What is Net Present Value (NPV)?
Net Present Value (NPV) measures whether an investment or project is worth pursuing by discounting all its future cash flows back to today's dollars and subtracting the initial cost. A positive NPV means the investment is expected to add value.
NPV is the sum of all a project's future cash flows discounted to present value, minus the initial investment; NPV = Σ CFt/(1+r)^t − C0. If NPV > 0, the investment is expected to be profitable.
- 1↓1. Forecast cash flowsEstimate the expected cash flow for every future period of the project.
- 2↓2. Choose a discount ratePick r — usually the cost of capital or required rate of return.
- 3↓3. Discount each cash flowDivide each period's cash flow by (1+r)^t to bring it to today's value.
- 4↓4. Sum the discounted flowsAdd all discounted cash flows together.
- 5↓5. Subtract the initial costNPV = sum of discounted flows − initial investment C0.
- 66. DecideNPV > 0 → accept the project; NPV < 0 → reject it.
Try it: interactive calculator
Step-by-step worked examples
A project costs $10,000 today and returns a single cash flow of $15,000 in 5 years. At an 8% discount rate, what is the NPV?
NPV = -C0 + CF/(1+r)^t NPV = -10000 + 15000/(1.08)^5 (1.08)^5 ≈ 1.4693 NPV = -10000 + 15000/1.4693 ≈ -10000 + 10208.80 = $208.80 Since NPV > 0, the project is worth pursuing
A project costs $50,000 today and produces cash flows of $20,000 at the end of each of the next 3 years. At a 10% discount rate, what is the NPV?
NPV = -C0 + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 NPV = -50000 + 20000/1.10 + 20000/1.21 + 20000/1.331 NPV = -50000 + 18181.82 + 16528.93 + 15026.30 NPV = -50000 + 49737.05 = -$262.95 Since NPV < 0, the project should be rejected
Two projects both cost $5,000. Project A returns $6,500 in 2 years; Project B returns $7,000 in 4 years. At a 6% discount rate, which has the higher NPV?
Project A: NPV = -5000 + 6500/(1.06)^2 = -5000 + 6500/1.1236 ≈ -5000 + 5785.26 = $785.26 Project B: NPV = -5000 + 7000/(1.06)^4 = -5000 + 7000/1.26248 ≈ -5000 + 5545.28 = $545.28 Project A has the higher NPV ($785.26 > $545.28), so it's the better choice
Flashcards
Quick quiz
Q1.A project has NPV = $500. What should you do?
Q2.In the NPV formula, what does C0 represent?
Q3.If the discount rate increases, what typically happens to NPV (holding cash flows fixed)?
Q4.Between two mutually exclusive projects, which is generally preferred?
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Common mistakes
Comparing raw future cash flows without discounting them. — Correct: Cash flows at different times must be discounted to present value before comparing them.
Forgetting to subtract the initial investment C0. — Correct: NPV is the discounted cash flows MINUS the upfront cost — not just the sum of discounted inflows.
Using the wrong discount rate (e.g. an arbitrary number). — Correct: Use the project's true cost of capital or required rate of return as r.
Thinking NPV = 0 means a bad investment. — Correct: NPV = 0 means the project exactly meets the required rate of return — it's break-even, not bad.
FAQ
What is Net Present Value (NPV)?
NPV is a project's discounted future cash flows minus its initial cost, showing how much value it's expected to add.
What is the NPV formula?
NPV = Σ [CFt/(1+r)^t] − C0, where CFt is the cash flow in period t, r is the discount rate, and C0 is the initial investment.
How do you calculate NPV?
Discount each future cash flow back to present value using (1+r)^t, sum them, then subtract the initial investment.
What are examples of NPV in practice?
Companies use NPV to decide whether to build a new factory, launch a product, or invest in equipment — accepting projects with NPV > 0.