# Pricing is … Quantitative

Hey quant jocks – Pricing is for you!

One of the great things about pricing is we get to play with spreadsheets: looking at historical transactions, calculating what will happen to profit when price change. For us quants, there is sheer joy in building a spreadsheet that models the business.

Yet, for the non-quants, the great thing is the math is usually easy. No calculus, trigonometry, or even geometry. Pricing just requires simple addition, subtraction and multiplication. Even the formulas are simple.

Profit = Quantity * (Price – Variable cost) – Fixed costs

How much simpler can it be?

The lesson? Use your numbers. The simplest and most important pricing calculation a small business needs to make is what happens when you change your price? If you’re not numerically inclined, here’s how to do that.

Step 1. Calculate your current profit level (using the formula above) with current prices and historical quantities sold.

Step 2. Calculate how many fewer you have to sell if you raise your price to make the same amount of profit. A little algebra shows that the formula is:

New qty = (Profit + Fixed costs) / (New price – Variable costs)

Let’s go through a quick example.

Current:

Qty = 100 widgets

Price = $1.50

Variable cost = $1.00

Fixed costs = $20

You are thinking about lowering your price to $1.25. How many widgets do you need to sell at $1.25 to make the same profit?

Step 1. Profit = 100 widgets * ($1.50 – $1.00) – $20 = $30

Step 2. New qty = ($30 + $20) / ($1.25 – $1.00) = 200 widgets

Wow, if this company lowers price by only $0.25 they have to double the number of widgets they need to sell to make the same profit.

Two lessons today. 1. Use your math when thinking about price changes. You will make better decisions. 2. Try not to lower prices if you can avoid it. It is usually much more difficult to make as much profit.

Mark Stiving, Ph.D – Pricing expert, speaker, author

Photo by Irargerich