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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Technical Screen rounds at Capital One.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Compute required output to recover 10% investment | Capital One Interview Question

Quick Overview

This question evaluates a candidate's ability to perform cost-volume-profit analysis and quantitative financial modeling, assessing skills in algebraic formulation of profit equations, capacity constraint evaluation, and derivation of generalized feasibility formulas.

Power Plant Profit Target and Capacity Feasibility

Context

You are evaluating a fossil-fuel power plant. The plant can sell all electricity it generates at the stated price. Annual economics:

Maximum output: 8.8 million MWh/year
Price: $40/MWh
Variable cost: $20/MWh
Lease: $5 million/month
Other fixed cost: $25 million/year
Initial investment (sunk for this analysis): $400 million

Tasks

Required output X (in MWh) for annual profit to equal 10% of the initial investment (i.e., $40 million). Write the annual profit equation and solve for X.
Check whether the required X is feasible given the 8.8 million MWh/year capacity. If infeasible, quantify the shortfall and state the maximum breakeven/profit achievable under the capacity constraint.
Generalize a formula for required output to cover a target annual return R (in $) given:
- price p ( $/MWh), variable cost v ($ /MWh), monthly lease L ( $/month), annual fixed cost F ($ /year), and capacity limit K (MWh/year). State feasibility conditions clearly.

Compute required output to recover 10% investment

Quick Overview