# Time Value Of Money(TVM)

Money has time value because a dollar or cash earned today is more valuable than if earned the next year. There are several reasons for this. Some of the reasons being:
• Generally individuals prefer current consumption than future consumption.
• Money invested today would generate positive returns tomorrow. A dollar invested today would grow to 1 + r% a year later.
• In an inflationary period, a dollar today represents a greater real purchasing power than a dollar a year hence.

Important points regarding TVM:
• Time Value of Money is a critical consideration in financial and investment decisions. It is an element of compound interest calculations used to determine future results of investments and of discounting, which is inversely related to compounding and is used to evaluate the future cash flow associated with capital budgeting projects.
• Most financial problems involve cash flows occurring at different points of time. These cash flows have to be brought to the same point of time for purposes of comparison and aggregation.

Time Lines and Notation:

When cash flows occur at different points of time, it is easier to deal with them using a time line. A time line shows the timing and the amount of each cash flow in a cash flow stream. Thus, a cash flow stream of \$5,000 at the end of each of the next four years can be depicted on a time line like this: (discount rate 10%)

Time Line

If cash inflows occur at the end of each period:

 0 1 2 3 4 10% 10% 10% 10% ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ \$ 5,000 \$ 5,000 \$ 5,000    \$ 5,000

If cash inflows occur at the beginning of each period:

 0 1 2 3 4 10% 10% 10% 10% ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ →→→→→→→→→→ ↓ \$ 5,000 \$ 5,000 \$ 5,000 \$ 5,000

Cash flows can be positive or negative. A positive cash flow is called a cash inflow and a negative cash flow is called a cash outflow. In evaluating capital budgeting proposals and other financing and investment decisions, the following aspects need to be considered:

• At what point of time is the cash inflow expected? If there are multiple cash inflows, at what points and periods of time would they occur?
• Is the cash outflow only required at year 0? Or does the project require cash outflows periodically? If yes, at what periods?
• Do the cash inflows and outflows occur at the beginning or end of the periods?
• What is the minimum rate of return expected out of a project? Or what return does that project generate? Does it at least recover the present value of the cash outflow and some reasonable profit?

Apart from answering the above questions, the time value of money concept is also used by individuals and other organizations for their personal investment and financing decisions. For example, an individual may be interested in knowing how much he needs to save per year to enjoy a certain amount of income during retirement period. A loan borrower may be interested to know how much he needs to pay in future including interest and principal. A depositor may be interested to know the future value of his investments. For answering all these questions, we employ the following concepts in Time value of Money:

• Future Value of Single/Multiple Cash flows.
• Future Value of an annuity.
• Present Value of Single/Multiple Cash flows
• Present Value of an annuity.

The cash flows occurring at different periods can be equated and compared using the following techniques:
• Compounding:

By compounding the present value of amount to a future date. This will include interest. Interest is compounded when the amount earned on an initial deposit becomes part of the principal at the end of first compounding period. The term principal refers to the amount of money on which interest is received.

• Discounting:

By discounting the future value of amount to the present date. Given a positive rate of interest, the present value of future rupees will always be lower. It is with the assumption that the decision maker has an opportunity to earn a certain return on his money.

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