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Management Accounting · Asset budgeting and investment appraisal

Net Present Value (NPV) Calculation Step by Step

Updated 11 October 2026 · Fact-checked

Net present value is the sum of a project's relevant future cash flows, each discounted to today's value at the cost of capital, minus the initial investment. If NPV is positive, accept the project because it adds value. If NPV is negative, reject it. If it is zero, the project just earns the required return.

Understand Net Present Value (NPV)

A dollar received today is worth more than a dollar received next year. You could invest it and earn a return. So you cannot add up cash flows from different years as if they were equal. You must convert them to a common point in time, which is today (Year 0).

This conversion is called discounting. You multiply each cash flow by a discount factor based on the cost of capital, which is the return the investors require. The result is the present value of that cash flow.

NPV is the total of all present values, with the initial outlay counted as a negative. A positive NPV means the project earns more than the required return, so it increases the wealth of the investors by that amount. This is why NPV is seen as the best appraisal method: it uses cash flows, accounts for the time value of money and links directly to shareholder wealth.

The skill the exam tests is choosing which numbers go into the calculation. Only relevant cash flows count. These are future, incremental cash flows caused by the decision. Sunk costs, allocated fixed overheads and non-cash items such as depreciation are left out. Financing costs such as interest are also left out, because the discount rate already allows for them.

Working capital needs care. Working capital needed for a year's activity is normally invested at the end of the previous year, so it is an outflow then. For example, working capital needed for Year 1 is an outflow at Year 0. The same amount is usually released at the end of the final year, as an inflow. Only the change in working capital each year is a cash flow, not the total balance.

Key formulas to remember

Net present value
NPV = Σ [Cash flow in year t × discount factor for year t] − initial investment
Treat Year 0 cash flows with a discount factor of 1.0. Outflows are negative, inflows are positive.
Discount factor
DF = 1 ÷ (1 + r)^n
r is the cost of capital as a decimal and n is the year. In the exam, discount factor tables are normally provided, so you rarely compute this by hand.
Annuity factor for a constant cash flow
Present value = annual cash flow × annuity factor (n years, r%)
Use only when the same cash flow occurs every year. The annuity factor is the sum of the discount factors for those years.
Decision rule
NPV > 0 accept; NPV < 0 reject; NPV = 0 indifferent
For mutually exclusive projects, choose the one with the highest positive NPV.
Working capital cash flow
Cash flow = −(closing requirement − opening requirement)
An increase in the requirement is an outflow. A decrease, including the final release, is an inflow.

How to solve Net Present Value (NPV) questions

Use the same routine for any NPV question. Set out a clear table so you can earn marks even if one figure is wrong.

  1. 1List the years across the top, starting with Year 0, and find the discount rate and any tax or inflation information.
  2. 2Pick out the relevant cash flows only. Include incremental revenues, incremental operating costs, capital cost and working capital changes. Exclude sunk costs, depreciation, apportioned overheads and interest.
  3. 3Place each cash flow in the correct year. Assume cash flows occur at the year end unless told otherwise, and the initial investment occurs at Year 0.
  4. 4Calculate working capital changes. Working capital needed for a year's activity is invested at the end of the previous year, so show the increase as an outflow then (Year 0 for Year 1 needs). Show the release as an inflow at the end of the final year.
  5. 5Multiply each net cash flow by its discount factor. Use an annuity factor if the flows are identical across years.
  6. 6Add the present values to get the NPV. Check the signs of your outflows.
  7. 7State the decision: accept if NPV is positive, reject if negative. For number entry questions, round as instructed.

Quickest way: Net cash flow row, then discount once

When to use it: Use this in the objective test when you have about 2 to 2.5 minutes per two-mark question and the cash flows are simple.

  1. Write one net cash flow per year in a single row. Combine sales, costs, working capital and capital items.
  2. Cross out anything irrelevant at once: depreciation, interest, sunk costs and apportioned overheads.
  3. Spot constant flows. Use one annuity factor instead of several discount factors.
  4. Multiply, add and subtract the investment. Check whether the answer is positive or negative and answer the question asked.
  5. Check the answer is sensible. If cash inflows total less than the investment before discounting, NPV must be negative.

Common mistakes in Net Present Value (NPV)

  • Including depreciation as a cash flow.

    Depreciation appears in the profit figures given in the question and looks like a cost.

    Fix: Depreciation is not a cash flow. Remove it. Use the actual cash paid for the asset at Year 0 instead.

  • Treating the whole working capital balance as the cash flow each year.

    Students forget that only the change affects cash.

    Fix: Work out the increase or decrease each year. Show the increase as an outflow and recover the total at the end of the project, if the question says it is released.

  • Including sunk costs or apportioned fixed overheads.

    These costs are mentioned in the question and seem connected to the project.

    Fix: Ask whether the cash flow changes because of the decision. If it would happen anyway, it is not relevant.

  • Deducting interest or financing costs from the cash flows.

    Students think interest is a cost of the project.

    Fix: Leave interest out. The discount rate already reflects the cost of finance, so including interest double counts it.

  • Using the wrong discount factor for the year or wrong table column.

    Time pressure and similar-looking numbers in the table.

    Fix: Label each year, the rate and the factor in your working. Remember that Year 0 has a factor of 1.0.

  • Giving the wrong decision or sign for the answer.

    Outflows are added instead of subtracted.

    Fix: Write outflows in brackets or with a minus sign. Do a quick sense check before you finalise.

Worked examples

Example 1

A project needs equipment costing $100,000 now. It will produce net cash inflows of $40,000 a year for 3 years, received at each year end. The cost of capital is 10%. The 3-year annuity factor at 10% is 2.487. Calculate the NPV and state whether to accept the project.

Show the solution
  1. Year 0 outflow: −$100,000, discount factor 1.0, present value −$100,000.
  2. Years 1 to 3 inflows are constant at $40,000, so use the annuity factor of 2.487.
  3. Present value of inflows = 40,000 × 2.487 = $99,480.
  4. NPV = 99,480 − 100,000 = −$520.
  5. The NPV is negative, so the project earns slightly less than 10%.

Answer: NPV = −$520. Reject the project.

Example 2

A company is considering a 3-year project. Equipment costs $200,000 now, with no resale value at the end. Annual sales revenue is $150,000 and annual cash operating costs are $60,000. Depreciation of $66,667 a year is included in the accounts. Working capital of $20,000 is needed at the start and is recovered at the end of Year 3. Cost of capital is 10%. Discount factors at 10%: Year 1 0.909, Year 2 0.826, Year 3 0.751. Calculate the NPV.

Show the solution
  1. Ignore depreciation because it is not a cash flow.
  2. Annual operating cash flow = 150,000 − 60,000 = $90,000.
  3. Year 0: equipment −200,000 and working capital −20,000, total −$220,000, factor 1.0, present value −$220,000.
  4. Year 1: 90,000 × 0.909 = $81,810.
  5. Year 2: 90,000 × 0.826 = $74,340.
  6. Year 3: operating cash flow 90,000 plus working capital release 20,000 = 110,000. 110,000 × 0.751 = $82,610.
  7. Total present value of inflows = 81,810 + 74,340 + 82,610 = $238,760.
  8. NPV = 238,760 − 220,000 = $18,760.

Answer: NPV = $18,760 positive. Accept the project.

Exam tips

  • Read for relevance first. Many wrong answers come from including depreciation, sunk costs, apportioned overheads or interest.
  • In multiple response questions, select exactly the number of items asked for. Check each option against the test: is it future, incremental and cash?
  • For number entry, follow the rounding instructions and give the sign. A negative NPV must be entered as negative.
  • Use the discount factor tables provided. Check the rate column and the year row before multiplying.
  • In multi-task questions, set out a neat table by year. Marks are often awarded for each correct cash flow and for the decision.

Practice questions from Asset budgeting and investment appraisal

Net Present Value (NPV) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Net Present Value (NPV): frequently asked questions

What is the NPV decision rule?

Accept a project if its NPV is positive, because it earns more than the required return. Reject it if NPV is negative. If NPV is exactly zero, the project earns just the required return, so it is a matter of other factors.

How do I treat depreciation in an NPV calculation?

Leave it out. Depreciation is a non-cash accounting charge. The cash paid for the asset is shown at Year 0 instead. If tax is in the question, depreciation may matter for tax relief, but that is beyond what you need unless the question specifically asks for it.

How do I treat working capital in NPV?

Include only the change in working capital each year. An increase is an outflow at the end of the previous year, so working capital for Year 1 is an outflow at Year 0. When the project ends, the working capital is normally released, which gives an inflow at the end of the final year.

Why are sunk costs and interest excluded from NPV?

Sunk costs have already been spent and cannot be changed by the decision, so they are not relevant. Interest is excluded because the discount rate already reflects the cost of finance. Including it would count the cost twice.