Exhibit 2
FAS 138 Benchmark Interest Value-Locked Debt Accounting Case:  
Two Confusing Concepts in FAS 133/138

Bob Jensen at Trinity University

Swap Curves and Amortization of Basis

Yield (Swap) Curves
In the introductory Paragraph 111 of FAS 133, the Example 2 begins with the assumption of a flat yield curve. A yield curve is the graphic or numeric presentation of bond equivalent yields to maturity on debt that is identical in every aspect except time to maturity. In developing a yield curve, default risk and liquidity, for example, are the same for every security whose yield is included in the yield curve. Thus yields on U. S. Treasury issues are normally used to plot yield curves. The relationship between yields and time to maturity is often referred to as the term structure of interest rates.

As explained by the expectations hypothesis of the term structure of interest rates, the typical yield curve is gradually increase relative to maturity. That is, in normal economic conditions short-term rates are somewhat lower than longer-term rates. In a recession with deflation or disinflation the entire yield curve shifts downward as interest rates generally fall and rotates indicating that short-term rates have fallen to much lower levels than long-term rates. In an economic expansion accompanied by inflation, interest rates tend to rise and yield curves shift upward and rotate indicating that short-term rates have increased more than long-term rates.

The different shapes of the yield curve described above complicate the calculation of the present value of an interest rate swap and require the calculation and application of implied forward rates to discount future fixed rate obligations and principal to the present value. Fortunately Example 2 assumes that a flat yield curve prevails at all levels of interest rates. A flat yield curve means that as interest rates rise and fall, short-term and long-term rates move together in lock step, and future cash flows are all discounted at the same current discount rate.

A yield curve is the graphic or numeric presentation of bond equivalent yields to maturity on debt that is identical in every aspect except time to maturity. In developing a yield curve, default risk and liquidity, for example, are the same for every security whose yield is included in the yield curve. Thus yields on U. S. Treasury issues are normally used to plot Treasury yield curves. The relationship between yields and time to maturity is often referred to as the term structure of interest rates. Similarly, an unknown set of estimated LIBOR yield curves underlie the FASB swap valuations calculated in all FAS 133/138 illustrations.  The FASB has never really explained how swaps are to be valued even though they must be adjusted to fair value at least every three months. Other than providing the assumption that the yields in the yield curves are zero-coupon rates, the FASB offers no information that would allow us to derive the yield curves or calculate the swap values in Examples 2 and 5 in Appendix B of FAS 133 and in other examples using FAS 138 rules.

The typical yield curve gradually increases relative to years to maturity. That is, historically, short-term rates are somewhat lower than longer-term rates. In a recession with deflation or disinflation the entire yield curve shifts downward as interest rates generally fall and rotates counter-clockwise indicating that short-term rates have fallen to much lower levels than long-term rates. In rapid economic expansion accompanied by inflation, interest rates tend to rise and yield curves shift upward and rotate clockwise indicating that short-term rates have increased more than long-term rates.

The different shapes of the yield curve described above complicate the calculation of the present value of an interest rate swap and require the calculation and application of implied forward rates to calculate future expected swap cash flows. Example 2 in Appendix B of FAS 133 assumed that a flat yield curve prevails at all levels of interest rates. A flat yield curve means that as interest rates rise and fall, short-term and long-term rates move together in lock step, and future cash flows are all discounted at the same current discount rate. The cash flows and values in the Appendix B Example 5, however, are developed from the prevailing upward sloping yield curve at each reset date.

The accompanying Excel workbook used the tool Goal Seek in Excel to derive upward sloping yield curves and swap values at the reset dates that generated the $4,016,000 swap value used in the FASB's Example 1 of Section 1 of the FAS 138 examples.  (ADD LINK HERE)

If you carefully study the yield curve tables in the Excel workbook, you will note that the forward rate is calculated in the following manner using the y(t) yield curve values:

ForwareRate(t) = [1 + y(t)]t/[1 + y(t-1)]^t-1 – 1

The ForwardRate(t) is the forward rate for time period t, y(t) is the multi-period yield that spans t periods, and y(t-1) is the yield for an investment of t-1 periods. For example, if 6.5% is y(t) and 6.0% is y(t-1). Thus, ForwardRate(2), the forward LIBOR for year 2, is calculated as follows

ForwardRate(2) = (1.065)2/1.06 – 1 = 0.07 or 7.0%

Having calculated a forward rate for each quarter from the rates in the trial yield curve, we can then ask Excel to give us the values of an upward sloping yield curve with forward rates that would calculate future expected swap cash flows whose present value is zero. The resulting yield curve,  equivalent rates, forward rates, expected swap cash flows are shown in the base examples in the Excel workbook.

Amortization of Basis Adjustments
In Example 2 of Appendix B of FAS 133, you will see values for "Amortization of Basis Adjustments" in the table in Paragraph 117.  These are simply put into the table, along with "Interest Accrued" amounts without ever explaining how to calculate those values or what they really mean.  In the Excel workbook accompanying this case you can trace how they are calculated and how they impact the journal entries.  They seem to add more confusion than they benefit users of financial statements since the amortization amounts have to be reset each year due to changing benchmarked carrying values of the debt.

The theory behind the amortization of basis adjustments is that, whenever carrying value of debt is revalued due to changes in benchmark rates, that change in value should be amortized over the remaining life of the debt rather than be charged each period.  Thus the change in the value of the debt due to changed benchmark rates can be amortized using the PMT function in Excel to compute the payment for each remaining period that will amortize that change in value.  As indicated above, however, the amortization must be reset each period that the rates change.

In the Excel workbook you are allowed to view the journal entries with or without the amortization of basis adjustments.  Basis adjustment in this case is simply a fancy way of saying that the i(t) index upon which carrying value of debt is being revalued changes and requires an adjustment in the carrying value.