Net Present Value – Definition

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Net Present Value Definition

Net present value (NPV) refers to the variance between cash flows over a period of time. It measures the difference between the present value of cash inflows and cash flows for a given time. NPV accounts for the value of time, value of money, and cash flows (inflows and outflows) in a given period of time. NPV is used for analyze how profitable an investment or project will be, investors or portfolio managers often use it in capital budgeting and investment planning.

The formula for calculating NPV in expressed in this equation;

Rt = net cash inflow – outflows during a single period

i = return that could be earned in alternative investments

t = number of time periods

NPV is calculated as the value of expected cash flows minus the present value of invested cash.

NPV = (Today’s value of the expected cash flows) – (Today’s value of invested cash)

When NPV is positive, it is an indication that the returns or discount rate generated by a project is higher that its planned costs. These values are expressed in dollars. A negative NPV however indicates that a net loss is likely to occur in the project. Oftentimes, investors consider investments with positive NPV because of high profitability.

A Little More on What is Net Present Value – NPV

One of the positioned maintained when calculating the NPV of an investment is the fact that a return (in dollars) earned on an investment in the future will not worth as much as the dollar earned in the present.  This difference or variation is accounted for using the discount rate element of the NPV formula. NPV also regard the present dollar is worth more than the same amount in the future.

For instance investor can choose to receive $105 in a year instead of receiving $100 today if there is nothing else to be done with the $100 that will bring more than the $5 return. Not all investors will accept to wait a year just to earn an additional 5%, especially if there is a tendency of earning 8% on another investment in the next year.

To calculate the net present value of an initial investment of $1,000,000 two things are important; to identify the time or period needed for the investment or project and also identifying the discount rate.

Identifying the number of periods (t): if an equipment is expected to generate a steady monthly cash flow for 5 years, then the number of periods will be 60. (12 months of a year multiplied by 5 years= 60). This should be included in the calculation of NPV.

Identify the discount rate (i): if an alternative investment is to generate 8% annually, this annual discount rate needs to be converted into a monthly rate because the equipment also generates a monthly cash flow. A monthly or periodic rate of 0.64% will be realized.

Step two: NPV of future cash flows

The net present value of future cash flows can be calculated on a spreadsheet or a calculator. If monthly cash flows are earned at the end of the month, and the first payment arrives one month after the equipment was purchased, this is a future payment that needs to be assigned with the time value of the money paid.

The calculation of the NPV will therefore be the present value of all the future cash flows (a total number of 60) subtracted from the $100,000,000 investment. This method of calculation is applicable when the equipment is directed to be worthless at the end of its life span.

After calculating the NPV and it turns to be positive, the equipment will be worth the purchase, if in the other hand the NPV is negative, the equipment should be avoided.

Net Present Value Drawbacks and Alternatives

There are some downsides of net present value, NPV depends on and draws its conclusions on assumptions, therefore, its calculations might fail to accurately gauge the profitability of an investment. Aside from this, there are unforeseen expenditures that can occur during the lifespan of a project and these might not be captured.

There are however other alternatives to NPV such as the payback method. The paid of time it will take for an original investment to be repaid is calculated in the payback method. This method only accounts for the time required to pay back an investment cost but  fails to account for the time value for money which is its major shortcoming.

Net Present Value vs. Internal Rate of Return

The Internal rate of return (IRR) of an investment is also called the discounted cash flow rate of return. Both IRR and NPV have certain similarities but the NPV of an investment can be reduced to zero when discount rate is applied.  IRR only measures the rate of return of an investment exclude other factors which are not internal when calculating the return.

Conclusion

The NPV of an investment accounts for the time value of money of the investment, it shows the present value of all future cash flows that an investment has. A positive NPV is an indication of significant of profitable return and good investment while investments with negative NPV are to be avoided.

Time value of money calculated using NPV can be compared to other alternative investments.

However, because NPV is based on assumptions on future events, it’s calculations are not always accurate.

References for Net present Value

Academic Research on Net present Value

Uses, abuses, and alternatives to the netpresentvalue rule, Ross, S. A. (1995). Financial management, 24(3), 96-102.

Fiscal implications of immigration—A net present value calculation, Storesletten, K. (2003). Scandinavian Journal of Economics, 105(3), 487-506.

The scheduling of activities to maximize the net present value of projects, Elmaghraby, S. E., & Herroelen, W. S. (1990). European Journal of Operational Research, 49(1), 35-49.

A compendium and comparison of 25 project evaluation techniques. Part 1: Net present value and rate of return methods, Remer, D. S., & Nieto, A. P. (1995). International journal of production economics, 42(1), 79-96.

Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints, Neumann, K., & Zimmermann, J. (2000). European Journal of Operational Research, 127(2), 425-443.

Free Cash Flow (FCF), Economic Value Added (EVA™), and Net Present Value (NPV):. A Reconciliation of Variations of Discounted-Cash-Flow (DCF) Valuation, Shrieves, R. E., & Wachowicz Jr, J. M. (2001). The engineering economist, 46(1), 33-52.

Scheduling a project to maximize its net present value: an integer programming approach, Yang, K. K., Talbot, F. B., & Patterson, J. H. (1993). European Journal of Operational Research, 64(2), 188-198.

On maximizing the net present value of a project under renewable resource constraints, Vanhoucke, M., Demeulemeester, E., & Herroelen, W. (2001). Management Science, 47(8), 1113-1121.

Project options valuation with net present value and decision tree analysis, De Reyck, B., Degraeve, Z., & Vandenborre, R. (2008). European Journal of Operational Research, 184(1), 341-355.

Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value, Hsieh, T. P., Dye, C. Y., & Ouyang, L. Y. (2008). European Journal of Operational Research, 191(1), 182-192.

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