Analyze Subscription, Insurance, App, and Card Cases

You are in a Data Scientist "power day" interview for a product analytics role. The interviewer gives you four independent business cases. For each one you are expected to **state your assumptions, define the metric or objective, write the governing formula, compute the answer where data is provided, and end with a recommendation**. Communicate as you would on a real power day: structure the math cleanly (fixed cost vs. unit economics), call out where an estimate is fragile, and connect each number back to a business decision. ### Constraints & Assumptions - The four subcases are independent — solve and present each on its own. - Use a **1-year horizon** unless a case states otherwise. - For the streaming case, "break even" means cumulative net contribution over the first 12 months equals the year-1 fixed costs (no discounting / NPV required unless you choose to add it). - Treat all probabilities, conversion rates, and spend figures as point estimates; part of a strong answer is noting which ones are uncertain or non-causal. ### Clarifying Questions to Ask - Streaming: is the $60\%$ free-to-paid conversion already net of trial fraud/abuse, and does CAC apply per *converted* subscriber or per trial start? - Insurance: are the segment failure probabilities modeled point estimates or observed frequencies, and how correlated are failures across customers (systemic weather events causing simultaneous payouts)? - Card: are the "after partnership" spend figures causal lift (vs. a holdout) or just pre/post observation that could include seasonality and selection? - Card campaign: are the $12\%$ and $7\%$ acquisition rates from a comparable past campaign, and do they reflect the same prospect quality? - General: what discount rate / NPV convention, if any, should I use for multi-year value, and over what horizon is "break even" judged? ### Part 1 — Streaming subscription break-even A media company is launching a new paid streaming service. Assume the following year-1 economics: - Fixed product and engineering launch cost: $12{,}000{,}000$ - Annual content licensing cost: $8{,}000{,}000$ - Fixed launch marketing cost: $5{,}000{,}000$ - Subscription price: $\$12$ per paid user per month - App store and payment processing fee: $10\%$ of subscription revenue - Variable streaming and support cost: $\$2.50$ per active paid subscriber-month - Customer acquisition cost (CAC): $\$18$ per converted paid subscriber - Monthly paid subscriber churn: $4\%$ - Free-trial-to-paid conversion rate: $60\%$ Tasks: 1. Compute the number of converted paid subscribers needed to break even over the first 12 months. 2. Compute the number of free-trial starts needed to generate that many paid subscribers. 3. Discuss whether the break-even subscriber count is reasonable. 4. If it is not reasonable, propose ways to make the launch economically viable. ```hint Structure the unit economics Separate the three **fixed** costs (which you sum once) from the **per-subscriber** economics. Build a monthly contribution margin per active subscriber *before* CAC, then bring in CAC as a one-time per-subscriber cost. ``` ```hint The churn trap A subscriber acquired in month 1 does **not** stay all 12 months at $4\%$ monthly churn. The expected number of active months in year 1 is the sum of monthly survival probabilities, $1 + (1-c) + (1-c)^2 + \dots$ over the first 12 months — a geometric series you should write out and close into a tidy form, not a flat multiply-by-12. ``` ```hint Funnel back-out Once you have the break-even *paid* count, divide by the trial-to-paid conversion rate to get trial starts. For reasonableness, compare the required trials to a plausible reachable market size. ``` #### What a Strong Answer Covers - Fixed costs summed once and held separate from the per-subscriber contribution margin. - A correct per-active-month margin (net of platform fee and variable cost) and CAC treated as a one-time per-converted-subscriber charge. - Churn modeled as a geometric decay of expected active months over 12 months, not a flat multiply-by-12. - A reasonableness judgment that compares required trial starts to a plausible reachable market, plus concrete viability levers ranked by leverage. ### Part 2 — Weather insurance profitability An insurance company is considering a weather insurance product. A customer prepays for 12 months. If a defined weather failure occurs during the year, the customer receives a benefit payment. Product economics: - Premium: $\$30$ per month, prepaid for 12 months - Servicing cost: $\$3$ per customer per month - Benefit paid if weather failure occurs: $\$8{,}000$ - Regulatory expense: $\$4$ per quarter per policy - Additional regulatory and administrative cost if a benefit is paid: $\$300$ Prospect segments: | Segment | Prospects | Estimated annual weather-failure probability | |---|---:|---:| | A | 20,000 | 1.0% | | B | 15,000 | 2.5% | | C | 8,000 | 5.0% | | D | 5,000 | 8.0% | Tasks: 1. What factors would you consider when defining the target customer? 2. What is the maximum annual weather-failure probability that still gives nonnegative expected profit per policy? 3. Compute expected profit per policy and total expected profit by segment. 4. Which segments should the company target to maximize expected profit? 5. Explain how you would present the cumulative-risk and cumulative-profit chart. 6. How could the company responsibly offer a product to high-risk segments C and D? ```hint Expected profit per policy Write per-policy expected profit as a function of failure probability $p$: a deterministic margin (premium minus the costs you always pay) minus $p$ times the cost you pay only when a claim happens. Set it $\ge 0$ to get the break-even $p$. ``` ```hint Marginal vs. cumulative For "which segments to target," compare each segment's expected profit per policy against the break-even threshold — the decision is **marginal**, not based on the cumulative average risk. A blended portfolio can look fine on average while the next segment added is value-destroying. ``` ```hint Serving C and D Three independent levers move a segment back above break-even: raise the **premium**, lower the **benefit**, or change the **probability** (deductibles, waiting periods, mitigation). Quantify at least the first two. ``` #### What a Strong Answer Covers - A per-policy profit function $\mathbb{E}[\pi] = (\text{deterministic margin}) - p \cdot (\text{claim cost})$, with the deterministic and claim-conditional costs cleanly split. - A correctly derived break-even probability and per-segment expected profit (per policy and in aggregate). - A *marginal* targeting argument — accept segments below the break-even threshold, not whatever keeps the blended average acceptable. - A clear description of the cumulative chart whose profit curve peaks at the optimal cutoff, plus quantified levers (premium / benefit) to rescue C and D and a note on correlated risk and adverse selection. ### Part 3 — Digital app product strategy Choose a digital app you know well and analyze it as if you were the product manager or product data scientist. Unlike Parts 1, 2, and 4, this part is qualitative and open-ended: there is no single correct app or answer, and you will be judged on the quality of your framework, metric choices, and reasoning rather than on matching a specific solution. Any well-known app is a valid choice as long as your analysis is coherent. Tasks: 1. Describe the app, the core user need, and why users like it. 2. List its major revenue streams. 3. Identify key competitors and the app's competitive advantages. 4. Propose one North Star metric and three supporting key metrics. 5. Discuss tradeoffs and guardrail metrics. 6. Propose six product-optimization ideas and explain how you would prioritize and test them. ```hint Pick a metric that captures value, not vanity A good North Star ties to *retained value delivered* (e.g. weekly engaged time from retained users), not a raw count. Pair it with an activation, a retention/churn, and a monetization metric, and name guardrails that prevent the team from gaming the North Star. ``` ```hint Prioritize and test explicitly Don't just list six ideas — prioritize with a named framework (e.g. RICE) and describe the A/B test: primary metric, guardrails, MDE / power, and what could confound it (novelty, seasonality, interference). ``` #### What a Strong Answer Covers - A coherent product description: user need, why users value it, and an honest competitive read (rivals + a defensible advantage). - A North Star tied to *retained value delivered* rather than a vanity count, paired with an activation, a retention/churn, and a monetization support metric. - Explicit guardrails that stop the team from gaming the North Star (quality, latency/reliability, support load, ecosystem health). - Six optimization ideas that are prioritized with a named framework (e.g. RICE) and made testable: primary metric, guardrails, power/MDE, and named confounds (novelty, seasonality, interference). > **Note for Part 3.** This part is qualitative and has no single correct answer — any well-known app is acceptable. It is scored on the *framework and reasoning* (a value-based North Star, sensible supports and guardrails, prioritized and testable optimization ideas), not on which app or specific metrics the candidate chooses. ### Part 4 — Co-branded credit card partnership A bank is considering a co-branded credit card partnership with a retail partner. The bank expects the partnership to increase spending among existing cardholders and to acquire new cardholders. Existing cardholder data: | Segment | Existing users | Monthly partner spend before | Monthly partner spend after | |---|---:|---:|---:| | Students | 100,000 | $40 | $55 | | Urban professionals | 60,000 | $120 | $180 | | Travelers | 20,000 | $300 | $420 | Assumptions: - Bank contribution revenue on incremental partner spend: $25\%$ - Bank-funded discount cost on incremental partner spend: $20\%$ - One-time partnership launch cost: $\$6{,}000{,}000$ - Each newly acquired cardholder contributes $\$300$ in annual profit before marketing cost Tasks: 1. What patterns do you observe across the three existing-user segments? 2. Compute annual expected profit from incremental spending by existing users. 3. Compute how many new users are needed to break even after accounting for existing-user profit. The bank is also considering a $\$200{,}000$ marketing campaign that reaches 100,000 eligible prospects. Campaign options: - **Option A:** Keep the $20\%$ discount. Expected acquisition rate is $12\%$. - **Option B:** Reduce the discount to $10\%$. Expected acquisition rate is $7\%$. For campaign analysis, assume each acquired user has $\$300$ annual gross contribution before discount cost and $\$600$ annual discount-eligible spend. Tasks: 1. Compare the two campaign options on expected year-1 profit. 2. Which option would you recommend? 3. What assumptions or risks could invalidate the comparison? ```hint Incremental, not total For existing users, profit comes only from the **incremental** spend (after minus before) — the pre-existing spend is already on the books. Apply the *net* margin (contribution revenue minus discount cost) to incremental annual spend. ``` ```hint Campaign decision For each option compute acquired users $=$ reach $\times$ rate, then net contribution per user $=$ gross $-$ (discount rate $\times$ eligible spend), then subtract the fixed $\$200{,}000$. Compare total profit *and* per-user margin — the higher-volume option and the higher-margin option may differ, and the "right" answer depends on the objective (year-1 profit vs. customer quality). ``` #### What a Strong Answer Covers - Profit on existing users computed from *incremental* (after − before) spend only, with the net margin (contribution revenue − discount cost) applied to the annualized incremental spend. - A correct break-even new-user count that credits the existing-user profit against the launch cost. - A campaign comparison that separates volume from per-user margin and lands a recommendation tied to the stated objective (year-1 profit vs. customer quality). - A named set of risks that could flip the call: non-causal acquisition rates, adverse selection / credit quality, cannibalization, and spend assumptions. ### What a Strong Answer Covers These dimensions span all four parts, on top of the per-Part rubrics above. - Formulas written before numbers, with fixed costs cleanly separated from per-unit (per-subscriber / per-policy / per-user) economics in every case. - A decision framed at the margin, not the blended average, wherever segments or options are ranked. - Causal humility throughout: which inputs are point estimates, which are non-causal (pre/post or historical rates), and how an A/B test or holdout would de-risk the call. - A clear recommendation per case, with the explicit condition under which it would flip and the single input the answer is most sensitive to. ### Follow-up Questions - For streaming, how would the break-even change if you modeled it on a lifetime-value (LTV/CAC) basis over 36 months with a discount rate, instead of a 12-month cumulative-cost basis? - For insurance, how do correlated (systemic) weather failures and adverse selection change your pricing and capital-reserve view versus the independent-risk assumption? - For the card partnership, how would you design a randomized experiment to measure the *causal* incremental spend and acquisition lift, and what guardrails (credit losses, delinquency, complaints) would you monitor? - Across all four cases, which single input is your answer most sensitive to, and how would you reduce uncertainty in it before committing budget?