The net present value (NPV) or net present worth (NPW)[1] applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

## Common pitfalls

• If, for example, the Rt are generally negative late in the project (e.g., an industrial or mining project might have clean-up and restoration costs), then at that stage the company owes money, so a high discount rate is not cautious but too optimistic. Some people see this as a problem with NPV. A way to avoid this problem is to include explicit provision for financing any losses after the initial investment, that is, explicitly calculate the cost of financing such losses.
• Another common pitfall is to adjust for risk by adding a premium to the discount rate. Whilst a bank might charge a higher rate of interest for a risky project, that does not mean that this is a valid approach to adjusting a net present value for risk, although it can be a reasonable approximation in some specific cases. One reason such an approach may not work well can be seen from the following: if some risk is incurred resulting in some losses, then a discount rate in the NPV will reduce the effect of such losses below their true financial cost. A rigorous approach to risk requires identifying and valuing risks explicitly, e.g., by actuarial or Monte Carlo techniques, and explicitly calculating the cost of financing any losses incurred.
• Yet another issue can result from the compounding of the risk premium. R is a composite of the risk free rate and the risk premium. As a result, future cash flows are discounted by both the risk-free rate as well as the risk premium and this effect is compounded by each subsequent cash flow. This compounding results in a much lower NPV than might be otherwise calculated. The certainty equivalent model can be used to account for the risk premium without compounding its effect on present value.[citation needed]
• Another issue with relying on NPV is that it does not provide an overall picture of the gain or loss of executing a certain project. To see a percentage gain relative to the investments for the project, usually, Internal rate of return or other efficiency measures are used as a complement to NPV.
• Non-specialist users frequently make the error of computing NPV based on cash flows after interest. This is wrong because it double counts the time value of money. Free cash flow should be used as the basis for NPV computations.

## History

Net present value as a valuation methodology dates at least to the 19th century. Karl Marx refers to NPV as fictitious capital, and the calculation as "capitalising," writing:[14]

The forming of a fictitious capital is called capitalising. Every periodically repeated income is capitalised by calculating it on the average rate of interest, as an income which would be realised by a capital at this rate of interest.

In mainstream neo-classical economics, NPV was formalized and popularized by Irving Fisher, in his 1907 The Rate of Interest and became included in textbooks from the 1950s onwards, starting in finance texts.[15][16]

## Alternative capital budgeting methods

• Adjusted present value (APV): adjusted present value, is the net present value of a project if financed solely by ownership equity plus the present value of all the benefits of financing.
• Accounting rate of return (ARR): a ratio similar to IRR and MIRR
• Cost-benefit analysis: which includes issues other than cash, such as time savings.
• Internal rate of return (IRR): which calculates the rate of return of a project while disregarding the absolute amount of money to be gained.
• Modified internal rate of return (MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes it is called Growth Rate of Return.
• Payback period: which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
• Real option: which attempts to value managerial flexibility that is assumed away in NPV.
• Equivalent annual cost (EAC): a capital budgeting technique that is useful in comparing two or more projects with different lifespans.

## References

1. ^ Lin, Grier C. I.; Nagalingam, Sev V. (2000). CIM justification and optimisation. London: Taylor & Francis. p. 36. ISBN 0-7484-0858-4.
2. ^ a b Berk, DeMarzo, and Stangeland, p. 94.
3. ^ erk, DeMarzo, and Stangeland, p. 64.
4. ^ Khan, M.Y. (1993). Theory & Problems in Financial Management. Boston: McGraw Hill Higher Education. ISBN 978-0-07-463683-1.
5. ^ Baker, Samuel L. (2000). "Perils of the Internal Rate of Return". Retrieved January 12, 2007.
6. ^ a b Serfas, Sebastian (2011). Cognitive Biases in the Capital Investment Context. Germany: Cabler Verlag. pp. 30–255. ISBN 9783834926432.
7. ^ Ngwira, Manase, Malawi, David (2016). Public Sector Property Asset Management. UK: Wiley-Blackwell. pp. 115–193. ISBN 978-1-118-34658-7.
8. ^ "Disadvantages of Net Present Value (NPV) for Investments". Investopedia. Retrieved 2022-04-30.
9. ^ Fioriti, Davide; Pintus, Salvatore; Lutzemberger, Giovanni; Poli, D. (2020-06-01). "Economic multi-objective approach to design off-grid microgrids: A support for business decision making (comparison of different economic criteria)". Renewable Energy. doi:10.1016/j.renene.2020.05.154. S2CID 224855745.
10. ^ Serfas, Sebastian (2011). Cognitive Biases in the Capital Investment Context. Germany: Gabler Verlag. pp. 32–255. ISBN 978-3-8349-6485-4.
11. ^ de Rus, Ginés (2021). Introduction to Cost-Benefit Analysis: Looking for Reasonable Shortcuts. Second edition, 2021. UK: Edward Elgar. pp. 136–245. ISBN 978-1-83910-374-2.
12. ^ Steven Buser: LaPlace Transforms as Present Value Rules: A Note, The Journal of Finance, Vol. 41, No. 1, March, 1986, pp. 243–247.
13. ^ Grubbström, Robert W. (March 1967). "On The Application of the Laplace Transform to Certain Economic Problems". Management Science. 13 (7): 558–567. doi:10.1287/mnsc.13.7.558. Retrieved 2022-06-27.
14. ^ Karl Marx, Capital, Volume 3, 1909 edition, p. 548
15. ^ Bichler, Shimshon; Nitzan, Jonathan (July 2010), Systemic Fear, Modern Finance and the Future of Capitalism (PDF), Jerusalem and Montreal, pp. 8–11 (for discussion of history of use of NPV as "capitalisation")
16. ^ Nitzan, Jonathan; Bichler, Shimshon (2009), Capital as Power. A Study of Order and Creorder., RIPE Series in Global Political Economy, New York and London: Routledge