# Net Present Value (NPV)

There are lots of comprehensive (but complicated sounding) financial definitions of present value and net present value. So rather than replicate those, here’s a rather simplified take on what they mean, with particular reference to electricity generation.

If you receive £1000 today, then you could invest that – let’s say you do so at a rate of 10%. In one year’s time, you have £1100. Another way of expressing that is to turn it around and say that £1100 received in a year’s time is worth £1000 in today’s money (present value) if discounted at a rate of 10% – so the latter is what we call a discount rate.

What if we receive another £1100, but in two years time? Discount that at the same rate and it gives us a lower present value: ~£909. That’s because if I had £909 today and it increased by 10% each year, it would have two years to grow: being worth £1000 by year one (£909 + 10% of £909) and £1100 by year two. [For the precise amongst you, the actual present value is £909.090909…]

Keep following that example or experiment with different discount rates and the conclusion is: the further forward in time you go and the bigger the discount rate you assume (i.e. how fast you think present money could grow), the more future money is reduced when expressed in present value terms.

For a power project, future money can include the revenue generated from selling electricity but can also include money spent (costs) on things like repairs or fuel. So you can calculate present values on cash flows which are positive (revenues) and cash flows which are negative (costs).

Do this for every year of an analysis period (e.g. the expected project lifetime), add the negatives to the positives and you have a measure of net present value, NPV. If, when all the numbers are converted back to present values, you’ve spent more than you’ve made, NPV will be negative. On the other hand, if the present values of all your revenues add up to more than the present values of all your costs, your NPV will be positive.

Unless you are involved in the financial modelling of power projects, the main reason to be aware of NPV is because a discount rate and present value analysis is used in calculations of a widely quoted metric: levelized cost of energy (LCOE). The choice of discount rate is often not clear when such figures are quoted, but can have a big impact on the result.