Net present value

How do you decide whether an investment to build, say, a combined heat and power station is worthwhile? What factors do you take into consideration? If you are making any capital investment decisions (e.g. building a power station, investing plant into extracting oil or building a dam), problems which most people do not come across in normal life can arise.

In reviewing the past performance of a business, you assess the amount of net assets employed and profits before and after tax each year. This is too simple for a capital investment, especially if the environment has to be taken into account.

Discounting is a simple concept, being the opposite of compounding:

Present > Compounding > Future

Value < or Discounting < Value

Compounding is used to determine the future value of present cash flows; discounting is used to determine the present value of future cash flows.

Compound interest is calculated by the formula:

Compound interest = I c = 1 + r t

(where r is the rate of interest per time period t)

Therefore, value in the final amount, Vfinal, is given by the following equation using the rate as a percentage and the initial value, Vinitial:

CVfinal=Vinital*[100%+rate100%]t

The compound discounting is calculated by the formula:

Compound discounting amount = Dc=11+rt

Therefore, present value =

PV=Vt1+rt

where Vt is the value of the item when it is realised at the future time t, and r is the fractional rate.

Or using the rate as a percentage:

PV=Vt*100%100%+ratet

Let's look at how this works in practice.