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.
Choosing between two projects with NPV, explained simply
When you can only do one of two projects, work out each NPV at the same discount rate and pick the higher one, as long as it's positive. In the example, at 10%, Investment 2 (NPV ≈ $115.70) beats Investment 1 (≈ $90.91), even though Investment 1 has the higher IRR (20% vs about 16.2%).
What this mutually exclusive projects lesson covers
- 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
NPV decision rule, explained
- CFₜ
- cash flow in year t
- r
- discount rate
- C₀
- initial investment
- NPV
- net present value at the same discount rate for both projects
How to choose between two investments step by step (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.
Investment 1 vs Investment 2
| Investment 1 | Investment 2 | |
|---|---|---|
| Cash flows | −$1,000 now, +$1,200 in Year 1 | −$1,000 now, +$1,350 in Year 2 |
| NPV at 10% | $90.91 | $115.70 |
| NPV at 15% | $43.48 | $20.79 |
| IRR | 20.0% | About 16.2% |
| Wins when the discount rate is | Above 12.5% | Below 12.5% |
What if your next idea is better? David's take
Investment 1 gives you your money back, plus profit, after one year. Investment 2 makes you wait two. At 10%, the textbook says wait. But the answer flips above 12.5%: if you can put Investment 1's $1,200 into a next project earning more than that, the fast one wins. That's how I think as a guerrilla producter: come in, make money in a burst, then move on to the next thing when the copycats arrive. The discount rate you choose should reflect what your next idea can really earn.
From David's concept: Guerrilla Producting. This is David's opinion, alongside the standard textbook answer above.
Harder questions on choosing between projects
Which project wins at a 15% discount rate?
Investment 1: its NPV is about $43.48 versus $20.79 for Investment 2. Above the 12.5% crossover rate, the ranking flips.
Why does the crossover rate equal 12.5%?
It's the rate where both NPVs are equal. Reinvesting Investment 1's $1,200 for one more year at 12.5% gives exactly $1,350, the same as Investment 2.
Should you ever trust IRR over NPV here?
For ranking mutually exclusive projects, NPV is the safer rule because it measures value added in dollars. IRR ignores scale and timing differences, which is exactly what goes wrong in this example at 10%.
Common questions on choosing between projects
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.