The 2.2:1 Ratio That Fails the Gate

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

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ADA · CALCULATION AUDIT

The 2.2:1 Ratio That Fails the Gate

A B2B IoT vendor spends $30,800 to win each new customer, then earns $50,000 in hardware plus $12,000/year of SaaS over a five-year relationship. Run through the chapter’s 40% and 80% margins, that lifetime value works out to $68,000, for an LTV:CAC of 2.2:1 — and the golden rule demands at least 3:1. This audit re-derives every step to ask whether the ratio really falls short of the gate, and by how much.

Companion to the chapter Go-to-Market Strategy — 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 acquisition cost. The middle card applies the page rule. The green card is ltv to cac ratio. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Walk the arrows. A higher acquisition cost pushes the ratio farther below the three-to-one gate.

Derive the baseline in four named moves

1
Name the input. The chapter baseline is 30800 USD.
2
Name the relationship. ratio = 68,000 USD lifetime value / CAC
3
Substitute with units. 68,000 / 30,800 = 2.21 times
4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change customer acquisition cost

Try Predict the direction of ratio = 68,000 USD lifetime value / CAC. Test another customer acquisition cost, then compare ltv to cac ratio.

Observe A higher acquisition cost pushes the ratio farther below the three-to-one gate. Reset customer acquisition cost to 30800 and compare ltv to cac ratio.

Explain A higher acquisition cost pushes the ratio farther below the three-to-one gate.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only customer acquisition cost moves here. Field effects named in the technical boundary stay fixed.

TryTreat the $30,800 CAC, $50,000 hardware sale, $12,000 annual SaaS, and five-year relationship as the fixed case; press Check derivation.

ObserveThe gross-profit ledger produces a 2.2:1 LTV:CAC result, visibly below the chapter's 3:1 gate.

ExplainHardware and SaaS margins, not revenue alone, form LTV; dividing that gross profit by CAC explains why the apparently large contract still fails.

Ada: The chapter builds a customer-acquisition cost from a $1.54M sales-and-marketing budget, then tests it against a five-year lifetime value. The verdict – 2.2:1 – falls below the 3:1 gate, so every step deserves a check, because this ratio decides whether the model ships as priced.

CAC from the budget: 1,540,000 / 50 = 30,800 per new customer.
Hardware gross profit at 40% margin: 50,000 x 0.40 = 20,000.
SaaS gross profit at 80% over five years: 12,000 x 5 x 0.80 = 48,000.
Lifetime value: 20,000 + 48,000 = 68,000.
LTV:CAC: 68,000 / 30,800 = 2.2078, which rounds to 2.2:1.

Every step holds. The design meaning is that 2.2 sits below the 3.0 threshold by arithmetic, not by opinion: to clear the gate the team must lift LTV to at least 3 x 30,800 = 92,400 or cut CAC to at most 68,000 / 3 = 22,667 – which is precisely why the chapter’s three remedies (channel partners to lower CAC, higher pricing, or a longer customer lifetime) are the only levers that move this number.

Technical boundaries
Churn timing, discounting, adoption ramp, sales capacity, payback cash timing, tax, and support cost are excluded from this five-year gross-profit ratio.

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.