Concept of Time Value of Money

Principle & Practice of Management

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Concept of Time Value of Money

“Money has time value” means that the value of money changes over a period of time. The value of a rupee, today is different from what it will be, say, after one year.

Factors Contributing to the Time Value of Money

Time Value of Money

Money has a time value because of the following reasons:
1. Individuals generally prefer current consumption to future consumption.
2. An investor can profitably employ a rupee received today, to give him a higher value to be received tomorrow or after a certain period of time.
3. In an inflationary economy, the money received today has more purchasing power than money to be received in future.
4. ‘A bird in the hand is worth two in the bush’: This statement implies that people consider a rupee today, worth more than a rupee in the future, say, after a year. This is because of the uncertainty connected with the future.
Thus, the fundamental principle behind the concept of time value of money is that a sum of money received today is worth more than if the same is received after some time. For example, if an individual is given an alternative either to receive Rs. 10,000 now or after six months; he will prefer Rs. 10,000 now. This may be because, today, he may be in a position to purchase more goods with this money than what he is going to get for the same amount after six months.
Time value of money or time preference of money is one of the central ideas in finance. It becomes important and is of vital consideration in decision making. This will be clear with the following examples.
Example 1: A project needs an initial investment of Rs. 1,00,000. It is expected to give a return of Rs. 20,000 p.a. at the end of each year, for six years. The project thus involves a cash outflow of Rs. 1,00,000 in the ‘zero year’ and cash inflows of Rs. 20,000 per year, for six years. In order to decide, whether to accept or reject the project, it is necessary, that the present value of cash inflows received annually for six years is ascertained and compared with the initial investment of Rs. 1,00,000. The firm will accept the project only when the present value of the cash inflows at the desired rate of interest is at least equal to the initial investment of Rs. 1,00,000.

Valuation Concepts or Techniques

The time value of money implies that:
1. a person will have to pay in future more, for a rupee received today and
2. a person may accept less today, for a rupee to be received in the future.
The above statements relate to two different concepts:
1. Compound Value Concept
2. Discounting or Present Value Concept

Compound Value Concept

In this concept, the interest earned on the initial principal amount becomes a part of the principal at the end of a compounding period.
Illustration 1:
Rs. 1,000 invested at 10% is compounded annually for three years, Calculate the compounded value after three years.
Amount at the end of 1st year will be: 1,100
[1000 × 110/100 = 1,100]
Amount at the end of 2nd year will be: 1,210
[1100 × 110/100 = 1,210]
Amount at the end of 3rd year will be: 1,331
[1210 × 110/100 = 1,331]
This compounding process will continue for an indefinite time period.
Compounding of Interest over ‘N’ years: The compounding of Interest can be calculated by the following equation.
A = P (1 + i)n
In which,
A = Amount at the end of period ‘n’.
P = Principal at the beginning of the period.
I = Interest rate.
N = Number of years.
By taking into consideration, the above illustration we get
A = P (1+i)n
A = 1000 (1 + .10)3
A = 1,331
Computation by this formula can also become very time consuming if the number of years increase say 10, 20 or more. In such cases to save the computational efforts, Compound Value table* can be used. The table gives the compound value of Re. 1, after ‘n’ years for a wide range of combination of ‘I’ and ‘n’.
For instance, the above illustration gives the compound value of Re. 1 at 10% p.a. at the end of 3 years as 1.331, hence, the compound value of Rs. 1000 will amount to:
10001 × 331 = Rs. 1331

Multiple Compounding Periods

A = (1 + i/m)m×n
A = Amount after a period.
P = Amount in the beginning of the period.
I = Interest rate.
M = Number of times per year compounding is made.
n = Number of years for which compounding is to be done.
Future Value of Series of Cash Flows
So far we have considered only the future value of a single payment made at time zero. The transactions in real life are not limited to one. An investor investing money in instalments may wish to know the value of his savings after ‘n’ years.