New Price = $2,300/(1-0,038) = $2390.85
Where do we get this number from and what does it signify? (Isn't the selling price $5,200)
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New Price
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Here, the assumption is that prices will fall as the companies want to gain market share 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.
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The new price is 42, the answer to all your questions.
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