Future Value
How much money will I have ONE year from today if I invest 100 dollars at an interest rate of 10%? Here, 10% is the annual return. The answer is 100 + 10% of 100 = 100 + 100 x 10% = 110. How much money will I have two years from now if I invest 100 dollars today at the same rate of return?
Value at the end of year 1 = 100 + 100 x 10% = 100 x (1 + 10%)
Value at the end of Year 2 = [100 x (1 + 10%)] + [100 x (1 + 10%)] x (1 + 10%) = 100 x (1 + 10%)2.
So, in general, the future value of P at the end of n years, at a rate of return of r, is:
FV = P x (1 + r)n
Present Value
Let’s ask the question in reverse. How much money should I invest to get 110 dollars in one year from today at a rate of return of 10%? We know that intuitively – it is 100. Formally, we get it by dividing 110 by (1 + 10%). By the way, 10% equals 0.1 (110/1.1 = 100). So the present value of 110 one year from now is 110 / (1 + 0.1). If we extend this further, the present value of C, n years from today, at a rate of return of r, is
PV = C/(1+r)n
Net Present Value
What is the present value (PV) of the future benefits that will happen in the following manner?
Year 1 = 200
Year 2 = 200
Year 3 = 200
Year 4 = 200
That must be PV of year 1 benefit + PV of year 2 benefit + PV of year 3 benefit + PV of year 4 benefit.
200/(1+0.1) + 200/(1+0.1)2 + 200/(1+0.1)3 + 200/(1+0.1)4 = 181.82 + 165.29 + 150.26 + 136.60 = 633.97.
The story is not over yet. What if I need to invest 500 dollars today to get the above benefits (200 dollars every year for 4 years)? Is it a good deal or a bad deal?
To get the answer, you estimate the present value of the future cash flows and subtract what is required to pay today. That is 633.97 – 500 = 133.97. Not bad. It is the net present value of this business.
The underlying principle behind these calculations is known as the ‘time value of money‘.
