The 6.67-Month Line That Decides the Business

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada 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.

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 cohort 1,000 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 cohort 1,000 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.

Every number above is taken from the chapter’s own material and re-derived step by step.