What does a negative NPV mean?

A negative NPV means the projected cash flows, discounted back to today, are worth less than the initial investment — the project destroys value at that discount rate. A positive NPV means the opposite: the project is expected to add value above what the same money would earn at your required rate.

Why is the first cash flow negative?

The first entry (period 0) is normally the upfront investment or cost, which is cash going out rather than coming in — entering it as a negative number is what makes the formula net the investment against the returns that follow.

How is NPV different from IRR?

NPV gives you a euro amount of value created at a discount rate you choose. IRR instead solves for the discount rate at which NPV is exactly zero — the break-even rate of return for the project. They use the same cash flows and formula, just solved for a different unknown.

What does a negative NPV mean?

A negative NPV means the projected cash flows, discounted back to today, are worth less than the initial investment — the project destroys value at that discount rate. A positive NPV means the opposite: the project is expected to add value above what the same money would earn at your required rate.

Why is the first cash flow negative?

The first entry (period 0) is normally the upfront investment or cost, which is cash going out rather than coming in — entering it as a negative number is what makes the formula net the investment against the returns that follow.

How is NPV different from IRR?

NPV gives you a euro amount of value created at a discount rate you choose. IRR instead solves for the discount rate at which NPV is exactly zero — the break-even rate of return for the project. They use the same cash flows and formula, just solved for a different unknown.

Giá trị hiện tại ròng (NPV)

Chiết khấu dòng tiền tương lai về hiện tại để biết dự án có tạo ra giá trị hay không.

The NPV calculator discounts a series of future cash flows back to today at your chosen rate and sums them with the initial investment, showing whether a project creates or destroys value.

ByHoang Truong

Tỷ lệ chiết khấu

Nhập dưới dạng phần trăm nguyên — ví dụ 10 nghĩa là 10%.

Dòng tiền

Phân tách các giá trị bằng dấu phẩy hoặc dòng mới

Giá trị đầu tiên là khoản đầu tư ban đầu (âm); mỗi giá trị tiếp theo là dòng tiền ròng của một kỳ.

Giá trị hiện tại ròng243 €

Tổng dòng tiền chưa chiết khấu500 €

Số kỳ3

Ví dụ minh họa

Sử dụng các số liệu ở trên:

Tỷ lệ chiết khấu: 1.000,0%
Dòng tiền: -1.000 €, 500 €, 500 €, 500 €

Giá trị hiện tại ròng243 €

Tổng dòng tiền chưa chiết khấu500 €

Số kỳ3

The formula

LaTeX

NPV = \sum_{t=0}^{n} \dfrac{CF_t}{(1+r)^t}

Variables

$C F_{t}$: Cash flow at period t (€)
$r$: Discount rate (%)
$t$: Period number (0, 1, 2, …)
$n$: Final period

What net present value means

Net present value (NPV) converts a series of future cash flows into a single number in today's euros. A euro next year is worth less than a euro today — it could have been earning a return in the meantime — so NPV discounts every future cash flow back to the present at a rate that reflects what your money could otherwise earn, then adds the results together along with the upfront investment (entered as a negative cash flow).

The result tells you directly whether a project creates value: positive NPV means the project is expected to earn more than your discount rate; negative NPV means it's expected to earn less. It's the workhorse metric of capital budgeting and shows up any time an exam question gives you a stream of projected cash flows and asks whether to invest.

How to calculate it

Lay out every expected cash flow by period, starting with period 0 — the initial investment, entered as a negative number.
Discount each period's cash flow back to today by dividing it by (1 + rate) raised to the power of the period number.
Add every discounted cash flow together, including the (already negative) period-0 investment. The sum is the NPV.

The discount rate should reflect your required return or cost of capital — a higher rate discounts future money more aggressively.
NPV assumes cash flows arrive at the end of each period and that the discount rate stays constant across the whole horizon.
A larger, positive NPV at the same discount rate means more value created, all else equal — but NPV in euros isn't directly comparable across projects of very different sizes (see the limitations below).

A worked example

Take a project needing €1,000 upfront, expected to return €500 at the end of each of the next three years, evaluated at a 10% discount rate. Discounting each €500: €500 ÷ 1.10 ≈ €454.55 in year one, €500 ÷ 1.10² ≈ €413.22 in year two, €500 ÷ 1.10³ ≈ €375.66 in year three. Adding those three discounted values (≈ €1,243.43) to the −€1,000 initial investment gives an NPV of approximately €243 — a positive result, so the project is expected to outperform the 10% hurdle rate.

Limitations to know

NPV in euros isn't directly comparable between projects of very different scale — a €10,000 project with €500 NPV and a €10,000,000 project with €500 NPV are not equally attractive, even though the number matches. NPV is also only as good as its inputs: the discount rate and every projected cash flow are estimates, and small changes to either can flip the sign of the result for a project that's close to break-even.

Câu hỏi thường gặp

Use your required rate of return, or cost of capital, for the type of project — usually WACC for a company investment, or a personal hurdle rate for individual decisions. A higher rate discounts future cash flows more heavily, so a riskier project needs a higher rate to compensate for that risk.