Evaluate Two Partnerships with Unit Economics and Break-Even Analysis

Solve two profitability scenarios. The first involves a restaurant weighing a discount-platform partnership, where different prescription-style service tiers carry different costs. The second involves a payments product that has a profitable credit option and a debit option that loses money.

Constraints and assumptions

• Use variables whenever a numeric input is missing; do not invent hidden source numbers.
• Keep revenue, variable cost, fixed cost, and one-time cost distinct.
• Specify whether customer counts are incremental or cannibalized from an existing channel.
• Any recommendation must include sensitivity analysis, not just a point estimate.

Clarifying questions to ask

• Does the partnership fee apply to gross sales, discounted sales, or per transaction?
• Which costs change by customer, tier, or payment product?
• Is break-even measured per day, per customer cohort, or across the contract term?

Part 1 — Restaurant partnership

Construct the daily profit equation before and after the partnership, solve for break-even volume, and solve for the mix of low-cost and high-cost service tiers needed to keep profit unchanged.

What this part should cover

• A full profit equation
• A symbolic derivation of break-even
• An expected-cost equation for the tier mix

Part 2 — Credit and debit products

Given current losses and the incremental contribution margin from one additional customer, calculate the number of customers required to break even. Explain how you would assess whether that result is operationally realistic.

What this part should cover

• Contribution margin for each incremental customer
• A check of the denominator and units
• Changes to pricing, cost, or product mix if acquisition alone is not realistic

What a strong answer covers

• Clear arithmetic and units
• Explicit incremental-versus-existing assumptions
• A recommendation that holds up across plausible ranges

Hint: Write the equation before substituting values. Name every revenue and expense term and its unit. This prevents mixing per-order margins with daily fixed costs or treating existing customers as incremental.

Follow-up questions

• How would cannibalization affect the recommendation?
• Which uncertain input has the highest information value?

Overview: A product analytics case about comparing partnership economics using transparent profit equations, contribution margins, and break-even thresholds. Candidates must separate fixed and variable costs, test customer-mix assumptions, and make a recommendation that survives sensitivity analysis.

Read the full product analyst interview experience this question came from.