Compute required output to recover 10% investment
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.
Capital One
Oct 13, 2025, 9:49 PM
Data Scientist
Technical Screen
Statistics & Math
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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.
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Generalize a formula for required output to cover a target annual return R (in $) given:
- price p ( /MWh), monthly lease L ( /year), and capacity limit K (MWh/year). State feasibility conditions clearly.
Solution
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