Net present value is the most important figure in this course. It converts every cash flow of a project, whenever it falls, into today’s money, adds them up and says in one number how much richer the shareholders will be if the project goes ahead.
If the number is positive, the project earns more than the cost of the money used and it adds value; if negative, it destroys value. Almost every later topic, from risk to leasing to capital rationing, builds on this calculation.
This topic explains how to calculate and interpret the net present value, the decision rules for one project and for mutually exclusive projects, a full worked example including working capital and scrap value, the sensitivity of the result to the discount rate, the advantages and limits of the method, and the case for discounted cash flow over non-discounting methods such as payback and the accounting rate of return.
The next topic covers the internal rate of return and compares it with net present value.
The net present value was the centre of the compulsory question in November Diet, 2025, Question 1 (30 marks): 16 marks for the calculation, then its sensitivity and the strengths of sensitivity analysis. Read the time value of money: discounting and annuities first.
In 30 seconds
Net present value (NPV) = present value of cash inflows − present value of cash outflows, discounted at the cost of capital (the return required by the investor). Rule: accept a project if the NPV is positive, because it adds that amount to shareholder wealth; among mutually exclusive projects choose the highest NPV.
Steps: list the relevant cash flows by year (including working capital and scrap value), apply the discount factors, sum, compare with zero. Advantages: uses cash flows and all of them, allows for the time value of money, is linked to shareholder wealth and is additive. Limits: needs an estimate of the cost of capital and of the cash flows, and gives an absolute figure.
discounted cash flow (DCF) methods beat payback and accounting rate of return (ARR) because they use cash flows, the time value of money and all returns.
Net present value
The net present value (NPV) method gives a present value to the expected costs and benefits of a project, using the cost of capital r as the return required by the investor or company. The NPV is the present value of the income or benefits minus the present value of the costs. A project adds value if its NPV is greater than zero, and it should then be undertaken.
A positive NPV of ₦1.7m means the project is expected to make the shareholders ₦1.7m better off in present terms, after earning the required return on the money invested.
- Identify the relevant cash flows for each year, from the previous topic: the initial outlay, annual net cash flows, working capital and its recovery, scrap value.
- Place each at its year: the outlay at time 0, the rest at year-ends.
- Multiply each by its discount factor at the cost of capital.
- Sum the present values to give the NPV, and apply the rule.
A worked example: Delta Packaging
Delta is considering a machine costing ₦7.5m. The project needs working capital of ₦1.0m at the start, recovered at the end of year 4. The relevant annual net cash flows are ₦2.6m, ₦3.1m, ₦3.4m and ₦2.8m in years 1 to 4, and the machine can be sold for ₦0.9m at the end of year 4. The cost of capital is 12%.
| Year | Item | Cash flow ₦m | Factor at 12% | present value (PV) ₦m |
|---|---|---|---|---|
| 0 | Machine and working capital | (8.5) | 1.000 | (8.50) |
| 1 | Net cash flow | 2.6 | 0.893 | 2.32 |
| 2 | Net cash flow | 3.1 | 0.797 | 2.47 |
| 3 | Net cash flow | 3.4 | 0.712 | 2.42 |
| 4 | Net cash flow 2.8 + scrap 0.9 + working capital 1.0 | 4.7 | 0.636 | 2.99 |
| Net present value | 1.70 | |||
The NPV is +₦1.70m, so the project should be accepted. If the cost of capital were 20% (factors 0.833, 0.694, 0.579 and 0.482), the NPV would fall to about +₦0.05m: the project is only just worth doing at that rate, which shows how sensitive the result is to the discount rate and leads to the internal rate of return in the next topic.
Choosing between projects
For a single project the rule is NPV above zero. For mutually exclusive projects (only one can be chosen) choose the highest NPV. For independent projects with no limit on funds, accept all with a positive NPV; where funds are limited the choice is more complicated, covered under capital rationing.
The case for discounted cash flow
| Method | Uses cash flows | Time value of money | All returns | Link to shareholder wealth |
|---|---|---|---|---|
| Payback | Yes | No | No: stops at payback | None |
| Accounting rate of return | No: profits | No | Yes, averaged | None |
| Net present value | Yes | Yes | Yes | Direct |
| Internal rate of return | Yes | Yes | Yes | Indirect |
DCF methods are superior because they use cash flows (the money actually invested and returned), allow for the time value of money, count all the cash flows of the project and use a discount rate that reflects the cost and risk of the funds, an objective basis, unlike the arbitrary maximum payback period or target ARR.
Advantages and limits of NPV
- Advantages: considers the time value of money; uses cash flows and all of them; measures the absolute increase in wealth; NPVs of separate projects can be added; consistent with the objective of maximising shareholder wealth.
- Limits: the cost of capital must be estimated and is assumed constant over the life; the cash flows are forecasts and treated as certain; it is harder to explain to non-financial managers than a percentage; and as an absolute figure it does not by itself show the scale of return per naira invested.
The ideas in more depth
Why the discount rate is the required return
The NPV asks whether the project earns more than the investors could earn elsewhere at similar risk. The discount rate is that alternative return. A zero NPV means the project exactly earns the required return, a positive NPV means it earns more, and the amount is the value created at today’s prices.
Why NPV and shareholder wealth are linked
If the market prices the company as the present value of its future cash flows, a project with a positive NPV raises the value of the company by about that amount, and so the share price. This is why NPV is the criterion consistent with the objective of maximising the wealth of the shareholders, studied at the start of the course.
Sources and references
- No accounting standard governs investment appraisal. The discount factor and annuity tables are given on the formula sheet of the paper.
These points are stated as at 5 November 2026.
Worked examples
Example 1: the NPV. Outlay ₦8.5m; present values of inflows 2.32, 2.47, 2.42 and 2.99. Required: the NPV.
- PV of inflows.
2.32 + 2.47 + 2.42 + 2.99 = ₦10.20m. - NPV.
10.20 − 8.50 = +₦1.70m: accept.
Example 2: year 4. Net cash flow ₦2.8m, scrap ₦0.9m, working capital recovered ₦1.0m; factor 0.636. Required: the present value.
- Cash flow.
2.8 + 0.9 + 1.0 = ₦4.7m. - PV.
4.7 × 0.636 = ₦2.99m.
Example 3: an annuity. ₦5.9m a year for 5 years at 10% (factor 3.791) plus ₦2m scrap (factor 0.621), outlay ₦18m. Required: the NPV.
- PV.
5.9 × 3.791 + 2 × 0.621 = 22.37 + 1.24 = ₦23.61m. - NPV.
23.61 − 18 = +₦5.61m.
How to answer in the exam
- Set out a table with year, cash flow, factor and present value, and total it.
- Use the annuity factor for level flows and show it.
- State the decision and its meaning: value added to shareholders.
- Comment on the weaknesses: the cost of capital, uncertainty, and the need for sensitivity analysis.
Common mistakes in the exam
- Forgetting to include the recovery of working capital or the scrap value.
- Discounting the initial outlay.
- Using a profit figure, not a cash flow.
- Choosing between exclusive projects on the internal rate of return (IRR) or on the size of investment.
- Stopping at the NPV without stating accept or reject.
- Saying that a negative NPV means a loss in the accounts, rather than a return below the required rate.
Quick revision
- NPV = PV of inflows − PV of outflows at the cost of capital.
- Accept if positive; among exclusive projects pick the highest.
- Include working capital and scrap value.
- DCF uses cash flows, the time value of money and all returns.
Practice questions
These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.
Recall check: multiple choice
Question 1. The net present value is:
- Total profit
- Total cash flow
- The present value of inflows less the present value of outflows
- The payback period
Show the answer
C. Discounted at the cost of capital.
Question 2. A project should be accepted if its NPV is:
- Negative
- Positive
- Zero always
- Equal to the cost
Show the answer
B. It adds value.
Question 3. The discount rate in an NPV calculation is:
- The required return or cost of capital
- The inflation rate only
- The tax rate
- The dividend yield
Show the answer
A. The return investors could earn elsewhere.
Question 4. A positive NPV means the project:
- Loses money
- Has no risk
- Pays back quickly
- Adds to shareholder wealth
Show the answer
D. By the amount of the NPV.
Question 5. Among mutually exclusive projects, choose the one with the:
- Lowest NPV
- Highest NPV
- Shortest life
- Lowest cost
Show the answer
B. Provided the NPV is positive.
Question 6. DCF methods are better than payback because they:
- Allow for the time value of money and all cash flows
- Ignore cash
- Are simpler
- Ignore risk
Show the answer
A. Payback ignores both.
Question 7. The initial outlay at time 0 has a discount factor of:
- 0.5
- 0
- 1.0
- 10
Show the answer
C. It is already at present value.
Question 8. A limitation of NPV is that:
- It ignores cash
- It ignores time
- It is a percentage
- It needs estimates of the cost of capital and the cash flows
Show the answer
D. Both are uncertain.
Question 9. The recovery of working capital at the end of a project is:
- Ignored
- An outflow
- An inflow in the final year
- Depreciation
Show the answer
C. It is discounted like other flows.
Question 10. NPV is measured in:
- Naira, an absolute amount
- Years
- Percentages
- Ratios
Show the answer
A. Unlike the internal rate of return.
Section B style: written questions
Question 11 (10 marks). (a) Define net present value and state the decision rule. (4 marks) (b) State THREE advantages of NPV. (3 marks) (c) State THREE reasons why DCF is better than payback. (3 marks)
Question 12 (15 marks). A project costs ₦18m. It gives ₦5.9m a year for 5 years and ₦2m scrap at the end of year 5. The cost of capital is 10% (annuity factor 3.791; year 5 factor 0.621). (a) Calculate the present value of the annual flows. (4 marks) (b) Calculate the present value of the scrap. (3 marks) (c) Calculate the NPV. (4 marks) (d) State the decision and its meaning. (4 marks)
A further written question
Question 13 (20 marks). Two mutually exclusive projects are evaluated at 12%. X costs ₦10m now and gives ₦4m a year for 4 years (annuity factor 3.037). Y costs ₦14m now and gives ₦5.0m, ₦5.5m, ₦5.5m and ₦5.5m (factors 0.893, 0.797, 0.712, 0.636).
(a) Calculate the NPV of X. (4 marks) (b) Calculate the NPV of Y. (8 marks) (c) State which to choose and why. (4 marks) (d) State TWO limits of the analysis. (4 marks)
Model answers
Show the model answer to Question 11
(a) The present value of inflows less the present value of outflows, discounted at the cost of capital (2); accept if positive (2).
(b) Time value of money; uses all cash flows; measures the increase in wealth; additive; consistent with shareholder wealth (1 each, any three).
(c) It uses the time value of money; counts all cash flows, not only until payback; has an objective discount rate (1 each).
Show the model answer to Question 12
(a) 5.9 × 3.791 = ₦22.37m (4).
(b) 2 × 0.621 = ₦1.24m (3).
(c) 22.37 + 1.24 − 18 = +₦5.61m (4).
(d) Accept: the NPV is positive, so the project is expected to add ₦5.61m to shareholder wealth after earning the 10% required return (4).
Show the model answer to Question 13
(a)
- 4 × 3.037 = 12.148
- NPV = 12.148 − 10 = +₦2.15m (4).
(b) 5.0 × 0.893 = 4.465; 5.5 × 0.797 = 4.384; 5.5 × 0.712 = 3.916; 5.5 × 0.636 = 3.498 (4); total 16.263 (2); NPV = 16.263 − 14 = +₦2.26m (2).
(c) Choose Y, the higher NPV, which adds most to wealth, provided the extra ₦4m can be funded (4).
(d) (2 marks each, any two) The cash flows and the rate are estimates; the risk of the projects may differ; the lives are equal here but replacement would matter if they were not.
Pathfinder on Net present value and the case for discounted cash flow
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Part (a) asks for the net present value of manufacturing a new product at a cost of capital of 5%, using the annuity factor, to show whether to proceed (16 marks).
Revise first: Net present value
Source: ICAN Pathfinder, Financial Management. Diets covered: Every diet in the Pathfinder, November Diet, 2025 and May Diet, 2026, was reviewed here. The diets listed above test this topic directly..
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