This paper investigates the implications for the nominal exchange rate of a Border Tax Adjustment (BTA) when there is BTA neutrality. A border tax adjustment is a change from an origin-based system of taxation, that taxes exports but exempts imports to a destination-based system that taxes imports but exempts exports. Both indirect taxes (e.g. a VAT) and direct taxes (e.g. a cash-flow corporate profit tax) can be subject to a BTA. In the US, a BTA for the corporate profit tax is under discussion. There is BTA neutrality when the real equilibrium, including measures of profitability and competitiveness, of an open economy is unchanged when it moves from an origin-based to a destination-based tax. The conventional wisdom on the exchange rate implications of a neutral BTA is that the currency of the country implementing the BTA will strengthen (appreciate) by a percentage equal to the VAT or CPT tax rate. The main insight of this note is that this 'appreciation presumption' is not robust, even when all conditions for full BTA neutrality are satisfied. Indeed, plausible alternative assumptions about constancy (or stickiness) of nominal prices support a weakening (depreciation) of the currency by the same percentage as the tax rate. On the basis on the very patchy available empirical information, it is not possible to take a view with any degree of confidence on the implications of a BTA for the nominal exchange rate, even if full BTA neutrality prevailed. Whether BTA neutrality itself is a feature of the real world is also a disputed empirical issue. Therefore, buyer (or seller) beware.