Business Math Series
Master the numbers that drive business success.
Most businesses fail not because they lack a good product, but because they don’t understand their numbers. This series demystifies the critical financial metrics, formulas, and frameworks that every entrepreneur, product manager, and business leader needs to know.
What makes this series different:
- Real-world examples from companies like Spotify, Netflix, Amazon, and WeWork
- Practical formulas with step-by-step breakdowns
- Visual explanations using diagrams and charts
- Calculator templates you can use for your own business
- Industry benchmarks to measure against
- Learn when to optimize for growth vs. profit
Who This Series is For
✅ Founders & Entrepreneurs — Understand if your business model is sustainable before you scale
✅ Product Managers — Make data-driven decisions about features, pricing, and growth
✅ Marketers — Calculate CAC, ROAS, and prove marketing ROI
✅ Finance & Strategy Teams — Deep dive into unit economics and profitability analysis
✅ Investors & Analysts — Evaluate businesses using the right metrics
✅ Anyone building or evaluating a business — Learn the language of business economics
Series Contents
1. Customer Economics: The LTV/CAC Framework That Predicts Success
What You’ll Learn:
- Customer Acquisition Cost (CAC) — by channel, cohort, and time period
- Lifetime Value (LTV) — simple and advanced formulas
- LTV:CAC ratio and what it really means
- Payback period — when you break even on a customer
- Churn rate (monthly vs annual, logo vs revenue)
- Cohort retention analysis
- Magic Number (SaaS efficiency)
- Negative churn and expansion revenue
Key Takeaway: Learn how to calculate whether acquiring customers will make or lose you money — before you spend millions on growth.
Real Examples: Spotify, Netflix, Dollar Shave Club, Slack
2. Profitability Metrics: Beyond ‘Are We Making Money?’
What You’ll Learn:
- Gross Margin vs Contribution Margin vs Operating Margin vs Net Margin
- EBITDA, EBIT, and why they matter
- Unit Economics at scale
- Rule of 40 (Growth% + Profit Margin%)
- Revenue per employee (RPE)
- When to optimize for growth vs profit
- Why profitable companies still fail
- When margins lie (Amazon’s 3% net margin but 26% ROIC)
Key Takeaway: Understand the hierarchy of profitability metrics and learn when low margins are acceptable vs. when they signal a broken business.
Real Examples: WeWork, Amazon, Shopify, Uber
3. Cash Flow & Financial Health: The Metrics That Keep You Alive
What You’ll Learn:
- Burn rate (gross vs net) and runway calculation
- Cash conversion cycle and working capital
- Operating cash flow vs profit
- Why profitable companies go bankrupt
- Cash flow forecasting
- Days Sales Outstanding (DSO) and Days Payable Outstanding (DPO)
- The growth trap: why faster growth can mean faster death
- Building cash flow resilience
Key Takeaway: Profit is accounting, cash flow is survival. Learn why profitable companies still fail and how to ensure you have enough cash to reach your goals.
Real Examples: Fast-growing SaaS company bankruptcy, Amazon’s negative cash conversion cycle, seasonal businesses
4. Growth Metrics: Viral Loops, Retention & Sales Efficiency
What You’ll Learn:
- Viral Coefficient (K-factor) — when K > 1, exponential growth
- Network effects quantified
- DAU/MAU ratio (stickiness metric)
- Net Revenue Retention (NRR) — the SaaS gold standard
- Gross Revenue Retention (GRR)
- Sales efficiency metrics (Magic Number)
- Lead Velocity Rate (LVR)
- Activation and engagement metrics
- Cohort analysis framework
Key Takeaway: Learn how Dropbox achieved 4000% growth by getting their viral coefficient above 1, and discover the retention metrics that separate world-class companies from the rest.
Real Examples: Dropbox’s referral program, Slack’s 93% DAU/MAU, Snowflake’s 158% NRR
5. Valuation & Investment Math: ROI, ROIC, and Returns That Matter
What You’ll Learn:
- NPV (Net Present Value) — the king of investment decisions
- IRR (Internal Rate of Return) — percentage returns
- ROIC (Return on Invested Capital) — operational efficiency
- ROE, ROA, ROI — when each metric matters
- Company valuation multiples (revenue vs EBITDA)
- Discounted cash flow (DCF) basics
- Capital efficiency and why it matters more than profit margin
- Cap table math and how dilution works
- Investment decision frameworks
Key Takeaway: Understand why Facebook paid $19B for WhatsApp, how Amazon achieves 26% ROIC with 3% margins, and learn the investment math that separates great acquisitions from terrible ones.
Real Examples: WhatsApp acquisition, Amazon’s capital efficiency, Instagram’s $1B exit that became worth $100B+
6. Industry-Specific Metrics: SaaS, E-commerce & Marketplaces
What You’ll Learn:
- SaaS: Quick Ratio, NRR, GRR, Expansion MRR, Magic Number
- E-commerce: AOV, Cart Abandonment, Repeat Rate, Conversion Funnel, Channel CAC
- Marketplace: Take Rate, GMV vs Revenue, Liquidity, Network Density, Supply/Demand Ratio
- What “good” looks like in each model (comprehensive benchmarks)
- When to track what metrics by stage
- Industry-specific red flags and warning signs
- Your metrics dashboard by business stage
Key Takeaway: Same metrics mean different things in different industries. A 70% gross margin is amazing for e-commerce but concerning for SaaS. Learn the benchmarks and metrics that matter for YOUR business model.
Real Examples: Uber’s 20-25% take rate vs eBay’s 10%, Airbnb’s liquidity metrics, DoorDash’s supply/demand balancing
Core Philosophy
1. Math Over Intuition
Business intuition is valuable, but metrics don’t lie. This series teaches you to:
- Measure what matters
- Calculate before you scale
- Predict outcomes with data
2. Unit Economics First
Before you worry about total revenue or valuation:
- Do you make money on each customer/transaction?
- What are your contribution margins?
- Can you profitably acquire customers?
If unit economics don’t work, scaling makes the problem worse.
3. Context Matters
Every metric has context:
- A 3% net margin is terrible for SaaS, great for retail
- 50% growth is amazing for a mature company, slow for a startup
- 10% monthly churn is catastrophic for consumer, normal for SMB
Know your industry benchmarks.
4. Growth vs. Profit is a Choice
You can optimize for growth or profit, but rarely both simultaneously. This series teaches you:
- When to prioritize growth (large markets, winner-take-most dynamics)
- When to prioritize profit (mature markets, limited capital)
- How to measure the balance (Rule of 40)
Prerequisites
Math Level: Basic arithmetic and percentages (middle school math)
Business Knowledge: Helpful but not required — concepts are explained from first principles
Tools: Spreadsheet software (Excel, Google Sheets) for calculator templates
Learning Path
Beginner Track
- Start with Customer Economics — Learn the fundamentals of CAC and LTV
- Move to Profitability Metrics — Understand the margin hierarchy
- Practice with the calculator templates provided in each post
Intermediate Track
- Calculate your own business metrics using the formulas
- Compare against industry benchmarks
- Identify which metrics need improvement
Advanced Track
- Build cohort retention models
- Create financial projections using these metrics
- Design A/B tests to improve key ratios (LTV:CAC, margins, etc.)
Calculator Templates
Each post includes calculator templates you can download and customize for your business:
- LTV/CAC Calculator — Model different scenarios for customer economics
- Churn & Retention Analyzer — Track cohort performance over time
- Margin Hierarchy Calculator — Calculate gross, contribution, operating, and net margins
- Rule of 40 Dashboard — Track the growth/profit balance
Real-World Case Studies
Throughout the series, we analyze real companies:
Success Stories:
- Netflix — 12.5:1 LTV:CAC, 2.5% monthly churn, content moat
- Slack — 15:1 LTV:CAC, -8% net revenue churn, 93% DAU/MAU ratio
- Shopify — 30% growth + 15% margin = 45% Rule of 40
- Amazon — 3% net margin but 26% ROIC through capital efficiency and negative cash conversion cycle
- Dropbox — 4000% growth by achieving K > 1 with referral program
- Snowflake — 158% Net Revenue Retention, expansion revenue dominates
- WhatsApp — Facebook’s $19B acquisition that became worth $100B+
- Instagram — $1B exit with zero revenue, 100x return in 11 years
Cautionary Tales:
- WeWork — $47B valuation with negative unit economics
- Groupon — High revenue growth, negative contribution margins
- Quibi — $1.75B raised, shut down in 6 months, never fixed unit economics
- Profitable SaaS bankruptcy — $10M revenue, 20% margins, but ran out of cash due to payment timing
- Yahoo selling Alibaba early — Missed $38.9B by selling before full potential realized
- Many startups — Mistook revenue growth for business health
Key Formulas Quick Reference
Customer Economics
$$ \text{CAC} = \frac{\text{Sales & Marketing Spend}}{\text{New Customers}} $$
$$ \text{LTV} = \frac{\text{ARPU} \times \text{Gross Margin %}}{\text{Churn Rate}} $$
$$ \text{LTV:CAC Ratio} = \frac{\text{LTV}}{\text{CAC}} \quad \text{(Target: 3:1 to 4:1)} $$
$$ \text{Payback Period} = \frac{\text{CAC}}{\text{Monthly Revenue per Customer} \times \text{Gross Margin %}} $$
Profitability Metrics
$$ \text{Gross Margin} = \frac{\text{Revenue} - \text{COGS}}{\text{Revenue}} $$
$$ \text{Contribution Margin} = \frac{\text{Revenue} - \text{Variable Costs}}{\text{Revenue}} $$
$$ \text{Operating Margin} = \frac{\text{Operating Income}}{\text{Revenue}} $$
$$ \text{Net Margin} = \frac{\text{Net Income}}{\text{Revenue}} $$
$$ \text{Rule of 40} = \text{Growth %} + \text{Profit Margin %} \quad \text{(Target: ≥ 40%)} $$
Cash Flow Metrics
$$ \text{Burn Rate} = \frac{\text{Cash Spent in Period}}{\text{Time Period}} $$
$$ \text{Runway (months)} = \frac{\text{Cash Balance}}{\text{Monthly Burn Rate}} $$
$$ \text{Cash Conversion Cycle} = \text{DIO} + \text{DSO} - \text{DPO} $$
Growth Metrics
$$ \text{Viral Coefficient (K)} = \text{Invites per User} \times \text{Conversion Rate} $$
$$ \text{NRR} = \frac{\text{Starting MRR} + \text{Expansion} - \text{Churn} - \text{Contraction}}{\text{Starting MRR}} $$
$$ \text{DAU/MAU Ratio} = \frac{\text{Daily Active Users}}{\text{Monthly Active Users}} \quad \text{(Stickiness)} $$
$$ \text{Quick Ratio} = \frac{\text{New MRR} + \text{Expansion MRR}}{\text{Churned MRR} + \text{Contraction MRR}} $$
Investment Metrics
$$ \text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t} - \text{Initial Investment} $$
$$ \text{ROIC} = \frac{\text{NOPAT}}{\text{Invested Capital}} \times 100% $$
$$ \text{ROE} = \frac{\text{Net Income}}{\text{Shareholders’ Equity}} \times 100% $$
Get Started
Begin with Customer Economics: The LTV/CAC Framework to master the most critical metrics for predicting business success.
Then progress through the series in order, or jump to the topic most relevant to your current challenges:
- Struggling with margins? → Profitability Metrics
- Running out of cash? → Cash Flow & Financial Health
- Want to accelerate growth? → Growth Metrics
- Evaluating investments? → Valuation & Investment Math
- Need industry benchmarks? → Industry-Specific Metrics
Remember: You can’t manage what you don’t measure. Let’s master the numbers together.
Feedback & Questions
Have questions about business metrics? Want to see a specific topic covered? Reach out via GitHub Issues or the contact page.
Happy calculating! 📊