TVA: Tax Valuation Adjustment#
Tax Valuation Adjustment, or TVA, is the adjustment for the effect of tax on the value of a derivative portfolio. The other adjustments are usually calculated before tax. In reality a firm pays tax on its profits, and that changes both the cash flows of the trade and the value of the other adjustments.
TVA is the least widely used of the XVAs. It is included here for completeness, and because it shows how far the logic of XVA can be taken.
Where tax enters#
A derivative affects the firm’s taxable income in several ways:
Trade cash flows: gains and losses on the derivative are taxed or are deductible, depending on the jurisdiction, the instrument and whether the trade is a hedge.
Funding: interest paid on funding is usually tax deductible, so the cost of funding after tax is lower than the headline cost. This reduces FVA and MVA.
Credit losses: a loss from a counterparty default may be deductible, which reduces the real cost behind CVA. Conversely, the gain from the firm’s own default in DVA is not realised cash and does not get a matching tax effect.
Capital: the cost of capital and the hurdle rate in KVA are generally after-tax measures, so a consistent treatment is needed.
The consequence is that the value of a trade to a firm paying tax can differ from the pre-tax value, and the other XVAs can be overstated if the tax shield is ignored.
How it is calculated#
A simple form scales the pre-tax adjustment by the tax rate:
where \(\tau\) is the marginal tax rate. In this form TVA is the difference between the after-tax and the pre-tax values, \(-\tau\) times the pre-tax adjustment.
A fuller treatment simulates the future taxable profit of the firm, as the benefit of a tax deduction only exists if there is income to deduct it against. A firm with losses or tax assets carried forward may not be able to use the shield at all, and the value becomes dependent on the firm’s whole tax position and not only on the trade.
Why it is rarely used#
TVA is not a standard part of most pricing and reporting frameworks, for several reasons:
the tax position is specific to the legal entity and not to the trade, so it is hard to attribute to a desk or a client
it depends on the firm’s future profits and on tax rules that change
fair value under IFRS 13 is meant to reflect an exit price to a market participant, and a firm-specific tax position is not part of that
the effect is usually small relative to the uncertainty in the other adjustments
It is therefore normally handled outside the trade-level valuation, in the treasury and tax functions, and is considered at the level of the entity.
A valuation control view#
For valuation control the main point is consistency and clarity of scope:
Pre-tax or after-tax: the framework should state which basis each adjustment is calculated on, so that the CVA, FVA, MVA and KVA are not mixed on different bases.
Where tax sits: if tax effects are included in any adjustment, for example in an after-tax funding cost or hurdle rate, this should be documented and approved.
Materiality: where TVA is ignored, the decision should be supported by an estimate of its size and reviewed periodically.