Question

3. 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 $4 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.

a. Assuming A&F’s gross profit margin is 60 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? (hint: assume an average selling price of $10)

Answer 1

At present

Price = $10 per unit

Gross profit margin = 60%

Gross profit = 60%*4 billion = $2.4 Billion

If decrease in price = 10%

Then,

New price = 10*(1-10%) = $9

Variable cost = $4

Sales volume required to achieve the same gross profit = 2.4/(9-4) = .48 Billion units

Revenue level at this sales volume = .48*9

Revenue level at this sales volume = $4.32 Billion

So, sales should increase by $.32 Billion to achieve the same gross profit in terms of absolute dollars.

Gross profit at this revenue = .48*(9-4) = 2.4 Billion ( same as old gross profit)