# Will the value of INR 100 today remain the same tomorrow? Imagine buying a bar of chocolate of Rs. 10 a couple of years back, as compared to today. Obviously, the size of a bar has reduced and it has become much thinner. What does this imply? The value of Rs.10 a few years back was more than it was today, i.e., it has much less purchasing power today. Many times we hear our grandparents moan about today and reminisce with pride, how, even 10 paisa had a lot of value in those times. And today, we see that even the 50 paisa coin has become extinct!

So how does this change occur? It is quite simple. As time progresses, the value of money is impacted by many factors such as inflation rate, government rules and regulations, forex policies, trade policies etc. Demand and supply of a product help determine the price in a free economy. Of course, in a mixed economy like India, there is government intervention in some commodities which regulates its prices.

When you deposit money in the bank for a couple of months, you expect a certain amount of interest? Why? Because you sacrifice your purchasing power for that period of time, and the value of that amount of money depreciates, hence you expect a compensation in the form of interest.

However, in practical scenarios, you need to take many complicated decisions in businesses. They have huge capital requirements for multiple projects. Hence, seeking loan at an appropriate rate and investing at the right place to generate more revenue is quite important. Hence, it is important to know the time value of money in these cases, to make smart investment decisions.

(A) Simple Interest

 Simple interest is the interest earned on only the original amount or principal. Simple interest (SI) depends on three variables: The principal (P) The interest rate per time period (i) The number of time periods over which the money remains invested (n) What would be the interest earned on Rs.10000 placed in a fixed deposit account earning simple interest @ 8% per annum after five years?Here P = Rs.10000 i = 8% n = 5 the value at present or at this point in time and Rs.14000 represents the Future Value of the investment (FV), that is the value of the investment in the future or later in time. The relationship between the two can be represented as below.

(B) Compound Interest

 In the case of compound interest, the interest earned on the principal is added back to the principal and interest is earned on both the principal and interest in the next time period. That is one earns interest on interest or there is a compounding effect. Compound interest also depends on three variables: 1) The principal (P) 2) The interest rate per time period (i) 3) The number of time periods over which the money remains invested (n) Given the above, the FV of the investment P after a year would be Principal plus interest earned FV= P+Pi=P(1+i) Now, this value becomes the principal for the next year. That means the interest added to the principal also earns interest. So the future value at the end of two years would be the new principal plus interest earned on the new principal. FV = P(1+i) + P(1+i)i =P(1+i)(1+i) = P(1+i)2 We can then obtain the general formula for compound interest over n periods as: FV= P(1+i)n What would be the future value of Rs.10000 placed in a fixed deposit account earning compound interest @ 8% per annum after five years? Here PV = Rs.10000 i = 8% n = 5 FV = PV (1+ 0.08)5 = Rs.14693

(C) Present Value and Discount Rate

• We can also do the reverse i.e. we can find the present value of a sum we are certain of getting in the future. In other words, the present value of a certain sum to be obtained in the future is the amount of money that must be invested today at a given interest rate over a given period of time in order to obtain the future value.
• This process of finding the present value of future cash flows is known as discounting i.e., the future cash flows are discounted to the present. The interest rate used in the discounting process is called the discount rate or capitalization rate. It is also called the opportunity cost or cost of capital or the required rate of return.

 Example: Find the present value of Rs.50000 to be received five years from now assuming a discount rate of 8%. n = 5 FV = 50000 i = 8% PV = 50000/ (1+0.08)^5 =50000/1.469 = 34029 The present value of Rs.50000 is Rs.34029 When there are multiple cash flows occurring in the future then the present value of these cash flows together can be obtained by finding the sum of the present values of each cash flow. PV total = PV1 + PV2 + P V3………..

The above examples were used to explain why it is important to calculate the time value of money in the field of investment banking, equity research, project finance, capital budgeting, etc. Time value of money is required is the basis of finance and it is important to understand the concept for all fields of the finance sector.

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