Pricing a Subscription Tier
A subscription language app has 10,000 paying users at $9 per month. Variable cost is $1.50 per user per month, and fixed costs are $40,000 per month. Monthly churn is 4% of active users, and the app currently adds 600 new subscribers per month. Management proposes raising the price to $12. A pilot suggests that at $12, 12% of existing users would cancel immediately, monthly churn among remaining users would stay at 4%, and new subscriber additions would fall 25% to 450 per month. Assume cancellations happen at the start of the month, churn applies to the surviving base, and new subscribers are added at month-end. Ignore taxes and acquisition costs. The finance lead wants a one-month comparison, not a long-run forecast, and asks whether the price increase raises contribution margin and operating profit. Contribution margin is revenue minus variable costs; operating profit subtracts fixed costs.
1. Calculate next month's ending subscriber count, contribution margin, and operating profit under the current $9 price.
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Current $9 plan:
- Start: 10,000.
- Churn: 4% × 10,000 = 400; survivors = 9,600.
- New subscribers: 600; ending = 10,200.
- Revenue: 10,200 × $9 = $91,800.
- Variable cost: 10,200 × $1.50 = $15,300.
- Contribution margin: $91,800 − $15,300 = $76,500.
- Operating profit: $76,500 − $40,000 = $36,500.
2. Calculate the same three figures under the proposed $12 price.
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Proposed $12 plan:
- Immediate cancellations: 12% × 10,000 = 1,200; survivors = 8,800.
- Churn: 4% × 8,800 = 352; survivors = 8,448.
- New subscribers: 450; ending = 8,898.
- Revenue: 8,898 × $12 = $106,776.
- Variable cost: 8,898 × $1.50 = $13,347.
- Contribution margin: $106,776 − $13,347 = $93,429.
- Operating profit: $93,429 − $40,000 = $53,429.
3. Should management raise the price based on this one-month analysis? Identify one risk that the calculation omits.
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On this one-month comparison, the price increase raises contribution margin by $93,429 − $76,500 = $16,929, and operating profit by the same amount. The break-even ending subscriber count at $12 is $76,500 / ($12 − $1.50) = 7,285.7. The plan produces 8,898, a cushion of about 1,612 subscribers. Equivalently, holding other assumptions, immediate cancellation would need to exceed about 29% before the contribution gain disappears: solve (10,000(1−c)×0.96)+450 = 7,285.7, giving c ≈ 28.8%. Recommendation: raise the price for the one-month window, but flag risks the calculation omits: long-run churn may rise, the 25% drop in new subscribers may compound, and brand or fairness effects are not priced. The analysis is a short-run contribution test, not a full valuation.