Subscription Metrics Guide: key equations & how to use them
Written by Michal Dallos

In this article we collected and explained the most relevant key metrics equations for subscription business. Note, that the business model related part explaining the economics behind subscription businesses can be found in the article Subscription Business Explained.

## Churn Rate, Customer Lifespan (CL), and Retention Rate (RR)

### What does Churn Rate, Customer Lifespan (CL) and Retention Rate Mean?

Churn rate (sometimes referred simply as ‘churn’ ) describes the fraction of subscribers who have dropped out over a specific time period, relative to the existing subscriber base. Retention rate is in contrast the fraction of remaining customers. Both values lie between 0 and 1, or after multiplication by 100% between 0 and 100%. They reflect the fraction (or percentage) of subscribers lost (churn rate) or subscribers retained (retention rate), rather than the absolute numbers. Note: Churn Rate and Retention Rate always add to 1, respectively 100%.

### How to Calculate Churn Rate and Retention Rate?

text{Churn }= frac{NC^{text{begin}}-NC^{end}}{NC^{text{begin}}}=frac{1}{text{CL}}

text{RR} = 1-text{Churn} = frac{NC^{end}}{NC^{text{begin}}}

where:
CL: stands for Customer Lifespan
RR: stands for Retention Rate
NCend: Number of customers at the end of a period
NCbegin: Number of customers at the beginning of a period

### Example of Churn Rate and Loyalty Rate Calculation

Monthly churn of 0.20 (or 20%) means that, starting from for example 100 subscribers at the beginning of the month, the company loses 20 subscribers over one month, resulting in 80 remaining subscribers: churn = (100-80)/100 = 0.2 (or 20%). Consequently the Custer Lifespan CL = 5 month = 1/0.2 and the retention rate RR is 80%.

## Customer Acquisition Costs (CAC)

### What does Customer Acquisition Costs (CAC) mean?

CAC represent the amount a company needs to spend in order to “acquire” a new customer in terms of getting them to buy a product. While in conventional one-time-sale businesses there is a need to “re-acquire” the customers over and over, the beauty of subscription businesses is that the customer remains with the company forever – or at least much longer than in the case of one-time-sales.

### How to Calculate Customer Acquisition Cost (CAC)?

 text{CAC} = frac{text{Marketing & Sales Expenses}} {NC^{text{new}}}

where:
NCnew: Number of new customers aquired
Marketing & Sales Expenses: consists of marketing- & sales-related salaries, costs of tools, and marketing expenditures. As CAC refers to the acquisition of new customers, only the corresponding one-time cost component should be included. Recurring costs of customer service, like server costs and support, should not be considered.

### Example of Customer Acquisition Cost (CAC) Calculation

Let’s assume you have contracted a marketing agency for EUR 2,400 a month to manage your campaigns in 3 channels. Further let’s assume that these agency costs are allocated by 1/3 to every channel. The direct campaign costs are EUR 3,500, EUR 5,000 and EUR 1,500 per channel, leading to the following new customer numbers in the corresponding channel: 500, 750 and 2.000. The CAC values per channel are:

CACCH1 = (800€+3,500€)/500 = 8.6 € per new customer acquired in channel 1
CACCH2 = (800€+5,000€)/750 = 7.74 € per new customer acquired in channel 2
CACCH3 = (800€+3,500€)/2,000 = 2.15 € per new customer acquired in channel 3

Note that stand-alone CAC values, without the corresponding profit generated per channel may result in misleading interpretations.

## Monthly Recurring Revenue (MRR)

### What does Monthly Recurring Revenue (MRR) means?

MRR is the revenue a company can expect every single month, hence it represents a company’s predictable income. It consists of all recurring payments like subscription fees, recurring add-ons, coupons and discounts; however one-time charges like set-up fees and nonrecurring add-ons are not included.

### How to Calculate the (Total) Monthly Recurring Revenue (MRR)?

 text{MRR}^text{TOTAL} = sum text{monthly recurring revenue}

alternatively we can also identify individual meaningful constributions to MRR:

 text{MRR}^text{new} = sum text{ MRR from new subscriptions of the month}

 text{MRR}^text{expansion} = sum text{MRR from subscr. upgrades & reactivations of the month}

 text{MRR}^text{contraction} = sum text{MRR from subscr. downgrades & cancelations of the month}

### Comments on Montly Recurring Revenue (MRR) Calculation

MRR is one of the most important KPIs for a subscription business. Hovewer, it is important to note that, in the case of subscription businesses providing tangible assets (for example food boxes, or cosmetics delivery), the MRR value should be evaluated together with the corresponding gross margin, in order to obtain an insight on the profitability rather than on the revenue only.

The breakdown of the MRR contributions into MRRnew, MRRexpantion, MRRcontraction provides an essential insight into the dynamics of the subscription development in your company:

• MRRnew provides one of the most direct growth level indicators allowing you to identify the most effective acquisition channels.
• MRRexpansion provides the sum over upgrades within the paid packages, free-to-paid upgrades as well as revenues from reactivation of previously cancelled subscriptions. It is important to ensure that the MRRexpansion is always higher than the MRRcontraction, otherwise the company is constantly losing subscription revenue.
• MRRcontraction consists of subscription revenue losses due to downgrades and cancellation of subscriptions. It is important to analyze and understand what the reason for downgrades or cancellations is. For example, if many subscribers cancel their subscription after only one month of membership, you observe a high value of MRRnew combined with a high value of MRRcontraction. In this case your marketing works well – you attract new subscribers. However, your value proposition lacks long-term attractiveness in keeping your subscribers.

## Gross & Net MRR Churn Rate

### What does Gross & Net MRR Churn Ratemean?

Gross MRR Churn Rate is a value describing the percentage reduction of the monthly recurring subscription revenues due to downgrades from higher to lower paid plans and cancellations.
Net MRR Churn Rate describes the monthly percentage net loss of the revenue by substracting the expansions of the subscriptions from the downgrades and cancellations.

### How to Calculate Gross MRR Churn Rate?

text{Gross MRR Churn Rate} = frac{text{MRR}^text{downgrade}+text{MRR}^text{cancellation}}{text{MRR}_text{begin}^text{TOTAL}}*100%

### How to Calculate Net MRR Churn Rate?

text{Net MRR Churn Rate} = frac{text{MRR}^text{contraction} – text{MRR}^text{expansion}}{text{MRR}_text{begin}^text{TOTAL}}*100%

### What does Customer Lifetime Value (LTV) mean?

Customer Lifetime Value LTV (or sometimes abbreviated as CLT) is one of the most important KPIs for subscription businesses quantifying how much profit or “value” a customer is bringing to your company. In a more precise textbook approach, the customer lifetime value is defined as present value of all future cash flows brought by a customer over his/her entire relation with a company.

### How to Calculate Customer Lifetimer Value (LTV)?

First let’s discuss the two most common equations used for calculating the LTV. The fist one is based on the ARPU and Churn values, while the second works with averaged Order Values, Gross Margins and Customer Lifespan values. It is worth noticing that the two formulas are equivalent: once referring to the same period Average Number of Transaction ANT times Average Order Value AOV results in total monthly Revenues MRRTOTAL. MRRTOTAL divided by the number of subscribers is exactly ARPU.

text{LTV} = text{ARPU} * text{CL}*text{GM} = frac{text{ARPU}*text{GM}}{text{churn}}

where:
ARPU: stands for Average Revenue per User
GM: stands for Gross Margin
churn: for the fraction of subscrubers leaving the subscription within a given time period

text{LTV} = frac{text{ANT}*text{AOV}*text{CL}*text{AGM}}{text{NC}}

where:
ANT: stand for the Average Number of Transactions per month
AOV: stands for Average Order Value per month
CL: stands for Average Customer Lifespan in months
AGM: stands for Average Gross Margin per month
NC: stands for Number of Clients

### Examples of Customer Lifetime Value (LTV) Calculation

Let’s take for example an company operating for the last 9 months with currently 300 subscribers, churn rate of 20%, and transaction data listed in the table.

Based on the monthly data provided, the Average Number of Transactions, ANT = 1.485/9 = 165 transactions per month.

The Average Order Value AOV of the last 9 month is AOV = 25,000/1,485 = 16.84 € per order.

The Average Gross Margin AGM is simply the montly average of the GM values, AGM = 0,33. The montly GM values are calculated form the Revenues and Cost of Sales values, for example for May: GM = (2,500-1,500)/2,500) = 0.40.

Based on the Churn Rate of the last 9 month of 20% we obtain an Average Customer Lifespan of ACL = 1/0.2 = 5 month.

Putting all the contribution together into the LTV formula we obtain:

text{LTV} = frac{text{ANT}*text{AOV}*text{CL}*text{GM}}{text{NC}} = frac{165*16.84*5 *0.33}{150} = 30.29

## Average Revenue per User (ARPU)

### What does Average Revenue per User (ARPU) means?

ARPU describes the revenue generated per user. As such it allows the management as well as investors to measure and optimize company’s revenue capability on the per-customer level and help forecasting future revenues streams. Further the ARPU value can be used internally to compare the revenue capability for various customer segments as well as externally to compare with competitors on the market.

### How to Calculate Average Revenue per User (ARPU)?

 ARPU = frac{text{Total Revenue}}{NC^{end}}

where:
NCend stands for the number of customers at the end of the period.
Note, that in case of high intra-period fluctuation averaged values should be used in order to avoid statistically misleading results.

### Examples of Average Revenue per User (ARPU) Calculation

Let’s assume an example app company generating last month 2,500 Eur in revenue with 24,500 active users. ARPU = 1,250 /24,500 = 0,051 Eur per user, or 5.1 Ct per user.

Market examples of ARPU may vary strongly over sectors as well as for individual companies. They start with 4 Ct per user for ‘simple’ app, for e-commerce stores may be as high as 100-300 USD. Facebook for example reported 2019 an ARPU of 29.25 USD. Additional industry examples can be found at Statista.

## Gross Margin & Revenue-Specific Margins

### What does Gross Margin (GM) mean?

Gross Margin is the revenue that a company retains, contributed from one or many revenue streams after direct expenses associated with those revenue streams are covered. The Gross Margin (GM) value can be calculated by the following general formula:

GM = TR – COGS

Often the %-value for the Gross Margins is used:

GM% = frac{TR – COGS}{TR}

Where:
TR stands for Total Revenue and is the sum of all revenue streams
COGS stands for Cost of Goods Sold and refers to all direct costs associated with manufacturing or reselling, packaging and delivering a product.

In traditional businesses, where physical goods are purchased by a one-time deal, the COGS value is rather easy to calculate. Simply add up the costs of the product, of packaging, and of delivery.

In subscription businesses (and service-related businesses), the traditional concept of COGS runs into the limit of its applicability and needs to be broadened towards a more general ‘Cost of Revenue’ framework.

### Total Revenue for Subscription Businesses

The revenue for subscription-based businesses consists typically of the following components:

TR = text{Recurring Revenue + Service Revenue + Other Revenues}

Where:
Recurring Revenue originates from the subscription fees
Service Revenue covers revenues from services provided on top of the subscription fee, such as individualization and customer-specific projects
Other Revenues sum up the remaining revenue streams from other business activities.

Note that if other types of revenues, such as transactional revenue or hardware revenue, are of significant importance, they should be categorized separately in the revenue listing.

### Cost of Goods Sold and Gross Margin for SaaS Businesses

For a subscription software company, or more generally speaking for a subscription service provider not connected with the delivery of physical goods, it can be challenging to determine which costs are to be included in the COGS. In this type of businesses, COGS is sometimes referred to as Cost of Revenue, which is a more suitable term capturing the essence of these costs.
Ask yourself the following question to determin which costs should be included into COGS:

‘If I don’t pay these costs, will I be able to provide my service to the client?’

If you don’t need to pay these costs for servicing your client, they should be included in other categories, like Opex, project costs or other. This means that upselling costs, internal administration costs and project costs should be excluded from COGS. For example, if an employee is active in both areas: customer support and upselling, his / her costs should be splitted accordingly.

Attention should also be paid to the software development costs: they should be included only on the level of amortizations for capitalized software development costs. In reality, many companies do not include them at all. In order to allow better benchmarking with competitors, you should calculate a COGS version without R&D amortization as well.

In a software subscription company the overall COGS consists typically of following elements:

COGS=
DevOps Costs, consisting of:
Hosting & Server Costs
3rd party software costs and royalties
R&D amortizations for capitalized SW dev.costs
Support and onboarding costs
Customer Success Management (CSM)
Service costs

In the next step we can further refine the calculations and obtain a more precise insight into the Gross Margin components. This can be done by grouping the revenues and the corresponding cost-to-revenue specific Gross Margins:

Typical value for SaaS businesses are Total Gross Margin ~70% (see the KeyBanc’s SaaS Survey 2019 for the median value of 73%) and Recurring Gross Margin about 75-90% (see the KeyBanc’s SaaS Survey 2019 for the median value of 78%).

### Gross Margin for Box Subscription Businesses

For box subscription businesses or more general subscription businesses related to physical goods delivery, the main differences are in the elements of GOCS. In case of box subscription businesses, it is favorable to group the individual elements into the following groups (see also the corresponding graphics):

COGS=
Product Costs
Fulfillment Costs

A real word example for the Gross Margin value of a box subscription company is HelloFresh, a German based food box delivery service. Acccording to its published data, it reports a Gross Margin of 20.3% in Q1/17 and 22.1% in Q2/17. The Gross Margin value of this type of businesses clearly varies more than that of SaaS businesses.