FAS 133 for Dummies - Accounting for Cash Flow Hedges

August 2, 2009

“We are limited, not by our abilities, but by our vision.” - Anonymous.

fas133_3GoldPeckers Incorporated is a manufacturer of golden jewelries based in the US of A.  To meet its production needs, GoldPeckers regularly source its raw materials (mostly Gold) from Ashanti Gold in Ghana West Africa.  Because of the increasing popularity of Gold as an alternative source of investment, the CFO of GoldPeckers, TFLASH is worried that the price of gold may shoot through the roof in the coming years.  Consequently, to hedge the anticipated adverse price movement, TFLASH entered into a forward contract as follows:

  • Spot Price of Gold = $954.50/Troy Ounce
  • Gold is measured in Troy Ounce and 1 Troy Ounce is 31.1034768 grams
  • Storage Cost/Troy Ounce is $28.00 (Storage Cost includes Insurance, Security etc)
  • Notional Unit is 10,000,000 ounces.
  • Risk Free rate is 3.88% (Assume that the risk free rate is constant throughout the life of the forward contract)
  • This is a three (3) year forward contract.
  • Use Discrete Compounding (We will solve another example using continous compounding in a future lesson).
  • For the purpose of illustration, assume that the hedge is fully effective in hedging the cashflow variability exposure.
  • Note that hedge accounting is not automatic, however, assume that GoldPeckers is eligible to use hedge accounting.
  • Spot Price of Gold in 1 year is $1,100.33
  • Spot Price of Gold in 2 years is $1,180.97
  • Spot Price of Gold in 3 years is $1,270.00
  • Forward contract was entered into on January 1, 2000

VALUATION & ACCOUNTING:

VALUATION:
To value a forward contract, we are going to use the Cost of Carry Method.

Under the Cost of Carry method:
VALUE OF A FORWARD CONTRACT PRIOR TO MATURITY:

The price of a forward is determined as follows:

F(0,T)  = S + C (0,T) (1+r)^T

The Net Present Value of the Storage Cost is Calculated as follows:

C (0,T) = C (1+r)^(- T)

The Fair Value of the Forward Contract is calculated as follows:

Vt(0,T) = S + C(t,T) - F(0,T)(1+r)^(- T-t)

VALUE OF A FORWARD CONTRACT AT MATURITY:

VT (0,T) = S - F(0,T)

Where:

  • F = Price of the forward
  • S = Spot Price
  • C = Cost of Carry
  • r = Risk Free Rate
  • V = Value of the forward
  • T = Maturity
  • t = A point in time before time T

Value of forward contract at initiation i.e. January 1, 2000:

On day zero (i.e. now) the PV of the cost of carry is calculated as follows:

C(0,3) = 28*1.0388^-1 + 28 * 1.0388^-2 + 28*1.0388^-3 = $77.99

On day zero (i.e. now) the price of the forward contract is calculated as follows:

F(0,3) = (954.50 + 77.90) *1.0388 ^3 = $1,157.29

On day zero, that is now, the value of the forward contract is zero (0).


Value of the forward contract after 1 year i.e. 12/31/2000:

C(1,3) = 28 * 1.0388^-1 + 28 * 1.0388^-2   = $52.90

F(1,3) = (954.50 + 52.90) * 1.0388^2 = $1,087.09

V(1,3) =  (1100.33 +52.90)  -  1,157.29 *1.0388^(-3-1) = $80.78

Value of the forward contract after 2 years i.e. 12/31/2001:

C(2,3) = 28 * (1.0388)^-1    = $26.95

F(2,3) = (954.50 + 26.95 )* 1.0388^1 = $1019.01086

V(2,3) = (1180.97+26.95)   -  1,157.29*1.0388^(-3-2) = $1,207.92 - 1,114.06 = $93.86

Value of the forward contract after 3 years i.e. 12/31/2002:

V(3,3) = $1,270.00 - $1,157.29 = $112.71

ACCOUNTING ENTRIES:

FAS 133 states that for a derivative designated as hedging the exposure to variable cash flows of a forecasted transaction (referred to as a cash flow hedge), the effective portion of the derivative’s gain or loss is initially reported as a component of other comprehensive income (outside earnings) and subsequently reclassified into earnings when the forecasted transaction affects earnings. The ineffective portion of the gain or loss is reported in earnings immediately.

January 1, 2000.

No entry required - just memorandum entry.

December 31, 2000 ( 1 year later)

The value of the forward contract is positive, therefore its a gain or better yet an asset and it is recorded as follows:

Dr.  Forward Contract Asset   (10M ounces * 80.78) = $807,800,000

Cr Unrealized Holding Gain/Loss (Other Comprehensive Income)   $807,800,000

(To record the increase in the fair value of forward contract as of 12/31/2000)

December 31, 2001 ( 2 years later)

Dr.  Forward Contract Asset   (10M ounces * (93.86 - 80.78))** = $130,800,000

Cr Unrealized Holding Gain/Loss (Other Comprehensive Income)   $130,800,000

(To record the increase in the fair value of forward contract as of 12/31/2001)

**Note that you only record the increase in fair value.

December 31, 2002 ( 3 years later)

Dr.  Forward Contract Asset   (10M ounces * (112.71 - 93.86))** = $188,500,000

Cr Unrealized Holding Gain/Loss (Other Comprehensive Income)   $188,500,000

(To record the increase in the fair value of forward contract as of 12/31/2002)

**Note that you only record the increase in fair value.

At 12/31/2002  10m ounces are purchased at $1,270 (Spot Price) for $12,700,000,000

Dr Gold Inventory  $12,700,000,000

Cr  Cash               $12,700,000,000


(To record the actual purchase of inventory - 12/31/2002)

In the same vein, forward contract is settled as follows:

Dr Cash ($1,270.00 - $1,157.29 = $112.71 * 10M)   $1,127,100,000

Cr Forward Contract Asset ($807,800,000+$130,800,000+$188,500,000)                    $1,127,100,000

(To record final settlement of forward contract - 12/31/2002)

NOTA BENE:
Please note that the Unrealized Holding Gain/Loss posted to OCI will not be taken into income until the hedged items affect earnings i.e. the Gold Inventory purchased are converted to finished goods and sold.  This will be illustrated in a future series.

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 :) . 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

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