When mobile growth teams calculate payback periods for user acquisition campaigns, many simply divide customer acquisition cost (CAC) by the initial subscription price. This elementary approach fails to capture the intricate cashflow realities of the Apple App Store and Google Play ecosystems.
In mobile subscriptions, cash realization is constrained by platform commission schedules, local value-added taxes (VAT), currency conversion haircut rates, refund allowances, and non-linear cohort renewal attrition.
The Four Deductions From Gross Subscription Value
To model true cumulative revenue per install, you must apply four essential deductions to every gross transaction before attributing it to a cohort payback curve:
Store Commission Tiering: Apple and Google deduct 30% for standard developers, decreasing to 15% under the Small Business Program or after a subscriber completes 12 consecutive months of an active subscription. If your financial model assumes a flat 15% fee across all months, year-one cash receipts will be overprojected.
Regional Tax Withholding: App stores remit digital services taxes and local VAT directly in many jurisdictions before transferring payouts. In certain European and Asian markets, this can reduce gross revenue by 18% to 25% prior to commission calculation.
Platform Refund Reserve: Apple manages customer refund requests directly without requiring publisher authorization. Across typical subscription apps, refunds range between 3% and 7% of gross transaction volume, with spikes occurring following trial-to-paid auto-renewals.
Merchant Payout Timing Delay: Store payouts operate on net-30 or net-45 schedules. A subscription billed on Day 1 is not liquid cash until 30 to 60 days later, affecting the working capital cycle required to fund continuous marketing campaigns.
Constructing the Shifted Beta-Geometric (sBG) Decay Function
Rather than assuming a constant 5% monthly churn rate, mobile cohorts exhibit strong heterogeneity: customers who renew in month six are intrinsically less likely to churn in month seven than a first-time subscriber in month two.
The shifted beta-geometric distribution captures this sorting effect. The probability of a subscriber churning at period $t$, given they have survived up to period $t-1$, is expressed as:
$$P(T = t \mid \alpha, \beta) = \frac{B(\alpha + 1, \beta + t - 1)}{B(\alpha, \beta)}$$
Where $\alpha$ and $\beta$ represent the shape parameters of the underlying Beta distribution fitted to historical cohort renewal points.
Step-by-Step Payback Horizon Calculation
To determine whether an acquisition cohort achieves full payback by Day 180 (D180), evaluate the following cumulative equation:
$$\text{Net ARPU}(180) = \sum_{t=0}^{180} S(t) \cdot \left[ R(t) \cdot (1 - c(t)) \cdot (1 - r(t)) \right]$$
- $S(t)$: Proportion of initial cohort surviving at day $t$.
- $R(t)$: Gross billing event triggered at day $t$.
- $c(t)$: Platform commission and tax rate at day $t$.
- $r(t)$: Expected refund and chargeback rate for transactions at day $t$.
When $\text{Net ARPU}(180) \ge \text{CAC}$, the cohort achieves capital recovery within six months. Any model that ignores $c(t)$ and $r(t)$ will systematically underestimate the required time-to-breakeven, leading to aggressive overbidding on acquisition channels.