Calculate Profitability with Different Pricing Schemes
Quick Overview
Evaluates subscription unit economics and break-even analysis under per-GB and two-tier pricing schemes. Strong answers compute monthly profit, fixed-cost leverage, and the paid-user percentage needed to break even.
Calculate Profitability with Different Pricing Schemes
Company: Capital One
Role: Data Scientist
Category: Analytics & Experimentation
Difficulty: easy
Interview Round: Onsite
##### Scenario
The startup tests different pricing schemes and needs unit-economics calculations to gauge profitability.
##### Question
Given 20 subscribers, $400 fixed cost, $5 variable cost per user, $1 per-GB price, and 15 GB average usage, compute monthly profit.
4) If subscribers double, does the firm break even?
6) With a free tier (cost $
1) and a paid tier (fee $54, cost $
5), what paid-user percentage is required for break-even?
##### Hints
Set up revenue and cost equations, subtract costs from revenue, and solve for zero-profit thresholds.
Quick Answer: Evaluates subscription unit economics and break-even analysis under per-GB and two-tier pricing schemes. Strong answers compute monthly profit, fixed-cost leverage, and the paid-user percentage needed to break even.
You are evaluating a subscription product's monthly unit economics. Unless otherwise noted, fixed cost is 400permonthandvariableservicecostis5 per user per month. In the base plan, users pay per GB. In the alternative plan, users are either free-tier or paid-tier users.
Constraints & Assumptions
Treat all costs and revenues as monthly.
Do not combine per-GB revenue with two-tier revenue; analyze each plan separately.
State whether total users are fixed when solving for the paid-user percentage.
Show formulas before interpreting results.
Clarifying Questions to Ask Guidance
Are the 20 users in the two-tier scenario the same total user count as the base plan?
Are fixed costs unchanged across pricing plans?
Does average usage remain the same when price changes?
Are acquisition, churn, or support costs excluded?
Part 1 - Base Per-GB Plan
Given 20 subscribers, 1perGBprice,15GBaverageusageperuser,fixedcostof400, and variable cost of $5 per user, compute monthly profit.
What This Part Should Cover Guidance
Compute revenue per user and total revenue.
Compute variable cost, fixed cost, total cost, and profit.
Interpret whether the product is profitable or losing money.
Part 2 - Scale Scenario
If subscribers double to 40 with the same usage and cost assumptions, determine whether the firm breaks even.
What This Part Should Cover Guidance
Recompute revenue, variable cost, fixed cost, total cost, and profit.
Explain why fixed-cost leverage changes the result.
State whether break-even is achieved.
Part 3 - Alternative Two-tier Plan
Free-tier users cost 1eachtoserveandproducenorevenue.Paid−tieruserspay54 each and cost $5 each. What paid-user percentage is required to break even? Provide the general formula and the value for 20 total users.
What This Part Should Cover Guidance
Define N as total users and f as the paid fraction.
Set profit equal to zero using paid revenue, paid-user cost, free-user cost, and fixed cost.
Derive the required paid fraction as a function of N.
Compute and interpret the 20-user case.
Follow-up Questions Guidance
What if free users have a conversion probability into paid users next month?
How would your answer change if variable cost increases with usage?
