Calculate net present value
Discount future net cash flows, subtract the initial outlay and interpret NPV using the supplied discount rate and assumptions.
Cambridge International AS & A Level Business 9609, 2026–2028 syllabus and 2029 syllabus, section 10.3.3. Ratio calculations use the formulae listed in the relevant Cambridge syllabus. Written practice is self-checked. Specialist review has not been completed for this lesson; these exercises do not award an official mark or establish exam readiness.
Before you begin
- Read the figures, dates and assumptions supplied in the question before calculating or interpreting an accounting result.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does NPV compare?
What you will learn
- Explain why future cash flows are discounted
- Calculate NPV from cash flows and discount factors
- Interpret positive, negative and uncertain NPV results
Discount future cash to a common date
Net present value (NPV) is the present value of expected future net cash flows less the initial investment. For each period, multiply the net cash flow by its supplied discount factor; add the present values and subtract the initial outlay.
A discount factor reflects the chosen discount rate and time period. Use factors provided in the question and align each factor with the correct year. Do not discount the initial outflow again if it is already at time zero.
Interpret the result within its assumptions
A positive NPV means the discounted inflows exceed the initial cost at the selected rate; a negative NPV means they fall short under those forecasts. If projects are mutually exclusive, compare their cash flows, scale, risk and constraints rather than choosing by sign alone.
NPV depends on uncertain demand, cost, timing, project life and the discount rate. Small changes can alter the result. NPV supports a decision; it does not prove that the forecast will happen or include every strategic and qualitative effect.
Pause and explain
A project has discounted inflows of $72,000 and initial outlay $80,000. What is NPV?
Worked example
A project costs $100,000 now. Net cash flows are $40,000 in year 1 at factor 0.91, $50,000 in year 2 at 0.83 and $50,000 in year 3 at 0.75. Calculate NPV.
Show the worked solution
- PV year 1=40,000×0.91=$36,400.
- PV years 2 and 3 are $41,500 and $37,500.
- Total PV=115,400; NPV=115,400−100,000=$15,400.
Answer NPV is positive $15,400 at the supplied factors. This result depends on the forecasts and discount rate.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A project costs $50,000. It returns $20,000 at factor 0.95, $25,000 at 0.90 and $20,000 at 0.85 in years 1–3. Calculate NPV.
Give me a hint
Discount each future flow separately, add, then deduct the initial cost.
Compare my reasoning
- PV1=20,000×0.95=$19,000.
- PV2=25,000×0.90=$22,500; PV3=20,000×0.85=$17,000.
- Total PV=$58,500; subtract $50,000.
NPV is $8,500, positive at the supplied factors.
Look for these in your work
- Each factor is paired with its year
- Discounted values are summed correctly
- Initial outlay is subtracted once
A project has an NPV of $12,000 at the firm's chosen discount rate. Explain what that indicates and one thing it does not prove.
Give me a hint
Interpret the discounted comparison, then state the forecast limitation.
Compare my reasoning
- Discounted expected net inflows exceed the initial outlay by $12,000.
- The result applies at the chosen rate and forecast cash flows.
- It does not prove the forecast or qualitative assumptions will hold.
At the chosen discount rate, expected discounted net inflows exceed the initial outlay by $12,000. It does not guarantee actual demand, costs or timing, nor does it show every strategic, legal or stakeholder consequence.
Look for these in your work
- Positive result is interpreted accurately
- Rate/forecast basis is included
- A real limitation is stated
Two mutually exclusive projects each have positive NPV, but one has a much larger outlay and the other has greater strategic value. What additional comparisons should managers make?
Give me a hint
A positive NPV is useful but does not resolve scale, constraints or strategic value.
Compare my reasoning
- Compare the absolute NPV and investment required.
- Check cash affordability, project risk and forecast sensitivity.
- Assess strategic fit, capacity, timing and the value of the alternative project.
Managers should compare NPV relative to the funds committed, affordability, cash timing, sensitivity to assumptions, risk, capacity and strategic fit. They should also consider the opportunity cost of rejecting the other positive-NPV project; the higher NPV alone may not settle the choice.
Look for these in your work
- Investment scale is compared
- Risk and affordability are considered
- Opportunity cost and strategic fit are included
Common mistakes
- Applying the wrong year's factor to a cash flow
- Subtracting the initial investment before adding discounted inflows inconsistently
- Interpreting a positive NPV as a guaranteed outcome
What can you explain now?
What does NPV compare?
Compare with the explanation
Present value of future net cash flows with the initial outlay
It discounts future flows to make a time-adjusted comparison.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do discount factors produce NPV, and which assumptions limit the meaning of a positive result?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.