The standard version, the five variants a data room will offer, and why the magic number and CAC payback are the same ratio.
The SaaS magic number is net new ARR in a quarter divided by sales and marketing spend in the previous quarter. On an illustrative company that added 3.0 million of ARR after spending 3.9 million on sales and marketing, the magic number is 0.77: each dollar of go-to-market spend bought 77 cents of new recurring revenue. The same quarter reads anywhere from 0.58 to 1.03 depending on the definition, so the definition matters more than the threshold.
Worked in full in The Growth Equity Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Growth investors use the magic number as a first screen of sales efficiency: is the company's next dollar of sales and marketing worth spending? It is quick to compute from a board pack, which is also why it is often computed inconsistently from one company to the next. The worked example below shows the standard version, the variants a data room will offer, and how the number connects to CAC payback.
| Quarter | Q0 | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|---|
| ARR at quarter end | 40.0 | 42.4 | 45.0 | 47.4 | 50.4 |
| GAAP revenue in quarter | 9.8 | 10.3 | 10.9 | 11.5 | 12.2 |
| Sales and marketing expense | 3.2 | 3.4 | 3.6 | 3.9 | 4.2 |
In Q4 the 3.0 million of net new ARR is made of 3.2 million from new customers and 0.8 million of expansion, less 1.0 million of churn. Gross margin is 75 per cent.
Magic number = (ARRq − ARRq−1) ÷ S&Mq−1
Revenue version = (revenueq − revenueq−1) × 4 ÷ S&Mq−1
Q4: (50.4 − 47.4) ÷ 3.9 = 3.0 ÷ 3.9 = 0.77. In Excel, with ARR in row 2 and S&M in row 4, quarters in columns B to F: =(F2-E2)/E4. The one-quarter lag is deliberate: spend in a quarter produces bookings in the next one. Use the company's actual sales cycle if it is much longer.
The revenue version is what you compute when the company does not report ARR: GAAP revenue rose 0.7 million in Q4, annualised to 2.8 million, over 3.9 million of S&M gives 0.72. It lags the ARR version because revenue recognises a new contract gradually.
| Definition | Numerator | Denominator | Magic number |
|---|---|---|---|
| Standard | Net new ARR, 3.0 | Prior-quarter S&M, 3.9 | 0.77 |
| Revenue-based | Revenue change × 4, 2.8 | Prior-quarter S&M, 3.9 | 0.72 |
| Same-quarter spend | Net new ARR, 3.0 | Current S&M, 4.2 | 0.71 |
| Gross-margin adjusted | Net new ARR × 75% | Prior-quarter S&M, 3.9 | 0.58 |
| Gross new ARR | New plus expansion, 4.0 | Prior-quarter S&M, 3.9 | 1.03 |
| Trailing four quarters | ARR Q4 less Q0, 10.4 | S&M Q0 to Q3, 14.1 | 0.74 |
Each version has a use. The gross new ARR version, 1.03, isolates the sales engine from churn, which is the customer success team's problem; it is the flattering number and the one most likely to appear in a management presentation. The gross-margin-adjusted version, 0.58, asks whether the spend is recovered in gross profit rather than revenue, which is what the investor ultimately cares about. The trailing four-quarter figure, 0.74, removes the seasonality that makes any single quarter noisy: here Q3 read 0.67 and Q2 0.76.
Rules of thumb often quoted put a magic number above 0.75 as a signal to spend more and below 0.5 as a signal to fix the engine before adding to it. They are conventions, not market data, and only meaningful on the standard definition. Always state which definition sits behind a number.
Turn the magic number upside down, adjust for margin and convert to months, and you get the CAC payback period: 12 ÷ (magic number × gross margin). On the standard figure, 12 ÷ (0.77 × 75%) = 20.8 months; on gross new ARR, 15.6 months. The two metrics should always tell the same story; if a deck shows a strong magic number and a long payback, one of them is on a different definition. CAC payback is worked in full in how to calculate CAC payback period.
Management proposes raising quarterly S&M from the current 4.2 million to 5.0 or 6.0 million. The magic number tells you what the next quarter has to deliver to justify it.
| Quarterly S&M | To hold 0.77 | To reach 1.0 |
|---|---|---|
| 4.2 | 3.23 | 4.20 |
| 5.0 | 3.85 | 5.00 |
| 6.0 | 4.62 | 6.00 |
At 6.0 million a quarter, holding efficiency means 4.62 million of net new ARR, 54 per cent more than the best quarter on record. Efficiency usually falls as spend rises, because the extra money goes to less productive channels and less experienced reps, so underwrite the plan on a lower number and test whether the return still works.
The common mistake is to compare magic numbers across companies without aligning the definition, or to use the current quarter's spend for a business whose sales cycle is two or three quarters long. A second is to divide by total S&M including brand and customer success spend for one company and by sales headcount cost only for another. Fix the numerator (net new ARR), the denominator (total S&M, prior quarter) and the window (trailing four quarters) before comparing anything. The related efficiency measure that uses cash burn rather than S&M is in how to calculate the burn multiple.
Compute the standard magic number, then show the gross new ARR and gross-margin-adjusted versions beside it, and the trailing four-quarter figure as the one to underwrite. Together they tell you whether growth is bought efficiently and whether churn is eating the sales engine's work. The return arithmetic that sits on top of these metrics is in the free workbook for this case.
A commonly quoted convention treats a magic number above 0.75 as a signal to invest more in sales and marketing and below 0.5 as a signal to fix efficiency first. These are rules of thumb, not market data. The illustrative company scores 0.77 on the standard definition, 0.74 over four quarters, which would sit just around the upper threshold.
ARR where the company reports it, because it captures a new contract in full in the quarter it is signed. The revenue version multiplies the quarterly change in GAAP revenue by four and lags behind: in the illustrative quarter it gives 0.72 against 0.77 on ARR, since revenue rose only 0.7 million while ARR rose 3.0 million.
They are the same ratio inverted. CAC payback in months equals 12 divided by the magic number times gross margin. A magic number of 0.77 at a 75 per cent gross margin is a 20.8-month payback; on gross new ARR, 1.03 corresponds to 15.6 months. If the two metrics disagree in a deck, they are on different definitions.
This article is one calculation from The Growth Equity Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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