The idea in plain language
Net present value (NPV) compares the present value of a project's future cash flows with its initial cost. Discounting puts cash flows received at different times onto a common basis: their value today.
A positive NPV means the modelled cash flows exceed the initial investment after accounting for the chosen discount rate. It is a model result, not a guarantee of profit.
Key points
- Discount every future cash flow to today.
- Subtract the initial investment once.
- Positive NPV means value is created at that discount rate.
The formula
NPV = Σ [CFₜ ÷ (1 + r)ᵗ] − C₀
Sum the discounted cash flows, then subtract the initial investment.
- CFₜ
- Cash flow in period t
- r
- Discount rate per period
- C₀
- Initial investment at time zero
DFₜ = 1 ÷ (1 + r)ᵗ
The multiplier that converts a period-t cash flow to today.
Match the discount rate to the timing of the cash flows and to the risk of the project. When the cash flows are annual, use an annual rate; when they are monthly, use a monthly rate.
A worked example
A project costs ৳10,000 today and generates ৳6,000 at the end of each of the next two years. At a 10% annual discount rate, year one is worth ৳6,000 ÷ 1.10 = ৳5,454.55 and year two is worth ৳6,000 ÷ 1.10² = ৳4,958.68.
The present value of the cash flows is ৳10,413.22, so NPV is ৳10,413.22 − ৳10,000 = ৳413.22. Use unrounded values and round only the final answer.
From the classroom to a decision
A business might use NPV to compare buying a machine with keeping existing equipment. The analysis should use incremental cash flows and account for relevant taxes, working capital, and any terminal value.
The discount rate should reflect the risk of the cash flows and the return available elsewhere. A higher rate shrinks the present value of distant cash flows the most.
Key points
- Use incremental, after-tax cash flows.
- Include working capital and terminal value when relevant.
- The discount rate is a judgement, so test it.
Common mistakes
Discounting accounting profit instead of cash flow, mixing monthly cash flows with an annual rate, and treating forecasts as certain can all distort the result.
Record the assumptions alongside the calculation. A single NPV figure hides the range of outcomes behind it.
Key points
- Cash flow, not profit.
- Consistent period and rate.
- A result is only as good as its assumptions.
02 / Calculate
Make the numbers yours.
Change an assumption and follow its effect. Cash flows occur at year-end; the initial investment occurs today. Amounts are in BDT.
A ৳10,000 investment with two year-end cash inflows of ৳6,000.
Net present value
Positive NPV৳413.22
The modelled cash flows exceed the investment after discounting at your chosen rate.
PV of future cash flows
৳10,413.22
Less initial investment
৳10,000.00
Follow each cash flow.
| Year | Cash flow | Discount factor | Present value |
|---|---|---|---|
| 1 | ৳6,000.00 | 0.9091 | ৳5,454.55 |
| 2 | ৳6,000.00 | 0.8264 | ৳4,958.68 |
Test the assumption
What if the rate changes?
The investment and cash flows stay the same. Compare nearby rates.
5% discount rate
৳1,156.46
Comparison scenario
10% discount rate
৳413.22
Your current assumption
15% discount rate
−৳245.75
Comparison scenario
This model uses 1–10 annual cash flows and a constant rate of 0–100%. Include taxes, working capital, and terminal proceeds in your cash-flow estimates; the calculator does not add them automatically.
03 / Apply
A machine purchase decision
A small manufacturer is considering a ৳120,000 machine. It expects incremental net cash savings of ৳45,000, ৳50,000, and ৳50,000 over three years, plus ৳15,000 from selling the machine at the end of year three.
The assumptions
- Use a 12% annual discount rate and year-end cash flows.
- The stated savings are already after tax.
- The resale value is net of tax and there is no extra working capital.
What to take away
01
The base case creates modelled value.
02
Weaker demand reverses the result, so test it.
03
A positive NPV is one input, not the whole decision.
Your turn
0 of 3 answered
01Question
A project costs ৳10,000 and returns ৳6,000 at the end of each of the next two years. At 10%, what is the NPV? Round to two decimals.
02Question
A project costs ৳8,000 and returns ৳5,000 at each year-end for two years. At 10%, what is the NPV? Round to two decimals.
03Question
For a project with positive future cash flows, what does a higher discount rate do to NPV?
Take it into the Lab
Experiment with the same idea.
The Lab turns this topic into a workspace: change the drivers, watch the statements move, and see the consequence before you commit to a decision.
What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
Open the labFormula lab
Understand, manipulate, observe, solve, then apply the formula to a decision.
Walk the formulaStatement playground
See how one driver propagates through the income statement, balance sheet, and cash flow.
Open the playgroundSources & further reading
OpenStax · Principles of Finance (free textbook) ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.