A wind turbine costs $10 million to construct and generates $1 million worth of electricity per year. When has the wind turbine paid for itself (what is the pay-back period)?

Question

A wind turbine costs $10 million to construct and generates $1 million worth of electricity per year.  When has the wind turbine paid for itself (what is the pay-back period)?

BlackTom AI · Accepted Answer

1) Relevant knowledge points and concepts:
Pay-back period (simple payback) is the time required for cumulative cash inflows (savings or revenues) to equal the initial investment. It is calculated as Initial Cost divided by Annual Cash Inflow when the inflows are constant each year. This is a simple, nondiscounted measure and ignores time value of money.

2) Step-by-step reasoning:
- Initial construction cost = $10 million.
- Annual value of electricity generated = $1 million per year.
- With constant annual returns, each year reduces the remaining unrecovered investment by $1 million.

3) Calculations with intermediate steps:
Payback period = Initial Cost / Annual Return
= $10,000,000 ÷ $1,000,000 per year
= 10 years.

You can also view this cumulatively: after 1 year: $1M recovered; after 2 years: $2M; ... after 10 years: $10M recovered, so the investment is fully paid back at the end of year 10.

4) Why the correct answer is correct:
Because the turbine produces a steady $1 million in value each year, it takes ten such annual amounts to sum to the $10 million expense. The simple payback formula directly yields 10 years, matching the cumulative-recovery interpretation.

5) Why other options would be incorrect:
No other answer choices are provided here, but common incorrect approaches include dividing incorrectly (e.g., $1M ÷ $10M = 0.1 year) or forgetting units. Another alternative metric is the discounted payback period, which accounts for the time value of money and could give a longer payback if discounting is applied—but that is not asked here. Any answer other than 10 years would contradict the simple arithmetic of $10M / $1M per year.

6) Conclusion:
The simple pay-back period equals 10 years, which matches the provided correct answer: 10 years.

A wind turbine costs $10 million to construct and generates $1 million worth of electricity per year. When has the wind turbine paid for itself (what is the pay-back period)?单项选择题

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