# Time Value of Money

Money has time value – Rupee available today has more value or is worth more than its value a year hence or in future. This is the fundamental idea behind time value of money.

**What is the logical reason behind the concept of time value of money?**

- Every human being in general prefers immediate consumption rather than postponing it to future.
- An investor would prefer to receive a Rupee today rather than a Rupee in future so that Rupee can be deployed for better productive use immediately – say by keeping it in a savings account that would generate positive returns. Rupee deployed in this fashion would be equal to (1+r) where r is the rate of interest.
- During inflationary periods, a Rupee today has higher purchasing power than a Rupee in future.

Time value of money has been universally accepted as the foundation for entire financial engineering in business finance, consumer finance and government finance.

Majority of the financial problems involve cash flows at various point of time. Different cash flows have to be brought to a common reference point of time in order to carry out comparison and summation. Compounding and discounting are the underlying tools for assessing the cash flows and for financial mathematics. These tools are useful in security valuation, project analysis, determining lease rentals, setting up loan amortization schedules, valuation of companies, choosing right financial instruments etc.

**Concept of Time Line**

When cash flows occur at different points of time, it is easier to handle with cash flows by using a time line. It shows the points of time and each cash flow in a cash flow stream.

For example – You are expecting a cash flow of Rs.50,000 at the end of each year for the next three years. On a time line, it would look as under.

**Explanation**

- 0 is the present time and hence does not require any adjustment for time value of money.
- Period of time and point in time are two different things.
- Period 1 is the first year and is the period between point 0 and point 1
- Cash flow at point 1 is the cash flow at the end of year 1.
- Cash flow at the end of year 1 is same as cash flow at the beginning of year 2.
- 12% is the discount rate. It may be same or it may be different from period to period.
- If the cash flow occurs at the beginning of the year instead of end of the year then the time line would look as under.
- Positive cash flow is termed as cash inflow and negative cash flow is termed as cash outflow.

Time line is the basic concept that further helps you to understand various interesting concepts of time value of money and the following formulas for financial mathematics.

- Present value of a single amount
- Present value of an annuity
- Present value of a growing annuity
- Present value of a perpetuity (perpetual annuity)
- Present value of a growing perpetuity (perpetual annuity)
- Future Value of a single amount
- Future value of an annuity
- Future value of a growing annuity
- Intra-year compounding and discounting
- Determining doubling period
- Determining growth rate
- Effective versus stated interest rates

**Summing Up:**

Be on the look out at Time Value of Money – Financial Mathematics to learn further concepts, formulas and applications of time value of money. You will also learn how to use spreadsheets to solve the problems of financial mathematics.

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