What is net present value?

Would you prefer $50 now, or $100 in 12 months time? If you live in the US or Australia, you'd prefer the latter. If you live in Zimbabwe or 1920's Germany, you'd much prefer the former. Why the difference?

Let's pretend your an investor who only invests in term (certificate) deposits, and the current interest rate is 10%. So $100 invested now will be worth $110 in 1 year. The future value (FV) is a function of current value (CV) and interest rate (IR) as follows:

FV = CV*(1+IR)
$110 = $100*(1+0.10)

Let's reverse the equation and find out what the CV of $100 in 1 years time is.

CV = FV/(1+IR)
CV = $100/(1+0.10)
CV = $91

This makes sense. If we put $91 in a term deposit at 10% for 1 year, we'd have $100 at the end.

We can also look out past 1 year by modifying the equation. Suppose we were promised $100 in five years time when the interest rate is 10%. How much is this worth?

CV = $100/[(1+IR)*(1+IR)*(1+IR)*(1+IR)*(1+IR)]
CV = $100/(1+0.10)^5
CV = $100/1.61
CV = $62.09

What this says is that if I took $62.09 and invested it for 5 years at 10% I would have $100 (the promised amount). But the really interesting thing is changes in CV as a result of IR. Suppose we look at an IR of 2% and 20% over 5 years with an FV again of $100.

CV = $100/(1+0.02)^5 = $90.57
CV = $100/(1+0.10)^5 = $62.09
CV = $100/(1+0.20)^5 = $40.19

The CV changes are dramatic, from -9% nominal, to -60%. The graph below shows the CV of a promised $100 in 5 and 10 years at different interest rates.
What is significant is just how quickly high interest rates reduce the current value of future money. This simple financial fact is one of the most important in finance. It helps us value bonds, shares and compare different investment opportunities. Check the articles index for more.