Pricing and sales volume part 2 - mechanics
Steven Forth is a Managing Partner at Ibbaka. See his Skill Profile on Ibbaka Talio.
Warning: this post is for people interested in the mechanics of pricing design. It gets into the weeds.
For most products in most markets the unit price changes with the volume purchased. These changes need to be designed into the pricing model. If not, they will emerge anyway in undisciplined discounting. This is the second of two posts on how to think through and design volume discounts.
Pricing and sales volume part 1 - framework
A general framework for understanding how and why price changes with volume and how to design pricing that responds to this. The design of pricing to volume relationships is a big part of pricing model design.
Pricing and sales volume part 2 - mechanics (this post)
This post looks at the mechanics of different ways to align unit price with sales volume, considering both smooth and stepped approaches.
How to design pricing for changes in volume
In the first post in this series we presented a general framework for managing the relationship between unit cost and volume. We suggested that you need to ask two key questions.
Should price change with volume? Why?
Consider all three possibilities.Unit price should go down with volume
Unit price should remain unchanged with volume
Unit price should go up with volume
If yes, should a stepped design or a smooth design? Why?
Smooth if you want to be able to optimize the algorithm and have a simple input-output pricing model
Stepped if there are changes in behavior across scale or the salesforce is most able to execute on this model
Now let’s dive into the details.
A bit more on the decision on a smooth or stepped design.
Use a smooth design when
There are no important changes in buying behavior across scales
You need to be able to optimize the curve algorithmically (this is much simpler with the smooth approach)
You are able to calculate the price in your pricing software, CPQ (configure price quote) platform or in a pricing and value management tool like Ibbaka Valio
You are able to include a pricing function in the pricing page on your website so that the potential buyer can enter a number and get a price
Use a stepped design when
There are important changes in buying behavior across scale that you want to reflect in the pricing model
Sales finds stepped tiers useful in closing deals or driving upsell
Design of smooth or algorithmic volume discount models for pricing
Once you have decided to use a smooth design the next decision is as to the shape of the curve. (Even when using a stepped design it is often useful to begin with the shape of the curve and then apply the steps to the curve, in the above figure, the steps were applied to the linear curve).
There are four possibilities:
Linear
Concave
Convex
Sigmoid
You are looking for the curve that will optimize volume, revenue or gross profit depending on your pricing strategy (there is generally no one curve that optimizes simultaneously for all three, the optimization is driven by assumptions about price elasticity and cross price elasticity and the distribution of opportunities by size).
The simplest approach is a linear model: choose a start point, pick another point, calculate the slope and extrapolate. This is seldom the price optimizing curve, but it is often a good place to start as you may have a sense of the best price at certain volumes.
A convex curve is used when you want the price to drop quickly early on and then flatten out at high volumes.
A concave curve is used when you want the price to stay relatively high for low volumes and then drop rapidly as higher volumes are reached.
There are many ways to generate concave or convex curves, but at Ibabka we generally use a log function.
A sigmoid curve is used when prices stays relatively high at low volumes, then drops off as volume increases, and price increases slow down again with higher volumes. The general equation for a sigmoid curve is
As on approaches a limit with the convex or sigmoid models one can either set a level at which prices no longer decline (a minimum price per unit, perhaps based on cost to serve) or have a level at which there is no charge for additional units (this is quite common in pricing for large enterprises who often demand a fixed price in return for buying at scale).
Design of stepped volume discount models
In some cases it is hard to make a smooth approach work and one can get a more effective design using a stepped or tiered model. This is especially true when there are important differences in buying behavior across scale. One can align tier transitions with changes in buying behavior. Changes in buying behavior include things like an individual purchasing for their own use, a manager buying for a team, a business unit leader buying for a business unit, a cross functional purchase, the level at which procurement gets involved, the level at which finance gets involved.
When using stepped models on needs to make the following decisions.
How many tiers (steps)
Price change across tiers
Additive or flat tiering
How to handle transitions between tiers in flat tiering
How many tiers (steps)
Generally one wants to keep the number of steps to 3 to 7, more than this becomes hard to model and optimize.
If you chose to use a stepped approach in order to align with changes the buying process with scale, then the number of transitions in the buying process determines the number of steps.
If there is no external reason to set the number of steps, Ibbaka generally models 3, 5 and 7 steps, allocates total revenue evenly across the steps, and then adjusts this base to optimize for volume, revenue or gross profit.
Price change across tiers
How much should the unit price go down at each tier? Here it helps to have tested smooth pricing models first and found the optimal curve. One can then approximate the curve with steps. The more steps, the closer the approximation, but of course having more steps also has a complexity cost, so you are looking at finding a balance.
One thing to look for is inflection points. The concave and convex curves have one inflection point, the sigmoid has two. Some pricing model designers put a step right on the inflection point. This makes mathematical sense, but in our experience there is a lot of variation in the area near inflection points so we tend to design steps that bracket these points. This can make it easier to design sales processes to support the transitional steps (the steps that include an inflection point).
Generally we set the price for a step at the average for what the price would be for the range when using smooth pricing.
Additive or flat tiering
There are two basic design styles in tiered pricing models: additive and flat tiering. Additive tiering is the best practice as it optimizes revenue, is generally felt to be fair and eliminates an additional design challenge of how to price incremental units. Let’s look at how this works for a simple example.
Additive price tiering: In additive tiering, the buyer pays the price for the number of units in each tier.
Flat price tiering: In flat tiering, the buyer pays the same amount for all units with the price beng based on the unit price for the cheapest tier. This looks like this.
The benefits of additive tiering build with scale and become larger with concave pricing models (which are more common than convex models in the wild).
How to handle transitions between tiers in flat tiering
If you study the above chart you can see the price anomalies associated with flat tiering in the dotted circles. These are surprisingly common but easily handled if one wants to use flat tiering (perhaps it is what sales insists on, or it helps sharpen the transitions between tiers, or one wants to leverage it to guide people into higher tiers).
The solution to this anomaly is to have a price for additional units included in the pricing model. The range for pricing these additional units is to use the price of the lower tier or to use the price on the upper tier. In the above pricing model, the range within which we would price 60 units (10 units above the 11-50 tier) is $9.00 per unit for a total additional price of $90 or $8.10 per unit for a total additional price of $81.00.
This is a range and you can set the price for additional units anywhere within this range. You set the price closer to $9.00 if you want to force buyers into the higher tier as soon as possible. Tiers are often associated with functional packages and there may be good reason to do this. We often use 1/3 as a good level at which to do this, so we would set the incremental price at $8.70. A more conservative approach is to use 2/3, in which case the price of incremental units would be $8.40.
Incremental pricing, if needed, and it is always needed with flat tiering, is dependent on the overall packaging and upsell strategy.
Final thoughts on pricing and volume
The relation between price and volume is one of the two central problems in pricing. (The other is the relation of price to value.) It requires a lot of thought and experimentation to get this right for your business as there are complex interactions. The most important of these interactions are
Price elasticity of demand and cross price elasticity (see Understand your market’s dynamics before you set pricing)
andVolume and Packaging - in most cases packages with more functionality are offered to buyers with higher volumes, though this does not have to be the case
Hopefully these two posts on pricing and sales volume will give you the guidance you need to think through your approach to this key pricing challenge. If not, well Ibbaka is happy to help.