What Is the Net Present Value (NPV) & How Is It Calculated? - Project-Management.info (2024)

When you perform a cost-benefit analysis and need to compare different investment alternatives with each other, you might consider using the net present value (NPV) as one of the profitability indicators. In project management, the NPV is commonly used and also listed in PMI’s Project Management Body of Knowledge (source: PMBOK®, 6th edition, part 1, ch. 1.2.6.4, p. 34). While the basic calculation – the sum of discounted cash flows – is comparatively easy, it is key to understand the assumptions, strengths and weaknesses of the NPV to make a reflected investment decision.

This article will introduce the net presentvalue, its formula as well as the required assumptions. This includes thedifferent components and pros and cons of this indicator and is furtherillustrated with 2 comprehensive examples. Thus, you will be able to apply theNPV in a sensible way when you compare different investment and project alternatives and when you present them to your stakeholders.

What Is the Net Present Value? The Definition.

The NPV represents the monetary value of aseries of future cash flows by today. All future cash flows are thereforediscounted with a predefined interest rate or discount rate. The NPV is part ofthe set of Discounting Cash Flows (DCF) methods.

The net present value is often used in thecontext of a cost-benefit analysis where it is a common indicator for theprofitability of project or investment alternatives:

• A positive NPV suggests that theinvestment is profitable, i.e. the return exceeds the predefined discount rate).
• The NPV is negative if expensesare higher or occur earlier than the returns. Thus, the investment does notyield the
• A net present value of 0indicates that the investment earns a return that equals the discount rate.

The Net Present Value (NPV) Formula

The formula for the calculation of the netpresent value is

where:

NPV = Net Present Value
NCF = Net Cash Flow of a period
i = Discount Rate or Interest Rate
RV = Residual Value
N = Total Number of Periods
t = Period in which the Cash Flows occur

These parameters are determined by certainestimates and assumptions which are discussed in the following section.

Components and Assumptions of the NPV Computation

The formula consists of three differentfundamental elements:

• the assumed cash flow of aperiod (for each period),
• the preset discount rate orinterest rate (for each period),
• the residual value at the endof the projection (optional).

The NPV calculation takes the point in timeinto account at which cash flows occur. With a positive discount rate (which isby far the most common use), earlier cash flows impact the NPV more than thoseof later periods. This can lead to a negative NPV even if the simple non-discountedsum of cash flows is positive or 0.

Cash Flows

Cash Flows used for NPV computations are usuallystemming from a business projection for an investment or a project opportunity.If you assess the value of a contract or a financial instrument with agreedupon payments, you will probably use those amounts though.

For instance, if you are planning a projectwith a one-year implementation time and 5 years use of the created result, yourprojected cash flows will be the estimated project cost in period 0 and 1 (initialinvestment) and the expected benefits and running cost as of period 1. Notethat the scheduling of activities and, subsequently, cash flows will have animpact on the overall NPV (source).

For the calculation of the NPV, a net cashflow estimation is basically sufficient. It does not change the result whetheryou discount net cash flows or whether you discount gross inflows and outflowsand offset the present values of both series.

However, if you intend to calculate the benefit-cost ratio in addition to the NPV, you will want to maintain a granularestimate of gross in- and outflows in your projection.

Discount Rate / Interest Rate

In the basic version of the NPV computation– which is usually applied for rough projections in early stages of a project –the discount rate remains constant for all periods and for all kinds of cashflows. It often represents the organization’s target return on investments orweighted average cost of capital (WACC).

In some areas, such as financial markets,the discount rates may vary among the different periods. They can, forinstance, represent a market interest rate curve or swap rate curve. Thoserates will then be used to price instruments and transactions.

In some cases, it may also be sensible touse different discount rates for different types of cash flows, e.g. distinguishedinto risk-free in- and outflows and those subject to higher risk.

An example of a very accurate yet rather complexapproach is the project option valuation with net present value and decisiontree analysis (read more on ScienceDirect).

While there are good reasons to do this incertain cases, complex calculation may often be over-engineered for small andmid-size projects, in particular in early stages. For such projects, interestrate changes or splits are often deemed less material compared to otherassumptions and insecurities of a forecast.

Residual value

When you are projecting cash flows for along time horizon, you will likely reach a point on the timeline where it isnot reasonable to continue the detailed benefit and cost forecasting, e.g. whenestimates lack accuracy or would require huge efforts. This is where theresidual value becomes relevant (source).

The residual value represents the remainingvalue of an asset, a project result or an intangible good at the end of thetime horizon of a projection.

In a construction project, for instance, aproject controller might decide to determine detailed cash flows (or benefitsand costs) for the years 1 to 10 of a projection. Subsequently, he would add aresidual value to the projection in order to account for cash flows occurringin the years 11 and later or for the expected market value of the asset at theend of year 10.

There are 3 different types of residualvalues that are typically used:

• Discounted infinite series of cashflows / perpetuity,
• Expected market value (salvagevalue),
• Cost of disposal,
• Zero.

Infinite Series of Cash Flows / Perpetuity

This method is sensible for investments andassets that provide returns for an infinite time. Examples are certain types ofassets with an infinite lifecycle, e.g. some financial instruments, (historic)buildings (arguable, but there are indeed historic buildings that lasted forcenturies) or farmland. Their returns are reflected in a residual value thatequals the present value of the perpetuity discounted to the last year of theforecast’s time horizon. It is calculated as follows:

ResidualValue = Net Present Value = perpetuity / interest rate

The calculation of this value requires 2assumptions: the constant perpetuity and the interest rate. The perpetuityreflects the constant net cash flow that is expected to occur after thedetailed forecasting period.

The interest rate can be the discount rateof the NPV calculation, sometimes increased by an add-on to take the insecurityof long-term planning into account. If cash flows are expected to increase overtime, e.g. in case of real estate investments, that growth rate is subtractedfrom the discount rate used for this calculation.

Most types of assets have a limitedlifecycle though. The other approaches to determine their residual value aretherefore more accurate. However, the present value of a perpetuity issometimes also used for those types of investment as a proxy, usually involvinga high interest rate (i.e. a lower present value) to account for the inaccuracyof the calculation.

Expected Market Value / Salvage Value as Residual Value

If it is intended to sell an asset at afuture point in time, it is reasonable to include the forecasted market valuein the NPV calculation. The future market value or salvage value needs to beestimated for this purpose.

Possible techniques include but are notlimited to the extrapolation of past market value developments, the use ofcertain depreciation rules/curves or the expected future book value.

In project management, this residual valuetype is used, for instance, if a projection covers the entire lifetime of aproduct. A market value can be reasonable in cases where a project result issubject to a license requirement that allows for a usage shorter than thelifecycle of the assets purchased or created.

Project Residual Value of 0

A residual value of 0 is typically assumedif the projection horizon ends at the end of – or even beyond – the expectedlifecycle of an asset or product. This may be applicable to fast-changing typesof assets, e.g. software and electronic devices.

A residual value of 0 can also be areasonable or conservative assumption if the future values or cash flows are highlyuncertain or subject to a high degree of ambiguity.

Negative Residual Value due to Disposal Cost

Some types of assets will cause disposalcosts when they are used up. These cost are also part of the cost-benefit assessmentof such investments. Examples could be projects and investments that involvetoxic material or constructions and structures that need to be removed eventually.

However, it is arguable whether these costsare classified as a negative residual value or a negative cash flow/cost in thedetailed forecast. As either understanding leads mathematically to the sameresult, we will skip further elaboration on that discussion. One way or theother, it is just important not to forget the disposal cost when projectingcash flows.

How to Calculate the Net Present Value in 6 Comprehensiveand Understandable Steps

Follow these 6 steps, use a calculation tool (such as Excel or our NPV calculator) and set aside a few hours to determine the NPVs of your project or investment options.

1. Determine the Expected Benefits and Cost of anInvestment or a Project over Time

The basis for the calculation of the netpresent value are the projected benefits and cost over time. Depending on thecharacteristics of an investment or project option, you will likely want toinvolve subject matter experts who help you project the monetary value of theexpected benefits and cost.

For this estimation, you can either developyour own estimation approach or refer to the following components that arecommonly addressed in a forecast:

• Initial investment: Outflows,project cost, allocated staff and all other types of resources that are used tocreate the results or assets subject to this analysis. Depending on the time oftheir occurrence, these outflows can be allocated to or split into period 0 andperiod 1 of the projection.
• Recurring benefits / inflowsfrom the investment or asset upon its completion.
• Recurring or running costs thatare necessary to maintain the asset.
• One-off cost and one-offbenefits / inflows within the time horizon.

All these components need to be estimatedand allocated to periods (typically years). Once you have completed thisgranular forecast, proceed with the next step.

2. Calculate the Net Cash Flows per Period

Calculate the sum of all inflows andoutflows for each period to determine the net cash flow of each period.

Alternatively, you can discount all grosscash flows (inflows as well as outflows) separately. Both ways will result inthe same NPV.

3. Set and Agree the Discount Rate

Following our previous explanations, youwill have to define an interest or discount rate which you will use for discountingthe cash flows.

There are numerous options of how to comeup with an appropriate discount rate. Some of the most common ways are:

• a company’s targetreturn-on-investment rate;
• the cost of capital, i.e. theaverage rate a company needs to pay on its liabilities and as return on equity;
• a market rate, i.e. an interestrate financial instruments with similar tenor and riskiness would yield;
• a risk-adjusted rate, i.e.consisting of a base rate (such as risk-free interest rate or a company’s costof capital) plus an add-on to take the specific risk of the endeavor intoaccount.

In addition, interest rates can vary amongthe cash flow sources and periods: a swap or yield curve can be used to achievean accuracy comparable to the valuation of financial markets instruments. Ifcertain elements of the projected cash flows are more certain (e.g. cost) thanother assumptions (e.g. sales revenue), the reflection of the different levelof risk in the respective discount rate can be considered (in that case, step 2needs to be modified in order to aggregate cash flows per period based on theirriskiness).

In theory, there are many different optionsand assumptions involved in the determination of the interest rate. In practicethough, a fixed interest rate – usually a company’s target return-on-investmentrate – is the most common discount rate type for NPV calculations used tocompare different project and investment options.

4. Determine the Residual Value

If necessary, estimate a residual value, as explained in the previous section. Consider the characteristics of the asset as well as the accuracy and reliability of a long-term forecast when you come up with a fitting residual value type. The following values can typically be used as residual values:

• a discounted infinite series ofcash flows / perpetuity after the time horizon of the detailed projection,
• the expected market value (orsalvage value) of an asset,
• the cost of disposal, or
• zero.

If you are choosing the present value of aperpetuity as your residual value, you will need to repeat step 3, thedetermination of a discount rate, for this calculation as well (read thedetails in the previous section).

In any case, make sure that the use andassumptions of a residual value are transparent and understandable forstakeholders. This is particularly recommended in cases where the residualvalue is one of the main drivers and components of the net present value. Thus,its rather rough assumptions might significantly impact investment decisions orthe selection of project options.

5. Discount the Cash Flows of Each and Every Period

Discount the net cash flows of each period,following the abovementioned formula. Use the interest rate determined in step3 and discount the residual value that you have calculated in the previousstep.

Alternatively, you can discount gross cashflows first, e.g. separately for inflows and outflows or for different levelsof riskiness.

6. Calculate the NPV as a Sum of Discounted Cash Flows

Whichever discounting method you have usedin the previous step, the Net Present Value is always the sum of all yourdiscounted cash flows.

You can then rank the differentalternatives by profitability, starting with the highest NPV.

When you are using this result for your stakeholder communication, make sure that you do not only present the calculated figure but also its underlying assumptions. This will allow them to get a full picture of the projection and ensure the comparability of different investment or project options.

Examples of NPV Calculations in Practice

This section contains 2 examples, aiming toillustrate the application of NPV calculations to real-life situations. Thefirst example comprises the comparison and selection of different project options.The second example elaborates on the use of perpetuities for infinite series ofcash flows.

Example 1: Comparing Net Present Values of DifferentSoftware Solutions

The following example will help youunderstand the calculation and the parameters that affect the NPV.

Estimated Cash Flows and Agreed Discount Rate

During the pre-project phase, a projectmanager is asked to compare the financial effects of 3 alternative softwaresolutions to facilitate the project sponsors’ decision-making.

The company’s expected return rate is 12% which is therefore the discount rate parameter of this NPV calculation. The investment and cost relate mainly to license, implementation, customizing and maintenance cost. The company intends to benefit from materialized efficiency gains as well as increased revenues as soon as the software helps enhance customer service.

The project manager is assessing thefollowing 3 options for a new software solution:

• Option 1 comprises buying an off-the-shelf solution that requires some customizing and an implementation time of 1-2 years.
• Option 2 is more comprehensive software solution that needs a shorter implementation time yet requires a higher initial investment. It would be ready to produce positive cash flows as of year 1.
• Option 3 involves an in-house development project at a lower cost which however takes more time. Benefits are expected from year 2 on.

For all 3 cases, the software is expectedto be replaced at the beginning of year 7 (i.e. immediately after year 6, theend of this projection) with no residual value.

Overview of Estimated Cash Flows

The subject matter experts involved in thecost-benefit analysis came up with the following estimated figures.

The following table compares the net cashflows of all three options.

At first sight, Option 2 seems to be themost promising one, given its high benefits and early break-even point in year1. Option 3, on the other hand, appears to be the least appealing alternative.

This perception is also reflected in thesimple sums of cash flows for each option: 7,500 for Option 2, 7,000 for Option1 and 6,000 for Option 3. However, the sum of non-discounted cash flows is notan appropriate type of value for comparing series of cash flows over time as itdoes not consider the points in time at which those cash flows occur. This iswhere the NPV method makes a difference.

Discounting Cash Flows and Calculating the NPV for EachOption

The next table contains discounted cashflows for each period and each option. They are calculated using the abovementionedformula, with the results summarized in the following tables.

The Net Present Value (NPV) is the sum offall discounted cash flows:

NPV (Option 1) = (- 5,000) + (- 4,464) + 1,594 + 3,203 + 2,860 + 1,702 + 1,520 = 1,415

NPV (Option 2) = (-185)

NPV (Option 3) = 1,765

Summary and Interpretation of Results

To compare the net present values anddetermine the best option (based on NPV), the alternatives are ranked by theirNPV in descending order.

In this case, Option 3 is the mostbeneficial alternative, followed by Option 1. The benefits (inflows) of Option2, on the other hand, do not even meet the expected rate of return which isindicated by a negative net present value.

These results are significantly differentfrom the simple un-discounted sums calculated in the previous section. This proves,once again, how important the time factor and the interest rate are when itcomes to assessing a series of cash flows.

Note that the NPV is only one part of acost-benefit analysis. There may be qualitative criteria (for software, e.g.the company’s target IT architecture, security considerations, ease of use andmaintenance, vendor rating etc.) as well as other calculation methods thatcould suggest a different ranking of those options.

Example 2) Calculating the NPV with a Perpetuity asResidual Value

The second example is an investment with aperpetuity as the residual value – a real estate investment, for instance.

The series starts with an initialinvestment of 1,000,000 that is incorporated as an outflow in year 0. The rentalincome is estimated at 60,000 in the first year with recurring cost (e.g.maintenance, management, taxes) of 10,000.

Both cash flow types are expected toincrease by 2% each year. The detailed forecast covers 6 years with a residualvalue calculated based on future returns. The discount rate is 5% and may, forinstance, represent the cost of funding and expected return.

The forecasted cash flows for the years 0 –6 are as follows:

After year 6, the net cash flow is expectedto be 55,000 with an expected annual growth of 1.5%. To account for the inherentinsecurity of long-term estimates, a risk add-on of 2% is added to the expectedreturn of 5%. The expected annual growth lowers the discount rate of theperpetuity (hence increases the present value) while the risk add-on increases therate (and lowers the present value):

The perpetuity as the residual value iscalculated by dividing the cash flow by the discount rate:

Residual Value = 55,000 / 5.5% = 1,000,000

This figure is the present value of theperpetuity at the end of year 6. It needs to be discounted – using the overalldiscount rate of 5% (alternatively, it could be discounted with 5.5% or anyother discount rate) – along with all other cash flows.

Once all numbers are calculated, the tablelooks like this:

The net present value of the investment isthe sum of all discounted cash flows:

NPV = (-1,000,000) + 47,619 + 46,259 +44,937 + 43,653 + 42,406 + 41,194 + 746,215 = 12,283

The positive NPV indicates a profitableinvestment.

Advantages and Disadvantages of the NPV

The net present value is a very common technique of cost-benefit analyses in finance, project management and various other economic areas. It takes the value of time and the expected return rate into account. One of the advantages for project managers and executives is that it produces only one figure per project and investment option that can easily be compared with other options. Lastly, it is fairly understandable which helps communicate the results of NPV-based cost benefit analyses.

However, the NPV comes with some disadvantages and weaknesses. It is broadly based on assumptions that can have a material, if not even game-changing, effect on the results. If the interest rate or the residual value are estimated, small changes to the parameters can heavily affect the present value. A methodological alignment of the calculation of different options and a high level of transparency on the assumptions can help reduce the risk of unintended or biased results. It also assumes that returns can be reinvested at the discount rate which might not always be the case in practice (source).

The net present value aggregates a numberof estimates into one catchy figure. While this increases understandability andkeeps things comparable and manageable, the information on the duration of therepayment of an initial investment is lost. Irrespective of economic figures,some decision-makers might prefer an option with high returns in early periodsover an option with a higher NPV but returns coming in in later periods. Thisdistinction is not possible when comparing project options solely based on theNPV.

Conclusion

The Net Present Value is a popular method of cost-benefit analyses as it is comparatively easy to understand and provides an accurate basis for comparing different project or investment alternatives. However, it requires a set of assumptions and comes with a number of weaknesses – one of which is the usually rough calculation yet high relevance of residual values for long-term investments.

Therefore, you should always maintain a critical view on the results and assumptions of NPV calculations. For investment decisions, it is not recommended to rely on only one single indicator. You should in fact use other quantitative and qualitative methods to assess alternative options as well.