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How do you compute expected return for two projects?

Last updated: Jun 21, 2026

Quick Overview

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.

  • easy
  • Capital One
  • Statistics & Math
  • Data Scientist

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.

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|Home/Statistics & Math/Capital One

How do you compute expected return for two projects?

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Capital One
Feb 12, 2026, 11:22 PM
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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 rrr 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?

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.

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.

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.

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?
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