FAS 133 for Dummies - Accounting for Equity Swaps (Part II)

January 31, 2010

“There are two types of people in this world -  the taker and the taken.  The taker who takes the most is the richest. “ - P. Diddy in the ABC Drama, A Raisin in the Sun.

nasdaq1000NEWENTRY llc entered into a 2 year fixed-rate equity swap as follows:

  • The aim of this exercise is to illustrate how to account for an equity swap designated as a fair value hedge.
  • However, how can you account for something if you don’t really know how it is  valued?
  • There is usually independence between accounting and pricing/valuation (one should at least hope so), however, the accountants should at least understand what is happening under the hood.
  • Notional is 100M USD.
  • Trade date is March 31, 2008.
  • Newentry llc is the fixed-rate receiver.
  • The fixed rate will be calculated based on market information (see below).  This is called “Pricing the Swap”.
  • The swap will have payment dates as follows:  (a) September 30, 2008 (b) March 31, 2009 (c) September 30, 2009 and (d) March 31, 2010.
  • The days to maturity for these payment dates as March 31, 2008 as follows: (a) September 30, 2008 - 183 days (b) March 31, 2009 - 365 days (c) September 30, 2009 and - 548 days(d) March 31, 2010 730 days.
  • The term structure of interest rate (LIBOR) on the payment dates as observed on March 31, 2008 were as follows (a) September 30, 2008 - 4.75% (b) March 31, 2009 - 4.85%  (c) September 30, 2009 - 5.23% and (d) March 31, 2010 - 5.45%.
  • Assume a 30/360 date convention.
  • Ignore dividend and taxation.
  • Also ignore transaction costs.
  • The stock index “NASDAQ 1000″ on March 31, 2008 was 2002.
  • Newentry’s reporting date is June 30, 2008 and the “NASDAQ 1000″index  on that date was 1750.
  • NASDAQ 1000 was 1770 on first payment date September 30, 2008, the first payment date
  • The term structure of interest rate (LIBOR) on the payment dates as observed on June 30 2008 were as follows (a) September 30, 2008 - 4.95% (b) March 31, 2009 - 4.99%  (c) September 30, 2009 - 5.29% and (d) March 31, 2010 - 5.55%.
  • The days to maturity for these payment dates as June 30, 2008 as follows: (a) September 30, 2008 - 92 days (b) March 31, 2009 - 274 days (c) September 30, 2009 and - 457 days(d) March 31, 2010 -  639 days.

Valuation of the Fixed-Rate Equity Swap:

  • Value of the swap at inception is zero as with any other type of swap.  As you move towards maturity this value changes depending on the volatility of the underlying and changes in interest rate.
  • For a fixed rate equity swap.  The “Fixed Rate” on the initiation date should be established - “Pricing the Swap”..

Calculation of Fixed Rate:

First we must determine the discount factors as of March 31, 2008 for 183, 365, 548 and 730 days as follows:

(a)  B (B,183) = 1/ (1+0.0475(183/360)) = 0.9764

(b)  B (B,365) = 1/ (1+0.0485(365/360)) = 0.9531

(c)  B (B,548) = 1/ (1+0.0523(548/360)) = 0.9262

(d)  B (B,730) = 1/ (1+0.0545(730/360)) = 0.9004

Using the formula below: R = 1 - B(0,t + n) / Sum of B(0, t + i)

R = The fixed rate on the swap = (Price of the swap not the value).
B (0, t +n ) = Discount factor on the last payment date.
Sum of B (0, t + i ) = Sum of discount factors for all payment dates.

R = (1 - 0.9764)/(0.9764 + 0.9531 + 0.9262 + 0.9004) = (1 - 0.9764)/(3.7561) = 0.006283.
Thus the fixed payment is $0.006283 per $1 of notional.

Then we must determine the discount factors as of June 30, 2008 for 92, 274, 457 and 639 days as follows:

(a)  B (B,92) = 1/ (1+0.0495(92/360)) = 0.98750

(b)  B (B,274) = 1/ (1+0.0499(274/360)) = 0.9634

(c)  B (B,457) = 1/ (1+0.0529(457/360)) = 0.9370

(d)  B (B,639) = 1/ (1+0.0555(639/360)) = 0.9103

Valuation of the fixed-rate swap on June 30, 2008:

From a fixed-rate receiver perspective:

V = B(j, t + n) - R (sum of B(j,t + 1) - (S (j)/S(0))

V = Value of the swap at a point in time.

B (0, t +n ) = Discount factor on the last payment date.

Sum of B (0, t + i ) = Sum of discount factors for all payment dates.

V = 0.9103 - 0.006283 ( 0.98750 + 0.9634 + 0.9370 + 0.9103 ) - ((1750/2002)) = $0.123100353/$1 notional principal.

ACCOUNTING ENTRIES - June 30, 2008:

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.

As of June 30, 2008 - Mark to Market Adjustment Resulting from a decline in the “NASDAQ 1000″ is ($1750/2002) -1 * 100M = ($12,587,412.59).

Dr Earnings - Unrealized Holding Gains - $12,587,412.59
Cr - Equity Investments - $12,587,412.59.
(To record the mark-to-market adjustments on the $100M investments in the NASDAQ 1000 as June 30, 2008)

Dr. Swap Asset (0.123100353 * 100M) - $12,310,035.3
Cr - Earnings - Unrealized Gains - - $12,310,035.3.

(To record increase in value of equity swap as of June 30, 2008)

Balance Sheet Presentation as of June 30, 2008:

Equity Investments        $100,000,000.00
Fair Value Adjustments ($12,587,412.59)
Net                                    87, 412,587.41

Swap Assets                   $12,310,035.3

Income Statement as at June 30, 2008:

Unrealized Holding Gain - 12,310,035.3.
Fair Value Adjustments - ($12,587,412.59)
Net loss                                ( $277,377.29)

Note that no payments are due until September 30, 2008 on the equity swap.  However, you should consider accruing and recording the anticipated receivable asset or liability on this date.  See below for calculation of net settlement on the first payment date

Calculation of Net Settlements at Payment periods (Note that payment is not due until September 30, 2008):

Assume that the NASDAQ 1000 index is at 1770 on September 30, 2008:

Payment based on equity index = (1770/2002) - 1 * 100M = ($11,588,411.59)
Note that this is a depreciation.  The fixed rate receiver - Newentry  llc ( who normally pays appreciation in the index) gets the depreciation in addition to the fixed payment.

Fixed payment to be received is 0.006283 * 100,000,000 = $628,300.00

Total payment to be received = $11,588,411.59 + 628,300.00 = $12,216,711.59

Bibliography:

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 :) .

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

Posted by Webmaster | Filed Under Business 

Comments

One Response to “FAS 133 for Dummies - Accounting for Equity Swaps (Part II)”

  1. FAS 133 - Accounting For Equity Swap : blackherald.com on February 14th, 2010 12:59 am

    [...] See FAS 133 for Dummies - Accounting for Equity Swaps is now available. [...]

Got something to say?