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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
