Customer equity and market value in the UK mobile industry
Inspired by Peppers & Rogers’ new book Return on Customer, we decided to calculate customer equity and return on customer equity for the UK mobile industry to see if we could measure the correlation with share price.
We chose the mobile industry because it publishes very detailed data on average customer metrics, including revenues, cost of acquisition and retention, and churn rates. This means that we can calculate reasonable value using publicly available information.
For this initial study, we chose three mobile companies: Vodafone, O2, and Virgin Mobile. They are three very different companies:

Vodafone (VOD.L), while UK headquartered has a very strong international presence with Germany as its biggest market (about 30% of revenues). With a market capitalization of almost £100bn it is by far the largest of the three. In 2004, it had revenues of about £34bn and losses of £9bn.

O2 (OOM.L) has international operations, but the UK is the largest market. It is capitalized at about £14bn, and it a profit of £0.2bn on revenues of £5.7bn in 2004.

Virgin Mobile (VMOB.L) is a UK based MVNO that focuses in prepaid customers. With a market capitalization of just over £0.7bn it is the smallest of the three. It had profits of £89m on £0.49bn revenues in 2004.
The three companies cover three orders of magnitude in terms of market capitalization and revenues, and the two main business models of operators and MNVO. Additionally, their performance on the London Stock exchange has been very different.
The main numbers we need from the companies’ annual reports are ARPU, SAC, and churn, as well as the number of active customers.
ARPU is the annual revenues per active unit (i.e. per SIM card). Active customers are normally defined as those who have generated a billing event in the last three months (or 90 days).
SAC is the cost of acquisition and retention per active customer (we combine the two; others may separate the acquisition costs, SAC, from the retention costs, SRC). Finally, churn is the ratio of active customers that leave in a year.
Definitions out of the way, let us make some assumptions for our efforts. We could naively define an individual customer’s equity as the ARPU divided by the churn rate. After all, 1/CHURN
is the number of years an average customer stays with the company, and ARPU is the revenue.
The first problem is that this definition does not take into account the time value of money. £1 today is better than £1 next year. We chose to use a discount factor of 10% (for no particular reason). If L=1/CHURN
is the customer lifetime, then
CE = ARPU * (1  (1CHURN)^L) / CHURN
is the customer equity on a revenues basis.
However, we really want profits per customer, as the book suggests. That is a little tricky. Organizations have all sorts of overheads. However, we can approximate using the SAC. This ignores all other expenses, including the expense of building the network. Maybe it is not fair, but that’s what we will use for this simple calculation. In this spirit,
CE = (ARPU  SAC) * (1  (1CHURN)^L) / CHURN
is the customer equity on a profits basis (for some definition of “profit”). There are all sorts of assumptions here, and we invite the reader to list them. To find the total enterprise customer equity, we multiply by the number of active customers (which of course introduces more assumptions about the constant size of the customer base).
Sticking to this model, we can calculate the customer equity and other interesting numbers, including the return on customer equity. In the following, we look at UK numbers only for the customer equity and derived numbers. Share price derived numbers are of course for the international groups.
In the UK for the year ended 31 March 2005, using 1 April share prices and comparing with the previous year, we find the following
Vodafone  O2  Virgin Mobile  

Market capitalization  £90.2bn  £10.6bn  £0.556bn 
Active customers  13,638,360  14,384,000  4,031,900 
Profit per customer  £273  £215  £101 
Lifetime customer value (CE)  £814  £559  £457 
Enterprise customer equity  £11.1bn  £8.0bn  £1.8bn 
Change in customer equity  (£550m)  (£132m)  (£249m) 
Return on customer equity (ROC)  27%  37%  8% 
If you try to plot changes in share price versus return on customer equity, you do not find much in terms of correlation.
But try to plot our customer equity value, with all its assumptions, against the market capitalizations of the companies. (In the graph below, we have 2004 and 2005 data for all three companies and additionally 2003 data for O2.)
This is surprising. There is so much wrong with this picture that I hardly know where to start.

We didn’t really expect a high correlation between group market capitalization and UK customer equity, given the different international exposure of the three companies.

We certainly did not expect an exponential relationship. This suggests that if O2 adds £5bn to their customer equity, then they will gain £90bn in market value while if Vodafone adds the same £5bn of customer equity they should win £900bn  ten times as much.

The relationship holds across the industry, but not within each company. The VMOB and VOD annual changes are almost orthogonal to the trend line.With the O2 historic data, it does look like the relationship holds over the years, across the industry, and within a single company.
I am confused. What is this? Please add a comment to explain. I bet there is something obviously wrong with this, but I can’t see it. Maybe we need to calculate customer equity taking into account tobe customers, but that then just becomes proportional to revenues, doesn’t it?
Some next steps to consider:

Does the correlation have predictive power? We will add 3 and Tmobile to the graph and see if they lie on the line.

Try with global customer equity instead of UK only. (This may help if the previous point fails: remember that VMOB.L is UK only, so we only have two points on the international line.)

Reduce to simpler causes. (Maybe Market Cap ~ Revenues ~ CE?)
Stay tuned.
"ROC" and "Return on Customer" may be a service mark, trademark, or registered trademark of Peppers & Rogers Group, Inc. in certain jurisdictions.