Given the following data: If net sales decreases by 10%, and cost of goods sold increases by 15%, gross margin would:

Question

Given the following data:  If net sales decreases by 10%, and cost of goods sold increases by 15%, gross margin would:

Quizplus · Accepted Answer

To solve this problem, we need to understand the formula for gross margin:

Gross Margin = Net Sales - Cost of Goods Sold

If net sales decrease by 10%, then the new net sales would be:

New Net Sales = Net Sales - 0.1*Net Sales = 0.9*Net Sales

If cost of goods sold increases by 15%, then the new cost of goods sold would be:

New COGS = COGS + 0.15*COGS = 1.15*COGS

Substituting these new values into the formula for gross margin, we get:

New Gross Margin = 0.9*Net Sales - 1.15*COGS

Now, we can simplify this expression by factoring out 0.9:

New Gross Margin = 0.9*(Net Sales - 1.278*COGS)

Notice that the factor in parentheses is less than the original gross margin, since we are subtracting a larger value (1.278*COGS) from the net sales. Therefore, the new gross margin is less than the original gross margin:

New Gross Margin < Gross Margin

To find the percentage decrease, we can use the formula:

% Decrease = (Original Value - New Value)/Original Value * 100

% Decrease = (Gross Margin - New Gross Margin)/Gross Margin * 100

% Decrease = (Gross Margin - 0.9*(Net Sales - 1.278*COGS))/Gross Margin * 100

Using the given data, we can calculate the original gross margin as:

Gross Margin = Net Sales - Cost of Goods Sold = 11ea84f5_9d4e_4e36_9a63_a9e10a4cbbfc_TB4002_00_TB4002_00_TB4002_00 - 3*TB4002_00 = 11ea84f5_9d4e_4e36_9a63_a9e10a4cbbfc_TB4002_00

Since we don't know the actual values of net sales and COGS, we cannot calculate the new gross margin or the % decrease exactly. However, we can still answer the question by using some estimation.

Assuming that net sales and COGS are roughly equal (which is a reasonable assumption for most businesses), we can estimate the original gross margin as:

Gross Margin ≈ Net Sales/2

Using this approximation, we can see that a 10% decrease in net sales would lead to a 5% decrease in gross margin (since net sales is roughly half of gross margin). On the other hand, a 15% increase in COGS would lead to a 15% decrease in gross margin (since COGS is equal to one third of gross margin). Therefore, the total % decrease in gross margin would be:

% Decrease ≈ 5% + 15% = 20%

Finally, we can use the formula for % decrease to find the % increase in gross margin:

% Decrease = (Original Value - New Value)/Original Value * 100

20% = (Gross Margin - New Gross Margin)/Gross Margin * 100

New Gross Margin = Gross Margin * (1 - 20/100)

New Gross Margin = Gross Margin * 0.8

Therefore, the new gross margin would be 80% of the original gross margin, which is a 20% decrease. But since the answer choices only allow for increase or decrease, the correct answer is D) decrease by 47.5% (rounded to the nearest choice).

Given the Following Data: If Net Sales Decreases by 10