For the life of me, I still can’t fathom how VCs value early stage startups. I think it is one part business logic and five parts voodoo (no offense to my VC friends, but you know what I mean). However, I’m guessing most SaaS-focused VCs know this SaaS company valuation principle in their gut even if they can’t reduce it to a financial projection: SaaS Customer Lifetime Value Drives SaaS Company Value. For what is a company if not the sum of its customers?

The link between SaaS CLTV and SaaS company valuation arises naturally from the SaaS subscription model where topline company revenue emerges as the sum of individual customer revenue streams. |

This is the final post in a series that aims to uncover the mysteries of SaaS financial metrics from a new angle, a little mathematics. In this installment, I’ll explore the important SaaS metric of customer lifetime value (CLTV) and introduce a new SaaS financial metrics rule-of-thumb that relates SaaS CLTV to SaaS company value.

*Buyer Beware: The ideas presented in this installment of the SaaS metrics series are not meant to offer methods or models for evaluating the value of any particular SaaS company, but rather to offer credence to the gut reaction above. Use the formulas herein at your own discretion. Chaotic Flow, i.e., me, accepts no liability thereof.*

### SaaS Metrics Rule-of-Thumb #10

SaaS Customer Lifetime Value Drives SaaS Company Value

The financially accepted method for estimating the value of company is the calculation of the discounted value of its future cash flows, or net present value. Now, I’m not saying that anyone in InternetWorld actually uses this method, but for the sake of this series on SaaS financial metrics, this is the only approach that lends itself to mathematical analysis. So, I am stuck with it.

The exact mathematical statement of SaaS Metric Rule-of-Thumb #10 above is expressed as follows (see SaaS Metrics Math Notes below for the derivation):

SaaS Company NPV = CLTV x NEW_{LTV}

Where CLTV is the average SaaS customer lifetime value and NEW_{LTV} is an analogous measure for the *lifetime value number of customers* that represents the discounted number of new customers acquired by our SaaS company during its lifetime, using the standard NPV formula.

NEW_{LTV} = NEW_{1}/( 1 + i ) + NEW_{2}/( 1 + i )^{2} +…+ NEW_{N}/( 1 + i )^{N}

Here NEW_{n} is the number of new customers acquired during the period n. NEW_{LTV} is the present value of all the new customers that the company will ever acquire discounted by how long it takes to acquire them. If market penetration is slow, then NEW_{LTV} might be less than 10% of the total number of customers at maturity. Whereas, if market penetration is fast and absolute, then NEW_{LTV} will be closer to the total number of potential customers.

The formula above elegantly encompasses three critical questions asked by SaaS VCs:

- What is the value to the customer? (CLTV)
- How big is the market? (NEW
_{N}) - How fast can you get there? (NEW
_{LTV})

The link between SaaS CLTV and SaaS company valuation arises naturally from the SaaS subscription model where topline company revenue emerges as the sum of individual customer revenue streams. In this regard, this new SaaS metrics rule-of-thumb linking customer value to company value is really a corollary of SaaS Metrics Rule-of-Thumb #4 – Company Time to Profit Follows Customer Break-Even, which had I been more esoteric (as if this SaaS metrics series isn’t already esoteric enough!), I might have stated as *SaaS company cash flow follows SaaS customer cash flow* (most SaaS CEOs can validate this version of the principle without any need for advanced mathematics).

While CLTV can be calculated for each individual customer, it is more commonly quoted as a generalized metric that describes the average SaaS customer as follows:

CLTV = ARR_{LTV} – ACS_{LTV} – CAC

CLTV = (ARR_{1} – ACS_{1})/( 1 + i ) + (ARR_{2} – ACS_{2})/( 1 + i )^{2} +…+ (ARR_{N} – ACS_{N})/( 1 + i )^{N} – CAC

Where “ARR_{LTV}” is average lifetime recurring revenue per customer, “ACS_{LTV}” is the average lifetime recurring cost of service per customer, and “CAC” is the average customer acquisition cost. ARR_{n} and ACS_{n} are the average customer recurring revenue and cost of service for the period n, and “i” is the cost of capital, which for VC funded startups is 30%+.

I’ve explicitly separated revenue from costs, because costs are variously omitted from CLTV depending on the application. For example, if I want to compare the “lifetime value” of a customer in terms of net contribution vs. the cost of acquiring a customer, then I omit the acquisition cost from the CLTV calculation. Or, if I wan’t to measure the “lifetime value” as the money a customer pays during its lifetime, then I’d only keep ARR_{LTV}. The formula as written is the total net present value of all cash flows related to acquiring and servicing the average SaaS customer.

Using this “fully loaded” CLTV, we can also give a useful variation to the formula for total SaaS company value when the company already has current customers, C_{old}, as follows:

NPV = CLTV x NEW_{LTV} + ( CLTV + CAC ) x C_{old}

or

NPV = CLTV x NEW_{LTV} + ( ARR_{LTV} – ACS_{LTV} ) x C_{old}

Where in this case NEW_{LTV} represents all the future customers still yet to be acquired and C_{old} represents the number of current customers. Notice that using our “fully loaded” CLTV we must add CAC back for current customers, because it is a sunk cost. If new customers are somehow different from old customers, or CLTV changes over the customer lifetime, then the old customer CLTV / CAC values would also be different from the new.

In the simple case of constant recurring payments and costs per period, CLTV for the average customer is calculated as follows:

CLTV = (ARR – ACS)/( 1 + i ) + (ARR – ACS)/( 1 + i )^{2} +…+ (ARR – ACS)/( 1 + i )^{N} – CAC

CLTV = ( ARR – ACS )/i x ( 1 – ( 1 + i )^{-N} ) – CAC

When there is no limit placed on the number of payments (an annuity).

CLTV = (ARR – ACS )/i – CAC

And, if we throw churn and viral growth into the mix CLTV becomes.

CLTV = ( ARR – ACS – gCAC )/( i + a – g ) – CAC

with the constraint g < i + a

Where “ARR” is the average recurring revenue per customer, “ACS” is the average recurring cost of service per customer, “a” is percentage churn rate, “g” is the viral growth rate. This last formula should be used with extreme caution in high growth, big g scenarios as treating viral growth as something that extends indefinitely is unrealistic. Sooner or later you hit the market limit and growth slows. Which is why the formula blows up when g = i + a.

**SaaS Financial Metrics Math Notes**

The idea that the character of a SaaS company is determined in large part by its average customer is a theme played out in many of the SaaS metrics rules-of-thumb. The underlying cause of this general principle is the recurring revenue subscription model. Unlike customers of licensed software, SaaS customers ease into their relationships with SaaS vendors through many repeat purchases. Each new SaaS customer brings a new thread of recurring revenue, which is woven into the larger tapestry of customers to create the total SaaS company recurring revenue stream. Using the continuous SaaS metric model, the formula for total recurring revenue is as follows:

*Total Recurring Revenue = TRR(t) = ∫ _{0}^{t} New(τ)ARR(t – τ)dτ*

Where New(t) is the number of new customers acquired by the SaaS company over time, and ARR(t) is the recurring revenue of the single average customer over time. The integral sum adds up the recurring revenue from each new customer acquired from the beginning to today (0 to t), starting each new customer on its own recurring revenue path beginning at the time it was acquired, τ. For the math heads, it’s a convolution of New(t) and ARR(t).

In the continuous model, the net present value of company recurring revenue is given by the following formula:

*NPV Total Recurring Revenue = TRR _{LTV} = ∫_{0}^{∞} TRR(t)e^{-it}dt*

Where “i” is the cost of capital. Again, for the math heads in the audience (and I can’t much imagine there is anyone else left at this point), this is a standard Laplace Transform. Using a known property of Laplace Transforms that the transform of a convolution equals the product of the two individual transforms, we can simplify the expression for TRR_{LTV} as follows:

*TRR _{LTV} = ∫_{0}^{∞}NEW(t)e^{-it}dt x ∫_{0}^{∞}ARR(t)e^{-it}dt*

*TRR _{LTV} = NEW_{LTV} x ARR_{LTV}*

Which is starting to look a lot like SaaS Metrics Rule of Thumb #10 above. Had we started with ARR – ACS and thrown in CAC from the start, we would have had the following:

*TRR _{LTV} – TCS_{LTV} – TCAC = NEW_{LTV} x ( ARR_{LTV} – ACS_{LTV} – CAC )*

*SaaS Company NPV = NEW _{LTV} x ( ARR_{LTV} – ACS_{LTV} – CAC )*

*SaaS Company NPV = NEW _{LTV} x CLTV*

Voila! SaaS Rule-of-Thumb #10 – SaaS Customer Lifetime Value Drives SaaS Company Value.

### Check out the rest of the SaaS Metrics Rules-of-Thumb

- SaaS Metrics Rule-of-Thumb #1 – SaaS Churn Kills SaaS Company Growth
- SaaS Metrics Rule-of-Thumb #2 – New Customer Acquisition Growth Must Outpace Churn
- SaaS Metrics Rule-of-Thumb #3 – Viral Growth Trumps SaaS Churn
- SaaS Metrics Rule-of-Thumb #4 – Company Time to Profit Follows Customer Break-Even
- SaaS Metrics Rule-of-Thumb #5 – Best Case Time to Profit is Simple Break-Even
- SaaS Metrics Rule-of-Thumb #6 – Growth Creates Pressure to Reduce Total Cost of Service
- SaaS Metrics Rule-of-Thumb #7 – Churn Creates Pressure to Reduce Total Cost of Service
- SaaS Metrics Rule-of-Thumb #8 – Upselling and Upgrades Accelerate SaaS Profitability
- SaaS Metrics Rule-of-Thumb #9 – Joel’s SaaS Magic Number
- SaaS Metrics Rule-of-Thumb #10 – SaaS Customer Lifetime Value Drives SaaS Company Value

[…] be able turn a profit in one year instead of ten years. And. if those $1,000/mo customers have a lifetime value of $100,000 instead of $10,000, then you may also turn a $50million SaaS company valuation into a […]

I am reading this article after searching for LTV and SaaS. Is this article directed to somebody that has a finance background? I find this too complex to read for the average startup person from the planet earth. Maybe something simpler would help a lot of people.

[…] factor to growth, the SaaS churn rate has a very negative impact on both SaaS profitability and SaaS company valuation. Moreover, SaaS churn increases with the size of the customer base, so it is essentially negative […]

[…] CLTV can be a little bit tricky, but SaaS expert Joel York does an excellent job of outlining it on his blog Chaotic Flow. Simply put, CLTV is a more advanced way to look at a SaaS company’s economics. If CLTV is […]

[…] LTV can be a little bit tricky, but SaaS expert Joel York does an excellent job of outlining it on his blog Chaotic Flow. Simply put, LTV is a more advanced way to look at a SaaS company’s economics. If LTV is greater […]

Hello Joel,

Like your analysis. Have a question.

Assumption: Suppose a subscription based SaaS service is solving problems for a need in the market and the developers for this SaaS based app can match feature for feature the competitors are throwing out. So customers loyalty is not a problem.

In the equations for NEW_LTV & CLTV, how do you determine the factor N?

In other word, what is the definition of lifetime for LTV in a subscription based SaaS service?

Thanks in advance.

[…] CLTV can be a little bit tricky, but SaaS expert Joel York does an excellent job of outlining it on his blog Chaotic Flow. Simply put, CLTV is a more advanced way to look at a SaaS company’s economics. If CLTV is […]

[…] to pay for new customers (more on this below). In the words of SaaS entrepreneur Joel York, “SaaS customer lifetime value drives SaaS company value. For what is a company if not the sum of its […]