
Making critical product decisions when your company is on a streak.

If most users pay nothing and software has almost no marginal production cost, what counts as a unit?
For a retention feature, the economic unit can be a subscriber-month.
| Input | Assumption |
|---|---|
| Fixed engineering cost | $5,000,000 |
| Monthly contribution | $6 |
| Monthly churn | 5% |
| Expected lifetime | 20 months |
Expected lifetime uses the steady-state approximation \(1/c\).
\[ L = \frac{1}{c} = \frac{1}{0.05} = 20 \]
\[ CLV = m \times L \]
\[ CLV = \$6 \times 20 = \$120 \]
\[ \text{Breakeven subscriber-months} = \frac{\$5{,}000{,}000}{\$6} = \mathbf{833{,}333\ \text{subscriber-months}} \]
What is a subscriber-month?
The feature postpones cancellation for exactly one month.
\[ \text{Value} = \mathbf{\$6} \]
The customer remains and again faces the normal 5% monthly churn rate.
\[ \text{Value} = \mathbf{\$120} \]
If a prevented cancellation restores the full expected remaining life:
\[ \text{Breakeven subscribers} = \frac{\$5{,}000{,}000}{\$120} = \mathbf{41{,}667} \]
This result is a shorthand for 41,667 customers × 20 months × $6.
Duolingo reported 8 million paid subscribers at the end of Q2 2024.
If the feature affects all 8 million:
\[ \frac{833{,}333\ \text{months}}{8{,}000{,}000\ \text{subscribers}} = 0.104\ \text{month per subscriber} \]
\[ 20.000 + 0.104 = 20.104\ \text{months} \]
\[ c_{new}=\frac{1}{20.104}=\mathbf{4.974\%} \]
Breakeven requires monthly churn to fall from 5.000% to about 4.974%.
The feature must create 833,333 additional subscriber-months.
| Subscribers affected | Added life needed per subscriber |
|---|---|
| 800,000 | 1.042 months |
| 2,000,000 | 0.417 months |
| 4,000,000 | 0.208 months |
| 8,000,000 | 0.104 months |
\[ \text{Added life needed} = \frac{833{,}333\text{ subscriber-months}} {\text{subscribers affected}} \]
What would Duolingo need to believe before committing $5 million?