FAS 133 for Dummies: Accounting for Fair Value Hedges (Example 2)
July 22, 2009
“We are what we repeatedly do. Excellence, then, is not an act, but a habit.” Aristotle (382-322 B.C.)
Gulf of Guinea (GoG) LLC is planning to build a new theme park for $2,000,000,000.00. In order to finance this project, GoG issued $2,000,000,000.00 for 1.5 years on January 1, 2000 and agreed to pay LIBOR plus 10bp. This bond was bought in its entirety by BHIB. Worried that interest rate may rise in the future, thus reducing the fair value of the bond bought from GoG, BHIB entered into an interest rate swap agreement as follows:
- BHIB to pay LIBOR plus 10bp for 1.5 years.
- Receive fixed at 6.0% for 1.5 years
- The LIBOR rates with continuous compounding for 6-months and 12-months maturities (i) 5.55% and (ii) 5.8%
- There are no transaction costs
- Interest rate is paid semi-annually and continuously compounded
- The 6-month LIBOR rate at the last payment date was 5.25% (semi-annual compounding).
- BHIB fiscal year end is June 30th
The value of the interest rate swap on January 1, 2000 is zero. Value of a swap at inception is zero. This is because if the value is not zero, there is an opportunity for arbitrage and based on the efficient market hypothesis, arbitrageurs will quickly take advantage of that opportunity and reset the price back to zero almost instantaneously (real time). No entries are required except memorandum entries.
VALUATION:
Value of the swap as of June 30th, 2000 is calculated as follows:
Where Bfix = Present value of bond with underlying fixed-interest payment
and Bfl = Present value of bond with underlying variable-interest payment
Where
K = Fixed payment made on each payment date
L = Notional principal in swap agreement
ti = time until maturity (over the life of the swap)
ri = LIBOR zero rate corresponding to maturity ti
e = exponential
Calculation of Bfix:
Calculation of Bfl:
NB: Note that continuous compounding method is theoretical construct and not really used in practice. Discrete compounding is more common because it accounts for day count convention etc.
Since BHIB is the fixed-rate receiver and floating rate payer under this swap agreement, BHIB has a gain of $4.9780078703879. This will result in booking a swap asset for $4.9780078703879 in BHIB books. In addition, net interest gain/loss will result from the swap agreement as follows:
Fixed Rate interest receivable = $60,000,000.00
Variable Rate + 10 basis point = $53,500,000.00
Net Interest Income from swap = $6,500,000.00
Gulf of Guinea LLC will pay interest on the $2,000,000,000.00 loan @ LIBOR plus 10 basis point.
![= [0.0565 * (6/12)] * 2,000,000,000.00 = 56,500,000.00](http://blackherald.egoong.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_980.5_95131af3c026ef3b0b87c7f3f88f2a1a.png "= [0.0565 * (6/12)] * 2,000,000,000.00 = 56,500,000.00")
ACCOUNTING ENTRIES:
FAS 133 states that:
For a derivative designated as hedging the exposure to changes in the fair value of a recognized asset or liability or a firm commitment (referred to as a fair value hedge), the gain or loss is recognized in earnings in the period of change together with the offsetting loss or gain on the hedged item attributable to the risk being hedged. The effect of that accounting is to reflect in earnings the extent to which the hedge is not effective in achieving offsetting changes in fair value.
Day 1 when loan was lent to GoG by BHIB:
Dr Bond $2,000,000,000.00
Cr Cash $2,000,000,000.00
(To record bond for $2,000,000,000 - January 1, 2000)
Day 1 when SWAP contract was entered.
(No entries required because this is just a memorandum entry).
Accounting Entries:
Dr Cash $6,500,000.00
Cr Income - Swap Interest Received $6,500,000.00
(To record NET SWAP Interest Received)
Dr Interest Income $56,500,000.00
Cr Income - Bond $56,500,000.00
(To record Interest Income Received on original bond acquired for $2,000,000,000.00 for 6 months)
Dr Swap Asset $4,978,007.87
Cr Unrealized holding gain/loss - income $4,978,007.87
(To record increase in FV of Swap Asset)
Change in FV of Loan = $2,000,000,000 - $1,997,298,773.51 = $2,701,226.49
Dr Unrealized holding gain/loss - income $2,701,226.49
Cr Bond $2,701,226.49
(To record decrease in FV of loan)
NET SWAP INTEREST INCOME:
Net Interest Income $6,500,000.00
LOAN INTEREST INCOME :
Accrued Interest Income $56,500,000.00
NET UNREALIZED HOLDING GAINS/LOSSES:
Increase in FV of swap asset $4,978,007.87
Decrease in Bond FV ($2,701,226.49)
Net Unrealized holding Gain $2,276,781.38
BALANCE SHEET PRESENTATION:
ASSETS:
Swap Assets: $4,978,007.87
Bond (Variable) $1,997,298,773.51
NET SWAP Interest Income Receivable $6,500,000.00
Interest Income - Cash $56,500,000.00
**Recalculate the FV of swap and bond every reporting period and repeat these entries.
Bibliography:
- Options, Futures and Other Derivatives “Fifth Edition” John C. Hull 2003
- Financial Accounting Standard 133 - AICPA
- Professional Risk Managers Handbook - Financial Instruments & Financial Markets (www.prmia.org)
NOTE: Thanks to our partners at Blackinsey & Company for providing the solution. Blackinsey & Company is a top tier strategy & management consulting outfit based in Washington, DC. This was created under creative commons and is copyleft. The interpretations and analysis presented in this article are purely for pedagogical exercise and Black Herald cannot be held responsible for any error of commission or omission. Thanks for visiting our website. You are always welcome . In the coming series, we will focus on cash flow and foreign currency hedges. We will also examine other types of derivatives namely forwards, futures, swaption, equity index and other exotic and examine different valuation tools including binomial theorem and Black-Scholes. Other third-party valuation tools will also be discussed.
If you like this article check out:
FAS 91 for Dummies and stay tuned for the following:
- FAS 133 for Dummies
- FAS 91 for Dummies (Sample with Prepayments)
- FIN 46 for Dummies
- FAS 115 for Dummies
- FAS 123(R) For Dummies
Comments
4 Responses to “FAS 133 for Dummies: Accounting for Fair Value Hedges (Example 2)”
Got something to say?
1. How did you arrive at 186,025427.30 for the Loan balance in the balance sheet?
2. You said LIBOR as at last payment date was 5.25% and GoG pays interest at LIBOR + 10bp. Why did you use 5.555 + 10bp instead of 5.25% + 10bp in calculating the original interest payable by GoG (just like we did in the FAS 133 part 1?)
3. The journal entry description for the 56.5M interest payable by GoG mentioned 6% fixed but the question says the loan was variable (LIBOR plus 10bp).
4. balance sheet description of the loan also called if 6% fixed? Is this loan fixed or variable?
RESPONSE -
@1 The $186,025,427.30 was inadvertently transferred from the first FAS 133 part 1 question and should have been updated to reflect the new value of the floating rate bond of $1,997,298,773.53 calculated in the solution above.
@2 Valid point - for the purpose of valuing the SWAP and calculating the interest on the bonds underlying the SWAP transactions you use LIBOR in arrears. However, for the purpose of calculating interest on the original bond, I used actual LIBOR on interest payment date. I guess this is debatable, depending on the terms of the bond indenture, however, it was an assumption I made, which is not explicit in the question.
@3. The Journal Entry description should have referred to the interest as variable i.e. LIBOR + 10%. But the calculated value is correct. Thanks.
@4. Same as #3 above thanks.
@1 - I thought as much. It must have been copied over from example 1.
@2 - I agree. I would go with interest date assumption based on my variable rate mortgage (LIBOR and some change).
@3 - You are welcome
@4 - ditto
Thanks for posting this FAS 133 stuffs. Makes it a lot clearer!
Hello I do not understand why BHIB entered into a swap to fix IR if they are going up - could you please detail a bit this
Because the higher the IR, the lower the bond price/value. BHIB purchased the bond, therefore, the bond is an asset in BHIB books, if interest rate goes up, the fair value of the bond declines, if IR falls the fair value of the bond goes up. There is an inverse relationship between bond price and IR…it is got to do with discounting concept……Therefore to hedge against fluctuation in the FV of its bond it entered into a fixed rate swap to pay LIBOR and receive fixed since the original bond already pays LIBOR essentially converting a floating rate bond to fixed rate bond …I guess you are confused between the coupon and the yield. The coupon determines the interest payment at every payment period, but the yield is what you use to value the bond. The yield is a transformation of the price of the bond, but because of convention instead of quoting bonds at dollar value they are transformed to yield, yield is quoted in % just like the coupon blah blah blah ……..search the internet for further explanations - search for term structure of interest rate.