NPV and IRR: How Companies Decide Which Projects to Take
Net present value (NPV) and internal rate of return (IRR) are the two most common tools for evaluating whether a project or investment is worth pursuing. NPV tells you how much value a project creates in today's dollars. IRR tells you what rate of return the project earns. Together, they give a company enough information to make a go or no-go decision.
Key takeaway: A positive NPV means the project creates value. An IRR above the company's cost of capital means the same thing. When the two metrics agree, the decision is straightforward.
Net Present Value (NPV)
NPV is the sum of all future cash flows discounted back to the present, minus the initial investment. If the result is positive, the project earns more than the discount rate and creates value. If it is negative, the project destroys value.
The formula is:
NPV = -C0 + CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n
- C0: The upfront investment (a cash outflow, so it is negative)
- CF1 through CFn: The expected cash flows in each future period
- r: The discount rate (typically the company's WACC)
- n: The number of periods
NPV in Action
A company is evaluating a new product line that requires a $500,000 upfront investment. The project is expected to generate cash flows over 5 years. The company's WACC is 10%.
| Year | Cash Flow |
|---|---|
| 0 | -$500,000 |
| 1 | $120,000 |
| 2 | $150,000 |
| 3 | $180,000 |
| 4 | $160,000 |
| 5 | $140,000 |
To calculate NPV, discount each future cash flow and subtract the initial investment:
| Year | Cash Flow | Discount Factor (10%) | Present Value |
|---|---|---|---|
| 0 | -$500,000 | 1.000 | -$500,000 |
| 1 | $120,000 | 0.909 | $109,091 |
| 2 | $150,000 | 0.826 | $123,967 |
| 3 | $180,000 | 0.751 | $135,237 |
| 4 | $160,000 | 0.683 | $109,282 |
| 5 | $140,000 | 0.621 | $86,929 |
| NPV | $64,506 |
The discount factor for each year is 1 / (1.10)^n. Multiply each cash flow by its discount factor to get the present value.
The NPV is $64,506. Since it is positive, the project earns more than the 10% cost of capital and creates value for shareholders. The company should take it.
How the Discount Rate Affects NPV
NPV is sensitive to the discount rate. A higher rate makes future cash flows worth less, pushing NPV down. A lower rate does the opposite.
Using the same project:
| Discount Rate | NPV |
|---|---|
| 6% | $129,190 |
| 8% | $95,488 |
| 10% | $64,506 |
| 12% | $35,965 |
| 14% | $9,623 |
| 16% | -$14,737 |
At 6%, the project looks very attractive. At 16%, it destroys value. Somewhere between 14% and 16%, NPV crosses zero. That crossover point is the project's IRR.
Internal Rate of Return (IRR)
IRR is the discount rate that makes NPV exactly equal to zero. It answers the question: what rate of return does this project actually earn?
Mathematically, IRR is the value of r that solves:
0 = -C0 + CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n
There is no algebraic shortcut for this equation. IRR is solved by trial and error or by using Excel's =IRR() function.
For the project above, the IRR is approximately 14.8%. This means the project's cash flows, discounted at 14.8%, have a present value exactly equal to the $500,000 investment.
The Decision Rule
The IRR decision rule is simple: if IRR exceeds the company's cost of capital (WACC), accept the project. If it falls below, reject it.
| Metric | Rule | This Project |
|---|---|---|
| NPV | Accept if NPV > 0 | $64,506 > 0 ✓ |
| IRR | Accept if IRR > WACC | 14.8% > 10% ✓ |
Both metrics agree. The project earns 14.8%, which is above the 10% cost of capital, and creates $64,506 in value.
NPV vs IRR: When They Disagree
NPV and IRR usually give the same accept-or-reject answer for a single project. But when comparing two mutually exclusive projects, they can rank them differently.
Consider two projects, both requiring a $200,000 investment at a 10% discount rate:
| Year | Project A | Project B |
|---|---|---|
| 0 | -$200,000 | -$200,000 |
| 1 | $180,000 | $50,000 |
| 2 | $60,000 | $80,000 |
| 3 | $30,000 | $120,000 |
| 4 | $10,000 | $90,000 |
| Metric | Project A | Project B |
|---|---|---|
| NPV (at 10%) | $42,593 | $63,199 |
| IRR | 25.8% | 22.3% |
Project A has a higher IRR (25.8% vs 22.3%). Project B has a higher NPV ($63,199 vs $42,593). Which is better?
NPV wins. NPV measures the actual dollar value created. Project B creates over $20,000 more in value even though Project A's percentage return is higher. The conflict arises because Project A returns most of its cash early (front-loaded), while Project B returns more cash overall but later (back-loaded). IRR favors the faster return. NPV favors the larger total value.
Key takeaway: When NPV and IRR disagree on ranking, follow NPV. It measures value creation in dollars, which is what shareholders care about.
Limitations of IRR
IRR has a few known problems that NPV does not share:
- Multiple IRRs. If cash flows switch between positive and negative more than once (for example, a project that requires a mid-life reinvestment), the equation can have multiple solutions. NPV always gives one answer.
- Reinvestment assumption. IRR implicitly assumes that interim cash flows are reinvested at the IRR itself, which may be unrealistically high. NPV assumes reinvestment at the discount rate, which is typically more conservative and realistic.
- Scale blindness. A $10,000 project with a 50% IRR looks better than a $10,000,000 project with a 20% IRR by the IRR metric alone. But the larger project creates far more value. NPV captures this; IRR does not.
Despite these issues, IRR remains widely used because it expresses returns as a percentage, which is intuitive and easy to compare across projects of different sizes. Most analysts use both metrics together.
NPV and IRR in Excel
In Excel, the NPV function calculates the present value of future cash flows (it does not subtract the initial investment automatically):
=NPV(rate, CF1:CFn) + C0
The IRR function finds the internal rate of return from a series of cash flows:
=IRR(C0:CFn)
For the original project example:
=NPV(10%, B2:B6) + B1
Where B1 contains -500000 and B2:B6 contain the year 1-5 cash flows. The result is $64,506.
=IRR(B1:B6)
This returns 14.8%.
Note that Excel's NPV function expects the first cash flow to start in period 1, not period 0. That is why the initial investment (C0) is added separately outside the function.
Why NPV and IRR Matter
These two metrics sit at the center of capital budgeting:
- Project evaluation: Should the company build a new factory, launch a product, or acquire a competitor? NPV and IRR provide the financial answer.
- Capital allocation: When a company has more good projects than it can fund, NPV ranks them by value created.
- Performance measurement: After a project is completed, comparing actual returns to the original IRR shows whether the investment delivered what was expected.
- Valuation: DCF models are just NPV applied to an entire company. The enterprise value is the NPV of all projected free cash flows.
Conclusion
NPV tells you how much value a project creates. IRR tells you the percentage return it earns. Use them together for a complete picture, and when they conflict on ranking, trust NPV.
For the fundamentals behind discounting, see our guide on time value of money. To understand where the discount rate comes from, see our guide on WACC. For calculating NPV and IRR in Excel, check out our finance Excel functions guide.
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