Syndicate
Calculating the Time Value of Money
The basic idea of the time value of money is that it is not the same to receive 100 dollars today than it would be to receive that same amount next year, since the one hundred dollars today can be invested at a risk free rate and the year that is to come we will have 103 dollars for sure. In other words, the Future Value (FV) or the value in the year to come, if one dollar is equal to the present value (PV) multiplied by one plus the yield we are hoping for K, for example:
FV = PV x (1 + K) = FV = 100 dollars x (1 + 0,03) = 103 dollars
In other words, it would be the same to receive 103 dollars the next year, as it would be to receive 100 dollars this year, if the risk free interest is of 3 of 100. if the risk free interest was for example, a 5 of 100 then it would be the same for us to receive 105 years the next year or 100 dollars today; but we would prefer to receive 100 dollars today than to receive 103 dollars the next year. In other words, if the risk free rate goes up we ask for more value of the dollars than we will receive in the future. Therefore, in order to find the present value of a future amount to be received, we discount the future value of a determined rate, which is the yield that we could obtain for sure. (Risk free yield).
If receiving 103 dollars were not a completely certain thing, in other words, if there were a risk involved, we would probably prefer to receive 100 dollars today instead of 103 “almost” sure dollars next year. However if we were offered 110 dollars with a good amount of probability – but not entirely sure – we would be indifferent about receiving 100 dollars today or 110 “almost” sure dollars the next year. With this what we are doing is that when uncertainty is seen (the possibility of not receiving 103 dollars), we use a greater discount rate K. In the example, the discount rate we use, or the yield we ask for that uncertainty is of 10 by 100.
If we invest our 100 dollars at a risk free rate for two years, its future value would be of:
FV = PV x (1 + K) = 100 dollars x (1 + 0,03) = 103 dollars
This would be the value of one year. This amount will be invested again during the second year and in the end we will obtain:
FV = 103 dollars x (1 + 0,03) = 106,09 dollars
In other words:
FV = PV x (1 + K) x (1 +K) = PV x (1 + K)
Out of which the present value can be cleared up from the formula.