**What Is Time Value Of Money?**

Time value of money’ is central to the concept of finance. It recognizes that the value of money is different at different points of time. Since money can be put to productive use, its value is different depending upon when it is received or paid.

In simpler terms, the value of a certain amount of money today is more valuable than its value tomorrow. It is not because of the uncertainty involved with time but purely on account of timing. The difference in the value of money today and tomorrow is referred to as the time value of money.

It is based on a simple theory- that states ‘the value of money you have now is greater than a reliable promise to receive the same amount of money at a future date’.

**This may be due**

Risk, i.e., uncertainty associated with future receipts or

Inflation causing the decline in purchasing power of money or

Reinvestment opportunities for funds received early.

It can be argued that the risk element associated with future receipt of money could be eliminated or reduced to a greater extent through suitable promises, insurance against default, etc., so that possibility of default (money not to be received in future) becomes quite remote. Naturally, the time value of money then becomes irrelevant.

Similarly, if it is assumed that the economy is free from inflation, then the value of money today and that of tomorrow may be taken to be the same and in this case also time value of money becomes irrelevant.

In spite of these two extreme assumptions, a rupee of today would be preferred to a rupee of tomorrow (i.e., future) because the rupee received today may be invested and its value tomorrow (in future) would be more (this is due to the fact that the rupee invested will fetch some interest).

It is only with respect to reinvestment opportunities of funds received early that future cash flows are taken to be less valuable than the present ones. Funds received today would earn a rate of return which may not be possible in case they are received later.

A simple example can be used to show the time value of money. Assume that someone offers to pay you one of two ways for some work you are doing for them: They will either pay you Rs1,000 now or Rs.1,100 one year from now.

Which pay option should you take? It depends on what kind of investment return you can earn on the money at the present time. Since Rs1,100 is 110% of Rs. 1,000, then if you believe you can make more than a 10% return on the money by investing it over the next year, you should opt to take the Rs.1,000 now. On the other hand, if you don’t think you could earn more than 9% in the next year by investing the money, then you should take the future payment of Rs.1,100 – as long as you trust the person to pay you then.

**Calculation:**

The present amount is called the present value, the future amount is called the future value, and the appropriate rate that relates the two amounts is called the discount rate.

**Present Value** = Future Value / (1 + Discount Rate)

**Future Value** = Present Value x (1 + Discount Rate)

Now, let’s look at time value of money examples. If you invest Rs100 (the present value) for 1 year at a 5% interest rate (the discount rate), then at the end of the year, you would have $105 (the future value). So, according to this example, Rs 100 today is worth $105 a year from today.

Rs.105 = Rs.100 x 1.05

Rs.100 = Rs.105 / 1.05

Likewise, Rs.100 a year from today, discounted back at 5%, is worth only $95.24 today.

Rs.95.24 = Rs.100 / 1.05

To calculate the time value of money for a period longer than one year, you simply raise the discount factor by the appropriate number of time periods. For example, to calculate the future value of $100 at 5% for 5 years:

Rs.127.63 = Rs.100 x (1.05)^{5}