The Greatest Equation in All of Pricing

I have lost track of the number of times I've heard a salesperson say something like "Let's lower the price and I'll make it up in volume." It's a seductive notion, right? On some level, there's the hope that the only thing keeping you from gobs of sales is that pesky price point. Taken to the extreme, if you lowered the price to $0 (or lower in some loss-leader situations) you'd sure move a lot of volume!

The problem with the above is that it rarely works out that way. In my experience, a price reduction only serves to dilute profit. Certainly, there can be some top line growth or improvement in margin percentage, but my scorecard says that profit is the reason I'm in business.

What about the other side of the coin? What if we want to see what would happen if we raise the price? Wouldn't it be great to have a quick way to set reasonable expectations about what volume we could afford to lose and still make a profit? There must be some sort of formula that can help us, right?!

The Volume Hurdle
We're going to use the Volume Hurdle formula to help illuminate both of the scenarios above. I've used the Volume Hurdle calculation numerous times to quickly show the high-level implications of what a price change could mean. Here's what the formula looks like:

%ΔQ ≥ -ΔCM/(ΔCM + CM_i)

Where Q = Quantity and CM = Contribution Margin (aka Price - Variable Cost). The subscript i = Initial in all subsequent examples (as in what is my initial contribution margin right now without making any price changes), and elsewhere I'm going to use a subscript f to indicate final/future (as in what would my future contribution margin be if I made a price change).

The whole idea is that this equation will show the change in quantity needed to break even based on the change in contribution margin. Let's work through a few examples to illustrate.

The preferred beer of pricing pro's everywhere.

Example: Beer Money
I sell bottles of beer for $4/each, it costs me $1/each to acquire them, and I sell 1,000 bottles on a given night. Beer makes people happy, and I'm a good guy that wants people to be happy. I want to sell MORE beer so I think I want to lower the price to $3/each. The cost remains the same in this example. How many bottles do I need to sell to break even from a profit perspective?

First, let's compute the CM in the initial state ($4 - $1 = $3), and what it will be in the future state once I reduce the price ($3 - $1 = $2).

Great! Because I sell 1,000 beers per night and I made a profit of $3 on each one, looks like my total contribution margin is $3,000.

The next task is to figure out how many bottles of beer I would need to sell at $2/each to break even. The simple math from here is to take the $3,000 profit I made, divide it by the $2 of profit per bottle, and I end up with 1,500.

Holy smokes! If I drop my price by 25% (from $4 to $3) I will need to sell 50% more beer (from 1,000 to 1,500) to break even from a profit perspective! Do I really think I can sell that much more beer? Probably not ethically, so I'd rather not drop my price.

An easier equation
Some of you caught that I pulled a shortcut when computing these numbers. I find the Volume Hurdle calculation a little clunky to use in its generalized format, so rearranged it looks like this:

Q_f ≥ CM_i/CM_f * Q_i

Why is this easier? In most real world applications I know how many units I'm selling now, I know my current price, and I know what price I think I want to charge. Now I can just plug and chug (heh!) to find the hypothetical quantity needed to support a price change.

Pictured above: A bear that would like to improve its profit margin.

Beer Money II: Cruise Control
As we discovered in the previous example, it would be tough for me to drop my prices and make more money. What if I raise my prices? How many fewer beers could I afford not to sell if my price per unit is higher? Assume the same as above (Price = $4/each, cost = $1/each, quantity sold = 1,000) but now I want to raise prices to $5/each. Let's throw that into the simplified equation and see what my future quantity (Q_f ) sold would need to be to break even.

Q_f ≥ ($4-$1)/($5-$1) * 1,000

This reduces to:
Q_f ≥ ($3)/($4) * 1,000
Q_f ≥ 750

Wow! I can afford to sell only 750 beers if I raise my price to $5. Now this is where intuition as a business owner needs to come into play. Do I really think I'm going to sell 250 fewer beers because people need to pay an extra buck? Probably not. So I'm going to move forward with the price increase.

But what about cost?!
I know what you're thinking because I hear it every time I've run through this example. If I sell fewer beers, won't my vendor get mad and jack up the price on me? Or if we consider the first example where we lowered price, couldn't I get a cost reduction if I move more volume? Sure, anything is possible. The beauty of the volume hurdle equation is that it can handle both of those scenarios because we're using Contribution Margin, which is computed with both price and cost.

Let's think about the first example again. Price from $4 to $3. Volume still 1,000. However, after speaking with the vendor about my plans to drive volume for them I can get a cost reduction from $1/each to $0.75/each.

Q_f ≥ ($4-$1)/($3-$0.75) * 1,000
Q_f ≥ ($3)/($2.25) *1,000
Q_f ≥ ~1,334

Ok, now we're getting somewhere. An extra 334 beers a night is still quite a bit, but it's more reasonable than an extra 500 a night in the first example. Maybe I can negotiate harder and get more off per unit, or I can get market funding to broaden my advertising reach to bring in more people, or maybe I can have the supplier front money for a ping pong table to bring in more foot traffic.

The point is I know what I'm up against if I lower my price, and I can bring hard numbers to a negotiation. Perhaps after running this exercise I say that I like where my price is right now and leave it alone. Sometimes the best decision you make is not to change. Cheers!