Evaluate payback and sensitivity for solar vs ethanol pilots
Overview
This question evaluates quantitative financial modeling and sensitivity analysis skills—specifically expected-value computation, simple payback estimation, and scenario-based risk quantification for renewable-energy pilots.
Capital One
Oct 13, 2025, 9:49 PM
Data Scientist
Technical Screen
Statistics & Math
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Renewable Pilot Evaluation — Payback and Sensitivity
Context
Two 1-year-operated pilot plants are being considered to add renewable capacity. Assume simple payback is calculated as:
- Simple payback (years) = Initial investment / Expected annual net cash flow
- Net cash flow = Revenue − Variable costs
- Ignore time value of money and fixed O&M (not provided). Electricity is sold at $40/MWh unless otherwise specified.
Plant Options
-
Solar pilot:
- Initial investment: $12.5 million
- Output: a fraction s of the year is “sunny” with 150,000 MWh/year; the remaining (1 − s) is “cloudy” with 50,000 MWh/year
- In a typical year: s = 0.75 (i.e., 75% sunny, 25% cloudy)
- Variable cost: $0/MWh
-
Ethanol pilot:
- Initial investment: $2.5 million
- Output: 100,000 MWh/year
- Variable cost: $30/MWh
Tasks
- Compute the expected annual MWh and the simple payback period (years) for each pilot at $40/MWh.
- Price sensitivity (ethanol): What electricity price P makes the ethanol pilot achieve a 2.0-year payback, holding other parameters constant?
- Resource sensitivity (solar): What is the minimum sunny-time fraction s (with output = 150,000 MWh at sunny times and 50,000 MWh at cloudy times) required for the solar pilot to achieve a payback of at most 3.0 years at $40/MWh?
- Considering commodity fuel price volatility and import risk for ethanol, and weather variability for solar, which pilot would you recommend and why? Support with calculations above and at least two quantified risk scenarios.
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