2006 Tax Ct. Memo LEXIS 155">*167  H. Guaranteed Mortgage Certificates (GMCs)GMC A 1975, GMC B 1975, GMC A 1976, GMC B 1976, GMC A 1977, GMC B 1977, GMC C 1977, GMC A 1978, GMC B 1978, GMC C 1978, GMC A 1979, GMC B 1979, and GMC C 1979 were certificates guaranteed by petitioner and denominated as representing an interest in a pool of single- family mortgages held by petitioner as trustee. 72006 Tax Ct. Memo LEXIS 155">*168  The terms of each GMC series obligated petitioner to pay interest at a rate stated on the face of its prospectus and to repay the face amount of the certificate to the holder. Principal payments were made annually. GMC holders received principal repayments in amounts equal to the greater of (1) minimum scheduled payments, or (2) monthly and other payments of principal petitioner received on the mortgages serving as collateral. Petitioner was unconditionally required to make annual principal payments to the GMC holders in an amount at least equal to the minimum levels specified, regardless of the amounts of principal received from the underlying mortgages. If mortgages that served as collateral paid down the principal amount faster than implied by the schedules of minimum payments, GMC holders received payments of principal at a faster rate than required by the schedule of minimum payments. GMCs holders had the option to require petitioner to purchase their certificates at the then-unpaid principal balance plus accrued interest at a future date specified by the prospectus.With respect to the 13 GMCs in issue, the put dates and the final maturity dates were as follows:  2006 Tax Ct. Memo LEXIS 155">*169       Debt          Put        ?  Final     Instrument         Date       Maturity Date     __________         ____       _____________     GMC A 1975        3/15/90        3/15/05     GMC B 1975        9/15/90        9/15/05     GMC A 1976        3/15/91        3/15/06     GMC B 1976        3/15/96        9/15/06     GMC A 1977        3/15/97        3/15/07     GMC B 1977        3/15/02        3/15/07     GMC C 1977        9/15/02        9/15/07     GMC A 1978        3/15/03        3/15/08     GMC B 1978        9/15/03        9/15/08     GMC C 1978        9/15/03        9/15/08     GMC A 1979        3/15/04        3/15/09     GMC B 1979        3/15/04       2006 Tax Ct. Memo LEXIS 155">*170   3/15/09     GMC C 1979        9/15/04        3/15/09With the possible exception of GMC B 1975, petitioner made minimum payments pursuant to the schedule for all GMCs on all payment dates after March 1980 through September 1993. 8 For GMC B 1975, petitioner made minimum payments on all payment dates after December 31, 1984.Petitioner initially funded the acquisition of the mortgages held as collateral for each of the CMOs and GMCs at issue by means other than the issuance of those particular CMOs and GMCs. When issuing its GMCs, petitioner disclosed that the proceeds would provide funds for petitioner to engage in additional activities consistent with its statutory purposes, including the purchase of additional mortgages and interests in mortgages and2006 Tax Ct. Memo LEXIS 155">*171  that some portion of the proceeds could be used to repay part of petitioner's borrowings. When issuing its CMOs, petitioner disclosed that the proceeds would be used to provide funds for the corporation to finance its purchase of the mortgages securing the CMOs.With respect to the CMOs and GMCs, petitioner received monthly payments of interest and principal on the mortgages that served as collateral. Petitioner made semiannual or annual payments of principal and interest to the CMO and GMC holders. Petitioner paid interest through the date of payment to the holders on the outstanding principal balance of the CMOs or GMCs, notwithstanding any receipt of principal amounts on the mortgages serving as collateral since the previous date of payment.Petitioner received spread and float income with respect to the CMOs and GMCs. Spread income is the amount by which the effective interest income rate on the mortgages serving as collateral exceeds the interest payments to the holders of the CMOs and GMCs. The float income is the interest on the monthly principal and interest payments that could be earned between receipt of the payments by petitioner and remittance to the CMO and GMC holders.2006 Tax Ct. Memo LEXIS 155">*172  The debt instruments in issue had issue dates, maturity dates, outstanding principal on December 31, 1984, effective contract rates, and market prices per $ 100 on January 1, 1985, as follows:                            Effective                     Principal    Contract   Market Price  Debt           Maturity    Outstanding   Interest   Per $ 100 onInstrument  Issue Date     Date    On 12/31/1984    Rate n.1    1/1/1985n.2__________  __________    ________   ____________   _________  ____________ G-15    11/19/1970   11/27/1995   $ 70,000,000     8.681   87.335069 G-16     8/2/1971    8/26/1996    82,500,000     7.813   81.835069 G-17     5/25/1972    5/26/1997   150,000,000     7.250   70.381944 F-12     2/25/1977    2/25/1985   200,000,000     7.407   99.906250 F-15     2/27/1978    5/28/1985   200,000,000     8.158   99.890625 F-8     11/25/1976   11/25/1985    40,000,000    2006 Tax Ct. Memo LEXIS 155">*173  8.442   99.187500 F-18     5/25/1979    2/25/1986   200,000,000     9.581   99.937500 F-11    10/25/1973   11/26/1993   400,000,000     7.412   77.000000 F-13     2/25/1977    2/25/1997   300,000,000     7.910   75.687500 D-2     3/30/1983    3/30/1990   300,000,000    10.937   98.062500ND 7/1/1975 11/1/1986 11,363,000 7.750   95.968750 CMO-A2    6/15/1983   12/15/1995   350,000,000    11.162   97.664063 CMO-A3    6/15/1983    6/15/2013   435,000,000    11.803   96.390625 CMO-C4    1/31/1984    1/31/2009    85,052,100    12.403   94.890625 Z-2     11/29/1984   11/29/2019   n.3/212,584,000    10.252    2.703125 Z-3     11/30/1984   11/30/1994    n.4/79,678,000    11.820   31.458333 CD-1    12/26/1978   12/27/1988   150,000,000     9.412   94.671875GMC A-75    2/25/1975    3/15/2005    98,100,000     8.200   92.437500GMC B-75    2/25/1975    9/15/2005    63,400,000     8.750   93.125000GMC2006 Tax Ct. Memo LEXIS 155">*174  A-76    2/25/1976    3/15/2006    70,600,000     8.550   92.593750GMC B-76    8/25/1976    9/15/2006    75,600,000     8.375   88.000000GMC A-77    1/25/1977    3/15/2007    77,600,000     8.050   88.937500GMC B-77    5/25/1977    3/15/2007    94,000,000     8.125   85.875000GMC C-77   11/25/1977    9/15/2007   108,200,000     8.200   83.468750GMC A-78    6/1/1978    3/15/2008   186,000,000     8.850   86.250000GMC B-78    9/1/1978    9/15/2008    98,800,000     9.000   87.218000GMC C-78    12/4/1978    9/15/2008    98,800,000     9.400   89.656250GMC A-79    2/1/1979    3/15/2009   114,000,000     9.875   92.125000GMC B-79    6/4/1979    3/15/2009   114,000,000    10.250   93.875000GMC C-79    8/2/1979    9/15/2009   114,000,000    10.000   91.937500n.1 See supra note 4.n.2 The market prices per $ 100 on Jan. 1, 1985, are based upon petitioner's calculations. Respondent's calculations of the market price per $ 100 on Jan. 1,1985, are slightly different. Respondent2006 Tax Ct. Memo LEXIS 155">*175  agrees that this difference is not significant.n.3 This figure represents the outstanding principal on Dec. 31, 1984. Because Z-2 did not pay interest periodically, the principal amount at maturity will equal $ 7 billion.n.4 This figure represents the outstanding principal on Dec. 31, 1984. Because Z-3 did not pay interest periodically, the principal amount at maturity will equal $ 250 million.II. Average Weighted Lives of the Debt InstrumentsThe average weighted life represents the time it takes for the average dollar of principal borrowed to be repaid to the lender. When principal repayment can vary, or when there is a chance an option will be exercised to retire the security early, the average weighted life is calculated using certain assumptions regarding principal payment rate and exercise timing. The expected remaining average weighted life of each debt instrument as of January 1, 1985, depends on: (1) The remaining term to maturity; (2) whether the debt was subject to any call or put options; and (3) whether any principal repayments would be made pursuant to either a mandatory schedule or terms that provided for repayment of principal on the debt based on the2006 Tax Ct. Memo LEXIS 155">*176  rate of principal repayments received on the mortgages serving as collateral. On January 1, 1985, the average weighted lives of petitioner's 30 debt instruments in issue were as follows:    Debt              Average weighted life    _____              _____________________    G-15               5 years,  5 months    G-16               6 years,  8 months    G-17               12 years,  5 months    F-8                    11 months    F-11               8 years, 11 months    F-12                    2 months    F-13               12 years,  2 months    F-15                    5 months    F-18               1  year,  2 months    D-2                5 years,  3 months    Z-2               34 years, 11 months2006 Tax Ct. Memo LEXIS 155">*177      Z-3                9 years, 11 months   ND 1 year,  8 months    CD-1               4 years,  0 months    GMC A 1975            3 years,  4 months    GMC B 1975            3 years,  9 months    GMC A 1976            3 years, 10 months    GMC B 1976            5 years,  6 months    GMC A 1977            4 years,  9 months    GMC B 1977            6 years,  3 months    GMC C 1977            8 years,  2 months    GMC A 1978            8 years,  5 months    GMC B 1978            7 years,  4 months    GMC C 1978            7 years,  4 months    GMC A 1979            6 years, 10 months    GMC B 1979            6 years, 10 months    GMC C 1979            7 years,  4 months   2006 Tax Ct. Memo LEXIS 155">*178  CMO A-2              5 years, 11 months    CMO A-3             17 years,  7 months    CMO C-4             14 years,  6 monthsIII. Tax ReturnsPetitioner claimed a tax basis for its favorable financing equal to its claimed fair market value at close of business on December 31, 1984. On its 1985 Federal income tax return, petitioner claimed that as of December 31, 1984, its favorable financing intangible assets had an aggregate amortizable value of $ 456,021,853. 92006 Tax Ct. Memo LEXIS 155">*179  Petitioner now claims that its favorable financing intangible assets had an aggregate amortizable value of $ 428,391,551 on January 1, 1985. 10OPINIONAs part of the legislation that subjected petitioner to Federal income taxation, Congress enacted a dual-basis rule for petitioner. DEFRA sec. 177(d)(2), 98 Stat. 711. Specifically, DEFRA section 177(d)(2)(A) provides:  (2) Adjusted basis of assets. --     (A) In general. -- Except as otherwise provided in     subparagraph (B), the adjusted basis of any asset of the     Federal Home Loan Mortgage Corporation held on January 1,     1985, shall --     (i) for purposes of determining any loss, be equal to the     lesser of the adjusted basis of such asset or the fair     market value of such asset as of such date, and     (ii) for purposes of determining any gain, be equal to the     higher of the adjusted basis of such asset or the fair     market value of such asset as of such date.The "special basis rules [were] 2006 Tax Ct. Memo LEXIS 155">*180  designed to ensure that, to the extent possible, pre-1985 appreciation or decline in the value of * * * [petitioner's] assets will not be taken into account for tax purposes." H. Conf. Rept. 98-861, at 1038 (1984), 1984-3 C.B. (Vol. 2) 1, 292.Section 167(a) allows taxpayers to depreciate property used in a trade or business, or held for the production of income, for exhaustion, wear and tear, and obsolescence. Section 167(g) provides that "The basis on which exhaustion, wear and tear, and obsolescence are to be allowed in respect to any property shall be the adjusted basis provided in section 1011 for the purpose of determining the gain on the sale or other disposition of such property." The depreciation of intangible assets is specifically addressed in section 1.167(a)-3, Income Tax Regs., which provides:  If an intangible asset is known from experience or other factors   to be of use in the business or in the production of income for   only a limited period, the length of which can be estimated with   reasonable accuracy, such an intangible asset may be the subject   of a depreciation allowance. * * 2006 Tax Ct. Memo LEXIS 155">*181  * An intangible asset, the   useful life of which is not limited, is not subject to the   allowance for depreciation. No allowance will be permitted   merely because, in the unsupported opinion of the taxpayer, the   intangible asset has a limited useful life. No deduction for   depreciation is allowable with respect to good will. * * *Petitioner's favorable financing intangible assets arise from debt obligations in existence on January 1, 1985, that required petitioner to pay interest to the holders at rates below-market rates on that date. In Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 129">121 T.C. 147, we held that "petitioner's adjusted basis for purposes of amortizing intangible assets under section 167(g) is the higher of regular adjusted cost basis or fair market value as of January 1, 1985." In 121 T.C. 254">Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 272, we held that "The right to use the proceeds of financing arrangements with below-market interest rates constitutes an economic benefit" and that "The benefit of petitioner's below-market financing can, as a matter of law, constitute an intangible asset which can2006 Tax Ct. Memo LEXIS 155">*182  be amortized if petitioner establishes a fair market value and a limited useful life as of January 1, 1985." In this opinion, we decide the fair market values and useful lives of petitioner's favorable financing assets.Both parties rely heavily on expert opinions and testimony to support their respective positions concerning the values and useful lives of the favorable financing intangible assets. "[W]e * * * consider expert opinion testimony to the extent that it assists us in resolving the issues presented". IT&S of Iowa, Inc. v. Commissioner, 97 T.C. 496">97 T.C. 496, 97 T.C. 496">508 (1991). We may exercise our broad discretion to accept or reject an expert's opinion in its entirety. Neonatology Assocs., P.A. v. Comm'r, 115 T.C. 43">115 T.C. 43, 115 T.C. 43">86 (2000), affd. 299 F.3d 221">299 F.3d 221 (3d Cir. 2002). Alternatively, we may selectively rely on those portions of an expert's opinion that we find most helpful to our decision. 97 T.C. 496">IT&S of Iowa, Inc. v. Commissioner, supra at 508; Parker v. Commissioner, 86 T.C. 547">86 T.C. 547, 86 T.C. 547">561 (1986). "[A]n objective reason for * * * [rejecting an expert's testimony] is that another expert's opinion is more persuasive." 86 T.C. 547">Parker v. Commissioner, supra at 562.2006 Tax Ct. Memo LEXIS 155">*183 "We are not bound * * * by the opinion of any expert witness where such opinion is contrary to our judgment." 97 T.C. 496">IT&S of Iowa, Inc. v. Commissioner, supra at 508.I. The Values of Petitioner's Favorable Financing Intangible AssetsA. Petitioner's Valuation of Its Favorable Financing Intangible Assets as of January 1, 1985The fair market value of property is a question of fact. Bank One Corp. v. Comm'r, 120 T.C. 174">120 T.C. 174, 120 T.C. 174">306 (2003); Estate of Jung v. Commissioner, 101 T.C. 412">101 T.C. 412, 101 T.C. 412">423-424 (1993); Estate of Newhouse v. Commissioner, 94 T.C. 193">94 T.C. 193, 94 T.C. 193">217 (1990). Fair market value is defined as "'the price at which the property would change hands between a willing buyer and willing seller, neither being under any compulsion to buy or sell and both having reasonable knowledge of the relevant facts.'" United States v. Cartwright, 411 U.S. 546">411 U.S. 546, 411 U.S. 546">551, 93 S. Ct. 1713">93 S. Ct. 1713, 36 L. Ed. 2d 528">36 L. Ed. 2d 528 (1973) (quoting section 20.2031-1(b), Estate Tax Regs.); 120 T.C. 174">Bank One Corp. v. Comm'r, supra at 209; 94 T.C. 193">Estate of Newhouse v. Commissioner, supra at 217; see also sec. 20.2031- 1(b), Estate Tax Regs.; sec. 25.2512-1, Gift Tax Regs. This is an objective standard2006 Tax Ct. Memo LEXIS 155">*184  that uses a hypothetical willing buyer and seller. Estate of Kahn v. Commissioner, 125 T.C. 227">125 T.C. 227, 125 T.C. 227">231 (2005). This Court considers all relevant evidence in the record when deciding the value of property. 120 T.C. 174">Bank One Corp. v. Comm'r, supra at 306; 101 T.C. 412">Estate of Jung v. Commissioner, supra at 431-432. As valuation is not an exact science, the taxpayer is not required to establish the precise value of the asset. See 101 T.C. 412">Estate of Jung v. Commissioner, supra at 423-424; Snyder v. Commissioner, 93 T.C. 529">93 T.C. 529, 93 T.C. 529">545 (1989). Furthermore, "A taxpayer is not required to use the most theoretically correct method * * * to establish the amount of depreciation to which he is entitled; rather, his method must be reasonable." 97 T.C. 496">IT&S of Iowa, Inc. v. Commissioner, supra at 522 (citing Citizens & S. Corp. & Subs. v. Commissioner, 91 T.C. 463">91 T.C. 463, 91 T.C. 463">514 (1988), affd. without published opinion 900 F.2d 266">900 F.2d 266, 919 F.2d 1492">919 F.2d 1492 (11th Cir. 1990)).Petitioner argues that the benefit of below-market interest should be measured by the present values of the difference between the contract interest rates on its debt instruments and market interest rates over2006 Tax Ct. Memo LEXIS 155">*185  the terms of the loans. Petitioner calculated that the January 1, 1985, fair market value of each favorable financing intangible asset was as follows:      Debt            Fair Market Value      ____            _________________      G-15              $ 8,865,451      G-16              14,986,068      G-17              44,427,083      F-8                325,000      F-11              92,000,000      F-12                187,500      F-13              72,937,500      F-15                218,750      F-18                125,000      D-2               5,812,500      Z-2               24,389,887      Z-3               1,448,674     ND 2006 Tax Ct. Memo LEXIS 155">*186  458,071      CD-1               7,992,188      GMC A 1975            7,418,813      GMC B 1975            4,358,750      GMC A 1976            5,228,813      GMC B 1976            8,342,336      GMC A 1977            8,146,021      GMC B 1977           12,825,330      GMC C 1977           17,407,946      GMC A 1978           24,814,023      GMC B 1978           12,413,781      GMC C 1978            9,776,662      GMC A 1979            8,521,734      GMC B 1979            6,626,888      GMC C 1979            8,946,893      CMO A-2             6,254,753?      CMO A-3             12,511,453      CMO C-4              623,683  2006 Tax Ct. Memo LEXIS 155">*187                    ____________       Total            428,391,551Petitioner relies on the expert opinion and testimony of Dr. Stephen M. Schaefer to determine the value of its favorable financing. Professor Schaefer received his doctor of philosophy at the University of London, Faculty of Economics. He currently serves as a professor of finance at London Business School and has been a visiting professor at seven universities around the world. Professor Schaefer has also served on the editorial boards of numerous publications, published two books, and published over 30 articles and notes relating to finance and economics.Professor Schaefer explained that the benefit of favorable financing is based on the difference between the interest payments on an existing debt obligation and the interest payments made at the prevailing market rate. The value of the favorable financing benefit equals the present value of this difference. When debt obligations are exchanged in a free market, the price paid for the debt instruments equals the fair market value of the future cashflows. The market price reflects uncertainties; for2006 Tax Ct. Memo LEXIS 155">*188  example, when a bond is prepayable, the market price incorporates the likelihood that the bond will be prepaid. A comparison of the adjusted issue prices of petitioner's debt instruments and the market prices indicates that petitioner's instruments were traded at a discount as of January 1, 1985. The difference between the adjusted issue price and the market price is the market discount. The discount reflects the present value difference between petitioner's contractual interest rate for each debt instrument and the market rate for comparable debt on January 1, 1985. From petitioner's perspective, the amount of the discount is the present value of the additional interest cost that the debtor would have to incur to borrow the amount of the existing debt at market rates.Professor Schaefer calculated the fair market value of the favorable financing inherent in each of the 30 debt instruments as of January 1, 1985, as the difference between the adjusted issue price per $ 100 of principal and the January 1, 1985, market price per $ 100 of principal, multiplied by the unpaid principal balance divided by $ 100. 11 Professor Schaefer's report provided the January 1, 1985, market price,2006 Tax Ct. Memo LEXIS 155">*189  adjusted issue price, and unpaid principal balance for the 30 debt instruments as follows:  Debt         Adjusted    Jan. 1, 1985     Unpaidinstrument      issue price n.1   market price n.2  principal balance__________      ___________   ____________   _________________ G-15         100.0000     87.335069     70,000,000 G-16         100.0000     81.835069     82,500,000 G-17         100.0000     70.381944     150,000,000 F-8          100.0000     99.187500     40,000,000 F-11         100.0000     77.000000     400,000,000 F-12         100.0000     99.906250     200,000,000 F-13         100.0000     75.687500     300,000,000 F-15         100.0000     99.890625     200,000,000 F-18         100.0000     99.937500     200,000,000 D-2          100.0000     98.062500     300,000,000 Z-2           3.0516     2.7031252006 Tax Ct. Memo LEXIS 155">*190     7,000,000,000 Z-3          32.0378     31.458333     250,000,000ND 100.0000     95.968750     11,363,000 CD-1         100.0000     94.671875     150,000,000 GMC A 1975      100.0000     92.437500     98,100,000 GMC B 1975      100.0000     93.125000     63,400,000 GMC A 1976      100.0000     92.593750     70,600,000 GMC B 1976       99.0348     88.000000     75,600,000 GMC A 1977       99.4349     88.937500     77,600,000 GMC B 1977       99.5190     85.875000     94,000,000 GMC C 1977       99.5574     83.468750     108,200,000 GMC A 1978       99.5909     86.250000     186,000,000 GMC B 1978       99.7826     87.218000     98,800,000 GMC C 1978       99.5517     89.656250     98,800,000 GMC A 1979       99.6002     92.125000     114,000,000 GMC B 1979       99.6881     93.875000     114,000,0002006 Tax Ct. Memo LEXIS 155">*191   GMC C 1979       99.7857     91.937500     114,000,000 CMO A-2        99.4511     97.664063     350,000,000 CMO A-3        99.2668     96.390625     435,000,000 CMO C-4        95.6239     94.890625     85,052,100n.1 The adjusted issue price is the unpaid principal balance minus the fraction of any unamortized original issue discount remaining as of the valuation date. For a debt instrument issued at a price that equaled its face value and for which there had been no redemption before Dec. 31, 1984, the adjusted issue price equals the initial face amount. The adjusted issue price listed above is the adjusted issue price per $ 100 of unpaid principal balance.n.2 The Jan. 1, 1985, market price equals the middle price -- this is the average of the bid and asked prices. With the exception of G-15 and G-16, Professor Schaefer used the average of the bid prices obtained by Arthur Andersen and petitioner from the Salomon Brothers, First Boston, Merrill Lynch, and Shearson Lehman investment banks as the bid price. See appendix. The bid prices for G-15 and G-16 equaled the average2006 Tax Ct. Memo LEXIS 155">*192  of the available prices.We find that petitioner's method of valuing its favorable financing intangible assets provides a reasonable estimate of fair market value. The Supreme Court in Dickman v. Commissioner, 465 U.S. 330">465 U.S. 330, 465 U.S. 330">337-338, 104 S. Ct. 1086">104 S. Ct. 1086, 79 L. Ed. 2d 343">79 L. Ed. 2d 343 (1984), indicated that the value of the right to use borrowed money is readily measurable by reference to current interest rates. See also Rev. Proc. 85-46, sec. 3.01, 1985-2 C.B. 507 (stating that the value of a gift below-market loan is "the difference between the rate at which the money is loaned and the prevailing market rate."). Similarly, we believe that the favorable financing aspect of petitioner's debt instruments may be valued by comparing petitioner's effective contract interest rates to the prevailing market rates for those instruments as of January 1, 1985. The market price of each of petitioner's existing debt instruments provides2006 Tax Ct. Memo LEXIS 155">*193  an accurate indication of the price at which investors would exchange the debt instruments. That price reflects the relationship between the contract rate of interest on the debt and the market rate of interest as of January 1, 1985. The market approach used by petitioner captures the values of the debt instruments using the prices at which willing buyers and sellers actually exchanged these instruments as of the valuation date. We find that the sum of the market discounts for petitioner's debt instruments provides a reasonable estimate of the present value of the interest costs petitioner saved by paying below-market interest rates on its outstanding debt instruments on January 1, 1985.B. Respondent's Position That Favorable Financing Has No ValueRespondent primarily argues that petitioner failed to show that the favorable financing intangibles had any value because: (1) Petitioner did not show it expected to receive a stream of income from the favorable financing intangible assets; (2) petitioner did not prove that it could realize the value of the favorable financing; (3) the favorable financing is a contra-liability, not an asset; and (4) petitioner could realize the value2006 Tax Ct. Memo LEXIS 155">*194  of favorable financing only by buying back its debt instruments in the market, which would be impractical because it would have to pay tax on the discharge of indebtedness.The main thrust of respondent's arguments is that petitioner's favorable financing is not an asset. We addressed this contention in Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 254 (2003). In that Opinion, we concluded: (1) That the right to use money at below-market rates is a valuable economic benefit in terms of the cost savings that can be achieved in income-producing activities; (2) that favorable financing is a benefit for which a third party would pay a premium if the favorable financing were included as part of a purchase transaction; (3) that petitioner's favorable financing arrangements on January 1, 1985, represented something of value; and (4) that the differential between the market rate of interest and petitioner's contract rate of interest serves as a measure of the economic value of that right on January 1, 1985. 121 T.C. 254">Id. at 260, 261. Nevertheless, we will briefly discuss respondent's arguments that petitioner's favorable financing had no value.1. Expectation of2006 Tax Ct. Memo LEXIS 155">*195  IncomeRespondent argues that the favorable financing intangible assets do not have any value because petitioner did not receive any additional income or earnings from these assets. Respondent relies on the expert opinion and testimony of Dr. Scott D. Hakala. 12 Dr. Hakala explained that "Intangible assets are defined as all elements of a business enterprise that exist in addition to monetary and tangible assets. Their existence is dependent on the presence, or expectation of earnings." (Fn. ref. omitted.)2006 Tax Ct. Memo LEXIS 155">*196  First, it seems clear that petitioner's favorable financing had a positive effect on its net income. To the extent that petitioner's financing costs were lower than they would have been had petitioner financed its operations with the market rates prevailing on January 1, 1985, its net income was enhanced. Second, respondent does not support with legal authority his contention that the value of the favorable financing intangible must be based on income. Indeed, courts have determined the value of similar intangible assets using cost savings methods. IT&S of Iowa, Inc. v. Commissioner, 97 T.C. 496">97 T.C. 514-515; Citizens & S. Corp. & Subs. v. Commissioner, 91 T.C. 463">91 T.C. 498.We have already held that petitioner's favorable financing constituted an economic benefit that can be an amortizable intangible asset if petitioner establishes a fair market value and limited useful life as of January 1, 1985. Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 272. We also concluded that the core deposit cases, which use cost savings to measure value, "support petitioner's position that favorable financing is an intangible asset subject to amortization." 121 T.C. 254">Id. at 264.2006 Tax Ct. Memo LEXIS 155">*197 Rather than addressing the valuation issue presently before the Court, respondent's argument seems to challenge our prior holdings.2. Realization of ValueRespondent argues that the favorable financing intangible assets do not have a fair market value and that any value is hypothetical because petitioner could not transfer favorable financing to a willing buyer. We might agree that petitioner's favorable financing could not be transferred by itself. However, we have previously rejected respondent's argument that favorable financing could not be valued because it could not be transferred except as part of a larger acquisition. Obviously, intangibles such as core deposits or deposit base 13 might have economic significance only in a larger context, but that does not prevent giving them a separate value. See Fed. Home Loan Mortgage Corp.  v. Commissioner, 121 T.C. 254">121 T.C. 266-267, where we stated:   We also cannot distinguish the cases involving deposit base for   the reason that those cases involved an acquisition of deposit   base in conjunction with a larger acquisition of assets of a   company. We might agree that, as a practical matter, a debtor's2006 Tax Ct. Memo LEXIS 155">*198     position with respect to its favorable financing would not be   transferred, except as a part of a larger acquisition of a   company or property. However, this is not, in our view,   determinative of the question of whether there exists an   amortizable asset of value. * * *2006 Tax Ct. Memo LEXIS 155">*199  3. Contra-Liability TheoryRespondent argues that petitioner's favorable financing is a contra-liability, not an asset. Respondent's expert Dr. Hakala explained that a contra-liability is a liability on the balance sheet that is misstated in some economic sense because the liability is worth less than face value and the liability has been marked to market. Dr. Hakala further explained that transferring the liability to the asset side of the balance sheet creates an unrealizable asset. As a result, respondent argues that the favorable financing intangible assets cannot be valued separately, without looking at the value of the underlying mortgages. According to respondent, petitioner's valuation method results in overvaluation, double counting of assets, and accounting irregularities because petitioner marks its liabilities to market without making the corresponding downward adjustment to its assets.a. Favorable Financing Is an AssetRespondent's contra-liability argument revisits the question of whether favorable financing can be an amortizable asset. We have already rejected respondent's argument that favorable financing is a liability. See Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 269,2006 Tax Ct. Memo LEXIS 155">*200  where we stated:   Respondent argues that petitioner's favorable financing   represents a "liability", not an "asset". Respondent claims that   petitioner is "attempting to adjust, for tax purposes, the asset   side of its balance sheet to account for an overstatement in   fair market value terms of its liabilities." We cannot agree  ? with respondent's proposed characterization of petitioner's   favorable financing as a liability. Indeed, as petitioner points   out, there is a valuable economic benefit associated with the   below-market interest rates on its financing arrangements as of   January 1, 1985. It is this economic benefit which petitioner   claims as an intangible asset and upon which it bases its   claimed amortization deductions.b. Favorable Financing Can Be Assigned a Separate ValueAs previously indicated, the fact that favorable financing could not be transferred apart from a transfer of other assets and liabilities does not prevent assigning it a separate value. At trial, petitioner's counsel developed the following hypothetical situation while examining respondent's expert, Dr. Herbert2006 Tax Ct. Memo LEXIS 155">*201  Kaufman: 14   Q: * * * The houses are both worth $ 300,000. They are identical.   They are next door to each other. They both have a "for sale"   sign in front of them. The first house just says, "For sale,   House, No Assumable Debt." The second house has "House for Sale   Plus 1 Percent Mortgage Assumable as Part of the Purchase."           *   *   *   *   *   *   *   Q: Do you believe the second seller is going to receive more   money at closing than the first seller?   A: Assuming that market interest rates are --   Q: They're five.   A: Sure.   Q: So the second seller would receive more money. Right?   A: I would think so.   Q: Why is that?   A: Because the assumable mortgage is in place.   Q: Does it have value?   A: The assumable mortgage?   Q: Yes.   A: Yeah. The value of the assumable mortgage with regard to the   house, which is the asset, --           *   *   *   *   *   *   *   A: -- has value.Further, Dr. Kaufman was asked and2006 Tax Ct. Memo LEXIS 155">*202  answered as follows:   Q: * * * Back to my other hypothetical about the two homes next   door to each other, let's assume you can't decide which house to   buy, the $ 300,000 one with no assumable mortgage or the $ 300,000   house with the 1 percent mortgage. Market rates are five.           *   *   *   *   *   *   *   Q: Do you think it's possible to calculate how much more you   would pay for that house with the assumable 1 percent mortgage?   Is that possible to do?   A: I think it's probably possible.   Q: But a buyer certainly would have the tools to determine how   much more to pay for the below-market financing. Is that right?   A: Not for the below-market financing; for the house with the   below-market.           *   *   *   *   *   *   *   A: Again, you keep wanting to separate. I can't separate that   because you're not going to buy a liability.   Q: Let's say the buyer hired an appraisal company and had in the   buyer's hand an appraisal saying the house is worth $ 300,000.  2006 Tax Ct. Memo LEXIS 155">*203  Right? How would the buyer decide how much more to pay for the   house with the 1 percent mortgage? It would determine the value   of the below-market mortgage and add that to the price. Isn't   that fair?   A: That's true, yeah.Like the purchaser and seller of the houses in the hypothetical situation, we think that petitioner can ascertain the value of the favorable financing. As we have mentioned, financial markets determined the current price of petitioner's debt obligations on the valuation date; a comparison of the contract price and the prevailing market price2006 Tax Ct. Memo LEXIS 155">*204  provides a reasonable measure of the value of the favorable financing associated with the debt instrument. Therefore, we disagree with respondent that a separate value cannot be assigned to petitioner's favorable financing.c. Double Counting the ValueRespondent also argues that petitioner's method of valuing its favorable financing overvalues and double counts petitioner's assets because petitioner's "real assets" -- the mortgages -- have lost value when compared to prevailing market rates.We think that respondent's concerns of double counting are misguided. When petitioner was chartered, it was exempt from Federal, State, and local taxation, except for real estate tax imposed by any State or local taxing authority. Congress enacted special legislation that subjected petitioner to Federal income taxation. In that special legislation, Congress created a dual-basis rule for petitioner's assets "to ensure that, to the extent possible, pre-1985 appreciation or decline in value of * * * [petitioner's] assets will not be taken into account for tax purposes." H. Conf. Rept. 98-861, supra at 1038, 1984-3 C.B. (Vol. 2) at 292. Just as this legislation applies to petitioner's favorable2006 Tax Ct. Memo LEXIS 155">*205  financing intangible assets, DEFRA section 177(d)(2) governs the adjusted bases of petitioner's so- called real assets. For the purposes of determining a loss, DEFRA section 177(d)(2)(A) provides that "the adjusted basis of any asset of * * * [petitioner] held on January 1, 1985, * * * be equal to the lesser of the adjusted basis of such asset or the fair market value of such asset" as of January 1, 1985. Congress created the special dual-basis rule specifically for petitioner when it became a taxable entity to ensure that pre-1985 appreciation or decline in value would not be taken into account for tax purposes. H. Conf. Rept. 98-861, supra at 1038, 1984-3 C.B. (Vol. 2) at 292. The adjusted basis rules of DEFRA section 177(d)(2)(A), which requires petitioner to calculate a loss using an adjusted basis equal to the lesser of fair market value or adjusted basis, address the kind of double counting that appears to concern respondent.4. Petitioner's Purchase of Its Debt Obligations Would Result in Discharge of Indebtedness IncomeRespondent appears to argue that the only way petitioner could realize the value of favorable financing would be to buy back its debt instruments at their2006 Tax Ct. Memo LEXIS 155">*206  discounted market prices. Respondent claims that this is impractical because petitioner would incur tax on the resulting discharge of indebtedness income.When a taxpayer repays a debt at a discount, the taxpayer normally realizes income from the discharge of indebtedness. See sec. 61(a)(12); United States v. Kirby Lumber Co., 284 U.S. 1">284 U.S. 1, 284 U.S. 1">3, 52 S. Ct. 4">52 S. Ct. 4, 76 L. Ed. 131">76 L. Ed. 131, 72 Ct. Cl. 739">72 Ct. Cl. 739 (1931). Section 1.61-12(a), Income Tax Regs., provides that "The discharge of indebtedness, in whole or in part, may result in the realization of income. * * * A taxpayer may realize income by the payment or purchase of his obligations at less than their face value." When a taxpayer receives borrowed funds, those funds are excluded from income because the taxpayer has an obligation to repay the funds. United States v. Centennial Sav. Bank FSB, 499 U.S. 573">499 U.S. 573, 499 U.S. 573">582, 111 S. Ct. 1512">111 S. Ct. 1512, 113 L. Ed. 2d 608">113 L. Ed. 2d 608 (1991). The rationale for including discharge of indebtedness in a taxpayer's income is that the taxpayer "realizes an accession to income due to the freeing of assets previously offset by the liability." Jelle v. Comm'r, 116 T.C. 63">116 T.C. 63, 116 T.C. 63">67 (2001) (citing 284 U.S. 1">United States v. Kirby Lumber Co., supra at 3).If petitioner entered2006 Tax Ct. Memo LEXIS 155">*207  the market and purchased its debt obligations for less than the amount that it had borrowed, petitioner would normally realize income equal to the difference between the amount it borrowed and the amount it paid to purchase its debt instruments. We think that respondent's argument that petitioner could have received discharge of indebtedness income by repurchasing its debt at a discount supports our conclusion that petitioner's favorable financing had value.C. Respondent's Argument That the Value of Petitioner's Favorable Financing Is Limited to the Value of Petitioner's Income SpreadAssuming, without conceding, that favorable financing is a valuable asset, respondent argues that the price an acquirer would pay to purchase petitioner's rights and obligations with respect to its CMOs or GMCs would not exceed the present value of petitioner's spread income associated with those instruments. As of January 1, 1985, respondent asserts that the present value of the spread related to petitioner's GMCs and CMOs equaled approximately $ 11.4 million and $ 7.2 million, respectively.Dr. Hakala concluded that favorable financing is not an intangible asset; however, Dr. Hakala found that petitioner's2006 Tax Ct. Memo LEXIS 155">*208  income spread has value because its assets and liabilities are closely matched. 15 According to Dr. Hakala, when previously issued debt is matched to income-earning assets, the issued debt does not have any intangible value by itself. In his report, Dr. Hakala explained that "what is of value to a potential buyer is the potential income stream between mortgages and obligations to holders of the securities."To determine the value of the income spread from the GMCs, Dr. Hakala used the net management and guarantee income 16 petitioner reported for the 6 months that ended June 30, 1985, and compared that to the average principal balance outstanding over that same 6-month period. He concluded that the management and guarantee income totaled $ 3.5 million. Dr. Hakala assumed general and administrative costs of 9 basis points annually and reduced the total value to incorporate the effect of taxes; these adjustments reduced the net management and2006 Tax Ct. Memo LEXIS 155">*209  guarantee income to $ 1.6 million. "Taking into account the actual runoff of each GMC and discounting to present value the future net spread income at the weighted average cost of capital results in a value of approximately $ 11.4 million for the spread associated with all of the GMCs." Dr. Hakala used the same analysis to find that the present value of the CMOs' future net spread income at the weighted average cost of capital equaled $ 7.2 million.We disagree with respondent that the value of petitioner's favorable financing intangible assets is limited to the value of the income spread. Dr. Hakala's income spread analysis is premised on his conclusion that favorable financing cannot be an intangible asset. However, in Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 272,2006 Tax Ct. Memo LEXIS 155">*210 we held that favorable financing was an economic benefit and that "the benefit of * * * below-market financing can, as a matter of law, constitute an intangible asset".Professor Schaefer explained that the income spread is a measure of petitioner's equity value, and that equity is different from the value of petitioner's assets, including the favorable financing intangible assets. Equity is generally described as the excess of the value of assets (tangible and intangible) over liabilities. The value of petitioner's favorable financing assets is the present value of the cost savings between the effective contract interest rate on petitioner's debt obligations and the prevailing market interest rates on equivalent debt obligations at the valuation date. To illustrate the differences between the value of an intangible asset and equity value, Professor Schaefer gave the following examples:   To illustrate this further, suppose a company has a long lease   on office space at $ 5 per square foot when the market price for   similar space is, say, $ 70. It is clear that this lease is   valuable to the company; if it did not own the lease at $ 5 per   square2006 Tax Ct. Memo LEXIS 155">*211  foot it would have to rent more expensive space and, as a   result, both the earnings and the value of the company would be   lower. Of course the price an acquirer would pay is the value of   the earnings stream from the whole company, i.e., its revenues   less its total costs, including the costs of space. However, it   is clear that paying $ 5 rather than $ 70 per square foot for   space increases the earnings of the company and therefore has   value to an acquirer.   Similarly, suppose two companies, A and B, have identical assets   and identical amounts of debt but pay different rates of   interest on their debt. Company A's liabilities pay the   Prevailing Market Interest Rate while company B's liabilities   pay a below-market interest rate. In this case, company B's   earnings will be higher than company A's and an acquirer would   clearly pay more for company B than for company A. The   difference in the earnings of the two companies is the   difference between interest payments at the Prevailing Market   Interest Rate (the rate on company A's liabilities) and the 2006 Tax Ct. Memo LEXIS 155">*212    lower rate on company B's liabilities. Thus, the difference   between the earnings of the two companies is equal to company   B's Favourable Financing benefits and the higher amount that an   acquirer would pay for company B over company A is the value of   company B's Favourable Financing Assets.To further rebut respondent's claim that favorable financing cannot exceed the value of equity, Professor Schaefer explained:   This claim is clearly flawed since all that is required for the   value of the Favourable Financing Assets to exceed the value of   equity is for the present value of the Asset Spread to   Market 17 to be negative. * * * the value of   Freddie Mac's equity is always equal to the present value   of its Asset Spread to Market plus the value of its Favourable   Financing Assets. Thus, if the present value of the Asset Spread   to Market is negative, the value of the Favourable   Financing Assets will exceed the value of equity. * * *2006 Tax Ct. Memo LEXIS 155">*213  In order to illustrate this point, Professor Schaefer used the following example:   A more concrete example is provided by the S&L crisis,which   featured negative Asset Spreads to Market, and therefore   Favourable Financing Assets with a higher value than equity. In   the early 1980s, when interest-rates rose sharply, the condition   of many S&Ls deteriorated as the value of their fixed-rate   mortgage assets fell. Suppose that, in September 1981   when mortgage rates were above 15%, an S&L held fixed-rate   mortgages paying a rate of 6% and therefore selling at around   40% of their face amount. Suppose further that this S&L was   fortunate in the sense that it was entirely financed with core   deposits * * * that paid 2%and therefore, despite earning 6% on   its assets when market rates were 15%, it nonetheless earned a   positive spread of 4% (equal to the rate on its assets of 6% less   2% paid on its liabilities).   To the extent that the core deposits remain in place,this S&L is   solvent. However, its positive net worth does not come from its   assets -- these have2006 Tax Ct. Memo LEXIS 155">*214  fallen in value by 60% -- but from its   liabilities. The total spread of 4% is made up of a substantial   and negative Asset Spread to Market of -- 9% (a 6% asset return   less a 15% market rate) and a large and positive   Favourable Financing benefit of 13% (the 15% market rate less   the 2% paid on deposits). The value of the Favourable Financing   Assets for this S&L (the present value of the 13% spread) would   clearly exceed the value of it sequity (the present value of the   4% spread).We must decide the value of petitioner's favorable financing intangible assets. Because income spread measures equity and not the value of individual assets, we find that the value of petitioner's favorable financing intangible assets is not limited to the income spread.D. Respondent's Argument That Taxes Reduce the Value of Favorable FinancingAssuming that petitioner's favorable financing intangible assets do have value, respondent argues that petitioner's calculations over- valued these assets because its method failed to incorporate the effect of taxes. In his rebuttal report, Dr. Hakala explained that "the reduction in the value of the2006 Tax Ct. Memo LEXIS 155">*215  liability would be partially offset by a deferred tax liability." Dr. Hakala calculated value by reducing the value of the intangible assets for income taxes and increasing the value by the tax shield. 18 After incorporating the tax effect, Dr. Hakala prepared a summary analysis of the favorable financing intangible assets using Professor Schaefer's market prices as follows:      Debt         Corrected Value      ____         _______________      G-15          $ 6,977,205      G-16          11,448,352      G-17          30,735,708      F-8            296,491      F-11          67,179,640      F-12            176,830      F-13          50,628,337      F-15            203,957      F-18            112,856      D-2           4,594,048      Z-2           14,598,063      Z-3         2006 Tax Ct. Memo LEXIS 155">*216    1,039,813     ND 405,439      CD-1           6,538,498      GMC A 1975        6,194,495      GMC B 1975        3,592,694      GMC A 1976        4,299,020      GMC B 1976        6,551,705      GMC A 1977        6,524,267      GMC B 1977        9,891,261      GMC C 1977       12,890,475      GMC A 1978       18,287,188      GMC B 1978        9,347,594      GMC C 1978        7,361,840      GMC A 1979        6,486,039      GMC B 1979        5,043,839      GMC C 1979        6,737,022      CMO A-2         4,862,086      CMO A-3         8,187,424      CMO C-4          420,731                ___________       Total        311,612,9172006 Tax Ct. Memo LEXIS 155">*217  Petitioner argues that its market-based valuation approach integrates the effect of taxes into the value of an asset. In other words, petitioner argues that the market prices of its debt instruments already reflect the tax considerations of buyers and sellers.In his rebuttal report, Dr. Hakala quoted the following excerpt from "Assets Acquired in a Business Combination to be Used in Research and Development Activities: A Focus on Software, Electronic Devices, and Pharmaceutical Industries" (2001) by the AICPA's IPR&D Task Force: "The task force believes that the valuation of an intangible asset would include (a) the expected tax payments resulting from the cashflows attributable to the intangible asset and (b) the tax benefits resulting from the amortization of that intangible asset for income tax purposes." At trial, Dr. Hakala was asked to read the two sentences that immediately followed the sentence he quoted in his rebuttal report: "'Including the tax affects [sic] in the valuation is common in the income and cost approaches. It is not typical in the market approach because any tax benefits would already be factored into the quoted market price through the negotiation of market2006 Tax Ct. Memo LEXIS 155">*218  participants during the bid and ask process.'"Petitioner's expert, Mr. Howard A. Scribner, 19 testified that taxes can affect the value of intangible assets but that the market approach incorporates taxes into the valuation. Specifically, Mr. Scribner was asked and answered as follows:   Q: Are taxes relevant or irrelevant in a market-based valuation   of an intangible asset?   A: A market-based intangible asset reflects the interactions of   buyers and sellers. All factors, including taxes, are reflected   in those prices.We agree with petitioner that the market approach of valuing an asset incorporates the effect of taxes. Respondent's expert relied on a source that states that the effect of taxes typically is not included in the market approach because the quoted market price already reflects taxes. Mr. Scribner confirmed that the market price incorporates the effect of taxes. We find that petitioner properly valued its favorable financing2006 Tax Ct. Memo LEXIS 155">*219  intangible assets using the market- based method and that no further adjustment is necessary to account for the tax effect.We agree that petitioner has proven that its favorable financing intangible assets have values that were reasonably estimated. We hold that the values of petitioner's favorable financing intangible assets are as follows:       Debt          Fair market value       ____          _________________       G-15           $ 8,865,451       G-16            14,986,068       G-17            44,427,083       F-8             325,000       F-11            92,000,000       F-12             187,500       F-13            72,937,500       F-15             218,750       F-18             125,000       D-2             5,812,500       Z-2         2006 Tax Ct. Memo LEXIS 155">*220     24,389,887       Z-3             1,448,674      ND 458,071       CD-1            7,992,188       GMC A 1975         7,418,813       GMC B 1975         4,358,750       GMC A 1976         5,228,813       GMC B 1976         8,342,336       GMC A 1977         8,146,021       GMC B 1977         12,825,330       GMC C 1977         17,407,946       GMC A 1978         24,814,023       GMC B 1978         12,413,781       GMC C 1978         9,776,662       GMC A 1979         8,521,734       GMC B 1979         6,626,888       GMC C 1979         8,946,893       CMO A-2           6,254,753       CMO A-3          12,511,453      2006 Tax Ct. Memo LEXIS 155">*221  CMO C-4            623,683                   ___________        Total          428,391,551II. Favorable Financing Intangible Assets Have a Reasonably Estimable Useful Life As of January 1, 1985To amortize favorable financing, a taxpayer must show that the intangible assets have limited useful lives, the duration of which may be ascertained with reasonable accuracy. Section 1.167(a)-3, Income Tax Regs., provides:  section 1.167(a)-3. Intangibles.  If an intangible asset is known from experience or other factors   to be of use in the business or in the production of income for   only a limited period, the length of which can be estimated with   reasonable accuracy, such an intangible asset may be the subject   of depreciation allowance. Examples are patents and copyrights.   An intangible asset, the useful life of which is not limited is   not subject to the allowance for depreciation. * * *"A taxpayer may establish the useful life of an asset for depreciation based upon his own experience with similar property, 2006 Tax Ct. Memo LEXIS 155">*222  or, if his own experience is inadequate, based upon the general experience in the industry." Citizens & S. Corp. & Subs. v. Commissioner, 91 T.C. 463">91 T.C. 500 (citing section 1.167(a)-1(b), Income Tax Regs.); Banc One Corp. v. Commissioner, 84 T.C. 476">84 T.C. 476, 84 T.C. 476">499 (1985) (citing section 1.167(a)-1(b), Income Tax Regs.), affd. without published opinion 815 F.2d 75">815 F.2d 75 (6th Cir. 1987). The taxpayer is not required to prove the precise useful life for purposes of depreciation -- a "'reasonable approximation'" of the useful life is sufficient. 91 T.C. 463">Citizens & S. Corp. & Subs. v. Commissioner, supra at 500; 84 T.C. 476">Banc One Corp. v. Commissioner, supra at 499 (citing Burnet v. Niagara Falls Brewing Co., 282 U.S. 648">282 U.S. 648, 282 U.S. 648">655, 51 S. Ct. 262">51 S. Ct. 262, 75 L. Ed. 594">75 L. Ed. 594, 1 C.B. 403 (1931), Super Food Servs., Inc. v. United States, 416 F.2d 1236">416 F.2d 1236 (7th Cir. 1969), and Spartanburg Terminal Co. v. Commissioner, 66 T.C. 916">66 T.C. 916 (1976)). The taxpayer must base the useful life estimation upon facts that existed at the valuation date. 91 T.C. 463">Citizens & S. Corp. & Subs. v. Commissioner, supra at 500; 84 T.C. 476">Banc One Corp. v. Commissioner, supra at 499.2006 Tax Ct. Memo LEXIS 155">*223 Taxpayers may use evidence of their subsequent experiences to corroborate their projections. 91 T.C. 463">Citizens & S. Corp. & Subs. v. Commissioner, supra at 500.Petitioner argues that on January 1, 1985, the reasonably estimated remaining useful lives of the 30 favorable financing intangible assets equaled the average weighted lives. Petitioner relies on the expert opinion and testimony of Mr. Howard A. Scribner. Mr. Scribner received a B.S.C. in accounting from Rider University and an M.B.A. in finance from Rutgers Graduate School of Management. He is also a licensed certified public accountant (C.P.A.) and an accredited business valuation specialist in the American Society of C.P.A.s. He is a partner in the Economic and Valuation Services practice of KPMG LLP. Mr. Scribner has more than 20 years of valuation experience involving intangible assets, debt, common and preferred stock, partnership interests, and stock options of privately and publicly held companies.Mr. Scribner determined that the estimated useful lives of the favorable financing intangible assets equal the average weighted lives of the debt obligations that give rise to them. According to Mr. Scribner, the estimated2006 Tax Ct. Memo LEXIS 155">*224  useful lives of the favorable financing intangible assets did not change on account of subsequent unforeseen events because   the interactions of market participants force the incorporation   of all known and expected information available at that date   into the existing prevailing market interest rate. Therefore,   the market consensus establishes the current market interest   rate to be the best estimate of the prevailing interest rate   over the life of the investment.Mr. Scribner states that the average weighted life represents the time it takes for the average dollar of principal borrowed to be repaid to the lender. The average weighted life is calculated by: (1) Multiplying the principal payment by the number of years or pro rata portion of a year that the principal amount has been outstanding, (2) adding the results for all payment periods, and (3) dividing that sum by the total principal paid. 20 For debt obligations that do not repay any principal until maturity, the average weighted life is the time remaining to maturity.2006 Tax Ct. Memo LEXIS 155">*225  The following example illustrates how Mr. Scribner's calculated the average weighted life for ND:        Years       Principal  Date    Outstanding (A)   Payment (B)    (A*B)/11,363,000 n.1  ____    _______________   ___________    _________________1/1/1985      --         --          --11/1/1985     0.8333     $ 1,407,703         0.1011/1/1986     1.8333      9,954,795         1.61                            ____ Total average weighted life               1.71n.1 This figure is the total principal outstanding on ND as of Dec. 31, 1984.Mr. Scribner estimated that ND had an average weighted life of 1.71 years, or 1 year, 9 months.When an issuer holds an option to repay debt, Mr. Scribner's report explains that the option may affect the average weighted life because the issuer may elect to redeem the instrument before maturity. Petitioner would elect to exercise an option to repay debt before maturity if it would save interest expense. 2006 Tax Ct. Memo LEXIS 155">*226  For example, petitioner would exercise the option to redeem the instrument before maturity when the interest rate of the instrument exceeded the market rate.Similarly, if the holder of a debt has a put option, the holder will exercise the option when the debt obligation pays interest at a rate below the market rate of interest because the holder could reinvest at a higher rate. Favorable put options would shorten the estimated remaining useful life of favorable financing intangible assets.Respondent argues that petitioner has not established a limited useful life for the favorable financing intangible assets because petitioner's calculations failed to consider the volatility of the markets, which may eliminate the benefit of these assets before the useful lives asserted by petitioner expire. Respondent's theory would seem to produce shorter useful lives for the favorable financing intangible assets, which would accelerate petitioner's depreciation allowance. 21 Instead, petitioner used a more conservative estimate of the useful life measured by the averaged weighted life.2006 Tax Ct. Memo LEXIS 155">*227  We disagree with respondent that petitioner failed to take market volatility into account when determining the useful lives of its assets. Mr. Scribner explained that the market incorporates all known information and expected information into establishing the prevailing market rates. Mr. Scribner concluded that "the market consensus establishes the current market interest rate to be the best estimate of the prevailing interest rate over the life of the investment."Because respondent contends that there is no fair market value to support the existence of the favorable financing intangibles, respondent offered no view as to their useful lives. Although Dr. Hakala disagrees that the average weighted lives equal the remaining useful lives of the assets, Dr. Hakala substantially agreed with the average weighted life calculations performed by petitioner's experts. We find that petitioner has proven that its favorable financing intangible assets have reasonably estimable useful lives equal to the average weighted lives of the debt obligations from which these assets arose. We hold that petitioner's favorable financing intangible assets had useful lives as follows:     Debt2006 Tax Ct. Memo LEXIS 155">*228            Average Weighted Life     ____           _____________________     G-15             5 years,  5 months     G-16             6 years,  8 months     G-17            12 years,  5 months     F-8                  11 months     F-11             8 years, 11 months     F-12                  2 months     F-13            12 years,  2 months     F-15                  5 months     F-18             1  year,  2 months     D-2             5 years,  3 months     Z-2             34 years, 11 months     Z-3             9 years, 11 months     ND 1 year,  8 months     CD-1             4 years,  0 months     GMC A 19752006 Tax Ct. Memo LEXIS 155">*229           3 years,  4 months     GMC B 1975          3 years,  9 months     GMC A 1976          3 years, 10 months     GMC B 1976          5 years,  6 months     GMC A 1977          4 years,  9 months     GMC B 1977          6 years,  3 months     GMC C 1977          8 years,  2 months     GMC A 1978          8 years,  5 months     GMC B 1978          7 years,  4 months     GMC C 1978          7 years,  4 months     GMC A 1979          6 years, 10 months     GMC B 1979          6 years, 10 months     GMC C 1979          7 years,  4 months     CMO A-2           5 years, 11 months     CMO A-3           17 years,  7 months     CMO C-4           14 years,  6 monthsIII. ConclusionPetitioner has proven that the favorable financing intangible assets have2006 Tax Ct. Memo LEXIS 155">*230  reasonably estimable values and ascertainable remaining useful lives in accordance with our findings. Since other issues in these cases remain unresolved, our conclusions, as stated herein, will be incorporated in a Rule 155 computation upon resolution of the remaining issues.APPENDIX: Investment Bank Bid PricesThe following table lists the investment bank bid prices obtained by petitioner and Arthur Andersen, which were used to value petitioner's favorable financing.___________________________________________________________________________                     Bid Price___________________________________________________________________________  Debt               Salomon      Merrill     ShearsonInstrument    First Boston    Brothers      Lynch      Lehman___________________________________________________________________________ G-15         --        --        --      87.250000 G-16         --        --        --      81.750000 G-17       70.3437502006 Tax Ct. Memo LEXIS 155">*231        --        --      70.250000 F-12       99.875000     99.812500      --        -- F-15       99.875000     99.812500      --        -- F-8        99.187500     99.093750      --        -- F-18       99.906250     99.812500      --        -- F-11       77.125000     76.625000      --        -- F-13       75.375000     75.750000      --        -- D-2        97.750000       --        --      98.125000 CMO A-2      97.468750     96.875000     96.625000    97.687500 CMO A-3      96.406250     95.687500     96.250000    95.218750 CMO C-4      95.906250     93.343750     95.375000    92.937500ND 95.562500       --        --      95.625000 CD-1       94.718750       --        --      94.500000 Z-2       2006 Tax Ct. Memo LEXIS 155">*232   2.500000       --        --      2.656250 Z-3        31.625000     31.000000      --      31.375000 GMC A 1975    n.1/92.062500       --        --        -- GMC B 1975    n.1/92.750000       --        --        -- GMC A 1976    n.1/92.218750       --        --        -- GMC B 1976    n.1/87.625000       --        --        -- GMC A 1977    n.1/88.562500       --        --        -- GMC B 1977    n.1/85.500000       --        --        -- GMC C 1977    n.1/83.093750       --        --        -- GMC A 1978    n.1/85.875000       --        --        -- GMC B 1978    n.1/86.843000       --        --        -- GMC C 1978    n.1/89.281250       --        --        -- GMC A 1979    n.1/91.750000       --    2006 Tax Ct. Memo LEXIS 155">*233      --        -- GMC B 1979    n.1/93.500000       --    ?     --        -- GMC C 1979    n.1/91.562500       --        --        --n.1 Mean of dealer bid prices obtained from First Boston and Salomon Bros.Footnotes1. Unless otherwise indicated, 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.↩2. This issue is one of several involved in these cases. See Fed. Home Loan Mortgage Corp. v. Commissioner, 125 T.C. 248">125 T.C. 248 (2005); 121 T.C. 129">121 T.C. 129 (2003); 121 T.C. 254">121 T.C. 254 (2003); 121 T.C. 279">121 T.C. 279 (2003); T.C. Memo. 2003-298↩.3. In this context, debt includes collateralized mortgage obligations (CMOs) and guaranteed mortgage certificates (GMCs).↩4. The effective contract interest rate is the adjusted coupon interest rate (or for zero-coupon bonds, the adjusted effective interest rate). The adjusted coupon interest rate equals the sum of the coupon rate of interest, the hedging gain or loss percentage, and any discount from the face value when the debt obligation was issued.↩5. The mortgages used as collateral for the outstanding CMOs as of Jan. 1, 1985, were entirely first lien, conventional residential mortgages having fixed rates of interest.↩6. In some cases, interest on the most junior class of bonds was not paid currently but accrued until the senior classes had been paid in full.↩7. Respondent issued to petitioner Priv. Ltr. Rul. 7607233060D (July 23, 1976), which states, in pertinent part:   Although the issuance of [Guaranteed Mortgage] Certificates   takes the form of a transfer to the Certificate holders by * * *   [petitioner] of undivided interests in the Mortgages, the terms   of the Certificates are such that for Federal income tax   purposes * * * [petitioner] will not be selling undivided   interests in the Mortgages but will be issuing debt obligations   for which the Mortgages held by the Trustee are security. * * *On May 13, 1983, respondent revoked this private letter ruling and related rulings. See Priv. Ltr. Rul. 8337016 (May 23, 1983). Respondent does not presently regard GMCs as debt for tax purposes; however, under the provisions of sec. 7805(b)↩, respondent has permitted petitioner to treat its GMCs issued before May 23, 1983, including all of the GMCs at issue in this case, as debt for tax purposes.8. Petitioner made minimum payments pursuant to the respective schedule on GMC A 1978, GMC B 1978, GMC C 1978, GMC A 1979, GMC B 1979, and GMC C 1979 on all payment dates from the inception of the GMC through March 1980.↩9. On its original Federal income tax returns for the years at issue, petitioner reported the aggregate adjusted bases of its favorable financing intangible assets as follows:               Aggregate adjusted               basis of favorable   Year         financing intangible assets   ____         ___________________________   1985             $ 456,021,853   1986              391,552,352   1987              337,931,651   1988              283,234,501   1989              237,398,945   1990              196,718,525Petitioner adjusted the bases of the favorable financing intangible assets for tax benefits received and the lost bases on retirements.↩10. Petitioner reduced the value of its favorable financing intangible assets using the valuation performed by Dr. Stephen M. Schaefer.↩11. FMV = (adjusted issue price per $ 100 - market price per $ 100) x (unpaid principal balance / $ 100).↩12. Dr. Scott D. Hakala received his doctor of philosophy, economics at the University of Minnesota. Dr. Hakala is currently a director and principal in CBIZ Valuation Group, LLC. His expertise includes: Corporate finance, restructuring and cost of capital; valuation of securities and business interests; valuation of intangible assets; analysis of publicly traded securities; economic loss analyses; wage and compensation determination; transfer pricing; and derivative securities. He has testified as an expert in over 60 cases in U.S. District Courts, this Court, and various State courts.↩13. The term "deposit base" represents the present value of the future stream of income to be derived from employing the core deposits of a bank. See Fed. Home Loan Mortgage Corp. v. Commissioner, 121 T.C. 254">121 T.C. 262. "Core deposits are a relatively low-cost source of funds, reasonably stable over time, and relatively insensitive to interest rate changes." Citizens & S. Corp. & Subs. v. Commissioner, 91 T.C. 463">91 T.C. 463, 91 T.C. 463">465 (1988). In First Chi. Corp. v. Commissioner, T.C. Memo. 1994-300, we defined core deposits as follows:   Core deposits can be an essential part of a commercial bank when   they represent a low cost and stable source of funds. Banks   typically invest the funds in loans or other income-producing   assets, and receive fees for services rendered to the   depositors. The excess of the income generated from the core   deposits over the associated expenses contributes to the   profitability of the bank. Core deposits are a separate and   distinct intangible asset with an inherent value because they   provide an inexpensive means to generate income. Therefore, when   one bank considers acquiring another bank, core deposits can   represent an attractive intangible asset and a reason for   acquiring a bank. [Fn. ref. omitted.]↩14. Dr. Herbert M. Kaufman received his Ph.D. in economics from the Pennsylvania State University. He is a professor of finance at Arizona State University, W.P. Carey School of Business. Dr. Kaufman's fields of specialization are: Investments; financial markets and institutions; monetary economics; and applied econometrics. He provided a valuation analysis of petitioner's asserted favorable financing intangible assets.↩15. Dr. Hakala indicates that the CMOs and GMCs are exactly matched.↩16. Management and guarantee income is the excess income/expense during a month from each GMC trust, including the excess of the effective interest income on mortgages backing the GMCs over the amount payable to GMC investors and short-term investments.↩17. Professor Schaefer describes Asset Spread to Market as follows:   the difference between the rate the firm actually earns   on its assets and the rate it would earn if it had to   invest in the market (at the Prevailing Market Interest Rate),   measures the benefit to the firm of the specific assets   it holds. I refer to this rate as the Asset Spread to Market. If   positive, this difference represents the "favourableness" of the   firm's assets, just as the difference between the market and   actual financing rates represents the "favourableness" of the   firm's liabilities. * * *↩18. The reduction of value for income taxes reflects the present value of cashflows on an after-tax basis. The tax shield is the amortized tax benefit associated with creating an intangible asset.↩19. See infra pp. 48-49.↩20. The average weighted life formula is as follows:        AWL = [sum] PMT x n           _____________              PPMT is the principal payment, n is the number of years that the principal amount has been outstanding, and P is the total principal paid.↩21. Respondent did not offer alternative useful life calculations for petitioner's favorable financing intangible assets.↩