##### Scenario A proposed renewable plant has: avg output 1,000 kWh, max capacity 8.8 M kWh/yr; land lease $5 M/mo; fixed cost $25 M/yr; VC $20/kWh; selling price $40/kWh; initial investment $400 M; target ROI 10 %/yr. ##### Question a) What is the minimum annual energy (kWh) the plant must generate and sell to achieve a 10 % annual ROI? b) Based on that quantity relative to the 8.8 M kWh capacity, would you approve the investment? ##### Hints ROI = annual profit ÷ initial investment. Annual profit = (price−VC)*Q − fixed − lease. Solve for Q, then compare with capacity ceiling.

Evaluates ROI and capacity feasibility for a renewable plant. Strong answers compute required annual profit, contribution margin, fixed costs, minimum energy output, maximum-capacity profit, and investment approval levers such as price, cost, capex, incentives, or technology changes.

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This is a easy difficulty Analytics & Experimentation question, commonly asked during Technical Screen rounds at Capital One.

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

Calculate Minimum Energy for 10% ROI and Investment Approval

You are evaluating whether a proposed renewable energy plant can achieve a 10% annual ROI based on annual operating profit before taxes and depreciation.

Given:

Selling price: $40/kWh
Variable cost: $20/kWh
Fixed operating cost: $25 million/year
Land lease: $5 million/month , or $60 million/year
Maximum annual capacity: 8.8 million kWh/year
Initial investment: $400 million
Target ROI: 10% per year on initial investment

Constraints & Assumptions

Use the annual capacity of 8.8 million kWh/year for feasibility.
Treat ROI as annual operating profit divided by initial investment.
Ignore taxes, depreciation, financing, and inflation.
Show units and intermediate calculations.

Clarifying Questions to Ask

Is the selling price really per kWh, or should it be per MWh?
Are fixed costs annual and fully allocated to this plant?
Is maximum capacity physically achievable every year?

Part 1 - Required Energy

What is the minimum annual energy the plant must generate and sell to achieve a 10% ROI?

What This Part Should Cover

Required annual profit from the target ROI.
Contribution margin per kWh.
Total fixed costs.
Solving profit = margin * Q - fixed_costs for Q .

Part 2 - Capacity Feasibility

Can the plant achieve the target ROI given the maximum annual capacity?

What This Part Should Cover

Compare required annual energy with max capacity.
Compute operating profit at maximum capacity.
Interpret whether the investment should be approved under the assumptions.

Part 3 - Approval Levers

If the plant cannot meet the target, what levers could make it feasible?

What This Part Should Cover

Higher price, lower variable cost, lower fixed cost, lower capex, subsidies, credits, capacity increase, or alternative technology.
Practicality and risk of each lever.

What a Strong Answer Covers

A strong answer calculates the required output cleanly, checks the capacity constraint, and turns the math into an investment recommendation with sensitivity levers.

Follow-up Questions

How would the answer change if price and variable cost were per MWh?
What selling price would be required at maximum capacity?
What is the largest fixed cost the project can support?