Net present value (NPV)

What NPV measures

Net present value compares the present value of a project's future cash inflows with the cost of the investment. Money received later is worth less than money today, so future cash flows are discounted at the cost of capital.

NPV = present value of future cash flows − initial investment

Step by step

1. Identify relevant cash flows: future, incremental cash flows only. Ignore sunk costs and depreciation.
2. Adjust for inflation: inflate each cash flow at its own rate if the question gives specific inflation rates.
3. Include tax: tax on operating cash flows, usually paid one year in arrears if the question says so, and tax relief on capital allowances.
4. Include working capital: an investment at the start and its release at the end.
5. Discount each year's net cash flow at the cost of capital and add them up.

Worked example

A project costs $100,000 now and returns $40,000 a year for three years. The cost of capital is 10%, and the three-year annuity factor at 10% is 2.487.

• Present value of inflows = $40,000 × 2.487 = $99,480.
• NPV = $99,480 − $100,000 = −$520.

The NPV is negative, so on financial grounds the project should be rejected, even though the undiscounted inflows of $120,000 exceed the cost.

Real and nominal rates

If the question gives a real cost of capital and inflation, convert with:

(1 + nominal rate) = (1 + real rate) × (1 + inflation rate)

For example, a real rate of 5% and inflation of 3% give a nominal rate of 1.05 × 1.03 − 1 = 8.15%.

Common mistakes

• Including depreciation as a cash flow.
• Mixing real cash flows with a nominal discount rate.
• Forgetting the release of working capital at the end.
• Giving a figure but no recommendation. Section C usually asks you to advise.

Where this leads

Investment appraisal is extended in ACCA AFM, with adjusted present value and multinational projects.