The Growth Equation: How Many New Customers Do You Really Need?

We've seen when customers leave, and that lesson from our first look at survival analysis is clear: churn is inevitable. The foundational question then becomes:

How many new customers do you need to bring in today to replace those lost and hit your growth goals?

But for businesses with limited resources, a deeper, more strategic question emerges: What is the most cost-effective blend of acquisition channels to secure those new customers?

The answer to this blending challenge shapes your budget, your marketing plan, and your team's focus for the year. Answering it with precision separates reactive businesses from those that execute with intention.

Coins balanced on a spoon above a calculator and paperwork, symbolizing customer acquisition cost and optimized growth strategy.

Eight Core Metrics That Drive Your Bottom Line

Most recurring revenue businesses (SaaS, platforms, memberships) track churn and acquisition on a monthly basis. Using a monthly period offers faster feedback loops and helps spot problems or opportunities earlier than annual tracking would. For this post, the baseline is one month, and we measure growth and churn Month over Month (MoM).

Why Monthly Matters: Quick feedback stops small leaks before they sink your ship.

For a business with 1,000 customers at period start and a 2% monthly churn rate, aiming for 0.8%, growth looks like this:

Metric	What it means	Example Calculation	Units	Why it Matters
Starting Customers (S)	Number of customers at period start	1,000	customers	Your growth baseline
New Customers Acquired (N)	Number of new customers added during period	28	customers	How fast you are accelerating
Customers Lost (L)	Number of customers lost during period	20	customers	Your biggest hidden costs
Ending Customers (E)	Ending Customers = S + N - L	1,008	customers	Your growth at the end of the period
Churn Rate (CR)	Churn Rate = L ÷ S	20 ÷ 1,000 = 2%	%/month	Measures retention health
Growth Rate (GR)	Growth Rate = (E - S) ÷ S	(1,008-1,000)/1,000 = 0.8%	%/month	Tracks true next expansion
Customer Acquisition Cost (CAC)	CAC = Total Sales & Marketing Expenses ÷ N	$5,600 ÷ 28 = $200	$/customer	Your effeciency per win
Average Revenue per Account (ARPA)	ARPA = Total Revenue ÷ E	$25,200 ÷ 1,008 = $25	$/month	Revenue potential per account

Spotlight on Month-by-Month Dynamics

Here's how that 2% churn and the target of 28 new customers play out over time. Notice that as your customer base grows, your churn in absolute numbers also increases, requiring slightly more new customers just to maintain the same growth rate.

Month	Customers at the Start of the Month	Churned	Target Customers at the End of the Month	Required New Customers
1	1000	20	1008	28
2	1008	20	1016	28
3	1016	20	1024	28
4	1024	20	1032	28
5	1032	21	1040	29
6	1040	21	1048	29

This approach focuses attention on the practical levers under control: customer engagement, retention, and sales. You can intuitively sense the interplay by plotting these numbers, either in Excel, Google Sheets, or Python.

The chart below visualizes the target growth line (what's needed to hit the goal) against a churn-only projection (what happens if acquisition lags - your nightmare scenario).

How to Optimize Every Single Dollar Budget—The Smart Way

With a finite budget and multiple channels—each with varying costs (CAC) and capacity limits—the strategic problem is squeezing maximum growth from every dollar. This immediately transitions the conversation from budgeting to solving an optimization challenge.

We must elevate the challenge:

Stop asking the baseline question, "How many new customers do we need?"

Start asking the strategic question: "What is the most cost-effective blend of acquisition channels to achieve our growth target within our operational constraints?"

This scenario is perfectly modeled as a blending problem. The mathematical tool best suited to provide the precise solution is Mixed-Integer Linear Programming (MILP). This technique ensures that your resource allocation is intentional and mathematically maximized.

You seek to maintain monthly customer growth (say, 0.8% MoM) with limited resources:

• Objective: Hit or exceed a target Ending Customers count for the month at minimum cost.

• Decision Variables: How many customers to acquire via each channel (Social, Paid, Outbound, Referral).

• Constraints:

  • Budget ceiling for acquisition.

  • Maximum new customers available per channel.

  • Each channel’s unique Customer Acquisition Cost (CAC).

  • At least X% of new customers from segments with lower churn (e.g., annual plans, high-LTV industries).

  • Subscription level mix (e.g., at least 30% must be on mid-tier plans and above).

Try This: Optimizing Your Customer Acquisition Mix

💡 Note on Attribution Simplification:

This example simplifies customer acquisition cost by assigning each channel a single fixed CAC. In real-world scenarios, multi-touch attribution models allocate credit across multiple marketing touchpoints influencing a customer’s journey. Our focus here is on illustrating the core MILP optimization concept clearly. Readers looking to analyze more complex attribution should consider dedicated multi-touch attribution frameworks alongside optimization.

Let's step into your shoes. You want a practical way to allocate your customer acquisition budget across channels, hitting your growth target while respecting constraints.

Your Turn:

Plug these numbers into Google Sheets or Excel—and watch Solver reveal your cheapest path to 28 new customers.

• Your growth target: Acquire 28 new customers this month to net 0.8% growth (from previous table).

• Budget ceiling: $4,000 total for new customer acquisition this month.

• Minimum referral customers (low churn segment): At least 20% of new customers should come via Referral.

• Channels available:

Channel	Max New Customers Based on Trend	CAC ($/customer)
Paid	15	250
Social	10	150
Referral	10	50
Outbound	5	100

Let's set this up in Google Sheets or Microsoft Excel (spreadsheet).

Solve, and view the optimal allocation of new customers by channel.

This is a blending model. You have different ingredients (customer acquisition channels) with unique costs (CAC) and availability (max customers per channel). The goal is to create the optimal recipe with the right mix of channels to meet a specific production target (your new customer goal) at the lowest possible cost.

Each channel represents a decision variable in your growth equation. By modeling these variables, you move from reactive spending to a data-driven acquisition strategy. This approach makes trade-offs explicit and aligns marketing, sales, and finance around a single, optimized plan.

Next Up

This post only addresses one part of the growth equation. The most durable businesses build a system that retains customers with the same precision used to acquire them. Next time, we will extend this quantitative approach to the art of retention.

Need help getting these numbers and plans in place?

Growth is too critical to leave to chance. Schedule a free consultation using coupon code OPTIMIZEGROWTH.

Get Your Smart Budget Plan Today