Calculate Payback Period for Solar and Corn Projects

Q: Calculate Payback Period for Solar and Corn Projects

This question evaluates financial analysis and unit-economics skills by requiring computation of simple payback periods for renewable energy projects, testing understanding of payback metrics, variable costs, revenue per unit, and comparative project economics.

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Question

Renewable Projects: Payback Period Comparison

Context

You are comparing two energy projects using a simple payback metric (years until cumulative profit equals the upfront investment). Assume:

Ignore discounting, taxes, depreciation, and fixed O&M; only variable costs matter.
"Units" refer to energy units sold at the stated price.
Solar has variable cost (VC) = $0 per unit.
Corn bio-power has VC = $30 per unit and constant output.
The corn plant's annual output level is not specified; compute its payback as a function of its annual units produced (Qc). If a specific Qc is provided (e.g., 150,000 units/year), plug it in.

Given

Solar project: upfront $12.5M; produces 75% of the year at 150,000 units (rate) and 25% at 50,000 units (rate); price =$ 40/unit; VC = $0/unit.
Corn bio-power project: upfront $2.5M; constant output (Qc units/year); price =$ 40/unit; VC = $30/unit.

Tasks

(a) Compute the payback period for the solar project.

(b) Compute the payback period for the corn project (as a function of Qc, and also give a numeric example for Qc = 150,000 units/year).

(c) Based on payback, which project should be chosen and why? State any conditions on Qc that affect the decision.

Calculate Payback Period for Solar and Corn Projects

Renewable Projects: Payback Period Comparison

Context

Given

Tasks

Solution

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