Percent changes, percentage points, and margins

Overview

A buyer at Ridgeway Office Products proposes adding 25% to a product's cost. She describes the result as a “25% margin.” Her manager needs to check the calculation before approving the price.

Both businesses and all figures in this lesson are fictional teaching assumptions.

Recall Lesson 022: Why did Meadow Soap need to distinguish cartons from individual bars before promising delivery? Today, the comparable question is what each percentage is measured against.

Percent change uses the starting amount

Percent means per hundred. A fraction of 0.25 equals 25%, or 25 out of every 100. To convert a fraction to a percentage, multiply it by 100. To use 25% in a calculation, divide by 100 to get 0.25.

The numerator is the amount being divided; the denominator is the number you divide by. It defines the comparison's base. For growth, that base is the starting amount:

Percent change = (new amount − old amount) ÷ old amount × 100.

If monthly revenue rises from $10,000 to $12,000, the increase is $2,000. Growth is $2,000 ÷ $10,000 × 100 = 20%. The starting revenue answers “20% of what?”

If revenue then returns to $10,000, the decline is $2,000 ÷ $12,000 × 100 ≈ 16.7%. The dollar movement is the same size, but the base changed. The symbol ≈ means approximately equal; we rounded the answer.

Compare matching periods and definitions. This formula assumes a positive starting amount. A zero starting value makes division impossible; a negative starting value can make an ordinary growth claim misleading. Report the amounts and explain the change instead.

Percentage points measure the gap between rates

A percentage-point change is the difference between two percentages. The UK's Office for National Statistics distinguishes this subtraction from a relative percent change. Source

If a customer renewal rate rises from 40% to 50%, it increases by 50 − 40 = ten percentage points. Relative to its starting rate, the increase is (50 − 40) ÷ 40 × 100 = 25%.

Both statements can be correct. “Up ten percent” would describe a different result: 40% × 1.10 = 44%. State the starting and ending rates when there is room, so the reader can see exactly what changed.

Margin and markup use different bases

For a product sale, gross profit is sales revenue minus the cost of the goods sold. In today's examples, that cost is the complete supplied product cost. Other business expenses, such as office rent and administration, remain to be deducted.

Gross margin expresses gross profit as a share of sales. Markup expresses the amount above product cost as a share of that cost. Business Victoria uses these different denominators in its formulas. Source

These formulas assume positive price and cost. Always name which margin you mean and which costs have been deducted. A 40% gross margin does not mean the business keeps 40% after every expense.

Worked example

You own Willow Lamp Shop. A lamp costs $60, including all costs assigned to the product, and sells for $100. Assume no discounts, returns, or sales taxes in these figures.

Gross profit per lamp is $100 − $60 = $40. Gross margin is $40 ÷ $100 × 100 = 40%. Markup is $40 ÷ $60 × 100 ≈ 66.7%. The same $40 produces two percentages because the bases differ.

Suppose the price rises to $120 while product cost stays $60. Price growth is ($120 − $100) ÷ $100 × 100 = 20%. Gross profit becomes $60, gross margin becomes $60 ÷ $120 × 100 = 50%, and markup becomes $60 ÷ $60 × 100 = 100%.

Gross margin rose from 40% to 50%: ten percentage points, or a 25% relative increase. A 20% price rise therefore did not produce a 20-percentage-point margin increase.

This arithmetic says nothing about how many lamps customers will buy at $120. A higher margin per sale can accompany lower total gross profit if enough sales disappear. Check demand and total dollars alongside the percentage.

To price from a target margin, identify the share available for cost. With a 25% gross-margin target, cost must be 75% of price. A $60 cost therefore requires $60 ÷ 0.75 = $80. Adding a 25% markup instead gives $60 × 1.25 = $75, leaving $15 ÷ $75 × 100 = 20% margin.