Exhibit 1
FAS 138
Benchmark Interest Value-Locked Debt Accounting Case:
Definitions of Basic Symbols
Bob Jensen at Trinity University
These tables do not define every term used in the case. Readers are referred to my FAS 39 and FAS 139/138 Glossary for more complete definitions and links to paragraphs in the standards and DIG issues. The link for this is at http://www.trinity.edu/rjensen/acct5341/speakers/133glosf.htm A short glossary is also provided in Exhibit 4.
|
Row |
Symbol |
Example and Explanation of Debt-Related Parameters |
|
120 |
PV | The present value of one or more payments in a stream of cash flows. This is a function in Excel that computes the present value of a specified annuity and principal for a known interest rate per period. The PV function is used primarily in this case to compute the various alternatives for "value." |
| 121 | PMT | Refers to the PMT function in Excel that calculates the annuity payment stream that equates a present value with a future value for a specified interest rate per period. The function is used in this case to compute the "Amortization of Basis Adjustments." |
| 125 | * | The * symbol is a multiplication indicator in this case. It helps avoid confusion of sorting out multiple parentheses and conforms to the accompanying Excel Workbook. |
| 200 | F(0) | = ($100,000,000), the liability of the hedged item at maturity. The -F(0) is called the "face" or "principal" of the debt. |
| 210 | T | = 5 years of the hedge contract. |
| 211 | D | = 2, the number of equally spaced time periods per year. |
| 212 | D*T | = 10, the number of total time periods before expiration, where t-1,...,D*T |
| 213 | APR | = annual percentage rate expressed in a percent per year. |
| 214 | D*f(0) | = .0.08000, the APR face (nominal, coupon) rate of the debt. |
| 215 | f(0) | = 0.04000, the face rate at t=0. This rate determines the cash flow stream other than the repayment of the principal at maturity. |
| 216 | f(0)*F(0) | = $4,000,000, the nominal (coupon) interest payment per period. |
| 217 | i(t) and I(t) | The i(t) rates comprise an interest rate index depicting either a U.S. Treasury risk-free rate or a LIBOR rate as discussed in Paragraph 17 of FAS 138. The corresponding I(t) present values of the debt's future cash flows are derived using the i(t) designated discount rate. |
| 220 | D*v(0) | = 0.08250, the effective rate of the debt at t=0 expressed as an APR |
| 221 | v(0) | = .04125, the effective
rate of the debt at t=0. The effective rate is a market rate that has the
following components in this case:
|
| 222 | V(0) | = ($98,992,418), the initial liability of the debt at the v(0) rate. In reality, v(0) is derived from the -V(0) proceeds of the debt issue. In other words, v(0) is the effective rate that discounts the stream of all contracted debt payments back to a present value of V(0). |
| 223 | -V(0) | = $98,992,418, the initial proceeds of the debt. These proceeds are dictated by both the full systematic risk and unsystematic risk components in the debt issue at t=0. |
| 224 | F(0)-V(0) | = $1,007,582,
the debt discount (premium) that arises whenever the effective v(0)
rate is not equal to the nominal rate f(0). The deepest
discount that can arise is to have f(0)=0 in a "zero-coupon"
debt instrument that pays zero interest each period until the last period
when the F(0) face of the debt is paid in full. In other words,
firms that have AAA credit ratings or CCC credit ratings can elect to
issue bonds at a discount or premium. Their credit standings do not
dictate the borrowing strategies.
FASB rules require that the F(0)-V(0) discount or premium be amortized over the life of the debt rather than be charged to earnings in one lump sum at t=0. |
| 225 | A(t) | = the amortization portion of F(0)-V(0) in period t. The unamortized discount or premium remaining is the F(0)-V(0)-SA(t) where the summation is for all periods up to and including period t. |
| 230 | v(t) and V(t) | V(t) is the "full" market value of the debt at time t, where the market is valuing the debt as an on-going obligation rather than one that is being liquidated prior to maturity. The V(t) market value is the present value of all remaining debt cash flows. The current effective rate that equates these cash flows with a V(t) present value is called the "full" effective rate at time t. Both v(t) and V(t) include both systematic risk and unsystematic risk components. They will go up and down and vary inversely with changes in the risk-free rates and the credit sector systematic rate changes in the economy. They will also vary with changes in the debtor's unique credit risk that may vary with production quality, production efficiency, labor strife, scandals, plant fires, weather, earthquakes, floods, etc. |
| 231 | u(t) and U(t) Treasury- Locks |
The U(t) is the present value of the remaining debt payments when discounted at the current risk free rate. For example, if the current U.S. Treasury rate is u(t), then -U(t) is the proceeds that the U.S. Government would receive if issuing debt having equivalent cash flows to hedged item in question. The difference between V(t) and U(t) is comprised of both systematic credit sector spreads and unsystematic, firm-specific spreads. If the debtor designates a FAS 133/138 "benchmark" rate as i(t)=u(t), the hedge is termed a "Treasury-Lock" hedge, because the only thing being hedged is the risk of variation in the risk-free rate component of v(t). When i(t)=u(t) is FAS 133/138 designated benchmark rate in a qualified Treasury-Lock hedge, the debt is carried on the balance sheet at the I(t)=U(t) present value of the future debt payments discounted at the l(t) rate. The FASB allows the i(t) hedging index to be the U.S. Treasury rate in a Treasury-Lock hedge. |
| 232 | l(t) and L(t) LIBOR- Locks |
The l(t) rate is the popular London Interbank Offered Rate (LIBOR) that is an index upon which many hedging contracts are based. It is greater than u(t) since it is not a risk-free rate. However, it is a worldwide rate that does not vary over particular credit sectors. Hence, when hedging with this LIBOR index, there remains some unhedged systematic risk in any particular credit sector. We will use the term LIBOR-Lock to depict a hedge based upon LIBOR. When i(t)=l(t) is FAS 133/138 designated benchmark rate in a qualified LIBOR-Lock hedge, the debt is carried on the balance sheet at the I(t)=L(t) present value of the future debt payments discounted at the l(t) rate. The only i(t) hedging index allowed for hedge accounting under FAS 133/138 is either the u(t) risk-free U.S. Treasury index or the l(t) popular LIBOR index. |
| 233 | s(t) and S(t) Systematic or Credit Sector Locks |
The s(t) rate is the theoretical systematic rate that accounts for all systematic risk factors such as system-wide risk-free rate and the sector-wide systematic risk of all firms in a particular credit sector. The s(t) rate differs from the v(t) full value rate only by the unsystematic rate components that vary from firm to firm in a given credit sector. The original FAS 133 only envisioned "fair value hedges" as hedges of S(t) present values of debt cash flow streams discounted at the s(t) total systematic risk rate. The problem is that interest rate indexes do not in general exist for each credit sector. |
| 234 | DIG E1 | The Derivative Implementation Group (DIG)
confused the issue of fair value hedging in the DIG Issue E1 that appeared
after FAS 133 was issued but before benchmarking was defined for hedge
accounting in FAS 138.
Paragraph 14 of FAS 138 states the following: Comments
received by the Board on Implementation Issue E1 indicated (a) that the
concept of market interest rate risk as set forth in Statement 133
differed from the common understanding of interest rate risk by market
participants, (b) that the guidance in the Implementation Issue was
inconsistent with present hedging activities, and (c) that measuring the
change in fair value of the hedged item attributable to changes in credit
sector spreads would be difficult because consistent sector spread data
are not readily available in the market. |
| 235 | v(t) and V(t) FullValue- Locks |
If a firm chooses to hedge the full value of a debt issue such that V(0)+HedgeValue is constant over the life of the debt, then the hedge really must be some type of an insurance contract rather than an interest rate hedge. The problem is that unsystematic risk components cannot be accounted for in market interest rate indexes. A full-value lock is tantamount to insuring against production disruptions, factory fire, labor strife, and the raft of other unsystematic risk factors that affect a particular debtor's credit standing. Such insurance contracts are covered by other FASB standards and were never covered by FAS 133/138 standards. |
| 236 | c(t) and C(t) | The C(t) value is the net carrying value of the
debt in the balance sheet. Under FAS 133/138 rules, the c(t)
discount rate corresponding to C(t) present values may be designated i(t)
benchmark rates set equal to u(t) risk-free rates, l(t) LIBOR rates, or
s(t) full systematic risk rates if there is a qualifying benchmark hedge
of "benchmarked" value under FAS 133/138 rules. If there
is no hedge or the hedge does not qualify for hedge accounting, then the
C(t) carrying value is amortized cost. The alternatives are as
follows depending upon whether the hedge qualifies for hedge accounting
under FAS 133/138 criteria for interest rate hedges: C(0)=V(0)
with no qualifying hedge for t=0 C(0)=V(0)+W(0)
with a qualifying hedge for t=0 Note that I(t) may be set equal to U(t), L(t), or V(t) depending upon the value-lock hedge that is chosen for the hedging contract. |
| 240 | Exogenous Parameters | Exogenous parameters are those parameters set by market forces outside the control of the debtor. Examples include u(t), l(t) and s(t) other systematic interest rate components of s(t). |
| 241 | Endogenous Parameters | Endogenous parameters dictated by the debtor in the debt contract. These include f(0), D, T, and F(0) parameters. |
| 242 | Mixed Parameters | Mixed parameters are jointly determined by a debtor and market forces. These include all other parameters defined above. For example, v(t) and V(t) full values are determined interactively by the F(0) face value and the f(0) face rate set by the debtor. However, what the market will lend for those parameters depends upon market forces at t=0. |
|
Row |
Symbol |
Example and Explanation of Swap-Related Parameters |
| 300 | Hedged Item | The benchmarked debt value as designated by I(0). Recall that I(0) may be designated as a risk-free U(0), a LIBOR-index L(0), or a full systematic risk S(0) present value. In this case it will be assumed that the hedged item satisfies all FAS 133/138 criteria in Paragraphs 21-27 as amended by FAS 138 Paragraph 4(b). |
| 301 | Hedge | The hedge is an interest rate swap having a fixed receivable leg and a floating swap payable leg based upon the designated i(t) index. |
| 305 | H(0) | = 1.0197. The H(0) parameter is a duration-weighted hedge ratio that determines the notional of the interest rate swap contract at t=0. |
| 306 | F(0)*H(0) | = ($101,970,000). The product of the face value of the debt and the hedge ratio determine what is called the swap's notional. Ideally, the hedged item's face liability is equal to the swap notional. However, when contracting swaps, it is not always possible to negotiate a hedge ration of 1.0000. |
| 310 | r(0) | = .04000. The r(t) swap receivable leg is assumed to have a fixed rate equal to the initial r(0) rate in this case. The annualized APR is D*r(0)=0.0800. |
| 315 | i(t)+p(0) | = i(t)+0.003925 is the swap payable leg rate that varies as a function of the i(t) designated benchmark rate in the swap hedge. In this example the p(t) payable increment is assumed to be fixed at p(0) when t=0. The annualized APR of p(t)=p(0) is D*p(t)=0.00785. |
| 318 | r(0)-i(t)-p(0) | Interest rate swaps are usually settled at the net rate determined by swap receivable rate minus the swap payable leg. In this particular swap, the debtor receives a net swap cash payment if r(0)>i(t)+p(0) and pays out when r(0)<i(t)+p(0). |
| 320 | X(t) | = [-F(0)*H(0)]*[r(0)-i(t)-p(0)]. This is the amount
of cash that the debtor either receives or pays out at time t under the
hedging swap contract. X(t) is simply the swap cash flow based
upon a fixed swap notional and a floating swap leg payable.
It is extremely important to note that swap cash flows are based upon ex post values of the i(t) swap valuation index. This is not the case for W(t) swap values defined below. |
| 325 | Basis Risk | This is the risk of an imperfect hedge due to having the
hedged value based on some index other than the i(t) index contracted
for the swap payable leg. For example, if the debt was based upon
some mortgage rate variable or a EURIBOR index and the swap payable leg
was based upon a LIBOR index, then a hedged swap carrying amount based
upon s(t) and some assumptions about unhedged credit sector risk faces
ineffectiveness of the hedge due to basis risk. In general, the
term "basis risk" means the hedged item and the hedge are
"based" upon two different rates. The effectiveness of a
hedge having basis risk depends upon how well the two bases are
correlated.
Basis risk underlies much of the criticism of the FAS 138 amendments by two of the dissenting Board members of the FASB. See the discussion following Paragraph 25 in FAS 138. |
| 330 | W(t) and Y(t) | W(t) is the ex ante swap value is the estimated value that
the debtor would receive or pay in the event of an early termination of
the swap when t<D*T. In practice, this W(t) swap value is
generally determined by yield curves of the i(t) swap index for all
future periods remaining under the swap contract. The yield curves
are sometimes called "swap curves," but that is simply another
term for the yield curves used to derive forward rates. A swap is
simply a portfolio of forward contracts. Yield (swap) curves are
derived from market transactions prices of forward contracts.
Typically, both the party and the counterparty to an interest rate swap
will go to some financial markets data service (e.g., Bloomberg) that
tabulates forward contracting prices and derives yield curves for common
interest rate indices such as LIBOR and U.S. Treasury indexes.
It is extremely important to note that X(t) swap cash flows are based upon ex post values of the i(t) swap valuation index. This is not the case for W(t) swap values that are derived from ex ante yield (swap) curves. The Y(t) is the swap value of a theoretically perfect swap having no ineffectiveness. It is derived by means of the shortcut method that always assumes that Y(t-1)-Y(t)=I(t)-I(t-1). The shortcut method is described below. |
| 340 | Ineffectiveness | A swap is perfectly effective when
W(t-1)-W(t)=I(t)-I(t-1). In other words,
the whole purpose of a value-lock hedge is to have the change in the
benchmarked value of the hedged item be exactly offset by a change in
the benchmarked value of the hedge (hedge values must be maintained at
current W(t) values on the balance sheet.
Ineffectiveness arises when the change in swap value does not exactly offset the change in benchmarked debt value. The FASB allows the debtor to define ineffectiveness and ineffectiveness tolerance. The debtor that hedges must test for ineffectiveness at least every three months under FAS 133/138 rules. Ineffectiveness that exceeds pre-defined tolerances must be booked charged to current earnings. |
| 344 | DELTA(t) | = the change in swap value divided by the change in debt value or some variation thereof based upon absolute values of the changes. The FASB suggests that a pre-defined tolerance of 0.80<DELTA(t)<1.25 is an acceptable tolerance such that ineffectiveness must be booked only when the observed ratio falls outside the tolerance limits. The debtor is not allowed to begin hedge accounting under FAS 133/138 rules unless hedge performance is expected to be within tolerance limits. It is somewhat common for economic hedges not to qualify for hedge accounting. |
| 345 | DELTA Error Tolerance |
Like most ratios, DELTA(t) can produce some misleading outcomes. If there is no change in the denominator (i.e., change in debt value), division by zero is undefined. Also, if the amount of inefficiency is very small, it is possible to get a very large DELTA(t) ratio that accompany insignificant amounts of value-lock hedging inefficiency. For example, suppose the ratio is 5.00 when the amount of inefficiency is only $10 in a company having $500 million in earnings. The FASB in at the bottom of Paragraph 5 in FAS 138 states that FAS 133/138 rules need not be followed to the letter for immaterial amounts. |
| 350 | Shortcut | The shortcut method is discussed in Paragraphs 68, 114,
and 132. Later on the DIG Issue E4 focused on circumstances where
all Paragraph 68 criteria were not met. FAS 138 discusses the
shortcut method in Paragraph 22.
Without getting bogged down in details at this time, suffice it to say that when the shortcut method is permitted, it saves the debtor a lot of time in testing and accounting for ineffectiveness every three months. Shortcut method hedges are assumed in advance to be perfectly effective. In this case, the shortcut method criteria in most instances are not met. However, the outcomes of the shortcut method are compared with ineffective outcomes. In essence, the shortcut method allows the debtor to assume shortcut swap valuations as if the swap values are perfectly effective each period. The change in the swap value on the balance sheet is always equal to the I(t-1)-I(t) changes in the benchmarked value of the debt. Technically there can be no ineffectiveness such that the change in actual swap values always perfectly offsets a change in debt values if the shortcut method is to be allowed. The FASB simply says that if this is to be the case, the debtor does not have to test for ineffectiveness during the hedging period. |