Bob Jensen at Trinity University
Note: This document was written prior to my documents of the SFAS 133 Glossary, What's Missing From SFAS 133, and my SFAS 133 tutorials. It will read better if and when I find the time to update Working Paper 231. You can find links to these and my latest SFAS 133 Tutorials at http://WWW.Trinity.edu/~rjensen/default3.htm
Trinity University Links of Interest for Working Paper 231
HTML Version: http://www.trinity.edu/~rjensen/231wp/231wp.htm
ToolBook Version: http://www.trinity.edu/~rjensen/acct5341/theory.tbk
Go to Book 1: derivg.tbk (Requires Asymetrix Neuron
Plugin)
MS Word Version: J:\\courses\acct5341\231wp\231wp.doc
Excel Spreadsheets: J:\\courses\acct5341\231wp\
In June 1996, the FASB issued ED 162-B Exposure Draft that proposed booking all financial instruments at "fair value" on the balance sheet and subsequent recording of changes in fair value as either current income or deferred income (classified as comprehensive income). In June 1998, the FASB issued SFAS 133 requiring fair value booking of derivative instruments. SFAS 133 offers no guidance beyond the previous FASB's SFAS 107 (1991) with respect to estimating fair value. SFAS 107, however, offers little help for estimating fair value of interest rate swaps since these swaps are nearly always private contracts that are not traded at all or are not traded in markets deep enough to provide fair value estimates.
The major purpose of this paper is to propose a legal settlement exit value estimation of fair value. An amortization (discount) alternative is introduced using changes in fair value. It will be argued that the legal settlement rate is more appropriate for the purpose of booking interest rate swap receivables/payables on the balance sheet. This rate is more in line with recent recommendations of mark-to-market or fair value reporting of derivatives. It has the added advantage of societal symmetry between what companies report as swap receivables and what other companies report as swap payables. Present methods for computing these amounts have societal asymmetries. It is also shown how the legal settlement discount rates can be adjusted for changing term structures of interest rates.
Lastly, the paper shows a graphical approach to interest rate risk driver sensitivity analysis in answer to a call for these types of analyses for interest rate swaps by the AAA Financial Accounting Standards Committee (1995b, p. 93). Requiring such graphs and related disclosures will help to overcome the primary criticism of SFAS 119 on derivatives. SFAS 119 stopped short of requiring quantitative disclosures of market risk exposures because the FASB had not yet decided upon a means of booking and amortizing fair values of all types of derivatives. The FASB's SFAS 133 rules do not resolve this controversy for interest rate swaps not traded in open markets. This paper recommends a means of both quantifying and graphing market risk exposures. The market risk variable to be quantified is defined in Equation (14). The market risk graph is illustrated in Exhibit 5 (View in a New Browser Window).
Money is a recursive function, defined, layer upon layer, in terms of itself. The era when you could peel away the layers to reveal a basis in precious metals ended long ago. There's nothing wrong with recursive definitions . . . But formal systems based on recursive functions, whether in finance or mathematical logic, have certain peculiar properties. Godel's incompletemess theorems have analogies in the financial universe, where liquidity and value are subject to varying degrees of definability, provability, and truth. Within a given financial system, (i.e., a consistem system of values) it is possible to construct financial instruments whose value can be defined and trusted but cannot be proved without assuming new axioms that extend beyond the system's reach.
G.B. Dyson, Darwin Among the Machines: The Evolution of Global Intelligence(Reading, MA: Addison-Wesly Publishing Company, 1997, p. 167)
The Securities and Exchange Commission (SEC) in early 1997 approved rules requiring greater disclosures about financial instruments derivatives such as interest rate swaps, forward contracts, options, foreign currency swaps, etc. Included in the requirements are "value at risk disclosures of potential loss in future earnings, fair values, or cash flows from market movements, including their likelihood of occurrence," as reported by the AICPA (1997). The Financial Accounting Standards Board (FASB) SFAS 133 proposes booking all financial instruments at "fair value" on the balance sheet and subsequent recording of changes in fair value as either current income (as additions or deductions from interest expense) or deferred income (classified as comprehensive income in owners' equity). Fair value is to be exit value in an unforced (non-exceptional bargain) sale. SFAS 133 offers little guidance beyond the previous FASB's SFAS 107 (1991) with respect to estimating fair value. SFAS 107, however, offers little help for estimating fair value of interest rate swaps since these swaps are nearly always private contracts that are not traded or are not traded in markets deep enough to provide reliable fair value estimates. This paper proposes a new method of estimating fair value of interest rate swaps and amortization based upon fair value changes. The method applies whether a swap qualifies as a deferred income hedge or does not qualify for income deferral. The method estimates interest rate swap value on the basis of interest rate movements in the economy. No consideration is given to credit risk, although credit risk is less serious in interest rate swaps due to the common practice of inserting "right of offset" clauses in swap contracts. Right of offset applies to both present and future swap cash flows. If one party to the swap defaults, the other party is thereby allowed to offset that default. Also, since no cash flows apply to notional amounts, credit risk is not as serious as in regular debt where the entire principal of a loan may be at risk. The notional amount (e.g., the $10 million notional in Exhibit 1 (View in a New Browser Window)) is the "paper" basis upon which the net swap cash flow pattern is determined. Also, swap contracts are often brokered through banks that insure against default on brokered swap contracts. Banks, in turn, hedge against losses with other contracts.
In this paper, the common practice of accounting for interest rate swaps will be termed the "Traditional OBSF" (off balance sheet financing) approach since the amounts of the swap receivable and the swap payable are neither posted to ledger accounts nor included among assets and liabilities reported on the balance sheet. The AICPA FITF (1994) report is highly critical of inconsistencies with the traditional OBSF accounting for interest rate swaps relative to accounting for other types of derivative financial instruments such as forwards and options. Writers such as Rue, Tosh, and Francis (1988) and Choi and Mueller (1992, pp. 573-581) argue for the merits of BSF (balance sheet financing) booking of interest rate swaps and including them on the balance sheet. Booking of interest rate swaps entails both the recording of the net present value of future swap cash flows and the amortizing of this balance subsequent to recording. The only method proposed for doing this in prior literature was proposed by Rue, Tosh, and Francis (1988, pp. 46-49). Their proposed method will be termed the "Present Value Estimation Via [Loan + Swap] Rate Method" for recording and amortizing a swap receivable/payable balance. Writers such as Choi and Mueller (1992, Chapter 12) call this the "fair value" accounting method for interest rate swaps, but the term "fair value" is somewhat misleading. The "fair value" term implies that current market prices exist, but this is not generally the case for interest rate swaps since such swaps are usually private contracts or are traded in markets too thin for accounting valuation estimates. Instead, swap receivable/payable balance sheet valuations are derived as present values of estimated future cash flows and estimated discount (amortization) rates. As a result, the recorded "fair value" can differ with the choice of a discount rate as well as on swap cash flow forecasts.
According to SFAS 133, the new standard for accounting for all derivative financial instruments will be to abandon the traditional OBSF swap accounting in favor of recording these instruments on the balance sheet at "fair value" BSF. Timing of income realization of a change in fair value depends upon whether the swap does or does not qualify as a hedge on a past or anticipated transaction.
The major purpose of this paper is to introduce a new fair value (legal settlement rate) method that makes different assumptions regarding discount (amortization) rates used in estimating interest rate swap receivable/payable balances. A legal settlement exit value discount (amortization) rate alternative to the [Loan + Swap] rate is proposed. Fair value under Method 4 below is deemed to be exit value based upon implied contractual terms if explicit terms to the contrary are not written into the contract. The spectrum of interest rate swap accounting methods compared in this paper are as follows:
Another purpose of this paper is to show how driver (e.g., LIBOR driver defined in Exhibit 1 (View in a New Browser Window)) sensitivity analysis can be graphically portrayed. This is relatively simple and important to do when reporting interest rate swaps. Present reporting does not usually make it clear which party to the swap has taken on the greater driver risks.
The issue of fair value reporting of interest rate swaps is important since interest rate swaps often comprise the largest proportion of corporate portfolios of derivative financial instruments. The AAA Securities and Exchange Liaison Committee (1995, p. 78) reports that much "of the attention of the SEC staff has been focused recently on the derivatives problem, perhaps best evidenced by the $157 million loss posted by Procter and Gamble in the first quarter of 1994, and comparable losses by Gibson Greeting Cards, Air Products, and others." Reporting has been inadequate for risk assessment. What were reported as "primarily hedges" by Procter and Gamble turned out to be hemorrhages. In 1993 and 1992, Sears Roebuck & Company reported losses primarily from interest rate swaps at levels of $400 million and $357 million with virtually no disclosure about risks of such losses. Moody's gave an AAA rating to Orange County bonds just prior to the declaration of bankruptcy. Purportedly external investors, bond rating services, and internal management had no information as to the extent of the interest rate risk exposure. In such circumstances, companies with complex interest rate risk exposures can get high, and possibly misleading, ratings. Financial risk disclosures vary greatly in practice. With all the emerging exotic derivatives contracts of the 1990s, risk has become more like Margaret Hungerford's beauty that "is in the eye of the beholder." Attempts to quantify risk are summarized in Estrella et al (1994) and Carey (1995). It is beyond the scope of this paper to review alternatives for quantifying portfolio risk. Probably the most difficult risks to quantify are internal control risks and legal exposure risks.
This paper shows a graphical approach to interest rate risk driver sensitivity analysis in answer to a call for these types of analyses for interest rate swaps by the AAA Financial Accounting Standards Committee (1995b, p. 93). Requiring such graphs and related disclosures will help to overcome the primary criticism of SFAS 119 on derivatives. SFAS 119 stopped short of requiring quantitative disclosures of market risk exposures because the FASB could not yet decide on a means of quantifying this exposure. For interest rate swaps, this paper recommends a means of both quantifying and graphing market risk exposures. The market risk variable to be quantified is defined in Equation (14). The market risk graph is illustrated in Exhibit 5 (View in a New Browser Window). Schrand (1997) provides empirical evidence that improved disclosures will provide value-relevant information about interest rate risk.
At present there are no rules for accounting for interest rate swaps. At present, firms may elect to use either OBSF or BSF disclosures where BSF disclosures entail recording of swap receivables/payables at estimated present values. Rue, Tosh, and Francis (1988, p. 46) are critical of the traditional OBSF approach and propose a BSF method that is equivalent to Method 2 described in greater detail below. The traditional method is seldom accompanied with fair (current) value disclosures in footnotes. The AAA Financial Accounting Standards Committee (1995a, p. 89) advocates fair value accounting. Fair value accounting on the balance sheet is also proposed by Ernst & Young partners Joseph and Wolthemath (1995) while still preserving hedge accounting treatments. SFAS 133 tries to accomplish that objective. The major controversy of that attempt lies in estimating fair value of derivatives such as interest rate swaps for which there are no markets in which to estimate fair values.
SFAS 133 requires that derivatives no longer be OBSF. Instead, the FASB proposes BSF booking of derivatives at fair values whether or not they qualify as hedges. Suppose the swap contract commences at time t=0 and ends at time t=n. Methods 2, 3, 4, and 5 valuation methods defined below are BSF methods that place swap receivable/payable amounts on the balance sheet:
1. At any time t, determine the net amount receivable or payable at time t under the swap contract of the firm. In an interest rate swap, the firm enters into a contract for gross swap receivables and gross swap payables, although cash settlements usually net out these gross amounts against one another. At the end of any period t, let R(t) and P(t) denote the ex post gross swap receivable and payable for period t under terms of the contract. The ex post net settlement swap cash flow received or paid out is as shown in Equation (1) below:
Equation 1:
X(t) = R(t) - P(t)
Unless noted otherwise, ex ante future net cash flows at t+1 through n are assumed to be equal to ex post X(t) amounts actually realized at time t.
2. If a(t) depicts the ex ante discount (amortization) rate at time t for periods t+1 through n, the ex ante swap receivable or payable is valued as the ex ante present value of an annuity for n-t periods remaining as shown in Equation (2) below:
Equation 2:
V(t) = X(t) {1 - (1+a(t) [t-n] ) } / a(t)
3. For historical cost amortization Methods 3 and 5, Equation 2 is modified as shown in Equation (3) below for the ex ante V(t):
Equation 3:
V(t) = X(1) {1 - (1+a(0) [t-n] ) } / a(0)
4. Let r(t) and p(t) depict the ex post contracted swap receivable and payable rates at the end of period t. Also let n(t) depict the ex post interest rate on the underlying notional bond or note liability of the firm. The [Loan + Swap] ex ante discount (amortization) rates are given by Equations (4) and (5) below for t from t+1 through n:
Method 2 a(t) = n(t) + [ p(t) - r(t) ]
Method 3 a(t) = n(0) + [ p(0) - r(0) ]
5. The time t legal settlement ex ante current and historical present values of gross swap receivable minus swap payable present values are given by Equations (6) and (7) below:
C(t) = R(t) {1 - (1+r(t) [t-n] ) } / r(t) - P(t) {1 - (1+p(t) [t-n] ) } / p(t)
Equation 7:
H(t) = R(1) {1 - (1+r(0) [t-n] ) } / r(0) - P(1) {1 - (1+p(0) [t-n] ) } / p(0)
6. The time t legal settlement ex ante discount (amortization) rates are the a(t) or a(0) internal rates of return that satisfy Equations (8) and (9) below:
Method 4 C(t) = X(t) {1 - (1+ a(t) [t-n] ) } / a(t)
Equation 9:
Method 5 H(t) = X(1) {1 - (1+a(0) [t-n] ) } / a(0)
Methods 2 and 4 qualify as BSF methods using "fair value" estimates. Methods 3 and 5 are BSF historical cost methods. Method 1 is the traditional OBSF method that does not book derivatives as assets and/or liabilities.
Given a V(t) ex ante present value of the swap receivable/payable, journal entries must be made at the end of each accounting period to amortize the V(t-1) valuation down to or up to the V(t) valuation. Account titles for such entries have not been standardized, but writers in the past have tended to use account titles such as "Swap Receivable," "Swap Payable," "Bond Premium," and "Bond Discount." Debits and credits to interest expense are typically used to adjust for the impact of the swap cash flows. In the illustrations below, account titles are modified somewhat by introducing the accounts deferred "Other Comprehensive Income" and realized "Swap Gain/Loss." Note that SFAS 133 would lump the "Swap Gain/Loss" account in with "Interest Expense" or "Expense." However, in this paper the realized income or expense on the swap is partitioned into the anticipated Interest Expense impact using interest rates at the beginning of the period. The "Swap Gain/Loss" account is booked for the difference between anticipated and actual interest rates during the period. These account titles seem to be somewhat more informative about interest rate change impacts on the swap transactions.
The most widely cited method for recording swap receivables/payables on the balance sheet is the Rue, Tosh, and Francis (1988, pp. 46-49) method. This entails discounting estimated future swap net cash flows at the [Loan + Swap] discount rate. One problem with the use of this discount rate is that what Company A reports as a swap payable to Company B is not the same amount as what Company B reports as a swap receivable from Company A. Until now, writers have failed to note that neither this method's swap receivable nor payable (equal to the present values resulting from these discount rates) is the amount that would likely be due or owing if the swap contract is terminated prematurely. Unless contract terms alter the settlement provisions, early settlement of an interest rate swap contract would likely entail a "legal settlement" that discounts the future swap receivable at the contracted r(t) swap receivable rate and discounts the future swap payable at the contracted p(t) swap payable rate. The reason is that these rates are specified in the swap contract and serve as the basis of cash flows. These, in turn, give rise to the C(t) legal settlement current present value defined above in Equation (6). Unless the swap contract explicitly provides a settlement formula, the C(t) valuation is the implied legal fair value at any time t. Of course, another settlement formula can be written into the contract. One such possible variation in contract terms for the Bloomberg Swaps Curve is noted near the end of this paper. With or without a Swaps Curve adjustment, this paper focuses upon the Method 4 alternative to the Method 2 Rue, Tosh, and Francis [Loan + Swap] rate.
The Method 2 [Loan + Swap} rate present values are confusing surrogates for fair values since each party in the swap contract has a different "fair value" of the same contract on the balance sheet. What one party discloses as a receivable is not generally equal to what the other party reports as a payable. It is contended here that with such differing valuations, the legal settlement valuation in Equation (6) is the logical compromise measure of fair value. As a result, [Loan + Swap] rate valuations are inconsistent with fair value recommendations of reporting financial instruments at exit (net realizable) values. If swap receivables/payables are reported on balance sheets, it would seem more consistent that these balances be set at the net difference of the present value of future swap cash receipts discounted at their contracted r(t) rate minus the present value of future swap cash payables discounted at their contracted p(t) rate. The legal settlement rate proposed in this paper is that rate that will discount net swap cash flows to such a present value. Consideration for term structure adjustments for contracted rates is given near the end of this paper.
An interest rate swap situation is described in Exhibit 1 (View in a New Browser Window). This is a typical vanilla swap contract. Proposed accounting journal entries under Methods 1, 2, 3, 4, and 5 are shown in Appendices 1 (View in a New Browser Window), 2 (View in a New Browser Window), and 3 (View in a New Browser Window). The swap cash flows ex post are as follows under the swap contract between Companies A and B in Exhibit 1 (View in a New Browser Window):
| Time | Symbol | Company A | Company B |
| t = 1 | X(1) = | $ 150,000 | ($ 150,000) |
| t = 2 | X(2) = | $ 100,000 | ($ 100,000) |
| t = 3 | X(3) = | $ 50,000 | ($ 50,000) |
| t = 4 | X(4) = | $ 0 | $ 0 |
| t = 5 | X(5) = | ($ 50,000) | $ 50,000 |
| t = 6 | X(6) = | ($100,000) | $100,000 |
| t = 7 | X(7) = | ($150,000) | $150,000 |
The possible amortization discount rates are listed below for Company A:
Co. A Method 2 |
Co. A Method 3 | Co. A Method 4 | Co. A Method 5 | |
| Present Value | Historical Cost | Present Value | Historical Cost | |
| Time | [Bond + Swap] a(t) | [Bond + Swap] a(0) | Legal Settlement a(t) | Legal Settlement a(0) |
| t = 0 | 8.00% | 8.00% | 24.41% | 24.41% |
| t = 1 | 8.00% | 8.00% | 23.84% | 24.41% |
| t = 2 | 8.50% | 8.00% | 23.97% | 24.41% |
| t = 3 | 9.00% | 8.00% | 24.08% | 24.41% |
| t = 4 | 9.50% | 8.00% | 00.00% | 24.41% |
| t = 5 | 10.00% | 8.00% | 24.25% | 24.41% |
| t = 6 | 10.50% | 8.00% | 24.32% | 24.41% |
| t = 7 | 11.00% | 8.00% | 00.00% | 24.41% |
The amortized valuations of the swap receivables/payables are shown below:
| Co. A Method 2 | Co. A Method 3 | Co. A Method 4 | Co. A Method 5 | |
| Present Value | Historical Cost | Present Value | Historical Cost | |
| Time | [Bond + Swap] V(t) | [Bond + Swap] V(t) | Legal Settlement V(t) | Legal Settlement V(t) |
| t = 0 | $ 780,956 | $ 780,956 | $ 481,284 | $ 481,284 |
| t = 1 | $ 693,432 | $ 693,432 | $ 454,758 | $ 448,769 |
| t = 2 | $ 394,064 | $ 598,907 | $ 274,700 | $ 408,316 |
| t = 3 | $ 161,986 | $ 496,819 | $ 120,039 | $ 357,989 |
| t = 4 | $ 0 | $ 386,565 | $ 0 | $ 295,377 |
| t = 5 | ($ 86,777) | $ 267,490 | ($ 72,628) | $ 217,480 |
| t = 6 | ($ 90,498) | $ 138,889 | ($ 80,438) | $ 120,568 |
| t = 7 | $ 0 | $ 0 | $ 0 | $ 0 |
As an illustration, the computation of the a(0) = 8.00% using Exhibit 1 (View in a New Browser Window) data in Equation (4), this Company A [Bond + Swap] discount (amortization) rate at t=0 is derived as follows:
Equation 10:
|
n(0) + [ p(0) - r(0) ] |
= |
9.5% + [ 9.5% - 11.0) ] |
= |
8.00% |
The Appendix 2 (View in a New Browser Window) V(0) = $780,966 swap receivable for Company A is the present value of seven X(0) = $150,000 annual swap cash flows discounted at the a(0) = 8.00% discount rate. For Company B, the t=0 [Loan + Swap] discount (amortization) rate is calculated below:
Equation 11:
|
n(0) + [ p(0) - r(0) ] |
= |
9.5% + [ 11.0% - 9.5% ] |
= |
11.0% |
The Appendix 2 (View in a New Browser Window) V(0) = $706,829 swap payable by Company B is the present value of seven X(0) = ($150,000) annual swap cash outflows discounted at the Company A a(0) = 11.00% rate. Because the above Method 2 discount (amortization) rates differ between Companies A and B, what Company A reports as a swap receivable at any point in time is not equal to what Company B reports as a swap payable, even though the future estimates of swap cash flow streams are identical for both firms (other than having differing signs). The reason is that the firms have differing [Loan + Swap] discount (amortization) rates.
In the case of Method 4, the Exhibit 1 (View in a New Browser Window) contract legally requires a R(0) = ($10,000,000)r(0) = $1,100,000 gross swap receivable annually for seven years. When discounted at the r(0) = 11.0% rate, these seven receivables have a Company A gross receivable of $5,183,415 that is the present value of gross amounts legally receivable from Company B at t=0. Similarly, Company A has a swap payable P(0) = ($10,000,000)p(0) = $950,000 gross swap payable annually for seven years. When discounted at the p(0) = 9.5% rate, these seven payables have a Company A gross payable of $4,702,131 that is the present value of gross amounts legally payable from Company B at t=0.
Since swap firms usually net out gross receivables against gross payables, the current legal settlement exit value at t=0 for Company A is the Equation (6) solution shown below:
Equation 12:
Company A Method 4 C(0) = $5,183,415 - $4,702,131 = $481,284
The corresponding discount (amortization) rate from Equation (8) is that a(0) that solves the following equation:
Equation 13:
Method 4 $481,284 = $150,000 {1 - (1+a(0) [0-7] ) } / a(0)
The solution to Equation (13) is a(0) = 24.41% for Company A. Using similar equations, this also becomes the solution for Company B. Thus, Company B's C(0) = $481,284 swap payable is exactly equal to Company A's C(0) = $481,284 swap receivable legal settlement (exit value) at t=0. This illustrates Method 4 has a societal symmetry that does not exist for Method 2 accounting for interest rate swaps. Method 4 is viewed in this paper as a better method under implied specifications for swap receivables and payables. It is viewed as "the legal settlement" exit value method unless exit values are explicitly stated in the contract to be something other than the present value of swap receivables minus the present value of swap payables.
The amortized balances of the present (current) value swap receivable/payable balances are compared graphically in Exhibit 2 (View in a New Browser Window) for Companies A and B. Similar graphical comparisons for the historical cost outcomes are provided in Exhibit 3 (View in a New Browser Window). Note in particular how the choice of a discount (amortization) rate affects the balance sheet rather dramatically. For example, the $481,284 swap receivable at the time 0 inception of the swap contract results in a legal settlement valuation much smaller than of the [Bond + Swap] valuation of $780,956. Similarly, Company B has a legal settlement swap payable of $481,284 in contrast to a $706,829 swap payable under the [Loan + Swap] rate swap payable. The accounting journal entries for all five swap accounting methods are shown in Appendices 1 (View in a New Browser Window), 2 (View in a New Browser Window), and 3 (View in a New Browser Window).
Note especially that, although the balance sheet is dramatically affected by the choice of an interest rate swap accounting method, there is no impact on the bottom-line net income. The net income impact is equal to the swap cash flows each year under any of these accounting methods. This impact is shown graphically in Exhibit 4 (View in a New Browser Window). It will be argued later that the Method 4 V(t) = C(t) valuations are closest to implied fair values unless contract clauses change the exit value terms.
The traditional OBSF (Method 1) interest rate swap journal entries are shown in Appendix 1 (View in a New Browser Window). Method 1 is appealing to many corporations because the swap receivables/payables do not appear on the balance sheet. This is especially appealing to firms wanting to keep debt off the balance sheet. Some analysts might argue that since the present values of the stream of cash flows on the original (notional) bonds or notes are not recorded at present values, why should they be recorded if the firm simply swaps those interest cash flows for the interest cash flows of another company? Furthermore, net income is affected by Method 1 no differently than it is under the alternative methods.
Analysts opposed to Method 1 argue that a firm is not swapping interest obligations having the same terms receivable vis-à-vis the terms payable. Comparing the two is like comparing apples and oranges. In Exhibit 1 (View in a New Browser Window), Company A initially is obligated with or without the swap to pay a fixed rate of 9.5% on $10 million in bonds. The interest rate swap dramatically changes the risk exposure of Company A. Company A has all the obligations that it had without a swap. In addition, it now is exposed to speculative or hedging gains and losses tied to changes in the LIBOR index (the current London InterBank Offering Rate that banks can borrow at in London) over the next seven years. In contrast, Company B has capped its risk exposure with the swap such that Company B no longer has any LIBOR risk exposure (LIBOR as defined in Exhibit 1 (View in a New Browser Window) is the index for the interest rate swap). Even when they are naked speculations, expected swap receivables and payables are not included on the balance sheet under traditional OBSF accounting (Method 1). Since the speculative interest rate risk exposures in some companies are in the millions or even billions of dollars, many analysts argue in favor of putting the swap receivables/payables on the balance sheet. The position taken by the AAA Financial Accounting Standards Committee (1995b) is that fair value accounting should be used whether or not the swap is a hedge against other contracts.
This method advocated by Rue, Tosh, and Francis (1988) and Choi and Mueller (1992, pp. 576-585) uses the discount (amortization) rate given in Equation (5). Proponents argue that this rate is consistent with the viewpoint that the purpose of the swap is to adjust the underlying notional bond rate by the difference between the p(t) swap rate payable minus the r(t) swap rate receivable. Discounting at this rate, however, does not usually give the present value of the amount that is actually owing under the swap contract at time t.
The Method 2 solutions are shown in Appendix 2 (View in a New Browser Window). The Company A and Company B current [Loan + Swap] amortization discount rates are listed below:
| Company A Method 2 | Company B Method 2 | |||
| Present Value | Present Value | |||
| Time | [Bond + Swap] a(t) | [Note + Swap] a(t) | ||
| t = 0 | .0800 | .1100 | ||
| t = 1 | .0800 | .1100 | ||
| t = 2 | .0850 | .1100 | ||
| t = 3 | .0900 | .1100 | ||
| t = 4 | .0950 | .1100 | ||
| t = 5 | .1000 | .1100 | ||
| t = 6 | .1050 | .1100 | ||
| t = 7 | .1100 | .1100 |
Several points should be noted about the above [Loan + Swap] discount (amortization) rates:
Method 3 is exactly the same as Method 2 in circumstances where interest rates remain unchanged for the life of the swap. In other words, it is "historical" in the sense that it computes the swap receivable/payable at any time t based on the initial swap a(0) discount rate for time 0 rather than a current value a(t) rate. All subsequent changes in this index affect amortizations under Method 2 but not under Method 3. Method 3 solutions are shown in Appendix 2 (View in a New Browser Window). This method has not been advocated in the literature, and it is a logical alternative to Method 2 only if settlement terms happen to specify settlement conditions consistent with this valuation method. This is possible if the swap contract calls for the [Loan + Swap] amortization rate but settles prematurely on the basis of initial time 0 cash flows and discount rates rather than current time t cash flows and discount rates. The historical cost method would, thereby, be consistent with the way bonds and notes are traditionally accounted for when settlements are based on historical cost amortizations.
Method 4 solutions are shown in Appendix 3 (View in a New Browser Window). This method uses the internal rate of return that solves Equation (8). It relies upon the swap receivable/payable valuations that discount the legally contracted swap receivable and payable back to the C(t) net current value defined in Equation (6).
The Company A and Company B legal settlement exit value amortization discount rates are as follows:
| Co. A Method 4 | Co. B Method 4 | |||
| Present Value | Present Value | |||
| Time | Legal Settlement a(t) | Legal Settlement a(t) | ||
| t = 0 | .2441 | .2441 | ||
| t = 1 | .2384 | .2384 | ||
| t = 2 | .2397 | .2397 | ||
| t = 3 | .2408 | .2408 | ||
| t = 4 | .0000 | .0000 | ||
| t = 5 | .2425 | .2425 | ||
| t = 6 | .2432 | .2432 | ||
| t = 7 | .0000 | .0000 |
Several points should be noted about the above legal settlement discount (amortization) rates:
Method 5 is exactly the same as Method 4 in circumstances where interest rates remain unchanged for the life of the swap. In other words, it is "historical" in the sense that it computes the swap receivable/payable at any time t based on the initial swap a(0) discount rate for time 0 rather than a current value a(t) rate. All subsequent changes in this index affect amortizations under Method 4 but not under Method 5. Method 5 solutions are shown in Appendix 3 (View in a New Browser Window). This method has not been advocated in the literature, and it is a logical alternative to Method 4 only if legal settlement terms happen to specify settlements consistent with this valuation method. This is possible if the swap contract calls for the legal amortization rate but must be settled on the basis of initial time 0 cash flows and discount rates rather than current time t cash flows and discount rates. The historical cost method would, thereby, be consistent with the way in which bonds and notes are traditionally accounted for when settlements are based on historical cost amortizations.
Appendices 2 (View in a New Browser Window) and 3 (View in a New Browser Window) contain journal entries that are in line with the Appendix B examples in the recent FASB Exposure Draft (1996b). Whereas the FASB examples take fair value as given, this paper proposes a method of deriving fair value for interest rate swaps. One minor departure in Appendices 2 (View in a New Browser Window) and 3 (View in a New Browser Window) is the partitioning of realized income loss into interest expense (based upon expected interest expense at the beginning of the period) and Gain/Loss on Swap (based upon unanticipated rate movements during the period). It is argued here that the partitioning of the swap cash flows (into that portion that would be interest expense without any change in LIBOR during the period and a second portion equal to the gain/loss resulting in a LIBOR change this period) is more informative about impacts of each period's change in LIBOR. The credit/debit to interest expense offsets a swap cash receipt/payment. Accordingly, this entry reflects the adjustment (of the underlying notional interest expense) on interest expense due to the swap. Appendix 2 (View in a New Browser Window) contains entries for Methods 2 and 3 [Loan + Swap] amortization rate alternatives. In Appendix 2 (View in a New Browser Window), the Interest Expense account is adjusted by only the a(t-1) rate multiplied by the V(t-1) swap receivable/payable balance at the beginning of period t. The added adjustment is called the "Gain/Loss on Swap" to reflect that this difference arose from the change in LIBOR during period t. Only if LIBOR remains unchanged will there be zero added "Gain/Loss on Swap." Even though these changes in account titles have no impact on bottom-line net income, there seems to be some merit in disclosing what portion of the adjustment arises if LIBOR remains stable and what portion arises due to the period's change in LIBOR. Use of "Other Comprehensive Income" for deferrals due to hedge accounting follows the recommended approach in Appendix B of the FASB Exposure Draft (1996b).
Appendix 3 (View in a New Browser Window) uses the same account titles as Appendix 2 (View in a New Browser Window). The implications are the most dramatic for the historical cost Method 5 amortizations. For example, in Appendix 3 (View in a New Browser Window), the interest expense adjustments are those that would have been obtained had LIBOR remained unchanged for all seven years of the swap agreement. The credits and debits to the "Gain/Loss on Swap" account thereby reflect the impacts of the changes in LIBOR on cash settlements.
The FASB Exposure Draft (1996b) and SFAS 133 recommend that changes in fair value of derivative financial instruments (after adjustments for swap cash settlements) be booked to current income and retained earnings unless the instruments qualify as hedges. In the case of hedges, the Exposure Draft recommends carrying the deferred gain/loss (i.e., "Other Comprehensive Income" in Appendix 2 (View in a New Browser Window)) as a separate equity account similar to what is already required in SFAS 52 for unrealized gains and losses on foreign currency translations. However, these special equity deferrals are to be added or deducted from the FASB's proposed "Comprehensive Income Statement" advocated by Beresford and Johnson (1996).
The AAA Financial Accounting Standards Committee (1995b, p. 93) makes the following recommendations:
In general, the Committee recommends that key "drivers" be identified that impact the risks and returns of derivatives. For example, for interest rate swaps, the key driver is fluctuations in interest rates perhaps tied to some index. The Committee recommends that the companies perform sensitivity analysis related to such drivers. Given that many derivative transactions are highly levered, such analysis seems necessary for gaining a complete understanding of the magnitude of the risk exposure. Moreover, if companies are appropriately managing risks by using derivatives, this information already should be available.
Given an n(t) bond/note notional loan interest rate and swap receivable, and swap payable rates of r(t) and p(t) respectively, the annual interest expense payment on the notional amount N(t) net of the swap cash received or paid out is Y(t) as defined below:
|
N(t) [ n(t) + p(t) - r(t) ] |
|
= |
n(t)N(t) - X(t) |
In Exhibit 5 (View in a New Browser Window), a graphical approach for driver sensitivity analysis is illustrated using Y(t) possible outcomes as a function of variations in the LIBOR index. The driver in this case is LIBOR as defined in Exhibit 1 (View in a New Browser Window). Exhibit 5 (View in a New Browser Window) dramatically portrays how Company A has taken on virtually all LIBOR risk while Company B has virtually no LIBOR risk even though its notional $10 million loan pays interest at the rate of [LIBOR + 1.5%]. The Exhibit 5 (View in a New Browser Window) graph shows the sensitivity of Company A risk and returns to possible LIBOR fluctuations. It also shows how all LIBOR risk has been swapped from Company B to Company A.
How much better it might have been for investors had Sears, Roebuck and Company provided a graph such as that in Exhibit 5 (View in a New Browser Window) to indicate the sensitivity of interest rate swap income and losses to changes in interest rates. Investors might then have been somewhat forewarned about how vulnerable Sears was to interest rate rises. In 1993 and 1992, Sears, Roebuck & Company reported losses primarily from interest rate swaps at levels of $400 million and $357 million with very little disclosure about risks of such losses.
The [Loan + Swap] and [Legal Settlement] methods are consistent with the FASB Exposure Draft (1996b) and SFAS 133 position that net income not be affected by fair value accounting for hedges. Derivatives qualifying as hedges recognize income or expense on a cash settlement basis with all other value changes being deferred in comprehensive income. For instruments that do not qualify as hedges, there can be no deferred income or expense since all changes in fair value are to affect current net income. The only change necessary for interest rate swaps that do not qualify as hedges would be to replace all deferred "Other Comprehensive Income" entries in Appendices 2 (View in a New Browser Window) and 3 (View in a New Browser Window) with realized "Gain/Loss on Swap" entries. There are to be no deferrals of changes in estimated fair values not qualifying as hedges. Only when a swap qualifies as a hedge will entries to "Other Comprehensive Income" be booked.
The illustration in Exhibit 1 (View in a New Browser Window) overlooks one possible objection to either Method 2 or Method 4 proposed for booking interest rate swaps at fair values. It is well known, in the theory of interest rate term structures, that interest rates vary with how distant the forecasted cash flows are in time relative to the present moment in time. Indeed, when contracting for interest rate swaps, both parties commonly consult the well-known Bloomberg Swaps (Yield) Curve. In the simple Exhibit 1 (View in a New Browser Window) illustration, a(t) rates were simply taken as given. In reality, they should be adjusted for term structures using the swaps curve agreed upon as the basis for negotiations when the swap contract was initiated. This swaps curve is likely to be the Bloomberg swaps curve. The a(t) rates could easily be derived for future r(t) and p(t) rates adjusted for term structures using the current swaps curve. The contact information for Bloomberg Financial Services is as follows: Bloomberg Financial Markets, 499 Park Avenue, New York, NY 10022; Telephone: 212-318-2000; Fax: 212-980-4585; E-Mail: feedback@bloomberg.com; WWW Link: <http://www.bloomberg.com/> and <http://www.wsdinc.com/pgs_www/w5594.shtml>. Various pricing services are available such as Anderson Investors Software at <http://www.invest-soft.com/products/p2653.shtml>. The legal settlement method proposed in this paper assumes that both parties agree to any term structure adjustment procedure that modifies early settlement modifications of contracted rates. Otherwise societal asymmetries arise if parties use different discount rates such that booked derivatives receivables do not equal booked derivatives payables.
In retrospect, after seven years of swap payments in Exhibit 1 (View in a New Browser Window), the net swap cash receipts minus the payments sum to zero for both Companies A and B. The ultimate net impact of the Exhibit 1 (View in a New Browser Window) swap on retained earnings is zero (i.e., see the ending balances of retained earnings in Appendices 2 (View in a New Browser Window) and 3 (View in a New Browser Window)). Hence from both cash flow and net income perspectives, both companies broke even on the Exhibit 1 (View in a New Browser Window) swap.
However, from an opportunity gain or loss perspective there is more to these swap results than appears in the ledgers and financial statements. Since Company B had to borrow $10 million and wanted no interest rate risk, the only known alternative without a swap would have cost $1,150,000 per year at an 11.5% rate. Because of the swap, Company B only paid $1,100,000 each year at a swap rate of 11.0%. As a result, Company B had an opportunity gain of $350,000 equal to $50,000 per year for seven years. Company B did much better than break even on the interest rate swap with Company A.
For Company A, it is more difficult to determine the opportunity gain or loss, because it is not clear whether Company A would have chosen a fixed or variable rate alternative when borrowing $10 million without an accompanying swap agreement. In Exhibit 1 (View in a New Browser Window) it is stated that Company A predicts that LIBOR will remain below 8.5%. Assuming that Company A would have borrowed at LIBOR + 1.0% without a swap agreement, Company A had an opportunity loss of 0.5% since the swap resulted in a payment to Company B at LIBOR + 1.5%. Under these assumptions, Company A had an opportunity loss of $350,000 equal to $50,000 per year for seven years. If LIBOR had remained unchanged for the entire seven years, it would have taken more than the first two years of $150,000 annual swap payments for Company A merely to recoup its opportunity loss. Of course, if LIBOR had remained unchanged over the seven years, Company A would have earned $1,050,000 equal to seven payments of $150,000 arising from virtually zero invested in the swap. Such are the opportunities and risks of speculation in interest rate swaps. As is evident in Exhibit 5 (View in a New Browser Window), it did not matter to Company B whether interest rates went up or down since Company B swapped out of interest rate risk.
Note that if there had been no change in LIBOR, Company A would have reported an accumulated $1,050,000 impact on retained earnings resulting from a successful swap. However, the accounting profits do reveal the opportunity loss of $350,000 that reduces the real economic gain to only $700,000 instead of $1,050,000 that is reported as swap profit. This illustrates the age-old failure of traditional accounting to reveal net opportunity gains and losses to investors. Investors only see the cash flow and accounting net results. In the actual circumstances of LIBOR increases of 0.5% per year and no hedge protections, Company A purportedly broke even according to the accountants but lost $350,000 according to the economists.
In cases where there are no market values upon which to book interest rate swaps, it is argued here that the proposed Method 4 Legal Settlement Exit (Liquidation) Value approach to estimating fair value is better than the only other method (i.e., Method 2) proposed to date. If swap contracts do not specify another liquidation formula, Method 4 is based upon the default amount owing at any point in time. Unlike Method 2, the fair value reported as a receivable by one party will equal the payable reported by the other party. Method 4 is more consistent with the intent of SFAS 133.
Choice of an accounting method dramatically affects the balance sheet largely due to the large amount of notional principal typically found in interest rate swaps. This makes the valuations of swap receivables/payables extremely sensitive to the choice of [Loan + Swap] versus legal settlement discount (amortization) rates. In this paper it is argued that Method 4 legal settlement rate accounting is more consistent with the fair value philosophy of valuing financial instruments at contracted exit values when market prices are nonexistent. Method 4, therefore, is viewed in this paper as a better method under implied contractual specifications for swap receivables and payables. It should be viewed as "the" fair value method unless exit values are explicitly stated in the contract to be something other than the present value of swap receivables minus the present value of swap payables.
Requiring graphs such as that illustrated in Exhibit 5 (View in a New Browser Window) will help to overcome the primary criticism of SFAS 119 on derivatives. SFAS 119 stopped short of requiring quantitative disclosures of market risk exposures because the FASB could not yet decide on a means of quantifying this exposure. For interest rate swaps, this paper recommends a means of both quantifying and graphing market risk exposures. The market risk variable to be quantified is defined in Equation (14). The market risk graph is illustrated in Exhibit 5 (View in a New Browser Window).
This paper does not adjust fair values for credit risk. Duffy and Huang (1996) provide a recent contribution on how to adjust discount rates for credit risk.