In the

last article we introduced the Customer Lifetime Value (CLV) formula of Gupta & Lehman, and we began to explain it, starting with the expected lifetime of a customer. So was that it? The lifetime value of a customer is expected length of the customer’s subscription times the profit you make on them each month. That is:

So if the churn rate is 10%, the CLV is 10 times the recurring margin, if the churn rate is 5% the CLV is 20 times the margin, and if the churn is 1% then the CLV is 100 times the margin. This approximation to CLV is widely used, but it has some serious flaws and as we will see it can significantly overstate CLV. This article will explain why.

## Discounting a Safe Cash Flow

As we all know, money promised in the future isn’t as good as cash in hand! So if you want to know the lifetime value of a customer you must “discount” future payments, or adjust them for the fact that you have to have to wait to receive the money (and for that matter may never receive it.) Both of these reasons, waiting and risk, contribute to making future money less valuable today and we will describe them in turn, below. This is an idea known to anyone who has taken a college level course in business or finance so if you already know what cash flow discounting is and why it is important you can skip this section – this article will just cover the basics.

Why is this subject important for subscriber acquisition and retention? Because if you’re thinking about spending some money to acquire or retain new customers you are going to spend that money

*right now* or very soon. But the money you will collect from those subscribers is going to trickle in over months or years. If you think the value of present and future dollars are the same you will reach incorrect conclusions about how to get the most value for your hard earned marketing budget.

To understand how to compare present and future money, you need to use a fundamental concept of finance, which is called cash flow discounting. The simplest version of this idea is this: if you have some money you can put it in a bank account and the interest makes the money grow over time. Now turn it around and imagine receiving money after waiting some period of time: money you have to wait for is worth less than money now because you could take less money today, invest it for the waiting period, and after that you would have the full amount. The amount you have to invest now in order to have the full amount after the waiting period is called the

*present value* of the future payment.

Let’s make a concrete example: If you are to receive say $100 at the end of the year, and interest rate is now 5%, it is the same as having around $95 today because if you had the $95 now you could put it in the bank and have $100 at the end of the year. The mathematics of how money grows with interest is described in the Appendix section below, and conversely how to calculate exactly the present value of money if you have to wait for it. This calculation depends on the interest rate that you could invest at. (If you want to know why $100 after a year with 5% interest is worth “around” $95 and not exactly $95 see the details in the appendix.)

Now an important point: what does a bank deposit and a subscriber to a service have in common? They both pay repeatedly, in installments. The periodic payments in both cases make up a “cash flow”. That is why we use the idea of cash flow discounting, borrowed from finance, to analyze the value of subscribers.

## Discounting a Cash Flow with Risk

Okay, that wasn’t too hard – you have to reduce the future money to be received by “discounting it”, which depends on the interest rate. That’s the basic idea. But here’s the catch: What we just said assumes that you will get the money in the future with 100% certainty, like in an FDIC insured certificate of deposit (CD). So the interest rate we were talking about is the rate on a safe deposit. But at the time of this writing in 2014, the interest rate on savings account is practically nothing, maybe 2%. What if instead of investing your money in a safe investment, you lent it to a more speculative venture, like lending your money to your friends crowd sourced loan on Prosper.com? You’d earn a higher interest rate, of course. These days a savings account may only give you 2%, but if you invest in a venture on Prosper.com you may

earn interest anywhere from 6% to 30%. That’s great if you get your money back, but if the borrower goes bust you’ll get much less, maybe nothing at all.

There is added risk, but notice that lending money to a small business venture is still similar to safe bank deposits and subscribers because you get paid periodic interest. That means that the same ideas apply, but because of the risk the interest rate should be larger. Lending at a higher interest rate, your money will grow faster if you make a risky loan, as long as you do in fact get paid. And the flip side is that money promised to you in the future by a risky investment is worth less today when you discount it than money promised by a safe investment. And here’s the point for customer lifetime value, if it’s not obvious already: cash expected from subscribers to a service should be considered like a risky investment and discounted at a high interest rate! Not the interest rate on a safe investment like a savings account.

The impact of a safe interest rate and a risky interest rate are shown in the table below. The way to read it is that $1 to be paid to you in 10 years by a safe investment (2% discount rate) is worth 82 cents today, but $1 to be paid to you in ten years by the risky investment (10% discount rate) is worth only 39 cents today – less than half as much.

**Table: Discount factors at different times for low (2%) and high (10%) discount rates**
What interest rate should you use to discount the future cash streams from subscribers to a service? If you don’t already have a system in place for choosing your own discount rates, we recommend discounting with the effective yield of a CCC junk bond, around 9-10% at the time of this writing. That’s probably too generous, meaning the rate for discounting subscriber payments should probably be even higher for most services. (That’s because CCC is just the worst rating for a rated company that issued a bond. Any company that can even issue a bond is way ahead of even smaller, risker ventures.) But the CCC bond rate has the advantages that the rate is

readily available in published sources, it will adapt to changing times, and CCC is pretty risky.

Adapting to changing times is important: if the economy goes into recession, many things will happen, most of them bad for your subscribers and for your business. As a result, you should probably discount expected payments more heavily if there is a recession. And in a recession, the CCC bond rate will rise, because all risky ventures are likely to have a tougher time so investors will demand a higher interest to loan to junk companies. So an increased CCC bond rate will automatically increase the discounting of future subscriber cash in an appropriate way. Why would you want to value your customers less in a recession? Because in a recession you should probably be more conservative with your marketing and retention spending : reducing the calculated value of your customers is a principled and objective way to do this. (You might argue that in a recession you will need to bolster your numbers by valuing your customers more highly. That’s great if you want to make a presentation to investors – just take a more careful approach when you decide how to spend those investor’s money!)

## Appendix: Mathematics of cash flow discounting

If you are mathematically inclined, the relationship can be expressed as:

where r is the annual interest rate (i.e. a percent as a decimal number like .02 for 2%) and N is the number of years.

*(1+r)*^{N} is the accumulated (compounded) interest rate. You can turn that equation around (by dividing both sides by the compounded interest rate) and write:

And now you can clearly see money in the future is worth less than money today because you divide the future dollars by the compounded interest you would accumulate over the time if you had the money today. (Note that

*(1+r)*^{N} is always greater than one whenever the interest rate is greater than zero, so future cash is always worth less than present.)