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Former BCG consultant with 3 years of experience in consulting; 50+ case interviews
Here, the assumption is that prices will fall as the companies want to gain marketshare by cost competition.
Based on this assumption, the answer assumes that gross margin of 3.8% stays the same (which is a significant assumption).
With a gross margin of 3.8%, this means that 96.2% of the price goes to cost. Costs, as calculated, are now $2300. Therefore, this leads us to the conculsion that the new price will be $2390.85. To calculate this, $2,300 / 96.2% (which is the equation shown in your question).
Of course, the earlier assumptions on gross margin staying the same are worth questioning.