Customer Lifetime Value

The last lesson handed us a retention curve — a decaying line showing how many of a cohort survive each month. This lesson collapses that whole curve into one number: the dollar value of a single customer across their entire life. We met a rough version of it back in unit economics as LTV (lifetime value — the total gross profit a customer generates before they cancel), the thing that, divided by CAC (customer acquisition cost), must stay above 3× for a healthy SaaS business.

But that LTV number has a hidden assumption baked in: it treats a dollar received two years from now as identical to a dollar in your pocket today. That is not how money works. This lesson fixes that.

Recap: the simple LTV formula

Start with the numbers from unit economics.

ARPU (average revenue per user — the average monthly subscription fee per customer) is $40. Gross margin (revenue minus the direct cost of delivering the service, expressed as a percentage of revenue) is 75%. So the monthly gross profit per customer — the amount left after paying for servers, support, and other variable costs — is:

monthly gross profit = ARPU x gross margin = $40 x 0.75 = $30

Churn (the fraction of customers who cancel each month) is 4%, meaning 96% stay — the retention rate (1 minus churn). If 4% of customers leave every month, the average customer lasts:

average lifetime = 1 / churn = 1 / 0.04 = 25 months

Multiply by monthly gross profit:

simple LTV = $30 x 25 months = $750

Mathematically this is a geometric series: $30 + $30 x 0.96 + $30 x 0.96^2 + ... which sums to $30 / 0.04 = $750. This formula assumes the customer could stay forever, which is why it is the optimistic ceiling.

Why that $750 is too high

Reason 1 — finite horizon

No business plans around receiving cash forever. A 24-month window is common in SaaS. Stopping at 24 months means we only sum the first 24 terms of that geometric series, so the result is smaller than $750.

Reason 2 — the time value of money (discounting)

A discount rate reflects the fact that money received in the future is worth less than the same amount today, for two reasons: risk (the customer might churn or the company might fold before that cash arrives) and opportunity cost (a dollar today can be invested and earn a return).

Applying a monthly discount rate of 1% means we multiply each future month’s cash flow by 1 / (1 + 0.01)^t, where t is the number of months from now. Month 0 (today) gets multiplied by 1. Month 1 gets multiplied by 1 / 1.01 ≈ 0.99. Month 12 gets multiplied by 1 / 1.01^12 ≈ 0.89. The cash flows shrink faster than retention alone would shrink them, so discounted LTV is lower still.

The present-value formula for each month’s contribution is:

month t contribution = monthly_gp x retention^t x (1 / (1 + r))^t

Summing over 24 months gives the discounted (present-value) LTV — what those future cash flows are worth in today’s dollars.

Three LTV numbers side by side

churn = 0.04
monthly_gp = 30.0
retention = 1 - churn      # 0.96 stay each month
r = 0.01                   # monthly discount rate (1%)

# 1. simple LTV: infinite horizon, no discounting
simple = monthly_gp / churn

# 2. finite LTV: 24-month horizon, no discounting
finite = sum(monthly_gp * retention**t for t in range(24))

# 3. discounted LTV: 24-month horizon, present-value cash flows
discounted = sum(monthly_gp * (retention**t) * (1/(1+r))**t for t in range(24))

print("simple LTV (infinite)   : $" + f"{simple:,.0f}")
print("finite LTV (24 months)  : $" + f"{finite:,.0f}")
print("discounted LTV (PV, 24m): $" + f"{discounted:,.0f}")

simple LTV (infinite)   : $750
finite LTV (24 months)  : $468
discounted LTV (PV, 24m): $427

The ranking is always discounted < finite < simple. Cutting off at 24 months drops LTV from $750 to $468 — we lose 40 months of tail revenue. Discounting those 24 months further to present value drops it again to $427. The $750 headline was never real; it was an accounting convenience.

What this means for your CAC budget

The 3× rule from unit economics says: keep CAC under one-third of LTV. Apply it to each number:

simple LTV $750    -> CAC budget < $250
finite LTV $468    -> CAC budget < $156
discounted LTV $427 -> CAC budget < $142

Which LTV you trust determines how much you will spend to acquire a customer. A team anchored to the $750 figure might spend $200 per customer and feel safe. A team using the discounted $427 figure caps spending at $142. The more conservative number is also the more honest one — it accounts for the fact that late cash flows may never arrive, and even if they do, they are worth less than early ones.

The decision rule is the same whatever method you use: keep CAC well under LTV. A more realistic LTV simply forces a more realistic CAC cap, which is the whole point.

Visualizing the decay

Each bar below is one month’s contribution to LTV. Retention alone makes the bars shrink left to right (fewer customers survive each month); discounting shrinks them a little faster still, because far-future dollars are deflated.

The early months dominate month for month — each one contributes more than any later month. Cumulatively, months 0–5 make up about a third of the total (34.8% of finite LTV, 37.3% of discounted); it takes roughly the first year to pass half. That front-loading is why churn in the first six months is so damaging — you lose the biggest contributions before anything has had time to accumulate.

Summary

The $750 number is useful as a back-of-envelope ceiling. The $427 number is the more defensible figure to use when setting a CAC budget.

In one breath

The simple LTV = monthly gross profit ÷ churn = $750 is the optimistic ceiling: it sums an infinite, undiscounted stream of cash. Two corrections bring it down to earth. Cap it at a realistic horizon (24 months) and it drops to $468 — you stop counting a tail you’ll never bank. Then discount each future month by 1/(1+r)ᵗ, because future money is worth less than today’s (risk + opportunity cost), and it falls again to $427. The ranking is always discounted < finite < simple, and early months dominate — which is exactly why first-six-month churn hurts most. Whichever number you trust sets your CAC ceiling via the 3× rule ($750 → $250, $427 → $142); the conservative figure is the honest one.

Practice

A question to carry forward

Look closely at what we just did. That $427 is an expected value — it already bakes in uncertainty. We didn’t claim each customer stays exactly 24 months; we weighted each future month by the probability they’re still around (retention) and by what that money is worth (discounting), then summed. CLV is a probability-weighted forecast wearing a dollar sign.

That same move — weighting each possible outcome by its probability and adding them up — is the engine behind almost every business decision made under uncertainty, not just customer value. So the question to carry forward is: how do you choose between options when you can’t know the outcome in advance — launch or wait, build or buy, settle or fight? That closes out the customer-analytics chapter and opens the next one, Decision Analysis, beginning with expected value: the single tool that turns a fog of probabilities into one comparable number per choice.