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 increase in sales equals?

The current gross profit is

​$2.7

billion. ​(Round to two decimal​ places.)

Set the initial price equal to​ $1.00. Then the new price is

​$. 90

​(Round to the nearest​ cent.)

The new gross margin percentage in decimal form equals 0.3889.

​(Round to four decimal​ places.)

The new sales level needed to maintain the original gross profit margin in terms of absolute dollars is $6.94 billion. ​(Round to two decimal​ places.)

The increase in sales equals? (as a decimal) in billions

Answer 1

It's not clear what needs to be calculated here as the value for current gross profit, new price, new gross margin percentage and new sales level needed to maintain the original gross profit margin is already given. Still, I'll try to show how these values arrived.

1. current gross profit = gross profit margin* sales = 45% * 6 billion = $2.7 billion

2. new price = 10% less than initial price = 1* (1-10%)= $0.9 per unit

3. initial cogs per unit = 55% * 1 = $0.55= new cogs per unit (same as variable cost depends on volume)

and new price = $0.9 per unit,

so current gross profit per unit =$0.9 -$0.55 = $0.35

so, new gross margin percentage = 0.35/0.9 = 0.3889 = 38.89%

4. new sales level needed to maintain the original gross profit margin in terms of absolute dollars  

= $2.7 billion / 38.89% = $6.94 billion

5. increase in sales = $6.94 billion - $6 billion = $0.94 billion