# Financial Management: Volume/Price/Mix

Post 2 in the series on management.

## Decomposing Revenue Change

Regardless of whether you are a retailer or an FMCG manufacturer, an airline or a hotel owner, an ad agency CEO or a news publisher, a lawyer or a doctor, if you want your company to make more revenue next year than you made this year, you can do one of two things (or, ideally, both): sell more goods (or services), or make more money per good you sell than you did this year.

Shockingly, many people overlook this basic fact — I know, because I have asked questions around it in interviews. Even when people get it, most are not sure how to breakdown revenue growth into these two drivers (volume and revenue/unit (note that I’m avoiding using “price” — the reason will become clear further on)).

Imagine than in year 1, you sell V1 units for P1 dollars each. Then, your revenue for Y1 is equal to P1 x V1, represented by the gray box in the chart below:

Now suppose that in year 2, you sell V2 units for P2 each. Your revenue for Y2 is P2 x V2, and your revenue growth is (P2 x V2) — (P1 x V1).

But how much of this growth came from the increase in revenue per unit, and how much from the increase in volume? This is a rhetorical question, as the chart gives away the answer:

- The effect of the increase in volume is represented by the blue rectangle, and is equal to (V2 — V1) x P1. The easiest way to think about this is that the volume effect is the impact of the increase in the quantity sold, had price remained constant.
- Similarly, the effect of the increase in price is shown as the yellow rectangle, and equals (P2 — P1) x V1.
- But there is a third rectangle, shown in green. This shows the interplay of the changes in price and volume, and is equal to (P2 — P1) x (V2 — V1) (though of course, the easiest way to calculate it is to take the total revenue delta and subtract the volume and pricing impacts, as calcualted above). Different people treat this in different ways; the most correct way is to call it out seperately as ‘interplay’, but personally I just attribute it to pricing, for simplicity’s sake. One could equally well attribute it to volume, split it 50/50 across the two, or split it based on the relative contribution of each driver. For example, if the change in volume has led to a $100 increase in revenue, the change in price to a $50 revenue increase, and the interplay to a $25 increase, one could attribute 2/3rds of that $25 to volume ($100 [the volume impact] / $150 [volume + pricing impact]).

You can find a Google Sheets file with an example here. Feel free to make a copy of it, and play around with the numbers in the yellow cells. Note that for the sake of neat numbers & charts, I used an example where both volume and revenue/unit drive growth. In practice, they could both be driving revenue decline, or one could be driving a decline, whereas the other driving an increase. The maths stays the same either way — but in the latter case, attributing the interplay to the two other factors based on relative contribution will give some very strange numbers — try it out!

One thing to note: the definition of volume is not always as straightforward as it might seem. For example, if you are running a consulting firm, how do you define volume? As the number of projects you complete in a given period, or as the number of man-hours you provide to your clients? If you are selling shampoo, is volume the number of bottles you sell, or the number of litres? The distinction can matter very much — though we will discuss the reasons for this in the next post in the series.

## Mix

Here’s an interview question (slightly paraphrased) I recently asked six different candidates, only one of whom got it right: imagine you run an airline. To keep things simple, suppose you only fly one route, say London to Athens. When looking at revenue change year over year for the month of June, you notice that you sold the same number of tickets both years (to your immense surprise, given COVID); moreover, the price you charged for each seat was also the same both years. Yet your revenue increased. How?

The answer (in case the section header hasn’t given it away) is mix. Mix refers to the impact of changes in relative contribution of the quantity of each product or service you offer to the total quantity sold; if different products have different prices, then changing their relative amounts sold between periods will cause revenue change, even if the total quantity of products sold and the price of each product remain constant.

So, in the example above, what might have happened is that more passengers booked business class seats instead of economy. Because business class tickets are more expensive than economy, if some passengers who booked economy in Year 1 switched to business in Year 2, the airline would make more money — even though the total number of tickets sold, and the price of each ticket, did not change.

(This is just one example of what could have driven the increase in revenue; another example is the time of day passengers chose to fly (a 2pm flight is probably more expensive than a 6am one, which requires you to get up at ungodly hours to get to the airport (personally, I just do not understand why people ever choose to take such early morning flights — I have refused to book flights before 9am at the earliest since I started booking my own tickets))).

Let’s take a closer look at how to seperate the effects of mix from those of price. Assume the following scenario: in Year 1, we sold 120 airplane tickets, and made $117/ticket on average, hence $14,000 in total. In Year 2, we again sold 120 tickets, but made $143/ticket on average, thus $17,200 in total.

Then, as we saw in the previous section, we can say that the growth in revenue can be solely attributed to the increase in revenue/ticket:

What we want to find out now is what drove this increase in revenue/ticket. To do this, we need to know how many economy and business class tickets we sold in each period, and what were their prices. We lay out this data in a table as follows:

We can immediately see that in this example we have both price and mix effects: price because the price of both economy and business class tickets has increased, and mix because even though the total number of tickets stayed the same, in Year 2 we sold more business tickets and fewer economy ones. This is why I avoided using the term ‘price/unit’ in the first section: because an increase in average revenue/unit may be driven by mix instead of price hikes.

Now, for the slightly complex part: instead of breaking down revenue delta to volume and revenue/unit, we now want to break it down to volume, pricing, and mix. To do this, we calculate these effects for the economy and business class tickets seperately, and add them up. First I will show the maths for doing this, and then I will (try to) explain the logic behind these calculations:

**Volume**: (Ticket type volume in Y2 — Ticket type volume in Y1) x (*Total*price/ticket in Y1). Pay attention here: we multiply by the average price/ticket for*all ticket types*in Y1, not the price/ticket for the particular type we are looking at. For example, the volume impact for Economy is (80–100) x $117 = -$2,333. Again, notice that we multiply by $117, not $100.**Price:**(Ticket type price in Y2 — Ticket type price in Y1) x (Ticket type volume in Y2). Note that here I’m following the convention I mentioned earlier of attributing the interplay effect entirely to price, to keep things simple.**Mix:**(Ticket type volume in Y2 — Ticket type volume in Y1) x (Ticket type price in Y1 — total ticket price in Y1). For example, the formula for the mix effect driven by economy tickets is (80–100) x ($100 — $117); this shows the mix effect due to the decrease in number of economy tickets relative to business class tickets. Note that both factors in this equation are negative, hence the mix effect is positive. This makes sense: selling fewer economy tickets relative to business tickets increases the average ticket price for the airline in Y2.

These are the results — which you can find here:

Why do we multiply by the total price/ticket to calculate the volume effect? This is so that we get the same answer we would get if we did the calculations at the total business level. Indeed, this way, the volume impact in Figure 4 is equal to that in Figure 2. Similarly, adding up the mix and price effects in Figure 4 is equal to the impact driven by revenue/unit in Figure 2.

If we *didn’t* do it this way, and calculated the volume impact using the ticket-type prices, it wouldn’t be immediately obvious whether the business is growing because we are serving more passengers, or because we are selling them more expensive seats; and the distinction matters very much: the cost an airline incurs for business class seats is not much higher than the one it incurs for economy seats. Growing through mix rather than volume is therefore (in general) much more profitable — and it is important for a company to be able to track this (remember the importance of tracking the right things!) and plan around it. It is similarly important to distinguish between price and mix — but I will discuss this in more detail in another post; for now, I want to focus on explaning how to calculate the two impacts.

(Also notice that if we add the volume and mix effects at the ticket-type level, we would get the same number as if we calculated the volume effect at the ticket-type level.)

Okay. So far so good. Unfortunately, things can get a bit trickier: companies rarely experience a single type of mix effect. In our example so far we assumed that our airline flies a single route; in reality, most airlines fly to many different destinations, and ticket prices vary widely across flight routes. If our airline adds a new route, say London to Dublin, then it will have two kinds of mix effects: those driven by ticket type, and those driven by destination. Nor is this all: there may be all sorts of other levels — for example, if the airline charges lower rates for children, we have passenger-age mix; if we charge different prices depending on whether passengers book tickets on our website or via a travel agency, we have sales channel mix; and so on and so forth.

There are two ways to deal with multiple-level mix. The first is to repeat the analysis above at each level; the second is to do the analysis at the leaf node level — i.e. at the greatest degree of granularity.

## Multi-layer Mix Analysis — Option 1

The figure below shows how to do the analysis at each level:

We start by doing the same analysis we did before, except we first do it at the destination level (let’s call this Level 1); in the second group of tables, we repeat the analysis, but at the ticket type level (Level 2) for passengers flying to Athens; and in the third group of tables, we do the same (still Level 2) for passengers flying to Dublin. Notice the following three things:

- Adding up the volume impacts at Level 2 (so $3,200 + $1,900) does
*not*equal the volume impact as calculated at Level 1. This is because to calculate the volume impact for Level 1, we multiplied the change in number of tickets sold by the average price for all tickets in Y1; when we do the same calculation for Level 2, we multiply the change in number of tickets sold by the average price for tickets to Athens or Dublin. - The price impact calculated at the Level 1 analysis is equal to the mix + price impacts calculated at Level 2. Why? According to the first table, the average ticket price for passengers flying to Athens went up, from $117 in Year 1 to $143 in Y2, causing a $3,200 increase in revenue. This is what is shown as ‘price impact’ in the first table. What the second table shows is what exactly caused this price increase: part of it ($1,200) was driven by actual price hikes, as the price of both business class and economy tickets went up. But another part ($2,000) was thanks to the fact that more passengers chose to fly business in Y2. These two
explain the increase in average price for Athens passengers.*together* - Mix means slightly different things when we look at it at the total business level (call this Level 0), at the destination level (L1) and at the ticket type level (L2). At L0 (i.e. the first row in the first table in figure 5), mix refers to the impact of the change in the average ticket price for
*the total business*due to the change in the destinations people travelled to; in the next two rows of the first table, mix does*not*refer to the change of that destination’s average price due to L2 mix changes — instead, it refers to the impact the change in number of tickets for the destination shown in each row drove for the level above.

## Multi-layer Mix Analysis — Option 2

The second option is to create one row for every destination & ticket type combination (or, more generally, one row for every possible combination of product attributes we wish to include in our analysis).

Here’s how this looks:

The maths is the same as before. Note that the volume impact is equal to the L1 calculation above, and the price impact is equal to the sum of the price impacts of the L2 tables.

The main difference between the two approaches is that the second one shows the mix impact each row contributes to the total business, whereas the first approach shows how much of each product attribute’s average revenue/unit has changed due to mix. For example, using the first approach, we know that the average price/ticket for Athens flight went up thanks to mix as well as thanks to pricing, and we know the size of that impact ($2,000); this is not evident in the second approach.

There is no right or wrong in choosing one of the two approaches — it mostly depends on what you are trying to do. One factor to consider is the org structure of your business. For example, if you have different division heads managing flights to different destinations, then the first approach probably makes more sense — using that, each division head can see the drivers of the changes in price/ticket for their part of the business.

This concludes the discussion on volume, price and mix; feel free to use the file linked above as a template to calculate the different impacts for your own business, and do let me know if you have questions or feedback (you can use the comment function below or email me at acatsambas [at] gmail[dot]com).

In the next post, we will look into pricing: how to determine the optimal price for a product, and different ways to change a product’s price (yes, there is more than one).