NPV: Investment 1 vs. Investment 2
When you can only pick one of two projects, they are mutually exclusive. The rule is simple: calculate each project's NPV at the same discount rate and choose the higher one. IRR can point the other way, but NPV gives the right answer because it measures value added in dollars.
What you will learn
- What mutually exclusive projects are and why ranking matters
- How to compare Investment 1 vs Investment 2 using NPV
- Why NPV and IRR can rank two projects differently
- What the crossover rate tells you
- How to set out the answer in an exam
The formulas
- CFₜ
- cash flow in year t
- r
- discount rate
- C₀
- initial investment
- NPV
- net present value at the same discount rate for both projects
Worked example
Investment 1 costs $1,000 and pays $1,200 in one year. Investment 2 costs $1,000 and pays $1,350 in two years. The discount rate is 10%. You can only do one. Which should you pick?
- Investment 1 NPV: 1,200 ÷ 1.10 − 1,000 = 90.91
- Investment 2 NPV: 1,350 ÷ 1.10² − 1,000 = 115.70
- IRRs: Investment 1 = 20.0%, Investment 2 ≈ 16.2%
- IRR prefers Investment 1, but NPV prefers Investment 2
- Crossover rate: 1,200 ÷ (1 + r) = 1,350 ÷ (1 + r)² gives r = 12.5%
Answer: Choose Investment 2 (NPV ≈ $115.70 vs $90.91). At any discount rate below the 12.5% crossover rate, Investment 2 adds more value even though its IRR is lower.
Common questions
What are mutually exclusive projects?
Mutually exclusive projects are alternatives where choosing one rules out the other, such as two different machines for the same job or two uses for the same piece of land. You must rank them, not just check whether each is acceptable.
Why do NPV and IRR give different rankings?
Conflicts usually come from differences in project size or in the timing of cash flows. IRR is a percentage, so it ignores scale, and it assumes cash is reinvested at the IRR itself. NPV measures dollar value added at the actual cost of capital.
Should I use NPV or IRR to choose between two projects?
Use NPV. When NPV and IRR disagree on mutually exclusive projects, the higher NPV project adds more value for shareholders. IRR is still useful as a quick check that a single project beats the hurdle rate.
What is the crossover rate?
The crossover rate is the discount rate at which two projects have exactly the same NPV. Below it, one project has the higher NPV; above it, the other does. You find it by setting the two NPVs equal or taking the IRR of the difference in cash flows.