SERIES ARTICLE

*Advances in Project Management Series*

**By Martin Hopkinson**

United Kingdom

A project may be worth doing provided that its costs are more than justified by its benefits. This principle lies at the heart of any project business case. If we can forecast the financial value of a project’s benefits, we can compare it to the project’s cost to test how attractive the business case is. NPV modelling is a way of performing this test. Its approach to discounting cash whereby future cash can be compared to today’s value is considered to make it a robust method for making financially-based project selection and approval decisions.

**The NPV method**

Today’s value of an amount of cash is its present value. If we know the cost of tying up cash or delaying its receipt, we can calculate the present value of cash at different points in the future. The rate of cost can be expressed as a discount rate. For example, if the discount rate (D) is 10%, the annual cost of tying up £100 cash is £10. On this basis, we would need £100(1+D) = £100(1+0.1) = £110 one year in the future to compensate for having £100 today. This is equivalent to calculating that the present value of £110 one year in the future would be £110/(1+D) = £100. Thus, if an amount of value of cash in one year in the future is written as C_{1} and its present value written as P_{1}, then P_{1} = C_{1} / (1+D). In general, since the associated costs accumulate at a compound rate, for a point in time that is n years in the future the present value P_{n} of an actual amount of cash C_{n} is calculated by the formula:

P_{n }= C_{n }/ (1+D)^{n}.

The Net Present Value (NPV) method for project financial modelling is usually applied by calculating the present value of the cash flow for each annual period of the extended project life cycle. Costs produce a negative cash flow, whist benefits contribute positively. The cash flow for each period can thus be calculated by deducting the cost forecast for that period from the cash value of the forecast benefits. Having calculated the present value for the net cash flow during each period the project NPV is calculated by summation. The formula for project NPV is thus:

using year-end discount factors, or

where:

C_{t} = the net cash flow over a period of time (typically 1 year),

t = the period of time during which that cash flow takes place,

D = the discount rate (rate of loss in the value of cash expressed as a percentage – typically per annum) and

n = the number of periods of time periods (typically years) over which NPV is calculated

The discount factor is the value by which a year’s cash flow is multiplied by to obtain its present value. In practice, many projects are modelled using year-end discount factors. However, on projects in which costs and benefits materialise continuously throughout each year, the use of mid-year discount factors is usually more appropriate.

**A Simple Example**

Figure 1 is a simple example that illustrates how NPV can be modelled. It is based on a project that is forecast to cost £2.5m over a two-year period and achieve benefits of £3.5m over a period commencing 18 months into the project and ending at the end of Year 5. An undiscounted forecast of the project’s net value would thus be £3.5m – £2.5m = £1m. Figure 1 shows how applying a discount rate of D = 4% affects this calculation. Note that the 4% rate used in the example above is comparatively low and reflects the use of constant cost forecasts for costs and benefits i.e. without the effects of inflation.

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About the Author

United Kingdom

**Martin Hopkinson** is the Director of Risk Management Capability Limited and has 30 years’ experience as a project manager, project risk management specialist and consultant. His experience has been gained across a wide variety of industries and engineering disciplines and includes multi-billion pound projects and programmes.

Martin’s first book, *The Project Risk Maturity Model*, concerns the risk management process. His contributions to Association for Project Management (APM) guides such as *Directing Change* and *Sponsoring Change* reflect his belief in the importance of project governance and business case development.

In his new book *Net Present Value and Risk Modelling for Projects* he brings these subjects together by showing how NPV and risk modelling techniques can be used to optimise projects and support project approval decisions. (To learn more about the book, click here.)