Evaluate ROI and payback for renewables

You are advising NorthGrid Energy on a utility-scale renewables investment. Unless stated otherwise, the Year-1 economics are: upfront capex of $50,000,000; fixed O&M of $2,000,000 per year; variable cost of $28/MWh; contracted PPA price of $40/MWh for the first five years; and maximum physical capacity of 800,000 MWh per year.

Define Year-1 ROI as $\frac{\text{Year 1 operating profit}}{\text{initial capex}}$.

Disregard taxes, depreciation, financing costs, and working capital.

Answer every part, showing formulas and numeric steps:

1. Which quantitative factors would you prioritize before modeling (at least 6)? For each, state the directionality—how an increase affects ROI—and how you would measure or validate it.
2. Calculate the minimum Year-1 MWh volume needed to reach a 10% ROI. If that volume exceeds capacity, quantify the MWh shortfall.
3. Suppose regulation limits Year-1 output to 500,000 MWh. a) With costs held constant, what PPA price (to the nearest cent) is required to still achieve a 10% ROI? b) With price held at $40/MWh, what maximum variable cost per MWh (to the nearest cent) would still produce a 10% ROI?
4. Compare two mutually exclusive build options with independent economics. Option A (Solar): capex $25,000,000; fixed O&M $2,000,000 per year; variable cost $0/MWh; expected output 300,000 MWh per year at $40/MWh. Option B (Biomass): capex $25,000,000; fixed O&M $1,000,000 per year; variable cost $30/MWh; expected output 1,100,000 MWh per year at $40/MWh. For each option, compute: a) Year-1 operating profit, b) simple payback period in years, and c) unit margin in $/MWh.
5. Which option would you recommend, and why? Justify your choice using unit economics, sensitivity to price and cost shocks, capacity risk, and operational complexity.
6. Provide a 30-second executive summary of no more than 90 words that states the recommendation, key assumptions, and the single largest risk.

Overview: This question assesses financial modeling and quantitative analysis skills for utility-scale renewable projects, including ROI and payback calculations, unit economics, capacity-constraint analysis, sensitivity analysis, and scenario comparison.