Is this project worth building? Cash flows, discounting and the cost of capital

Lay out a wind farm’s cash year by year, discount it, and read NPV, IRR and payback

Analyst lesson A1 of Energy Systems, Step by Step: build a wind farm’s yearly cash flows, discount them at the cost of capital, and read NPV, IRR, payback and a tornado chart.
  • Analyst · L2
  • 30 min guided · about 45 min practice
  • After lesson 7 and K3

A 150 MW wind farm in seven moves (real 2025 dollars)

  1. Year 0 spends $256.8M on building the farm. Years 1 to 30 each sell $22.2M of power at $50/MWh and spend $5.2M on upkeep: $17.0M net.
  2. Discounted at 4% a year, the 30 net years are worth $294.3M today, so the net present value (NPV) is +$37.5M.
  3. The discount rate is what the money costs. With loans at 5% and owners at 10% (nominal, both held fixed), 60% loans give 4.39% real and an NPV of +$24.1M; 40% loans give −$5.7M.
  4. The NPV reaches zero at 5.17%, the internal rate of return (IRR).
  5. The cash put in is back in year 16 (year 24 discounted). With a 20-year life, payback is still year 16, but the NPV is −$25.5M.
  6. The NPV crosses zero at a price of $45.11/MWh, lesson 7's levelized cost of the same farm.
  7. Swung across its range, the capacity factor moves the NPV most ($204.5M), then the discount rate ($170.0M) and the price ($153.6M).
Year Cash Worth today at 4% Running sum Running sum, discounted
0 −$256.8M −$256.8M −$256.8M −$256.8M
1 $17.0M $16.4M −$239.8M −$240.4M
2 $17.0M $15.7M −$222.8M −$224.7M
10 $17.0M $11.5M −$86.6M −$118.7M
16 $17.0M $9.1M $15.5M −$58.5M
24 $17.0M $6.6M $151.7M $2.7M
30 $17.0M $5.2M $253.8M $37.5M

With JavaScript on, you build these cash flows step by step, with charts, sliders and a tornado chart.

  • One price year: every dollar is a real 2025 dollar, so every rate is a real rate (inflation taken out), as in lesson 7 and toolbox K3.
  • Building cost $1,712 per kW and fixed upkeep $34.57 per kW a year: EIA, AEO2026 assumptions, Table 3 (2025 dollars, April 2026).
  • Capacity factor 33.8%: EIA, Electric Power Annual, Table 4.08.B (U.S. wind, 2025; October 2026).
  • 4% real over 30 years, as in lessons 7, 12 and 13: a round rate inside the range of the 2025 ATB (NLR, September 2026).
  • Illustrative: the loan and owner rates (5%, 10%), the 150 MW size and the $50/MWh price, fixed in 2025 dollars as a contract indexed to inflation would be.
  • Left out: taxes, tax credits, depreciation, interest during construction, output that falls with age, and the loan's own repayment schedule. These are the project's cash flows before any loan payments.

Need a refresher? Toolbox K3 (present value and the annuity factor) and lesson 7 (LCOE and the WACC blend).

What you just did, as diagrams

Cash flow
Money in minus money out, year by year: the outlay in year 0, then sales minus upkeep.
Net present value
Every year's cash discounted to today and added up, the outlay included: +$37.5M for the farm at 4%.
WACC
The blended rate the project pays lenders and owners: its discount rate.
Internal rate of return
The rate at which the NPV is exactly zero: 5.17% for the farm.
Payback
The first year in which the running sum of cash reaches zero: year 16, or year 24 discounted. It ignores every year after.
Break-even price
The price that gives an NPV of zero: $45.11/MWh, the farm's LCOE.
Yardstick This farm
Net present value at 4% +$37.5M
Internal rate of return 5.17%
Simple payback year 16
Discounted payback at 4% year 24
Break-even price $45.11/MWh
Go deeper · AnalystWhat these cash flows leave out
  • Taxes and credits. A real project pays income tax and may earn tax credits; depreciation lowers the tax. They change the cash every year, which is why agencies’ numbers differ from these.
  • The money’s mix. Step 3 held both rates fixed. More loans make the owners’ share riskier, so owners ask more: the real WACC may fall less than the slider shows, or not at all.
  • Loan size. Lenders cap a loan by the cash that must repay it, so the loan share is not free to choose.
  • Two views of one project. These are the project’s cash flows before loan payments, discounted at the WACC. Owners also judge their own cash after loan payments, at their own rate: the owners’ IRR.
  • Where it stops. Loan sizing and capital structure stay at awareness level in this course (side shelf X5). No investment advice.
Go deeper · ModelerNominal cash flows, spreadsheets and models
  • Real or nominal, never mixed. Here prices stay in 2025 dollars and the rate is real. A nominal analysis inflates each year’s cash and uses a nominal rate, \((1 + \text{nominal}) = (1 + \text{real})(1 + \text{inflation})\) (K3): the same NPV.
  • A flat contract price. The $50/MWh here is fixed in 2025 dollars, as a contract indexed to inflation would be. A price flat in nominal dollars buys less each year, so its real revenue falls.
  • Spreadsheets. A spreadsheet’s NPV function counts its first value as year 1, so add the year-0 outlay outside it: NPV(4%, years 1 to 30) − 256.8. IRR takes all 31 years, year 0 included.
  • Inside a model. A planning model charges each MW a yearly cost instead (K3, lesson 13): with these inputs, 1 MW of wind costs $133,575 a year, and \(133{,}575 \div (0.338 \times 8{,}760) = 45.11\) $/MWh, the break-even price.
  • Where it goes. Modeler lesson M11 puts a project’s cash flow inside the optimization.

Check yourself

Myth or fact? “Of two projects, the one with the higher IRR is the better one to build.”

  • Myth
  • Fact
Answer

Myth, when only one can be built. A 20 MW farm at a 43% capacity factor returns 8.12% but adds $18.9M; the 150 MW farm returns 5.17% and adds $37.5M. NPV counts the size.

Myth or fact? “A project that pays back early enough is worth building.”

  • Myth
  • Fact
Answer

Myth. With a 20-year life the farm still pays back in year 16, yet its NPV is −$25.5M: payback ignores the time value of money and every year after it.

Myth or fact? “A positive NPV means the project makes money every year.”

  • Myth
  • Fact
Answer

Myth. Year 0 is −$256.8M. The NPV is one sum of all years at today's value, +$37.5M at 4%.

Myth or fact? “If a project's IRR is above its discount rate, its NPV is positive.”

  • Myth
  • Fact
Answer

Fact, for cash like this farm's: one outlay, then only positive years, so the NPV falls as the rate rises. Projects with later outlays can have several IRRs, or none.

The money costs 7% real instead of 4%. Is the farm still worth building at $50/MWh?

  • Yes: its NPV is +$37.5M
  • No: its NPV is −$45.6M
  • Yes: it still pays back in year 16
  • It cannot be told without taxes
Answer

No: at 7% the NPV is −$45.6M, because 7% is above the farm's 5.17% IRR. +$37.5M is the NPV at 4%; simple payback does not depend on the rate.

The farm costs $256.8M and nets $17.0M a year. In years, how long until its cash is back, not discounted?

  • 8.56 years
  • 12.00 years
  • 15.09 years
  • 30.00 years
Answer

15.09 years: 256.8 ÷ 17.02 = 15.09, so the running sum first reaches zero in year 16.

Build it yourself · about 20 minutes

Rebuild the farm in a spreadsheet (toolbox K7) and check this page.

  1. Row 1 holds the headers: Year in A1 and Cash ($M) in B1. Years 0 to 30 go in A2 to A32.
  2. Cash: −256.8 in B2 (year 0), then 22.2066 − 5.1855 in B3 to B32 (years 1 to 30).
  3. NPV: =NPV(4%, B3:B32) + B2 gives 37.53. IRR: =IRR(B2:B32) gives 5.17%.
  4. Change the price to $45.11 (sales 20.0348): the NPV should be about zero. Then try a 20-year life.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
+$37.5M The 150 MW farm's net present value at 4% real and $50/MWh (2025 dollars). This lesson's model (price and size illustrative)
5.17% Its internal rate of return: the rate at which the NPV is zero. This lesson's model
Year 16 · year 24 Its simple and discounted payback. This lesson's model
$45.11/MWh Its break-even price, lesson 7's LCOE: $133,575 a year per MW ÷ 2,960.88 MWh per MW. Lesson 7, from EIA, AEO2026 assumptions, Table 3 (PDF) · April 2026
4% · 30 years The real rate and life of lessons 7, 12 and 13. NLR, 2025 ATB · September 2026 (4%: a round value inside its range)

Next

A2 · Who carries the risk? Power purchase agreements and risk allocation

Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.