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Calculate profit and break-even across pricing models

Capital OneData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question evaluates understanding of unit economics, break-even analysis, and pricing-model effects on profitability by requiring computation of revenue, variable and fixed costs, and profit under per-GB and two-tier pricing scenarios.

You are analyzing a cloud-storage startup that currently charges unit-based pricing only. Use the following data and assume no other revenues or costs:

  • Subscribers: 20
  • Fixed monthly cost (FC): $400
  • Variable cost per user (VC_user): $5
  • Price to customers: $1 per GB
  • Average usage: 15 GB per user per month Assume identical usage across users. (a) Compute monthly revenue, total variable cost, total cost, and profit. Show formulas and intermediate steps. (b) Explain numerically why the firm operates at a loss or profit. Which lever (price, usage, user count, FC, or VC_user) most impacts the sign and magnitude of profit here, and why? (c) If subscribers double (same usage distribution), does the firm break even? If not, compute the exact subscriber count required for break-even under this model. (d) The company considers a two-tier model that replaces per-GB revenue: Free tier ($0 revenue, $1 cost per free user per month) and Paid tier ($54 revenue per paid user per month, $5 cost per paid user per month). Fixed cost remains $400. For T = 20 total users, what minimum paid-user percentage is required to break even? Derive the general formula for the minimum paid share as a function of T. (e) If only 25% of users convert to Paid, how many total users are required to break even under the two-tier model? Provide the inequality you solve and the smallest integer solution.