Net Present Value

Turn future cash flows into one decision today

Finance FundamentalsProject Valuation & DCFFree preview

⏱️ About 16 min

A project costs $10,000 today and returns $4,000 a year for three years. At an 8% cost of capital, is it worth doing - and by how much?

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The big idea: Net present value discounts every future cash flow back to today at the cost of capital, subtracts the up-front investment, and gives one number: create value when it is positive, destroy value when it is negative.

🎯 By the end, you'll be able to

Write NPV as the sum of discounted cash flows minus the investment.
Compute the NPV of a multi-year project at a given discount rate.
Apply the accept-if-positive decision rule.

📎 Helpful to know first

The Module 1 lessons on present value and discounting.

Every cash flow is worth less the later it arrives

A project is a stream of future cash flows bought with money spent today. Because a dollar next year is worth less than a dollar now, you cannot simply add the cash flows up. You discount each one back to today, then compare the total with what you paid.

\[ NPV = \sum_{t=1}^{n} \dfrac{CF_{t}}{(1 + r)^{t}} - CF_{0} \]

Reading the formula

$CF_{t}$ is the cash flow in period $t$, $r$ is the discount rate (the cost of capital), $n$ is the project life, and $CF_{0}$ is the up-front investment. Each future cash flow is divided by $(1+r)^{t}$, so cash further away is discounted more heavily.

⚠️ The decision rule

Accept the project when $NPV > 0$: the discounted cash flows more than repay the investment at the required return. Reject it when $NPV < 0$. A zero NPV means the project earns exactly the cost of capital.

🎮 NPV Profile Explorer LIVE

Predict first: Predict first: as the discount rate rises, does the NPV of a project rise or fall?

The NPV profile - net present value as the discount rate changes; the zero line marks where the project breaks even.

📝 Worked example: A project costs $10,000 today and returns $4,000 at the end of each of the next 3 years. The cost of capital is 8%. What is the NPV?

1. Discount each cash flow: $4000/1.08 = 3703.70$.
2. $4000/1.08^{2} = 4000/1.1664 = 3429.36$.
3. $4000/1.08^{3} = 4000/1.259712 = 3175.33$.
4. Sum of present values: $3703.70 + 3429.36 + 3175.33 = 10308.39$.
5. NPV: $10308.39 - 10000 = 308.39$.

✓ NPV = $308.39 (positive, so accept the project)

✏️ Practice: Same project ($10,000 cost, $4,000 for 3 years), but now the cost of capital is 12%. Is the NPV positive or negative?

💡 Hint

Discount at 12%: $4000/1.12 + 4000/1.12^{2} + 4000/1.12^{3} - 10000$.

Answer

Negative: NPV = -$392.67, so reject.

Check your understanding

1. A project should be accepted when its net present value is:

A positive NPV means the discounted cash flows more than repay the investment at the required return, so the project creates value.

2. Raising the discount rate applied to a project generally:

A higher discount rate shrinks every discounted future cash flow, so the NPV falls.

✅ Key takeaways

NPV discounts every future cash flow to today and subtracts the investment.
NPV $= \sum CF_{t}/(1+r)^{t} - CF_{0}$.
Accept when NPV is positive; a higher discount rate lowers NPV.

➡️ NPV tells you whether a project pays at a given rate; the next lesson asks what single rate makes NPV exactly zero - the internal rate of return.

Want to test yourself on this? Try the Finance Fundamentals Aptitude test →