How to calculate a weighted average?
In this video, we go through examples of calculating a weighted average
from the world of financial analysis.
Let’s start off with calculating the weighted average revenue growth for a company consisting
of three business units: Business Unit A generating $800 million revenue in year 0, and Business
Unit B and C generating $100 million revenue each.
Business Unit A is large and stable, but has no revenue growth.
Business Units B and C are much smaller,
but have more attractive growth rates of 10% and 20%.
What is the revenue growth for the company as a whole?
The easiest way to calculate the weighted average revenue growth is to first translate
the percentage growth to absolute amounts.
The 0% growth of Business Unit A equates to $0 extra revenue.
10% growth in Business Unit B equals $10 million in incremental revenue.
20% growth in Business Unit C equals $20 million.
If we sum this across the business units, we get to $30 million revenue growth for the
company in total.
$30 million revenue growth on a base number of $1 billion equals 3%.
A second way to calculate the weighted average revenue growth is to look at the relative
contribution of each of the business units.
In terms of relative size, Business Unit A brings $800 million out of the total $1 billion
in revenue for the company, or 80% of the total.
Multiply that 80% relative size by 0% revenue growth.
Business Unit B brings $100 million out of the total $1 billion in revenue for the company,
or 10% of the total.
Multiply that 10% relative size by 10% revenue growth.
Business Unit C, like Business Unit B, brings 10% of the total revenue.
Multiply that 10% relative size by 20% revenue growth.
Now sum the percentages: 0% + 1% + 2% equals 3%.
Let’s see what happens in the second year.
Now the year 1 revenue numbers are the base for the calculation.
Let’s assume that each individual business unit grows at the same rate in year 1 as in
year 0: 0% for Business Unit A, 10% for Business Unit B, 20% for Business Unit C. Will the
weighted average total revenue growth for the company be the same or different from
the year before?
Let’s calculate the absolute amounts again.
The 0% growth of Business Unit A equates to $0 extra revenue.
10% growth in Business Unit B on top of the $110 million,
equals $11 million in incremental revenue.
20% growth in Business Unit C on top of the $120 million equals $24 million.
If we sum this across, we get to $35 million revenue growth for the company in total.
$35 million revenue growth on a base number of $1030 million equals 3.4%.
Even though each division grows at the same rate as in the prior year, due to the mix
change of the revenue the company now achieves 3.4% revenue growth instead of 3%!
Business Unit B and C become bigger as a percentage of the total.
Let’s now calculate the weighted average Gross Margin for the same company.
The largest business unit, Business Unit A, generates a Gross Margin of only 20%.
Business Unit B has a Gross Margin of 60%.
Business Unit C has a Gross Margin of 80%.
What is the weighted average Gross Margin for the company as a whole?
Just like in the revenue example, the easiest way to calculate this is to translate the
percentages to absolute amounts.
$800 million revenue in Business Unit A at 20% Gross Margin equals $160 million.
$100 million revenue in Business Unit B at 60% Gross Margin equals $60 million.
$100 million revenue in Business Unit C at 80% Gross Margin equals $80 million.
If we sum this across the business units, we got to $300 million Gross Margin for the
company in total.
$300 million Gross Margin on a revenue base of $1 billion equals 30% Gross Margin.
A second way to calculate the weighted average Gross Margin is to look at the contribution
of each of the business units.
In terms of relative size, Business Unit A brings $800 million out of the total $1 billion
in revenue for the company, or 80% of the total.
Multiply that 80% relative size by 20% Gross Margin.
Business Unit B brings $100 million out of the total $1 billion in revenue for the company,
or 10% of the total.
Multiply that 10% relative size by 60% Gross Margin.
Business Unit C, like Business Unit B, brings 10% of the total revenue.
Multiply that 10% relative size by 80% Gross Margin.
Now sum the percentages: 16% + 6% + 8% equals 30%.
Let’s see what happens in the next year.
Now the year 1 revenue numbers are the base for the calculation.
Let’s assume that each individual business unit has the same Gross Margin percentage
in year 1 as in year 0: 20% for Business Unit A, 60% for Business Unit B, 80% for Business
Unit C. Will the weighted average Gross Margin percentage for the company be the same or
different as in the year before?
Let’s calculate the absolute amounts again.
$800 million revenue in Business Unit A at 20% Gross Margin equals $160 million.
$110 million revenue in Business Unit B at 60% Gross Margin equals $66 million.
$120 million revenue in Business Unit C at 80% Gross Margin equals $96 million.
If we sum this across the business units, we got to $322 million Gross Margin for the
company in total.
$322 million Gross Margin on a revenue base of $1030 million equals 31.3% Gross Margin.
The conclusion of our analysis: Revenue growth in higher margin business units drives the
corporate Gross Margin % increase.
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Thank you for watching.