# 3.2 The time value of money, discounting and present value

Many projects involve cash flows that occur over several years and, in order to accurately assess the benefit that will be received from projects, it is necessary to take into account the time value of money. The time value of money reflects the fact that cash flows in the future are less valuable than those that take place immediately. The further into the future they occur, the larger the discount needs to be to reflect the greater reduction in value. Discounting each future cash flow in proportion to how far it occurs in the future allows us to compare all the future cash flows which result from taking on a project on an equal basis.

This equal basis is called the present value of the future cash flows, and which is the equivalent value of each future cash flow if it were paid or received today. By converting each future cash flow into its present value, you can compare future cash flows that occur at different points of time in the future on a like-for-like basis. Converting a cash flow to its present value is achieved by discounting using the discount rate, which is the annual discount that must be applied to future cash flows. This technique can be applied to two types of decisions in project appraisal, which are discussed below.

## Determining whether or not a project should proceed

The NPV (net present value – the total sum of all the positive and negative relevant future cash flows) of a project is calculated. A project will add value to an organisation when its net present value is positive. Note that net present value is not simply totalling all cash flows from a project to see if they are positive: because of the time value of money, cash that is received a long time in the future has significantly less value than cash paid out now. So a project that produces a lot of cash inflows sometime in the future may have positive* net cash flows*; however, when the time value of money is taken into account the *net present value* may actually be negative.

A very simple example of this would be if a company offered to pay you £110 in 10 years’ time, if you invest £100 with them now. Despite the net cash flow being £10, this is clearly not a good investment. Inflation over 10 years will mean that £110 in 10 years has significantly less present value than £100 now. (And this is without taking into account the additional risk that you do not receive the money back, for example if the company goes bankrupt over the 10 years and you lose your initial £100.)

## Choosing between projects

Sometimes, there is more than one project available and only one can be chosen (perhaps the projects are mutually exclusive, or they both achieve the same objective in different ways).

When appraising several projects, not only do you have the problem that the actual cash flows cannot simply be added together, but also that different projects will last for different lengths of time and have different patterns of cash outflows and inflows over the lifetime of the project. Using net present value makes it easy to compare the relative value that each project will provide to the organisation. Once you have discounted the cash flows into present values the rest is simple: simply find the net present value for each project and the highest net present value is the best option, at least economically, as it produces the most value for the organisation.