# Time Value of Money

Capital expenditures involve costs and benefits over time. For example, if an investor wants to go in for a sugar factory, he would incur capital expenditure in the purchase of land, construction of buildings, buying of plant and machinery, purchasing of sugarcane, payment of wages and salaries to the employees. While some of this expenditure is non-recurring, others are recurring expenditures. Further even all non-recurring expenditures may not be incurred in a particular month or a year but rather spread over a number of years. Once the project is commissioned, it would generate output in the form of sugar and molasses, which would be forthcoming year after year until the project terminates. Thus, investment projects are associated with costs and benefits which are spread over a period of time.

Analysis of an investment project involves comparison of costs and benefits associated with it. It is not only the amount of costs and benefits that are relevant for this purpose, but also the timings of their occurrences. This is because money has time value for the following reasons:

(a) Earning power of money
(b) Inflation/deflation
(c) Uncertainty

Whenever there are investment opportunities money has the earning power. The earning power is represented by the opportunity cost of money, the least of which would be the rate at which banks accept deposits. By this virtue, todayâ€™s sum of money is equivalent to a larger sum in the future.

Money is needed not for its own sake but for its purchasing power, which varies inversely with the price level. Thus, when one considers the use or value of money, it changes with inflation and deflation for a given sum. In particular, during inflation, todayâ€™s sum of money is equivalent to a larger sum in the future and quite the reverse holds good during deflation. This is easy to see. Thus, for example, if the price of, say, rice is Rs 8 per kilogram today and Rs 10 per kilogram after one year, then Rs 100 equals 12.5 kilogram of rice this year and 10 kilogram next year. Incidentally, note that the price of rice is taken just for illustration purpose. The relevant price is the weighted average price of goods and services on which the investor spends his money income.

Investment as a rule deals with the future and the future is uncertain. Investment is concerned with commitment of funds today with the expectation of receiving a stream of benefits in the future. Thus, it involves a trade-off between a certain sum today and an uncertain series of sums in the future. Uncertainty is undesirable in the sense that given a particular amount, an individual would always prefer receiving it right now instead of receiving the equivalent amount at a future date. This is because â€˜a bird in hand is worth two in the bushâ€™. Thus, due to uncertainty, todayâ€™s sum of money is equivalent to a larger sum in the future.

During the period of inflation, all the three factors representing the time value of money, work in the same direction â€“ todayâ€™s money is worth more than the equivalent amount in the future and thus money gains in value over time. But during deflation, while money gains in value over time due to its earning power and uncertainty associated with the future, it loses in value due to falling prices. Further, there is no guarantee that the gain and loss either just cancels out or one is always larger than the other, and consequently nothing unambiguously can be stated regarding the direction of change in the value of money over time during deflation.

Since investment involves expenditures and revenues over time, it is imperative to adjust for the time value of money for conducting a meaningful investment analysis. The adjustment for the earning power of money is made through the principles of compounding and discounting, which can, in fact, be also used to adjust for inflation/deflation as well as uncertainty. A discussion on these follows:

Compounding Principles (an illustration):

Under the compounding principle, the future value of a present sum is found, given the earning power (interest rate) of money and the frequency of compounding. For example the value of Rs 100 of today after one year, given the rate of interest of 10% per year and the compounding to be done once in a year, equals

Rs 100 + 0.10 (100) = Rs 100 (1 + 0.10) = Rs 110

The value of this sum after two year equals

Rs. 110 + 0.10 (110)
Rs. 110 [ 1 + 0.10]
Rs. 100 (1 + 0.10 ) (1 + 0.10)
Rs. 100(1 + 0.10)2
Rs 121

Similarly the value of the sum after three years equals Rs 100 (1 + 0.10)3 and so on.

Y = X (1 + i) T

Y = Final sum
X = Present sum
i= Interest rate per period (year)
T = Number of periods (year).

Thus the value of Rs. 100 after 7 years, interest rates being 10% equals Rs. 194.87.