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What is Net Present Value (NPV)?

Q: What is a good discount rate?

Typically the company's weighted average cost of capital (WACC) or the investor's required return.

Net Present Value (NPV) is a method to evaluate the profitability of an investment by calculating the present value of all future cash flows minus the initial cost. It accounts for the time value of money — the principle that money today is worth more than the same amount in the future.

Short answer

NPV is the difference between the present value of cash inflows and outflows: NPV = ∑[CF_t / (1+r)^t] − I₀, where CF is cash flow, r is the discount rate, and I₀ is the initial investment.

Cash flows discounted over time

x: Year · y: Discounted Cash Flow ($)

Try it: interactive calculator

Net Present Value

-48,719.52$

= (10,000/(1+8)**1 + 12,000/(1+8)**2 + 14,000/(1+8)**3 + 12,000/(1+8)**4 + 11,000/(1+8)**5) - 50,000

Initial Investment50,000 $Year 1 Cash Flow10,000 $Year 2 Cash Flow12,000 $Year 3 Cash Flow14,000 $Year 4 Cash Flow12,000 $Year 5 Cash Flow11,000 $Discount Rate (%)8 %

Step-by-step worked examples

A $50,000 investment returns $10k, $12k, $14k, $12k, $11k in 5 years at 8% discount rate. Find NPV.

Year 1: 10000/(1.08)^1 = 9259
Year 2: 12000/(1.08)^2 = 10288
Year 3: 14000/(1.08)^3 = 11135
Year 4: 12000/(1.08)^4 = 8810
Year 5: 11000/(1.08)^5 = 7507
NPV = (9259+10288+11135+8810+7507) - 50000 = -3001

Initial cost $20,000, returns $6k/year for 5 years at 5% rate. NPV?

Year 1: 6000/1.05 = 5714
Year 2: 6000/1.1025 = 5442
Year 3: 6000/1.1576 = 5183
Year 4: 6000/1.2155 = 4937
Year 5: 6000/1.2763 = 4703
NPV = 25979 - 20000 = 5979

$30,000 investment, $8k in Y1, $8k in Y2, $20k in Y3 at 10% rate. NPV?

Year 1: 8000/1.1 = 7273
Year 2: 8000/1.21 = 6612
Year 3: 20000/1.331 = 15026
NPV = (7273+6612+15026) - 30000 = -1089

Flashcards

Quick quiz

Q1.$10k investment, returns $3k/year for 4 years at 10% rate. NPV?

Correct answer: A. Year 1: 3000/1.1 = 2727; Year 2: 3000/1.21 = 2479; Year 3: 3000/1.331 = 2254; Year 4: 3000/1.4641 = 2049. Sum = 9509 − 10000 = −491. (Calculator will verify exact.)

Q2.What does a positive NPV indicate?

Correct answer: B. Positive NPV means the investment returns MORE than the required rate.

Q3.Discount rate increases. NPV will…

Correct answer: C. Higher discount rate makes future cash flows worth less in today's money.

Q4.NPV formula uses present value because…

Correct answer: B. $100 today ≠ $100 in 5 years due to inflation and opportunity cost.

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Common mistakes

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Ignoring the time value of money and adding raw cash flows. — Correct: Always discount future cash flows using the discount rate.

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Using the wrong discount rate. — Correct: Use the investor's required rate of return or company cost of capital.

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Accepting projects with NPV < 0. — Correct: Only accept if NPV > 0; it means value is created.

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Forgetting to subtract the initial investment. — Correct: NPV = PV of inflows − initial outlay.

FAQ

What is net present value?

NPV is the sum of discounted future cash flows minus the initial investment, showing whether a project adds value.

What does NPV formula mean?

NPV = ∑[CF_t / (1+r)^t] − I₀ calculates present-day worth of all future cash, adjusted for risk and time.

How is NPV used in business?

To decide whether to accept or reject a project. Accept if NPV > 0; reject if NPV < 0.

What is a good discount rate?

Typically the company's weighted average cost of capital (WACC) or the investor's required return.