Net present value (NPV) is the sum of a project's future relevant cash flows discounted at the cost of capital, less the initial outlay. The examiner likes it because it tests relevant costing, discounting and consistency of rates all in one short question.
The rule
Include only incremental future cash flows: use opportunity cost for assets the company already owns, and ignore sunk costs, book values and costs that do not change. Discount each cash flow at the cost of capital, using an annuity factor for level annual flows. NPV = PV of inflows less PV of outflows. Accept if NPV is positive. Discount money (inflated) flows at the money rate and real flows at the real rate. With tax, inflate everything and use the money rate, because capital allowances are fixed in money terms.
Worked example
A project needs a new machine costing $400,000 now. It earns sales of $220,000 a year for 4 years, with cash operating costs of $90,000 a year. These are nominal figures, the first flows arise at the end of year 1, there is no scrap value and no tax. Cost of capital is 10% and the 4-year annuity factor is 3.170.
Net annual cash flow = $220,000 - $90,000 = $130,000.
PV of inflows = $130,000 x 3.170 = $412,100.
NPV = $412,100 - $400,000 = $12,100.
The NPV is positive, so the project is acceptable because it adds $12,100 to shareholder wealth.
Remember: only incremental future cash flows count, so use the opportunity cost of owned assets (for example the $30,000 sale proceeds, not the $50,000 book value), ignore sunk costs, and always match real flows with the real rate and money flows with the money rate.
Where candidates lose marks
Including sunk costs such as a market research fee already paid, or using book value instead of the opportunity cost of an existing asset.
Adding up cash flows without discounting, or discounting sales only and forgetting the operating costs.
Stopping at the PV of inflows and forgetting to deduct the initial outlay.
Discounting current-price flows at the money rate, or assuming real flows at the real rate still work when tax allowances are fixed in money terms.
Try it: 4 questions
Green Thumb Garden Centre Ltd is evaluating a new landscaping service. The project would use a delivery machine the company already owns, which has a book value of $50,000 and could be sold for $30,000 now if not used on the project. It would also use existing permanent staff whose time is already paid and who have no alternative use. A market research study costing $20,000 was paid last month. The project requires a new licence costing $10,000 a year, payable annually in advance with the first payment at time 0. What is the total relevant cash outflow at time 0?
Answer: C. Rule: only incremental, future cash flows count. Use opportunity cost for existing assets and ignore sunk costs and non-cash or unchanged items. Relevant at time 0: machine at opportunity cost $30,000 (sale proceeds forgone), plus first licence payment $10,000 = $40,000. Excluded: book value $50,000 (not a cash flow), staff time (already paid, no alternative use, so no incremental cost) and the $20,000 research (sunk). Wrong options: $30,000 omits the licence fee payable at time 0. $60,000 includes the sunk research ($30,000 + $10,000 + $20,000); the book value error ($50,000 + $10,000) gives the same figure. $80,000 uses book value and includes the sunk research.
Pollen Seeds Co, a seed producer, is appraising a packaging machine costing $400,000 now. It will generate sales of $220,000 a year for 4 years, with cash operating costs of $90,000 a year. Both figures are nominal (already inflated), the first cash flows arise at the end of year 1, and the machine has no scrap value. There is no taxation. The company's cost of capital is 10%, and the 4-year annuity factor at 10% is 3.170. What is the project NPV?
Answer: B. Rule: NPV = PV of net cash inflows less initial outlay. Net annual cash flow = $220,000 - $90,000 = $130,000. The PV of the 4-year annuity = $130,000 x 3.170 = $412,100. NPV = $412,100 - $400,000 = $12,100 (positive). Wrong options: $120,000 adds the net cash flows undiscounted ($130,000 x 4 - $400,000), so it ignores the time value of money. $297,400 discounts the sales only ($220,000 x 3.170 = $697,400, less $400,000), so it forgets the operating costs. $412,100 is the PV of the net inflows but does not deduct the $400,000 initial outlay.
Brandt Co, an electronics assembler, is appraising a new assembly line. All cash flows have been forecast in current prices. All costs and revenues are expected to inflate at the same uniform rate, and a real cost of capital is available. Management wants the simplest approach that is still consistent. The project will pay corporation tax, and tax-allowable depreciation is based on the original cost of the equipment. Which TWO of the following statements are correct?
Select the two that apply (each shows on its own).
Answer: B, D. Rule: real flows must be discounted at the real rate and money flows at the money rate. Real flows at the real rate give the same NPV as money flows at the money rate only when every item inflates at the same rate and no cash flow is fixed in money terms.
Correct: - Option B: with uniform inflation and no tax, the two methods are equivalent. - Option D: capital allowances are fixed in money terms, based on historic cost, so they do not inflate. Converting them to real terms is awkward and error-prone, so inflate all flows, apply tax and allowances in money terms, and discount at the money rate.
Wrong: - Option A mixes real flows with a money rate. This is inconsistent and understates NPV, and it is not 'prudent', just wrong. - Option C ignores that the allowances do not inflate, so the tax saving is misstated in real terms. - Option E is too absolute, because the real rate is valid when no tax or other money-fixed flows are involved.
A trainee at Circuit Co, an electronics assembler, has appraised a project at the firm's WACC of 10%. The trainee included a year 0 outflow of $200,000, then deducted $30,000 a year of depreciation and $10,000 a year of interest costs as annual cash costs, and obtained a negative NPV. Which TWO of the following identify errors in the trainee's working?
Select the two that apply (each shows on its own).
Answer: A, B. NPV uses only incremental cash flows. Depreciation is an accounting allocation, not a cash flow, so it must be excluded (only tax relief on capital allowances is relevant when tax is included). Interest is a financing cost; discounting at the WACC already charges for the cost of finance, so deducting interest as well double counts it. Wrong options: the $200,000 is a future incremental investment at the start of the project, not a sunk cost. Including depreciation as a cost is the very error made. Raising the rate to allow for interest would double count finance costs again.
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Accept a project if its NPV is positive when discounted at the cost of capital, because it increases shareholder wealth. If NPV is negative, reject it. If projects are mutually exclusive, choose the one with the highest positive NPV.
Which cash flows are relevant in an NPV calculation?
Only future, incremental cash flows. Use opportunity cost for existing assets, such as the sale proceeds forgone, and exclude sunk costs, book values, and costs already paid with no alternative use, such as existing staff time.
Should I use the real or money discount rate for NPV?
Use the money rate with money (inflated) cash flows and the real rate with real cash flows. If there is tax, inflate the flows and use the money rate, because capital allowances are based on historic cost and do not inflate.