FX differences with put option fair value accounting

In an earlier posting, “How do you calculate exchange gains and losses when using Fair Value Accounting?”  I considered how to apply the statutory rules for computing exchange gains and losses when a company is using fair value accounting.  A recent conversation with my partner Iain Hill, who leads our Finance & Treasury Network brought out some subtle points not addressed in the previous posting.

Structure under discussion

Iain was considering the situation illustrated below:

In this case, UK Co owns a subsidiary in the USA with net assets of, say $100.  In order to hedge the translation risk (see posting “Should companies hedge against translation risk?”) it purchases an American out of the money put option over $100 with a life of 18 months.  For example, if the spot exchange rate is £1=$2, the option exercise price may be at a rate of £1=$2.10.  Several points should be noted:

(a) The company remains exposed to translation risk if the dollar weakens against sterling, until the dollar falls to the £1=$2.10 rate.

(b) Choosing an out of the money option reduces its cost, (the option premium) compared with an option whose strike price is equal to the spot exchange rate.  For illustrative purposes, assume that the company pays £5 to purchase the option.

(c) As an American option, it can be exercised at any time in its life, as opposed to a European option which can only be exercised on the expiry date.

(d) If the dollar strengthens, the company will benefit from the increase in the sterling value of the $100 net assets of the US Subsidiary.  That opportunity is the commercial compensation for suffering the cost of the option premium.

Experience of exchange rate movements

Assume that the 18 month option was taken out on 2 July 2007 and expires on 2 January 2009, and that UK Co has a calendar year end, with the following pattern of exchange rate movements.  (This is not a forecast of future exchange rates but an illustration!)

2/7/2007  say £1=$2.0
31/12/2007  £1=$2.099
31/12/2008  £1=$2.0
2/1/2009  £1=$2.0

The value of the option will change in a non-linear way as time passes and exchange rates change:

- As time passes, the time value of the option will decay.  Market experience indicates that the decay is slow at first and then rapid as expiry approaches.  The time value of an option is equal to its total value less its intrinsic value (value represented by the difference between the current price of the underlying item and the exercise price).   In the example, the option never has any intrinsic value at the key dates, so all of its value is time value.

- As the exchange rate approaches the strike price, the value of the option increases and vice versa.

The value of the put option is diagrammed below, using illustrative numbers:

While all of the numbers are hypothetical, it should be noted that as the exchange rate changes from £1=$2 to £1=$2.099 the option is assumed to increase in value by a smaller amount (£1) than the diminution in the value of the underlying $100 (£2.36).  It is typically the case with an out of the money option that its market price will change by less than the change in value of the underlying item.

Accounting

In the consolidated accounts of UK Co, assumed to be prepared under IFRS, it can designate the option as a hedge of the net assets of the US subsidiary, provided that the effectiveness requirements in IAS 39 are met.  IAS 39 normally requires the entire fair value of the hedging instrument to be designated for hedging purposes.  However, in the case of options, IAS 39 paragraph 74 permits a company to split the value of an option between its intrinsic value and its time value, with only the intrinsic value being designated as a hedge.

Assuming that the IAS 39 hedging effectiveness criteria are met, the accounting can be summarised as follows:

(a) No splitting of option value

The consolidated accounts of UK Co would show the following translation differences going through reserves:

(b) Alternative – Option value split between intrinsic value and time value

Under the assumed facts, all of the value of the option is time value, as the option is never in the money.  This time value would be recognised in the profit and loss account, while the retranslation of the net assets of the US subsidiary would be recognised in reserves, as follows:

    

Applicable tax rules

From a tax perspective, it is important to split the value changes in the option between exchange gains and losses and other value changes.  The reason is that exchange gains and losses will be disregarded for tax purposes because the put option is acting as an economic hedge of the foreign exchange risk associated with the equity investment in the US subsidiary. See posting "The Tax Law on Foreign Exchange Net Investment Hedging".

Conversely, any value changes in the option that are not exchange gains and losses represent taxable income/deductions as the put option is a derivative contract within the rules set out in FA 2002 Sch 26.

What determines the value of a currency option?

As with any other tradeable contract, the market value of an option is what other people are prepared to pay for it in an open market transaction.  However, one needs to consider theoretical valuation models, not least because they are used by market participants to decide what prices to seek/offer for options being sold/bought.

One of the leading theoretical models for options is the Black-Scholes model developed by Fisher Black and Myron Scholes.  While the mathematics of the model are complex, what matters in the current context are the inputs that the model uses, which are (click to enlarge image):

One of these inputs, the exercise price, is fixed, while the others vary over time which is the reason for the time suffix.

Application of the tax rules to this option

For simplicity, in the following discussion it is assumed that Vt, Rt and It remain fixed throughout the period.  Accordingly, the only variables that change over the life of the option are the time left until expiry and the spot exchange rate.

(a) First accounting period 2/7/07 – 31/12/07

The option has increased in value by £1, rising from £5 to £6.  However, if the spot exchange rate had remained unchanged, the option would have decreased in value, as the time left until expiry would have reduced, and other relevant factors such as volatility are assumed to be unchanged.

Accordingly, the value increase attributable to movements in the spot exchange rate from £1=$2.0 to £1=$2.099 must be greater than £1.  The legislation, the Loan Relationship and Derivative Contracts (Exchange Gains and Losses using Fair Value Accounting) Regulations 2005, SI 2005 No 3422 anticipates this outcome in Regulation 9(2) “where the exchange gain exceeds the fair value profit, the difference between the two is the residual loss”.

An approach to calculation to quantify the exchange gain was discussed in the previous posting.  Under that approach one would recompute the value of the option on 2/7/07 using all of the relevant inputs such as Vt, Tt Rt  Vt, measured at 2/7/07, but using as an input St,(the spot exchange rate) as it stands at the period end, 31/12/07.  This will give a value for the option of greater than £5, say £X, and the exchange gain was then proposed as £X - £5.  For example, £X may be £6.50, so the exchange gain would be £1.50, which then means that by subtraction there would be a residual loss of 50p.  The £1.50 exchange gain would be disregarded, while the 50p residual loss is deductible.

(b) Second period 1/1/08 – 31.12.08

During this period, the value of the option falls to, say, 1p.  A non-zero value is assumed, as the option still has two days to expiry so a sharp exchange rate change could cause it to become valuable.  Over this period, the option has fallen in value by £5.99, and exchange rates have moved.  How much of the £5.99 loss is a foreign exchange loss?

If the spot exchange rate at 31/12/08 had remained at the period’s opening value of £1=$2.099, close to the strike price, then the option would be worth more than 1p, perhaps say 3p.  This 2p difference is the only part of the fall in value of the option that is due to movements in spot exchange rates.  The rest of the £5.99 fall in value, specifically £5.97, has arisen from the effluxion of time which has caused the “time value” of the option to waste away.  Accordingly, the 2p foreign exchange loss should be disregarded, while the £5.97 residual loss should be deductible.

Unfortunately, if one applies the methodology proposed in the earlier posting, one gets an answer which is inconsistent with the fundamental analysis given above.  On 31/12/2007 the option is worth £6.  If ones uses the assumed valuation model, using all input variables as at 31/12/2007 apart from the rate of exchange, and inputs the 31/12/2008 exchange rate of £1=$2.0, the value of the option should be computed as being some number under £5.

(All of the option valuation inputs are the same as on the purchase date of 2/7/2007 except that the time to expiry has reduced by six months, from 18 months to 12).  Accordingly the previous methodology will produce a figure for the exchange loss of at least £1 (£6-£5) whereas on a fundamental analysis very little of the loss in 2008 arises from exchange rate movements.  Accordingly, while the methodology seemed sound for the currency swaps discussed in the previous posting, it breaks down in the case of options due to the complex way that their values change in response to external circumstances.

Conclusion

From my perspective, the key message from the above analysis is the importance of considering the issue from a fundamental perspective.  Options have very different characteristics from swaps, and their values vary in a non-linear way as the price of the underlying asset changes.  Accordingly, simply applying a calculation method which was appropriate in a different scenario (currency swaps) risks giving a clearly incorrect answer, as above when analysing the 2008 period.

The outcomes given by applying the tax rules may themselves appear anomalous, in that the 2007 value change is considered largely non-taxable due to the application of the disregard regulations while most of the 2008 value change is considered tax deductible.  However, this answer appears consistent with the scheme of the legislation, which excludes from taxation value changes in the hedging instrument which arise from spot exchange movements, but which does not exclude value changes arising from the other causes such as the passage of time.

Comments

[Bradley Anderson 30 Aug 2007 17:55:56]

Mohammed, thanks for your comprehensive example.

In one of your scenarios you've included changes in the time value of the option as part of the effective hedging relationship. PwC publicly stated that such treatment is acceptable under IAS 39 (see PwC Applying IFRS Solution 81.32 on the PwC website).

Given that the IFRIC has recently discussed (and subsequently rejected from their agenda) this issue, is likely that PwC will change their viewpoint on this issue?

[Mohammed Amin 4 Sep 2007 10:19:30]

As the questioner mentions, whether this issue should be taken onto its agenda has been discussed by the International Financial Reporting Interpretations Committee (IFRIC), as noted in the May 2007 and July 2007 editions of IFRIC Update. IFRIC has reached a tentative agenda decision not to take the issue onto its agenda. In July 2007, IFRIC revised the basis for such a decision, stating that it was because the International Accounting Standards Board (IASB) has recently decided to propose an amendment to IAS 39 to clarify what risks and cash flows can be designated as hedged risks and hedged portions of risks for hedge accounting purposes and that the Board's project would specifically address this issue.

We will continue to monitor developments at the IASB on this issue and await the publication of the proposed amendment to IAS 39. Meanwhile, PwC's current view is that the time value of a purchased option can, in the right circumstances, be treated as an effective component of a cash flow hedge relationship if the designated risk exposure has been defined as 'one-sided.' Additional material on hedging is set out on our Applying IFRS website.

[Linus Ericsson 28 Dec 2007 08:53:54]

Mohammed,

What is your opinion after the latest Exposer Draft "Exposures Qualifying for Hedge Acounting"? Is it still possible to include the time value in the hedge (given that the effectivness criteria are meet)?