The 6.67-Month Line That Decides the Business
The 6.67-Month Line That Decides the Business
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
The 6.67-Month Line That Decides the Business
A firm gives away a $40 tracker and earns just $6/month in margin, so the device loses money until that subsidy is repaid. The chapter runs two 1,000-device cohorts past the same payback point — one stays 24 months and nets $104, the other churns at 4 months and loses $16 — and concludes that churn alone flips the business from profit to loss. So where exactly is the break-even line that decides it, and which side does each cohort sit on?
Companion to the chapter Asset Tracking Unit Economics Contracts — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is customer life. The middle card applies the page rule. The green card is unit contribution. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 24 months.
- 2
Name the relationship. contribution = months x 6 USD/month - 40 USD subsidy
- 3
Substitute with units. 24 x 6 - 40 = 104.00 USD
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change customer life
Try Predict the direction of contribution = months x 6 USD/month - 40 USD subsidy. Test another customer life, then compare unit contribution.
Observe A device earns only after customer life crosses the 6.67-month break-even line. Reset customer life to 24 and compare unit contribution.
Explain A device earns only after customer life crosses the 6.67-month break-even line.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Ada: The chapter says churn “flips the business from profit to loss,” and there is an exact line hiding behind the phrase “about 7 months” — every device in both cohorts sits either above it or below it. Let me find that line and price both cohorts against it.
Start with the payback, carried to full precision:
$40 / $6 = 6.67 months(the chapter rounds up to about 7)
That 6.67 is not merely a payback figure; it is the break-even retention threshold. A subscriber who leaves before month 6.67 has not repaid the subsidy, and one who stays past it begins to earn. Now price the two 1,000-device cohorts against that line:
- Cohort A stays 24 months, comfortably past 6.67: per device
24 x $6 - $40 = 144 - 40 = +$104; across the cohort1,000 x 104 = +$104,000. - Cohort B churns at 4 months, short of 6.67: per device
4 x $6 - $40 = 24 - 40 = -$16; across the cohort1,000 x (-16) = -$16,000.
Same $40 subsidy, same $6 margin, same 1,000 units — the only thing that changed is whether the average life cleared the 6.67-month bar, and that single fact swings the cohort result by 104,000 - (-16,000) = $120,000.
The design lesson follows directly: because the whole model pivots on one break-even line, the levers worth pulling are the ones that move a customer across it — a minimum-term contract that guarantees at least seven billed months, a smaller subsidy that lowers the bar, or longer device life that raises the odds of reaching it. Headline activation growth is the one number that cannot help, because it counts devices on both sides of the 6.67-month line as if they were the same.
The break-even model deliberately does not simulate discounting, support and cloud cost, returns, cohort-varying churn, payment failure, tax, or hardware replacement; margin is a fixed six dollars per billed month.
Work the audit first, then check the displayed derivation.
Every number above is taken from the chapter’s own material and re-derived step by step.