Question

Abercrombie​ & Fitch, once the favorite of loyal​ teens, is considering lowering prices on all items it sells in an effort to win them back after several years of sales declines.​ A&F's total sales were ​$6 billion last​ year, but they have been declining in the face of a weak economy and an intensively competitive retail environment. Price reductions are often effective in increasing​ sales, but marketers need to analyze how much sales must go up before a price reduction pays off and increases revenue enough to make the it worth doing. Assuming​ A&F's gross profit margin is 45 percent and cost of goods sold represents the only variable​ cost, by how much must sales increase to maintain the same gross profit margin in terms of absolute dollars if​ A&F lowers prices by 10 ​percent?

The current gross profit is?

Answer 1

The current gross profit			=	Sales * Gross profit margin
			=	$6,000,000,000*45%
			=	$              2,700,000,000.00
Let the unit price be $100
Gross profit per unit			=	$100*45%
			=	$                                    45.00
Variable cost			=	Selling price-Gross profit
			=	$100-$45
			=	$                                    55.00
New unit price			=	Current price -10% of current price
			=	$100-10% of $100
			=	$90
New gross profit margin			=	Sale price-variable cost
			=	$90-$55
			=	$35
New gross profit margin (%)			=	(New Gross profit/new sales price)*100
			=	($35/$90)*100
			=	38.8889%
New sales (for maintaining the same gross profit)				current gross profit/New gross profit margin
			=	$2,700,000,000/0.388889
			=	$              6,942,855,159.18
Theremay be little difference due to decimal places
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