{"id":1478,"date":"2021-12-16T15:27:30","date_gmt":"2021-12-16T15:27:30","guid":{"rendered":"https:\/\/sellingsherpa.com\/?p=1478"},"modified":"2024-03-07T12:50:50","modified_gmt":"2024-03-07T17:50:50","slug":"computing-customer-lifetime-value-cltv","status":"publish","type":"post","link":"https:\/\/sellingsherpa.com\/index.php\/2021\/12\/16\/computing-customer-lifetime-value-cltv\/","title":{"rendered":"Computing Customer Lifetime Value (CLTV)"},"content":{"rendered":"
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Simply stated, customer lifetime value (CLTV) is an estimate of the total profit an account will generate over the course of their relationship with your company. Corporations and their investors often compute the ratio of CLTV to customer acquisition cost (CAC) to measure the health of a company’s go-to-market motion. CAC includes the sum of all sales and marketing costs. <\/p>\n\n\n\n

Conventionally, a LTV:CAC ratio over 3.0 is considered healthy. According to a 2017 study by McKinsey, 40% of SaaS businesses have ratios above three. The average ratio is 3.4 and the median, a better measure given the right skew of the distribution, is 2.8.<\/p>\n\n\n\n

Because CLTV is an estimate and because there are multiple ways to compute it, I feel it is better to focus on improving the number over time rather than simply trying to hit a particular number.<\/p>\n\n\n\n

In this post, I’ll focus on computing CLTV and leave CAC for a later time. Beware, there is math, but I’ll explain anything complex from first principles. Also, I’m going to use annual numbers but the concepts apply to any duration you choose.<\/p>\n\n\n\n

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Source: Fuel by Mckinsey<\/a>, May 2017<\/figcaption><\/figure>\n\n\n\n

Method 1: A Simple Approach<\/h2>\n\n\n\n

Let’s ease in by assuming one only knows two things: annual recurring revenue (ARR) and the customer retention rate (CRR). CRR is the percentage of customers who renew each year. One will also hear the team customer churn rate (CCR) mentioned which is simply equal to 1-CRR.<\/p>\n\n\n\n

I’ve only just gotten started but must inject a brief digression to explain CRR in the context of the manifold ways of measuring retention. Assume a company starts the year with 100 accounts at a uniform ARR of $100 each. Hence, total ARR is $10,000. <\/p>\n\n\n\n

At the end of the year, assume 10 accounts cancel, 80 accounts each increase from $100 to $130, and 10 accounts each decrease from $100 to $85. With these assumptions, the CRR is 90% since 90 of the 100 accounts remained as clients. <\/p>\n\n\n\n

The starting ARR dropped by $1,000 for the 10 lost accounts, increased by $2,400 for the 80 accounts that upgraded, and dropped by $150 for the 10 accounts that downgraded.<\/p>\n\n\n\n

Net retention rate (NRR) is a dollar measure of retention that includes cancellations, upgrades, and downgrades (but excludes dollars from signing new logos). In this scenario, ARR increased from $10,000 to $11,250 reflecting an NRR of 112.5%. As you can see, it is possible for NRR to exceed 100% and in fact should for any healthy SaaS business. NRR is sometimes called uncapped dollar retention or uncapped wallet retention.<\/p>\n\n\n\n

Gross retention rate (GRR) is a complementary measure of dollar retention that includes cancellations and downgrades but does not include upgrades (and still does not include new logo ARR). Due to the ceiling placed on upgrades, GRR is sometimes called capped dollar retention. Excluding upgrades, ARR changed from $10,000 to $8,850 yielding a GRR of 88.5%. As GRR does not include upgrades, it cannot exceed 100%. GRR is a more conservative measure of the health of a business since it does now allow upgrades to mask the impact of downgrades and cancellations.<\/p>\n\n\n\n

Now, let’s get back to determining CLTV for a single account. Assume, once again, that the account starts the year at $100. We know the probability we will retain the account is the CRR. Hence, in Year 2, the expected ARR for the account, assuming no upgrades or downgrades, is simply ARR*CRR = 100 * 0.90 = 90. In Year 3, the expected ARR is the year 2 ARR again times the probability of retaining the account = (ARR*CRR)*CRR = (90)*0.90 = 81. <\/p>\n\n\n\n

If we continue this indefinitely, we end up with the following:<\/p>\n\n\n\n

\"CLTV=ARR+ARR*CRR+ARR*CRR^{2}+ARR*CRR^{3}+...<\/p>\n\n\n\n

Pulling the ARR out front, this is the same as :<\/p>\n\n\n\n

\"CLTV=ARR*(1+CRR+CRR^{2}+CRR^{3}+...<\/p>\n\n\n\n

The term in parentheses is recognizable to mathletes as an infinite geometric series \"1+x+x^{2}+x^{3}+...\" which reduces to \"\frac{1}{1-x}\" as long as the absolute value of x is less than 1, or \"|x|<1\"<\/p>\n\n\n\n

Recognizing that CRR = x, we have our Method 1 CLTV formula:<\/p>\n\n\n\n

\"CLTV=\frac{ARR}{1-CRR} <\/p>\n\n\n\n

or equivalently, <\/p>\n\n\n\n

\"CLTV=\frac{ARR}{CCR}<\/p>\n\n\n\n

Plugging our example numbers into this equation yields:<\/p>\n\n\n\n

\"CLTV=\frac{100}{1-0.90}=1,000<\/p>\n\n\n\n

This is as good as time as any for another brief sidebar. Notice the term \"\frac{1}{1-0.9}=10\". This means the expected customer lifetime is 10 years. To conceptualize this, recall that we start out with 100 accounts and we lost 10 in the first year. If we continue to lose 10 more each year, then we will be down to 0 by year 10.<\/p>\n\n\n\n

Method 2: Factoring In Cost to Serve<\/h2>\n\n\n\n

Method 1 uses a lot of simplifying assumptions. One big assumption is that value in a given year is equal to ARR. Even in the absence of upgrades or downgrades this is a problem since it does not account for the cost to serve (CTS) a customer in a given year. <\/p>\n\n\n\n

Letting CTS be a percentage of ARR, the actual amount we make in Year 1 is ARR-CTS*ARR=ARR(1-CTS). The term in parentheses (1-CTS) has a common name, gross margin (GM) so we will switch to that. Now our CLTV calculation looks like this:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)+(ARR*GM)*CRR+(ARR*GM)*CRR^{2}+(ARR*GM)*CRR^{3}+...<\/p>\n\n\n\n

Similar to before, we pull (ARR*GM) out which gives us:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)*(1+CRR+CRR^{2}+CRR^{3}+...<\/p>\n\n\n\n

Applying the infinite geometric series trick again, we get our Method 2 CLTV formula:<\/p>\n\n\n\n

\"CLTV=\frac{ARR*GM}{1-CRR}<\/p>\n\n\n\n

or equivalently, <\/p>\n\n\n\n

\"CLTV=\frac{ARR*GM}{CCR}<\/p>\n\n\n\n

Using our existing numbers and a typical SaaS gross margin of 80% yields:<\/p>\n\n\n\n

\"CLTV=\frac{100*0.8}{1-0.90}=800 <\/p>\n\n\n\n

Method 3A: Incorporating ARR Growth<\/h2>\n\n\n\n

Method 2 is a vast improvement but still fails to account for ARR growth in accounts over time. I’m going to call this factor G. One might be tempted to use NRR for this factor but that would be incorrect since it takes into account cancellations but we’ve already done that with CRR. <\/p>\n\n\n\n

Going back to our prior example, we want to include the ARR for accounts that either upgraded or downgraded but exclude lost accounts from both the numerator and denominator. Completely excluding the 10 that cancelled, we went from $9,000 to $11,250, or G=125%. As expected, this is higher than the NRR of 112.5% we computed earlier. We will express G in decimal form as G=1.25.<\/p>\n\n\n\n

Since the growth factor (G) starts in Year 2 and compounds thereafter, the CLTV series looks like this:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)+(ARR*GM)*G*CRR+(ARR*GM)*G^{2}*CRR^{2}+(ARR*GM)*G^{3}*CRR^{3}+... <\/p>\n\n\n\n

Dusting off our algebra textbook again, note that \"a^{x}b^{x}=(ab)^{x}\" so:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)+(ARR*GM)*(G*CRR)+(ARR*GM)*(G*CRR)^{2}+(ARR*GM)*(G*CRR)^{3}+...<\/p>\n\n\n\n

Once again, we have an infinite geometric series but this time x=G*CRR giving our our Method 3A CLTV formula:<\/p>\n\n\n\n

\"CLTV=\frac{ARR*GM}{1-G*CRR}<\/p>\n\n\n\n

Using our assumptions yields:<\/p>\n\n\n\n

\"CLTV=\frac{100*0.8}{1-(1.25*0.90)}=\frac{80}{1-1.125} <\/p>\n\n\n\n

Mission control, we have a problem! How can CLTV be negative with healthy margins and ARR growth? The problem here is that the infinite geometric series reduction only applies if<\/strong> the “x” term in \"\frac{1}{1-x}\" has an absolute value less than<\/strong> 1. Here, G*CRR=1.25 so we cannot use the Method 3A CLTV formula and need to apply a different approach.<\/p>\n\n\n\n

Method 3B: Brute Force CLTV Calculation<\/h2>\n\n\n\n

In the situation where we cannot use the infinite geometric series reduction, we will need to calculate CLTV via brute force by computing the sum:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)+(ARR*GM)*(G*CRR)+(ARR*GM)*(G*CRR)^{2}+(ARR*GM)*(G*CRR)^{3}+...<\/p>\n\n\n\n

By convention, the number of terms to compute equals the lifetime \"\frac{1}{1-CRR}=\frac{1}{CCR}\" which in this case is 10. The calculation is shown in the table below. (Note: We have 10 periods but we starts at period 0 since the payment for Year 1 is upfront.) As shown in the table below, we compute CLTV of $1,438 using Method 3B.<\/p>\n\n\n\n

\n
\n
Period (P)<\/strong><\/td>ARR<\/strong><\/td>ARR*GM<\/strong><\/td>\"(G*CRR)^{P}\"<\/strong><\/td> \"(ARR*GM)[(G*CRR)^{P}]\" <\/strong><\/td><\/tr>
0<\/td> 100 <\/td> 80 <\/td>1.0<\/td>80.0<\/td><\/tr>
1<\/td> 100 <\/td> 80 <\/td>1.1<\/td>90.0<\/td><\/tr>
2<\/td> 100 <\/td> 80 <\/td>1.3<\/td>101.3<\/td><\/tr>
3<\/td> 100 <\/td> 80 <\/td>1.4<\/td>113.9<\/td><\/tr>
4<\/td> 100 <\/td> 80 <\/td>1.6<\/td>128.1<\/td><\/tr>
5<\/td> 100 <\/td> 80 <\/td>1.8<\/td>144.2<\/td><\/tr>
6<\/td> 100 <\/td> 80 <\/td>2.0<\/td>162.2<\/td><\/tr>
7<\/td> 100 <\/td> 80 <\/td>2.3<\/td>182.5<\/td><\/tr>
8<\/td> 100 <\/td> 80 <\/td>2.6<\/td>205.3<\/td><\/tr>
9<\/td> 100 <\/td> 80 <\/td>2.9<\/td>230.9<\/td><\/tr>
<\/td><\/td><\/td>Total<\/strong><\/td>1,438<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n

Method 3C: Time Bound LTV<\/h2>\n\n\n\n

With a fixed number of periods, one can also use the following using net dollar retention (NDR):<\/p>\n\n\n\n

\"CLTV=\frac{ARR}{\#<\/p>\n\n\n\n

Method 4: Applying an Interest Discount Rate <\/h2>\n\n\n\n

Most companies tend to stop at Method 3A or 3B but financial analysts typically convert future cash flows to present values by applying an interest discount rate (i), often referred to as the weighted average cost of capital (WACC). To understand this, imagine you wanted to have $100 in the bank a year from now, how much would you need to deposit if the interest rate were 5%? You’d need \"\frac{100}{1+0.05}=95.24\" <\/p>\n\n\n\n

By analogy, the amount a company earns in Year 2 (ARR*GM*G) needs to be discounted the same way as \"\frac{ARR*GM*G}{1+i}\". Interest compounds year after year (like the G factor) so we have:<\/p>\n\n\n\n

\"CLTV=(ARR*GM)+(ARR*GM)*G*CRR\/(1+i)+(ARR*GM)*G^{2}*CRR^{2}\/(1+i)^{2}+(ARR*GM)*G^{3}*CRR^{3}<\/p>\n\n\n\n

After applying, yes, you guessed it, the same infinite geometric series reduction, we get CLTV Method 4:<\/p>\n\n\n\n

\"CLTV=\frac{ARR*GM}{1-\frac{G*CRR}{(1+i)}}<\/p>\n\n\n\n

In SaaS, 20% is a reasonable cost of capital assumption (source<\/a>). To be safe, let’s ensure we can use the infinite geometric series reduction by computing x:<\/p>\n\n\n\n

\"\frac{G*CRR}{1+i}<\/p>\n\n\n\n

Since this has an absolute value less than 1, we are good to compute CLTV using Method 4 (otherwise, we’d simply need to use brute force as we did in Method 3B but applying Eq. 4.1).<\/p>\n\n\n\n

\"CLTV=\frac{100*0.8}{1-\frac{1.25*0.9}{(1+0.2)}} <\/p>\n\n\n\n

Final Thoughts<\/h2>\n\n\n\n

Using the various methods, CLTV ranged from $800 to $1,438. Most folks calculate the CLTV:CAC ratio. Just for the sake of argument, assume the sum of all sales and marketing costs is $250 per account. This implies a CLTV:CAC range of 3.2 to 5.8 with our range of methods.<\/p>\n\n\n\n

As I mentioned at the start of this post, CLTV is an estimate that depends heavily on the model chosen so it is more important to improve the metric over time than to target any single value. <\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

Simply stated, customer lifetime value (CLTV) is an estimate of the total profit an account will generate over the course of their relationship with your company. Corporations and their investors often compute the ratio of CLTV to customer acquisition cost (CAC) to measure the health of a company’s go-to-market motion. CAC includes the sum of […]<\/p>\n","protected":false},"author":1,"featured_media":1513,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","_monsterinsights_skip_tracking":false,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-1478","post","type-post","status-publish","format-standard","has-post-thumbnail","category-uncategorized","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t