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Compute required output to recover 10% investment

Capital OneData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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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.

Energy One operates a fossil-fuel plant with these economics: maximum output 8.8 million MWh/year; electricity sale price = $40/MWh; variable cost = $20/MWh; lease cost = $5 million/month; other fixed costs = $25 million/year; initial investment = $400 million.

  1. How many MWh of production (X) are required for annual profit to cover 10% of the initial investment (i.e., $40 million), assuming the plant can sell all generated electricity at the stated price? Show the profit equation and solve for X.
  2. Verify whether the required X is feasible given the annual maximum output constraint; if not, explain the shortfall and the breakeven that is achievable.
  3. Generalize a formula for the required output to cover a target return R (in $) given price p, variable cost v, monthly lease L, annual fixed cost F, and capacity limit K. State any feasibility conditions clearly.