You've been through this drill before, haven't you? Your CMO or CEO or CFO wants to know "what would happen if we cut twenty percent from the marketing budget?".
This is where you use the square root rule to your advantage, allowing you to give a "back of the envelope" answer to questions that require a lot of time and energy.
Assume you spent $1,000,000 on marketing last year, generating $3,000,000 sales. Your profit factor is 35%, yielding profit of $3,000,000 * 0.35 - $1,000,000 = $50,000 .
What would happen if you cut 20% from your marketing budget.
Step 1: Sales = (($800,000 / $1,000,000) ^ 0.5) * $3,000,000 = (0.894 * $3,000,000) = $2,683,282. The "0.5" number is the square root ... you are taking the square root of the ratio in change of marketing spend. In this case, a 20% reduction in spend yields a 10.5% reduction in sales.
Step 2: Profit = $2,683,282 * 0.35 - $800,000 = $139,149.
In other words, you'd lose a little over $300,000 in sales, but profit would increase by nearly $90,000.
The square root rule allows you to play these "what if" scenarios ... and the scenarios are important. Sr. Management needs to get directional answers quickly. You don't want to do a ton of work, only to have the CFO tell you to run a new scenario where you cut marketing expense by 33%.
Is the square root rule 100% accurate? Absolutely not. In fact, there are times when it is blatantly inaccurate (affiliate marketing, shopping comparison sites, e-mail marketing).
When your leadership team needs an immediate answer, at an aggregate level, this rule of thumb works well.