## December 11, 2008

### Rule Of Thumb For Marketing ROI / Profit

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.

1. Anonymous12:20 PM

If I understand this concept, the formula you propose makes the assumption that decreasing circulation increases profitability.

In other words, as circulation decreases, the response rates go up as the marginally profitable names are dropped from the mailing list.

The other key assumption is that circulation costs remain constant as mailing volumes decrease.

As you say, no formula is perfect. But for some clients, the solution is simpler because circulation is not maxed out.

Even assuming level circulation costs, a strait formula of 20% reduction in budget reduces sales by 20% and profits by 20% works equally well.

This yields a profit of \$40,000 instead of \$50,000 if the budget goes down by 20%. I think this fairly represents a likely outcome.

If I maintain the testing budget regardless of the 20% cut, then the profits will likely drop well below the \$40,000.

Such simplicity may not satisfy the CFO or other decision makers in some cases. But I think for some advertisers, this simpler approach works just as well.

2. Your assumptions in the first three paragraphs are correct.

In my example, I am raising change in advertising by the power of 0.5.

In your example, you are raising change in advertising by the power of 1.0.

For every company, there is a rule of thumb that works, using power functions of 0.3 or 0.5 or 0.7, or in your example, 1.0.

And if you don't know the specific power function to use, I advocate defaulting to 0.5.

3. Anonymous3:20 PM

I think it is much more than rule of thumb. If one plots incremental costs VS incremental sales or profit or any utility function, it is a nonlinear function, often approximated by a parabola type curve(2nd order function). The above two cases represent the two sides of the curve, where incremental sales are increasing with incremental costs (hence you didn't reach the optimum point yet), and incremental sales start decreasing with incremental costs.

Thank you.

4. Certainly!