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EXECUTIVE EDUCATION SERIES: Understanding Interest Rate Derivatives
Presented by: Shareholders Tim Woods,
Mike Loritz and James Comito
May 9, 2013
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Before We Get Started…
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This webinar is eligible for CPE credit. To receive credit, you will need to answer periodic polling questions throughout the webinar.
External participants will receive their CPE certificate via email immediately following the webinar.
CPE Credit
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The information in this Executive Education Series
course is a brief summary and may not include all the details relevant to your situation.
Please contact your MHM service provider to further
discuss the impact on your financial statements.
Disclaimer
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Today’s Presenters
Mike Loritz, CPA Shareholder 913.234.1226 | [email protected] Mike has 17 years of experience in public accounting with diversified financial companies and other service based companies, including banking, broker/dealer, investment companies, and other diversified companies ranging from audits of public entities in the Fortune 100 to small private entities. He is a member of MHM's Professional Standards Group, providing accounting knowledge leadership in the areas of derivative financial instruments, investment securities, share-based compensation, fair value, revenue recognition and others.
Tim Woods, CPA Shareholder 720.200.7043 | [email protected] A member of MHM’s Professional Standards Group, Tim is a subject matter expert for derivatives and hedge accounting. He also has extensive experience in leasing transactions, fair value, stock-based compensation, and complex debt and equity transactions. Tim has worked in public accounting, consulting, and private industry for the past 20 years, focusing on outsourced CFO consulting and financial statement audits for small and mid size privately held companies. He has extensive experience in accounting for business combinations and variable interest entities, as well as with issues in leasing, revenue recognition, and foreign exchange.
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Today’s Presenters
James Comito, CPA Shareholder 858.795.2029 | [email protected] A member of MHM’s Professional Standards Group, James has expertise in all aspects of revenue recognition, business combinations, impairment of goodwill and other intangible assets, accounting for stock-based compensation, accounting for equity and debt instruments and other accounting issues. Additionally, he has significant experience with a variety of other regulatory and corporate governance issues pertaining to publicly traded companies, including all aspects of internal control. In addition, James frequently speaks on accounting and auditing matters at various events for MHM.
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Today’s Agenda
1
2
3
Interest Rate Risk – Risk Management
Hedge Accounting
Valuation & Fair Value Issues
RISK MANAGEMENT
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Common Types of Derivatives
Option-Based Interest rate cap or floor Put or call option (equity)
Currency
Forward Agreements
Forward Rate Foreign exchange
Commodity
Future Agreements Equity
Currency Commodity
Swaps Interest rate
Currency Commodity
Credit Default
Forward Based
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Most common is a plain vanilla interest rate swap where:
A Company agrees to pay cash flows equal to interest at a predetermined fixed rate on a stated notional principal for a stated period and, in return, the Company receives interest at a floating rate on the same notional principal for the same period of time.
Company can be the fixed rate payer and the floating rate receiver or vice versa.
Interest Rate Swaps
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For example:
Company XYZ has outstanding $10,000,000 of non-amortizing variable rate debt for which interest payments are due on a quarterly basis. The note accrues interest at the 3 month London Interbank Offered Rate (“LIBOR”) plus 5% and matures via a bullet payment in 5 years.
In this case, in order to hedge the Company’s interest rate risk, the Company would enter into a 5 year interest rate swap for a notional amount of $10,000,000 at a swap rate (fixed rate) of 1.50%.
Interest Rate Swaps
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Example cont’d:
The Company would pay the fixed rate of 1.5% on the $10,000,000 notional amount on a quarterly basis and would receive the 3 month LIBOR rate on a quarterly basis. The LIBOR received is set a quarter prior to payment so the payment is made 3 months in arrears. Accordingly, the Company knows 3 months in advance what the payment will be.
Payments are settled on a net basis so if the 3 month LIBOR is greater than 1.5% then the Company will receive a payment.
Therefore, the Company has effectively turned its variable rate debt into fixed rate debt with an effective interest rate of 6.5% (1.5% fixed + 5% spread).
Interest Rate Swaps
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Example cont’d:
FIXED RATE PAYMENT = $10,000,000 * .015 / 4 = $37,500
VARIABLE RATE PAYMENT = $10,000,000 * 3 MONTH LIBOR (3.0%) or .03 / 4 = $75,000
THEREFORE COMPANY RECEIVES:
$75,000 - $37,500 = $37,500 AT QUARTERLY SETTLEMENT. THE FIXED RATE PAYMENT WILL BE $37,500 AT EACH SETTLEMENT
THE VARIABLE RATE PAYMENT IS THE MOVING COMPONENT AS THE THREE MONTH LIBOR WILL CHANGE.
Interest Rate Swaps
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An interest rate cap is an option that provides a payoff when a specified interest rate increases above a certain level (the cap rate). The specified rate is a floating rate that is set periodically.
Interest Rate Cap Agreement
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Interest rate caps can be described by a “term sheet”
Interest Rate Caps – Terms
Maturity (for example - 5 years)
Notional amount (usually set equal to borrowed amount)
Strike price (sometimes called the protection level)
Frequency (how many payments per year) • Payments per year times maturity tells you how many caplets
Basis (how you’re going to count days)
Underlying rate (usually LIBOR of some maturity)
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For Example: Company XYZ has outstanding $10,000,000 of non-amortizing variable rate debt for
which interest payments are due on a quarterly basis. The note accrues interest at the 3 month LIBOR plus 5% and matures via a bullet payment in 5 years.
In this case, in order to hedge the Company’s interest rate risk, the Company would purchase a 5 year interest rate cap agreement for a notional amount of $10,000,000 which has a cap rate of 1.5% (for example) and designated maturities of 3 months. For purposes of this example, the purchase price is $200,000 for the interest rate cap agreement.
Therefore, given that the Company purchased an interest rate cap agreement with a term of 5 years and quarterly settlements, the interest rate cap agreement is comprised of 20 individual cap agreements, or “caplets”, that are settled on a quarterly basis. As with the interest rate swap, the cap rate is set 3 months prior to settlement and as such, the settlement amount is known 3 months in advance.
Interest Rate Cap
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For Example cont’d: With an interest rate cap, the Company that purchased the cap agreement
will only receive a payment if the 3 month LIBOR closes above the cap rate. At no time will the Company be required to pay additional funds at any of the caplet settlements.
For example, if the 3 month LIBOR rate closes at 3%, the Company will receive a payment equal to (3% - 1.5%) *10,000,000 / 4 = $37,500.
Therefore, the Company has ensured that the effective rate of its debt will not go above 6.5% (LIBOR of 1.5%, the cap rate, plus the 5% margin on the underlying debt). However, the Company’s effective rate can go as low as the market will take it, which is not the situation with the interest rate swap.
Interest Rate Cap
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The swap rate is the fixed rate of interest that the receiver (variable rate payer) demands in exchange for the uncertainty of having to pay the short-term 3 month LIBOR (floating rate) over the term of the swap.
Therefore, at the time that the interest rate swap is entered, the total present value of the fixed rate payments to be received (made) is equal to the expected value of the variable rate payments to be made (received). As such, at the date the swap is entered the value of the swap is $0, which is why there is no purchase price for the swap (without commissions).
Risk Characteristics of Interest Rate Swaps
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1) interest rate risk
2) credit, or counterparty,
risk
Risk Characteristics of Interest Rate Swaps
Two primary risks:
Interest Rate Risk: • When a company enters into an interest rate swap for purposes of risk management,
they are stating that they are comfortable with the effective interest rate that has been set as a result of entering into the swap. • From the standalone viewpoint of the swap only, swaps entail interest rate risk. • However, when viewed in conjunction with the cash flows of the underlying debt being
hedged, the variable rate receiver has effectively locked in the hedged interest rate at the time the swap was entered into as the any fluctuations in the variable rate being received will be offset by the variable rate being paid on the underlying debt and the Company is effectively left with the fixed rate + the margin on the underlying debt.
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Credit, or Counterparty, Risk
Swaps are also subject to the counterparty’s credit risk: the chance that the other party in the contract will default on its responsibility.
• Banks that deal in LIBOR and interest rate swaps generally have very high credit ratings of double-A or above – It is still higher than that of a risk-free U.S. Treasury bond.
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Pros • No upfront cash outlay • Effective hedging
vehicle • Locks in an effective
rate
Cons • No upside participation • Mark to Market
accounting can have large effect on net income
• Credit, non-performance risk
Pros and Cons – Interest Rate Swaps
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An upfront premium is required to purchase a
cap.
The value of a cap depends upon the
variability of interest rates; that is, the projected
volatility of interest rates, over the life of the cap.
The longer the maturity of the cap, the more
expensive.
A cap provides “insurance” against higher interest
rates.
The farther out-of-the-money a cap is, that is, the
higher the cap rate, the cheaper it will be.
Interest rate caps are option products, and as such, share certain common characteristics with all options:
Risk Characteristics – Caps
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• The only value at risk with an interest rate cap is the premium paid for the cap agreement.
• The value of the interest rate cap agreement will increase with increases in interest rates and will decrease with decreases in interest rates.
• All other aspects of the value of the interest rate cap are the same as for other types of options: Increase in interest rate volatility increases
the value of the interest rate cap Increase in term, increases the value of the
interest rate cap Increase in cap rate, decreases the value of
the interest rate cap And vice versa
Risk Characteristics – Caps
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Pros • Effective interest rate
risk hedging vehicle with participation in gains from decrease in interest rates.
• Can only lose premium paid, cannot go to below zero (re: no liability treatment)
• Caps interest rate
Cons • Upfront cash outlay • Mark to Market
accounting can have large effect on net income although losses only to the extent premium paid.
• Credit, non-performance risk
Pros and Cons – Interest Rate Caps
HEDGE ACCOUNTING
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? From an economic
standpoint, hedging is using derivative instruments to offset risks (or volatility) that are present in a company’s business model in order to maintain a predictable outcome.
• Fair value: maintain the fair value of an item
• Cash flow: achieve predictable cash flows
From an accounting standpoint, there are specific criteria that must be met prior to a company’s implementation of hedge accounting
What is Hedging?
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Derivatives that are accounted for as freestanding are recorded at fair value at each reporting date with the change recorded in earnings.
Derivatives that are accounted for as hedging instruments are also recorded at fair value; however, the accounting for the impact to earnings is based upon the type of hedge that has been implemented.
Regardless of whether hedge accounting is utilized, ALL derivatives are recorded on the balance sheet at their estimated fair value.
What is Hedging?
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Fair value hedge - Economic purpose is to enter into a derivative instrument whose changes in fair value directly offset the changes in fair value of the hedged item (i.e. item has fixed cash flows).
Foreign currency hedge - If the hedged item is denominated in a foreign currency, then an entity may designate the hedge as either of the above or a net investment hedge.
What is Hedging?
Cash flow hedge - Economic purpose is to enter into a derivative instrument whose gains and losses on settlement directly offset the losses and gains incurred upon settlement of the transaction being hedged.
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Fair value hedge In a fair value hedge the gain or loss on a derivative instrument designated and qualifying as a fair value hedging instrument as well as the offsetting loss or gain on the hedged item attributable to the hedged risk are recognized currently in earnings in the same accounting period.
Intent is to convert a fixed cash flow instrument with a variable fair value to a fixed fair value.
EXAMPLE: FIXED RATE DEBT Special treatment = Hedged Item
Types of Hedging
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Types of Hedging
Cash Flow Hedge In a cash flow hedge, the effective portion of the gain or loss on a derivative instrument designated and qualifying as a cash flow hedging instrument shall be reported as a component of other comprehensive income (outside of earnings) and reclassified into earnings in the same period or periods during which the hedged forecasted transaction affects earnings.
Any portion of the derivative instrument that is designated as a cash flow hedge that is determined to be ineffective should be recognized in earnings immediately.
Intent is to convert a variable cash flow instrument to a predictable set
of cash flows.
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Contains explicit guidance regarding the application of hedge accounting models, including documentation and effectiveness assessment requirements. One of the fundamental requirements of ASC 815 is that formal documentation be prepared at inception of a hedging relationship.
Stresses the need for the documentation to be prepared contemporaneously with the designation of the hedging relationship.
ASC 815
ASC 815
Hedging is a Privilege, Not a Right!
Formal Documentation Under ASC 815 Hedge Documentation
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You can replace this text with
your own text. Keep the text
short and simple
You can replace this text with
your own text. Keep the text
short and simple
Hedging relationship
Documentation must include:
Hedge Documentation
• Identification of the hedging instrument • Identification of the hedged item or forecasted
transaction(s) • Identification of how the hedging instrument’s
effectiveness in offsetting the exposure to changes in the hedged item’s fair value (fair value hedge) or the hedged transaction’s variability in cash flows (cash flow hedge) attributable to the hedged risk will be assessed.
• How ineffectiveness will be measured
Entity’s risk management objective and strategy for
undertaking the hedge
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Both at the inception of the hedge and on an ongoing basis, the hedging relationship is expected to be highly effective in achieving Offsetting changes in the fair value attributable
to the hedged risk during the period that the hedge is designated (in the case of a fair value hedge) or
Offsetting cash flows attributable to the hedged risk during the term of the hedge (in the case of a cash flow hedge).
An assessment of effectiveness is required whenever financial statements or earnings are reported; at least every three months.
Hedge Documentation – Effectiveness Assessment
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Sample Company XX (Company) intends to enter into a transaction with Counterparty A (Counterparty) as part of the Company’s overall risk management policies and intends to designate an interest rate swap as a hedge of the exposure to changes in cash flows resulting from changes in interest rates associated with the Company’s variable rate debt.
Cash Flow Example - Documentation
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Risk Management Objective The Company’s risk management objective is to reduce exposure to the
variability in cash flows (interest payments) associated with changes in the 3 month LIBOR benchmark interest rate on $10 million of outstanding principal of the Company’s note payable to Bank A. The Company intends to hedge its exposure to changes in the benchmark interest rate by entering into a pay fixed, received variable (3 month LIBOR) interest rate swap. The variable leg of the swap is intended to offset changes in the cash flows attributable to changes in the 3 month LIBOR benchmark interest rate.
Cash Flow Example - Documentation
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Hedged Item The Company is hedging the changes in cash flows, associated with
changes in the 3 month LIBOR rate only, on the monthly variable rate interest payments beginning on January 1st, 2011 and the 1st of each month thereafter on the Company’s $10 million in outstanding debt with Bank A.
Based on the Company’s internal evaluation, the future interest payments associated with the outstanding debt with Bank A are assessed as probable of occurring as the debt is not callable by the lender and the Company intends for the debt to remain outstanding throughout the hedged period (maturity). Additionally, we have assessed the counterparty credit risk and determined that the likelihood the counterparty would default on any payments due under the contractual terms of the hedging instrument is not probable (ASC 815-20-35-15).
Cash Flow Example - Documentation
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Hedged Item Therefore, the Company has elected to ignore the impact of changes in
the counterparty credit risk as well as the Company’s non-performance risk in the assessment of effectiveness and ineffectiveness. As a result, changes in the fair value of the hedging instrument related to counterparty credit risk and non-performance risk will be included as a component of accumulated other comprehensive income (AOCI) until the hedged cash flows impact earnings.
Hedging Instrument The hedging instrument is the pay fixed, received variable interest rate
swap with Counterparty A.
Cash Flow Example - Documentation
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Effectiveness Assessment: The Company will perform the initial and on-going effectiveness
assessment through a regression analysis of the monthly change in the actual interest rate swap and a perfectly effective hypothetical (PEH) swap designed to entirely offset the changes in cash flows as a result of changes in the 3 month LIBOR. The regression analysis will use a minimum of 60 monthly data points (length of the hedging relationship) prior to the hedging relationship.
When correlating the actual swap value to the perfectly effective hypothetical derivative instrument, the R2, or coefficient of determination, which is the R, or coefficient of correlation, squared, should be equal to or greater than 0.8. The R2 factor should be greater than (0.8) and less than or equal to 1.25 in order to be considered highly effective.
Cash Flow Example - Documentation
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Effectiveness Assessment: Additionally, the Company will update the assessment of
the probability of the hedged cash flows occurring and the assessment of counterparty and non-performance credit risk on a quarterly basis. To the extent the hedged cash flows remain probable of occurring, and counterparty default is not probable, the Company will exclude the impact of changes in counterparty credit risk from the valuation of the perfectly hypothetical derivative and actual derivative for purposes of the effectiveness and ineffectiveness testing.
Cash Flow Example - Documentation
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Ineffectiveness Assessment: The Company will use the cumulative dollar-offset method to
assess the ineffectiveness on a quarterly basis. The Company will compare the change in the value of the actual interest rate swap with the change in the fair value of the perfectly effective hypothetical swap (a swap assuming the same critical terms as the hedged item). The actual interest rate swap will be recorded at the credit adjusted fair value on the balance sheet with an offsetting entry to other comprehensive income.
The amount of ineffectiveness to be recorded equals the lesser of
the cumulative change in the fair value of the actual interest rate swap or the cumulative change in the fair value of the perfectly effective hypothetical swap
Cash Flow Example - Documentation
VALUATION ISSUES
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ASC 820, provides a fair value hierarchy under which among other items, derivatives, must be measured and disclosed.
Given that interest rate swaps and caps into which your companies will enter will not be able to be valued by obtaining market quotes, the fair values must be estimated via cash flow and option pricing models.
Typically, your banker will provide a statement of the fair value of these instruments, however, if considered material in relation to your financial statements, your auditors will need to audit that value and it is rare that the banker will provide them access to their pricing models as they are typically deemed to be proprietary.
Valuation
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Therefore, in the situation of a non-publicly traded entity, the auditor may be able to estimate the value of the interest rate swap and/or cap for the Company, in the context of auditing the confirmation received from the bank. However, auditors cannot derive the valuation assumptions for management.
Valuation
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Valuation – Interest Rate Swaps
Interest rate swaps are valued by taking the net present value of the estimated cash flows over the life of the swap.
Given that the fixed rate payments are known, the variable rate payments must be estimated. • The future variable rate payments can
be estimated by extracting the forward rates for the variable rate and using these as our estimates of the variable rate that will be in effect at settlement.
• By definition, a forward interest rate is the interest rate for a future period of time that is implied by the interest rates prevailing in the market today.
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1 2 3 4 5 6 7 8 9 10 11Swap Rate: 2.60% Annualized Period Present
3 Month LIBOR 3 Month LIBOR Payer Receiver Value ofTotal Period Notional Forward Forward Fixed Floating Net Discount Net
Date Days Days Principal Rate Rate Cash Flow Cash Flow Cash Flow Factor Cash Flow12/31/2012 $10,000,000
3/31/2013 90.00 90.00 $10,000,000 2.0000% 0.5000% ($64,110) $50,000 ($14,110) 0.99502 ($14,039)6/30/2013 181.00 91.00 $10,000,000 2.2500% 0.5625% ($64,822) $56,250 ($8,572) 0.98946 ($8,482)9/30/2013 273.00 92.00 $10,000,000 2.5000% 0.6250% ($65,534) $62,500 ($3,034) 0.98331 ($2,984)
12/31/2013 365.00 92.00 $10,000,000 2.7500% 0.6875% ($65,534) $68,750 $3,216 0.97660 $3,141($22,364)
Therefore, based upon the following swap terms:
Notional Amount: $10,000,000Swap Rate: 2.60%Fixed Rate Payer: XYZ Company & Floating Rate ReceiverFloating Rate Payer: ABC Bank & Fixed Rate ReceiverSettlement: Every 3 monthsFloating Rate: 3 month LIBORMaturity: 12/31/2013
The value of the interest rate swap to XYZ Company is as follows: ($22,364)Which would be recorded as follows as of 12/31/12, assuminghedge accounting has not been elected: Unrealized loss - derivatives $22,364
ST Derivative Liability $22,364
Valuation – Interest Rate Swaps – NO CVA Example
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As stated before, over the counter derivatives (not actively traded), must have the counterparty valuation adjustment (CVA) factored into fair valuation estimate of the derivative. With interest rate swaps, the CVA is representative of the credit risk of the counterparty. For interest rate swaps, as there are 2 parties, there are 2 CVA factors: 1 for the bank and 1 for the counterparty (although for swaps with projected net cash flows that are either all outflows or all inflows, the CVA for the party paying the cash flows is the only applicable CVA). The CVA is the rate that represents the credit risk of the counterparty and is added to the risk free rate to calculate the applicable discount factor for each projected net cash flow over the life of the interest rate swap.
Valuation – Counterparty Valuation Adjustment
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Valuation – Interest Rate Swaps – with CVA Example
1 2 3 4 5 6 7 8 9 10 11Swap Rate: 2.60%
CVA XYZ Co 2.00% Fixed payer Annualized Period PresentCVA ABC Bank 1.00% Floating payer 3 Month LIBOR 3 Month LIBOR Payer Receiver Value of
Total Period Notional Forward Forward Fixed Floating Net Discount NetDate Days Days Principal Rate Rate Cash Flow Cash Flow Cash Flow Factor Cash Flow
12/31/2012 $10,000,0003/31/2013 90.00 90.00 $10,000,000 2.0000% 0.5000% ($64,110) $50,000 ($14,110) 0.99038 ($13,974)6/30/2013 181.00 91.00 $10,000,000 2.2500% 0.5625% ($64,822) $56,250 ($8,572) 0.97957 ($8,397)9/30/2013 273.00 92.00 $10,000,000 2.5000% 0.6250% ($65,534) $62,500 ($3,034) 0.96761 ($2,936)
12/31/2013 365.00 92.00 $10,000,000 2.7500% 0.6875% ($65,534) $68,750 $3,216 0.96386 $3,100($22,207)
Therefore, based upon the following swap terms: Valuation w/o CVA factor ($22,364)CVA $157
Notional Amount: $10,000,000Swap Rate: 2.60%Fixed Rate Payer: XYZ Company & Floating Rate ReceiverFloating Rate Payer: ABC Bank & Fixed Rate ReceiverSettlement: Every 3 monthsFloating Rate: 3 month LIBORMaturity: 12/31/2013
The value of the interest rate swap to XYZ Company is as follows: ($22,207)Which would be recorded as follows as of 12/31/12, assuminghedge accounting has not been elected: Unrealized loss - derivatives $22,207
ST Derivative Liability $22,207
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Given that interest rate caps are options, we must use an option pricing model to estimate the fair value thereof.
The most widely used option pricing model for interest rate caps is a derivation of the Black Scholes Option Pricing model, called the Black option pricing model.
Valuation — Interest Rate Swaps
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While going through the math that is behind the valuation of an interest rate cap using the Black Model is beyond the scope of this webinar, we will touch upon the variables that must be input / estimated for the Black Model.
Valuation — Interest Rate Swaps
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flag = "caplet" for pricing European call options on interest ratesX = option strike price (e.g. 2.6%)ndays = the number of days in the protection period ( = life of option)basis = the number of days used in the forward market for quoting interest rates
( e.g., 360 days or 365 days)ep = length of the exposure period (also called the reset period), measured in
years (e.g., 0.5 yrs, or 2.75 yrs, etc.)z = the continously compounded zero coupon rate over the exposure periodf = the forward rate over the protection (or reset period) periodVol = volatility of the forward interest rate
Exposure Period
t=0 t= 6
Protection Period
t = 1 year
f = z=
Life of
Valuation – Interest Rate Caps
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1 2 3 4 5 6 7 8 9 10 11 12 13 14
X ndays basis ep z f VolNotional: $10,000,000 # of Days # of Days (Reset zero Forward VolatilityBase Rate: 3 month LIBOR Option In In Fwrd Period) Rate for Rate for 3 mn LIBOR Value
Life of Strike Protection Market Exposure Exposure Protection Forward Caplet ofPeriod From To Days Caplet Price Period Quotes Period (yrs) Period (yrs) Period (yrs) Rate Price Caplet
31-Dec-12 31-Mar-13 90.00 0.3 2.60% 90.0 360.0 2.00% 60.00%1 1-Apr-13 30-Jun-13 90.00 0.5 2.60% 90.0 360.0 0.3 2.25% 2.25% 60.00% 0.0003628 $3,6282 1-Jul-13 30-Sep-13 91.00 0.8 2.60% 91.0 360.0 0.5 2.38% 2.50% 60.00% 0.0009437 $9,4373 1-Oct-13 31-Dec-13 91.00 1.0 2.60% 91.0 360.0 0.8 2.50% 2.75% 60.00% 0.0015457 $15,457
$28,522
Therefore, in this example, the Company has purchased an interest rate cap for a periodof 1 year, with 3 remaining settlements. The notional amount is $10,000,000 and the cap rate is 2.60%.Given the forward rate curve as of 12/31/12 (hypothetical not actual), and an estimated volatiltiyof the 3 month LIBOR of 60%, the total value of the entire interest rate cap agreement is $28,522
Valuation – Interest Rate Caps
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As we can see from the example, the most important variables that are input into the Black model are as follows: Forward curve – 3 month LIBOR – obtained from observed
market rates as of the valuation date
Volatility for the underlying, in this case the 3 month LIBOR rate – volatility is an estimate which as with any estimates, needs to be that amount that we most expect to occur in the future. This can be obtained from historical data representing the actual volatility that has occurred over a period consistent with the term of the interest rate cap agreement. Or volatility can be estimated using the implied volatility in the valuations of similar actively traded instruments.
Interest Rate Caps - Volatility
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Futures contracts are actively traded instruments in the marketplace on certain regulated exchanges.
Futures contracts allow the buyer (seller) to purchase (sell) a stated notional amount of a certain commodity, currency, financial instrument, etc… at a stated price over a designated period of time.
Futures contracts may be entered and exited at anytime during the life of the futures contract provided that the buyer (seller) is willing to accept a net settlement of the value of the futures contract, and not physical settlement (receipt of the actual underlying).
The prices of futures contracts are based on the current spot price and can be estimated from the spot price using the risk free rate, the dividend or stated interest rate on the underlying (if any), costs of storage, and convenience cost.
Futures Contracts
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Therefore, using the following formulae, the value of a futures contract can be derived from the current spot price of the underlying and compared to the actual future price to identify any opportunities in the marketplace:
Futures Contracts
Futures prices with:T = Time to maturityS = Current Spot price of Underlyingr = risk free rate for TI = Known income provided by underlyingq = Known convenience income or yieldc = costs of carrying the commoditye = 2.71828^ = to the power of
F = Se^rT Provides no incomeF = (S - I)e^rT Provides income with present value = IF = Se^(r-q)T Provides yield = to q%F = Se^(r+c)T Cost to maintain = c%
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EXAMPLE – value of futures contract
Futures Contracts
Futures prices with: VARIABLES FOR CONTRACTT = Time to maturity 1S = Current Spot price of Underlying $1,578.00 GOLD - 1 ozr = risk free rate for T 0.13%I = Known income provided by underlying 0q = Known convenience income or yield 0c = costs of carrying the commodity 0e = 2.71828 2.71828^ = to the power of
ACTUAL per CME $1,588.00F = Se^rT Provides no income $1,580.05 = 1580*(2.71828)^(.0013*1)F = (S - I)e^rT Provides income with present value = IF = Se^(r-q)T Provides yield = to q%F = Se^(r+c)T Cost to maintain (storage) = c%
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Forward Contracts • Therefore, although forward contracts may impose
explicit times for settlement (e.g. at the maturity of the contract), the formula for calculating the value of a forward contract is the same as the formula for calculating the value of a futures contract, except for one difference – CREDIT RISK
• Given that futures contracts are traded on organized exchanges, the requirement for initial and maintenance margin limits the credit risk associated with these contracts and, as such, credit risk is generally not considered in the valuation of futures contracts.
• However, assuming that a forward contract meets the definition of a derivative, and if the underlying is consistent with the underlying of an actively traded futures contract, it is likely that this is the case, the holder of the forward contract must take into account the credit risk of the counterparty, when determining the value of the forward contract. That is, the CVA must be added to r when discounting the value of the contract.
NOTE: you must take into account the presence of credit enhancements when valuing the contract. e.g. collateral, letters of credit, guarantees, master netting arrangements, etc…
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Options on Futures and Forward contracts have the same properties as options on any financial asset (e.g. stocks) and can, provided that the options are European, that is, they can only be exercised at maturity of the contract (or at a certain date) be valued using the Black Scholes Option Pricing Model (or a derivation thereof, the Black model).
Therefore, a European call and put option can be valued using the following formulae:
Options on Futures and Forward Contracts
Black Scholes Option Pricing Model for Futures Contracts:EXAMPLE:
c = e^-rT[F*N(d1) - K*N(d2)] call = $1.05p = e^-rT[K*N(-d2) - F*N(-d1)] put = $3.35
whereN(d) N(-d)
d1 =[ln(F/K) + σ^2*T/2] / σ*SQRT(T) 0.072169 N(d1) = 0.528766 0.471234d2 =[ln(F/K) - σ^2*T/2] / σ*SQRT(T) = d1 - σ*SQRT(T) -0.07217 N(d2) = 0.471234 0.528766
EXAMPLE: PUT - CALL PARITY, requires that:European call and put option on an oil futures contract c + Ke^-rT = p + Fe^-rtT = 0.333333 Time to expirationF = 60 Current Futures price We can use put-call parity to findK = 60 Exercise price mispriced options in the market.r = 0.09 Risk free rateσ = 0.25 Volatility of Oil Futures Contracte = 2.71828
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We can also calculate the values of options on futures contracts using lattice based models (binomial and trinomial models) and simulation.
However, this is beyond the scope of this webinar.
Options on Futures and Forward Contracts
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Given the decrease in interest rates experienced over the past year, the current index for swap rates is very low from a historical perspective.
Current swap rate (www.federalreserve.gov) 4/5/13 – Fixed for 3 month LIBOR
Interest Rate Swaps – Current Market Rate
Current swap rate (www.federalreserve.gov)
4/5/13 – Fixed for 3 month LIBOR 1 year .32% 2 year .37% 3 year .48% 4 year .65% 5 year .87% 7 year 1.33%
10 year 1.87%
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The requisite hedge accounting
documentation
Maintenance of hedge accounting - Effectiveness testing,
ineffectiveness - Additional transactions
Accounting and reporting
(disclosures)
Valuation Structuring and risk management
Sensitivity analyses
CBIZ & Mayer Hoffman McCann P.C.
MHM’s Derivatives Assistance Group
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If You Enjoyed This Webinar…
Join us for these related EES courses: 8/1: Commodity Hedging – A Risk Management Tool Against
Price Volatility of Commodities 10/10: Hedge Accounting – What is it? And is Now the
Time?
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Questions?
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Today’s Presenters
Mike Loritz, CPA Shareholder 913.234.1226 | [email protected] Mike has 17 years of experience in public accounting with diversified financial companies and other service based companies, including banking, broker/dealer, investment companies, and other diversified companies ranging from audits of public entities in the Fortune 100 to small private entities. He is a member of MHM's Professional Standards Group, providing accounting knowledge leadership in the areas of derivative financial instruments, investment securities, share-based compensation, fair value, revenue recognition and others.
Tim Woods, CPA Shareholder 720.200.7043 | [email protected] A member of MHM’s Professional Standards Group, Tim is a subject matter expert for derivatives and hedge accounting. He also has extensive experience in leasing transactions, fair value, stock-based compensation, and complex debt and equity transactions. Tim has worked in public accounting, consulting, and private industry for the past 20 years, focusing on outsourced CFO consulting and financial statement audits for small and mid size privately held companies. He has extensive experience in accounting for business combinations and variable interest entities, as well as with issues in leasing, revenue recognition, and foreign exchange.
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Today’s Presenters
James Comito, CPA Shareholder 858.795.2029 | [email protected] A member of MHM’s Professional Standards Group, James has expertise in all aspects of revenue recognition, business combinations, impairment of goodwill and other intangible assets, accounting for stock-based compensation, accounting for equity and debt instruments and other accounting issues. Additionally, he has significant experience with a variety of other regulatory and corporate governance issues pertaining to publicly traded companies, including all aspects of internal control. In addition, James frequently speaks on accounting and auditing matters at various events for MHM.
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