How do you compute expected return for two projects?
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Technical Screen
## Case: A TV studio's project & divestiture decisions under uncertainty
You are the CEO of a media/streaming company. You run an existing TV show, **"Analyst,"** and you are weighing a new project, **"Shark Bank."** Over the interview you will reason through several connected decisions: whether to keep "Analyst" on the air, which project earns a higher expected return, how to improve "Analyst's" profitability, and finally whether to sell "Analyst" when a competitor makes a concrete cash offer.
This is a structured business case. The interviewer expects you to drive the analysis: ask for the data you need, lay out a framework, do the arithmetic when numbers are given, and defend a recommendation.
### Constraints & Assumptions
- Two candidate projects: **"Analyst"** (existing, can be continued, kept, or sold) and **"Shark Bank"** (new).
- The remaining economic life of "Analyst" is **2 years** (relevant to Parts 2 and 4).
- All cash figures are in USD. Treat the discount rate $r$ as something you must ask for or assume explicitly; if unstated, you may reason in undiscounted terms but should flag the simplification.
- The interviewer may withhold some inputs (e.g., success probabilities) on purpose — part of the test is asking for them rather than assuming.
### Clarifying Questions to Ask
Before diving in, scope the whole case with questions such as:
- What is the objective — maximize total expected profit, maximize value per dollar of capital, or manage cash/liquidity?
- Is capital constrained — i.e., can the company fund "Shark Bank" *and* keep "Analyst," or is it one-or-the-other?
- What discount rate / cost of capital should I use, and over what time horizon?
- For each project, what are the possible outcomes (success / moderate / failure), their cash flows, and — critically for "Shark Bank" — the probability of each? (Do **not** assume 50/50.)
- Are the subscriber and contribution figures total-over-horizon or per-year?
---
### Part 1 — Whether to keep "Analyst" on the air
You must decide whether to **cancel or renew** "Analyst." What factors would you consider, and how would you organize them into a recommendation?
```hint Where to start
Organize the drivers along the two halves of profit — **revenue** sources and **cost** drivers — then add the external lens the interviewer is fishing for.
```
```hint Don't forget the external view
Beyond the show's own P&L, think about **market trend / competitive landscape**, audience shift to other formats, and how the show feeds the broader subscriber funnel.
```
#### What This Part Should Cover
- A clear **revenue vs. cost** decomposition (subscriptions/ads/licensing/merch vs. production, talent, marketing).
- **External / market factors**: industry trend, competition, audience taste shifts — not just the show's standalone economics.
- **Cross-project / portfolio** effects: opportunity cost of the slot, capital, and talent vs. alternatives like "Shark Bank."
---
### Part 2 — Expected return: which project to pick
You are given (or can request) an exhibit of possible outcomes and associated profits/cash flows for each project. Compute and compare the **expected return** of "Analyst" and "Shark Bank," then state which you would pick and why.
```hint Definition
Expected return is a probability-weighted average: $EV=\sum_i p_i \cdot \text{Profit}_i$, with $\sum_i p_i = 1$. If cash flows span years, discount them and compute expected **NPV**.
```
```hint The trap
For "Shark Bank," explicitly **ask the interviewer for the success/failure probabilities** — do not assume 50%. If they won't give them, find the **break-even probability** that equalizes the two projects and sensitivity-test around it.
```
#### What This Part Should Cover
- Correct expected-value (and, if multi-year, NPV) formula applied with the **given** probabilities, not assumed ones.
- A clean **comparison and pick** with the decision rule stated (higher expected NPV when risk-neutral and capital-unconstrained).
- **Risk and sensitivity**: variance / downside, and a break-even probability or scenario test rather than a single point estimate.
---
### Part 3 — How to improve "Analyst's" profitability
List concrete levers to raise "Analyst's" profitability, on both sides of the P&L.
```hint Structure
Same revenue/cost split as Part 1, but go one level deeper: enumerate each **revenue stream** and how to grow it, then each plausible **cost component** and how to trim it. Be ready to reason about costs from common sense (production, talent, marketing, distribution) even without an exhibit.
```
#### What This Part Should Cover
- **Revenue levers** across multiple streams (pricing/subscription, advertising, licensing/syndication, merchandising, international).
- **Cost levers** grounded in a sensible cost structure (production, talent/cast, marketing, distribution/platform) — willingness to reason about costs even when not given them.
- Awareness of **trade-offs** (e.g., cutting marketing may reduce subscribers; cost cuts that erode quality can shrink revenue).
---
### Part 4 — Selling "Analyst": is the $51M offer worth taking?
A competitor offers **$51M today** to buy the "Analyst" project. Use the following:
- Remaining economic life of "Analyst": **2 years**.
- Selling causes a loss of **1.5 million subscribers**, each worth **$32** of contribution (assume this is the *total* contribution per subscriber over the relevant horizon unless you state otherwise).
- "Shark Bank" will generate **$22M total profit over 2 years** (already net of costs).
Show how you would decide whether to sell using an **NPV / expected-value** framework, and list the strategic considerations that could change the decision.
```hint Set up the comparison
Compare **value of selling** (cash received, minus value given up like lost subscriber contribution, plus costs avoided) against **value of keeping** (the project's remaining NPV). Sell only if $NPV_{sell} > NPV_{keep}$.
```
```hint Anchor the lost-value number
Compute what selling costs you: **value the subscriber loss** (lost count × contribution per subscriber) and compare that figure to the cash offer. Whether "Shark Bank" belongs in the analysis depends on whether selling actually frees capital you'd otherwise lack.
```
```hint Beyond the arithmetic
A close numeric result means qualitative factors decide it — **liquidity/financial distress** raises the value of cash today; option/franchise value and competitor harm push the other way. There's no single "right" answer; defend whichever side you take.
```
#### Clarifying Questions for this Part
- Is the **$32** total over the 2-year horizon or per year? (Per-year would roughly double and require discounting.)
- Are there **production/marketing costs avoided** by selling that should be added to the sell side?
- Could the company **pursue "Shark Bank" without** selling "Analyst," or is capital the binding constraint?
#### What This Part Should Cover
- A correct **sell-vs-keep NPV framework** with the lost-contribution figure ($\approx\$48\text{M}$) computed and placed correctly.
- Explicit handling of where the **$22M "Shark Bank"** profit does (or does not) belong — only relevant under a capital constraint.
- A **defended recommendation** plus strategic factors (liquidity, option/franchise value, competitive risk, measurement error, deal structure) and a **break-even sale price** framing.
---
### What a Strong Answer Covers
These dimensions span all four parts:
- **Candidate-driven structure**: asks for missing inputs (especially "Shark Bank" probabilities and the discount rate) instead of silently assuming them.
- **Numerical rigor with stated assumptions**: every formula is accompanied by the assumptions it rests on (probabilities, horizon, discount rate, total-vs-per-year).
- **Business judgment beyond the math**: market/competitive context, portfolio/capital constraints, and a willingness to take and defend a position when the numbers are close.
### Follow-up Questions
- The interviewer pushes: *"What if the company is in financial distress — would you sell then?"* How does liquidity / a higher effective discount rate change your Part 4 answer?
- At what **sale price** would you be indifferent between selling and keeping "Analyst"? Derive the break-even threshold.
- How would you **stress-test** the project choice in Part 2 if you learned the "Shark Bank" success probability was overstated by 20 percentage points?
Quick Answer: This question evaluates a candidate's ability to compute expected return and net present value by modeling probabilistic outcomes, cash flows, discounting, and decision criteria for comparing an existing asset versus a new project.