Discounting Principle

One of the fundamental ideas in economics is that a rupee tomorrow is worth less than a rupee today. This seems similar to the saying that a bird in hand is worth two in the bush. A simple example would make this point clear. Suppose a person is offered a choice to make between a gift of Rs. 100 today or Rs. 100 next year. Naturally he will choose the Rs. 100 today.

This is true for two reasons. First, the future is uncertain and there may be uncertainty in getting Rs. 100 if the present opportunity is not availed of. Secondly, even if he is sure to receive the gift in future, today’s Rs. 100 can be invested so as to earn interest, say, at 8 percent so that. one year after the Rs. 100 of today will become Rs. 108 whereas if he does not accept Rs. 100 today, he will get Rs. 100 only in the next year. Naturally, he would prefer the first alternative because he is likely to gain by Rs. 8 in future. Another way of saying the same thing is that the value of Rs. 100 after one year is not equal to the value of Rs. 100 of today but less than that. To find out how much money today is equal to Rs. 100 would earn if one decides to invest the money. Suppose the rate of interest is 8 percent. Then we shall have to discount Rs. 100 at 8 per cent in order to ascertain how much money today will become Rs. 100 one year after. The formula is:

 V = Rs. 100 1 + i

where,

V = present value

i = rate of interest.

Now, applying the formula, we get

 V = Rs. 100 1 + i = 100 1.08

If we multiply Rs. 92.59 by 1.08, we shall get the amount of money, which will accumulate at 8 per cent after one year.

92.59 x 1.08 = 99.0072

= 1.00

The same reasoning applies to longer periods. A sum of Rs. 100 two years from now is worth:

 V = Rs. 100 = Rs. 100 = Rs. 100 (1+i)2 (1.08)2 1.1664

Similarly, we can also check by computing how much the cumulative interest will be after two years. The principle involved in the above discussion is called the discounting principle and is stated as follows: “If a decision affects costs and revenues at future dates, it is necessary to discount those costs and revenues to present values before a valid comparison of alternatives is possible.”

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