Present Value

The present value concept can be seen as being the opposite of the future value concept. As a sum of money invested today will tend to grow in future, so a sum of money to be received in the future will be worth less in today’s terms. The current value of any future cash flow is referred to as its present value. Present value is one of the most important concepts in finance, as it allows future cash flows from an investment to be compared with present capital investment requirements to determine whether the investment will be profitable.

The future value equation, as discussed above, is:

Future Value = Present Value * ( 1 + i ) ^ t

Therefore, the present value is:

Present Value = Future Value / ( 1+i ) ^ t

In other words, the future value of a cash flow is multiplied by a factor of 1 / (1 + i) ^ t to arrive at the present value. Provided that ‘i’ is positive, the future value will always be greater than the present value. As such, 1 / (1 + i) ^ t is generally known as the discount factor and ‘i’ is known as the discount rate or cost of capital, generally expressed in percentage terms.

For most projects, there will tend to be a major capital investment at the start, and then a number of cash payments at a series of future dates. Depending on these dates, the future cash flows will be discounted by different factors to bring them back to their present value. The sum of all the present values of cash flows for an investment, including any initial payments, is referred to as the net present value. For a given discount rate, i, if the net present value is positive then the project will be accepted, as it produces a net positive present value for the company.

In order to calculate the net present value, it is important to be precise about the data being used. For example, any depreciation should not be counted in the calculation, as it is not a cash flow. In addition, any cash flows which have already been made, such as R&D, should not be included as they cannot be recovered and are not relevant to the decision. They are said to be sunk costs. Finally, it is important to be absolutely certain of when each payment is received, and hence which discount factor should be applied. The best way to achieve this is to use a time line and discount each value according to its position on the time line.

Note also that, in the same way that many universities will provide interest factor tables, they will also provide discount factor tables showing values of 1 / (1 + i) ^ t for a variety of time periods and interest rates.

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