One way to maintain exclusivity for a brand is to raise its price. That's what

luxury fashion and leather goods maker Louis Vuitton did. The company

did not want the brand to become overexposed and too common, so it

raised prices $15$ percent and is slowing its expansion in China. The Louis

Vuitton brand is the largest contributor to the company's $$13\mathrm{.}3$ billion

revenue from its fashion and leather division, accounting for $$8$ billion of

those sales. It might seem counterintuitive to want to encourage fewer

customers to purchase a company's products, but when price increases,

so does the product's contribution margin, making each sale more

profitable. Thus, sales can drop and the company can still maintain the

same profitability as before the price hike. If a company's original

contribution margin was $40\%,$ calculate the new contribution margin if price

is increased $15\%.$

Set the initial price equal to $$1\mathrm{.}00.$ Then the variable cost is $$.($Round

to the nearest cent.$)$