subscriptions.ltv-cac

export function ltvCac(arpa: Money, grossMarginBasisPoints: number, monthlyChurnBasisPoints: number, cac: Money): LtvCac

/** Unit economics for one average customer. */
export interface LtvCac {
  /** ARPA x gross margin / monthly churn, rounded half-up; null when churn is 0 */
  readonly ltv: Money | null;
  /** LTV / CAC, rounded half-up; 30000 is 3x; null when churn or CAC is 0 */
  readonly ltvToCacBasisPoints: number | null;
  /** CAC / (ARPA x gross margin), rounded up to whole months; null when ARPA x margin is 0 */
  readonly paybackMonths: number | null;
}

import { ltvCac } from "#fune/subscriptions.ltv-cac@^1";

import { roundDiv } from "./math_round_div.ts";  ← from math.round-div ^1.0.0 · built alongside by fune
import { type Money, assertSameCurrency, money } from "./money_amount.ts";  ← from money.amount ^1.0.0 · built alongside by fune
import { type LtvCac } from "./subscriptions_ltv_cac_types.ts";

const MAX_EXACT = 9007199254740991;

function checkRate(name: string, value: number): void {
  if (!Number.isInteger(value) || value < 0 || value > 10000) {
    throw new RangeError(`${name} must be between 0 and 10000, received ${value}`);
  }
}

/**
 * LTV, LTV:CAC and CAC payback, each computed as one exact division from the
 * inputs so no figure inherits another's rounding.
 */
export function ltvCac(arpa: Money, grossMarginBasisPoints: number, monthlyChurnBasisPoints: number, cac: Money): LtvCac {
  assertSameCurrency(arpa, cac);
  if (arpa.minor < 0 || cac.minor < 0) {
    throw new RangeError(`ARPA and CAC must not be negative, received ${arpa.minor} and ${cac.minor}`);
  }
  checkRate("gross margin basis points", grossMarginBasisPoints);
  checkRate("monthly churn basis points", monthlyChurnBasisPoints);
  // Monthly margin per account, in minor units x 10000.
  const margin = arpa.minor * grossMarginBasisPoints;
  if (margin * 10000 > MAX_EXACT || cac.minor * 10000 > MAX_EXACT || monthlyChurnBasisPoints * cac.minor > MAX_EXACT) {
    throw new RangeError("amounts too large for exact arithmetic (2^53 - 1)");
  }
  const churn = monthlyChurnBasisPoints;
  return {
    ltv: churn === 0 ? null : money(roundDiv(margin, churn, "half-up"), arpa.currency),
    ltvToCacBasisPoints: churn === 0 || cac.minor === 0 ? null : roundDiv(margin * 10000, churn * cac.minor, "half-up"),
    paybackMonths: margin === 0 ? null : roundDiv(cac.minor * 10000, margin, "up"),
  };
}

Install

fune build

With that line in your source, in a TypeScript project (language typescript in fune.project), fune build resolves it and its 2 dependencies, pins them in fune.lock, downloads only the TypeScript package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. Or pin a range in fune.project and build in one step:

fune add subscriptions.ltv-cac

The manifest, vectors and README with only the TypeScript implementation. Install it without the registry with fune add ./subscriptions.ltv-cac-1.0.0-typescript.fune, or fetch it from a terminal with fune pull subscriptions.ltv-cac@1.0.0:typescript.

The whole function, every language, is one file too: subscriptions.ltv-cac-1.0.0.fune, 14,952 bytes, sha256 725964865268be00d902a309ce0d11889e068dda8249a82b4d7074e26c23c6ae. It installs into a project of any language.

// fune: before subscriptions.ltv-cac

// fune: after subscriptions.ltv-cac

// fune: replace math.round-div in subscriptions.ltv-cac
// fune: replace money.amount in subscriptions.ltv-cac

// fune: step subscriptions.ltv-cac after <n|label>

More from the author

LTV is ChartMogul's published formula ("LTV = ARPA x Gross Margin / Customer Churn Rate"): a customer who pays ARPA a month and churns with probability c each month stays 1/c months on average, and only the gross margin of what they pay is value. CAC payback is the usual gross-margin-adjusted form: how many months of margin it takes to earn back what it cost to win the customer. With ARPA 100.00, an 80% margin, 2.5% monthly churn and CAC 1,200.00, LTV is 3,200.00, the ratio is 2.67x and payback is 15 months.

Rounding. Each figure is one exact integer division from the inputs, never built from another rounded figure: LTV is rounded half-up to the minor unit, the ratio half-up to a basis point (30000 is 3x, the common target), and payback is rounded up to whole months, because a customer who has paid back 12.5 months of CAC has not paid it back after 12.

Zeroes are answers, not errors. With no churn the simple formula has no finite lifetime, so LTV and the ratio are null; with no CAC the ratio is null and payback is 0 months; with no margin (or no revenue) payback is null, because it never happens.

The formula assumes churn is constant over a customer's life, which in practice overstates LTV: churn is usually highest in the first months. Use monthly figures for all three rates; for annual churn, convert first.

Errors: a negative ARPA or CAC, rates outside 0 to 10000, amounts in different currencies, and inputs so large the intermediate products leave the exact integer range (2^53 - 1) that all three languages share.

Sources: ChartMogul, "Customer Lifetime Value (LTV)", https://chartmogul.com/saas-metrics/ltv/ (formula and LTV:CAC ratio).

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