How can a depreciation in the home currency impact the trade balance?

The trade balance is defined by the difference in value of exports minus imports. Now a depreciation in a the home currency means it that one unit of foreign currency (lets say $) can now purchase more £'s and consequently £1 now is worth less in $.It follows that since $1 can purchase more £'s, exports are more attractive to foreign consumers, thus more exports are purchased. Similarly, since £1 can now purchase less in terms of $'s, imports are less attractive and more expensive to domestic consumers thus less are purchased. It follows that the value of exports have increased, and the value of imports decreased leading to an improvement in the trade balance.