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Financial Concepts
Time Value of Money
Money has time value.
A rupee today is more valuable than a rupee a year hence. This is because of
the following reasons:
- Individuals, in general, prefer current consumption to future consumption.
- Capital can be employed productively to generate positive returns.
- In an inflationary period, a rupee today represents a greater real purchasing power than a rupee a year hence.
The following are the basics involved in the concept of time value of money.
- Calculating the future value of a single cash flow.
- Calculating the future value of a stream of periodic cash flows.
- Calculating the present value of a single cash flow.
- Calculating the present value of a stream of periodic cash flows.
Calculating the future value of a single cash flow: The future value of a single cash flow would be equal to the principal amount invested and the interest earned on it. The interest can be either simple interest or compounded interest.
The general formula for the future value of a single cash flow is: FVn = PV (1+k)n
Where,
FVn = Future value n years hence
PV = Cash Flow today (present value)
K = Interst rate per year
Calculating the future value of a stream of cash flows: A stream of equal periodic cash flows is also called an Annuity. The premiums paid or payable for a life insurance policy are an example of annuity. The future value of a stream of equal periodic cash flows can be calculated step by step manually as follows.
- Step 1: Calculate the future value at the end of the first period. The future value of such amount is equal to the amount invested in the first period plus the interest earned on it during the first period.
- Step 2: Calculate the total amount outstanding at the beginning of the second year. The total amount invested in the second period is equal to the future value of the first period (calculated in Step 1) plus the amount invested in the second period.
- Step 3: Calculate the future value at the end of the second period. The future value at the end of the second period is equal to the total amount invested in the second period (calculated in Step 2) plus the interest earned on it during the second period.
- Step 4: Continue the above process till the end of the period under consideration.
The above procedure is difficult as it is time consuming. A simpler method, which is always used, is given below:
The general formula for the future value of a stream of cash flows is: FVAn = A[(1+k)n-1/k]
Where,
FVAn
A = Constant Periodic Cash Flow
K = interest rate per period
N = Duration of the annuity
Calculating the present value of a single cash flow: The present value of a single cash flow is the current discounted value of the cash flow.
The general formula for the present value of a single cash flow is: PV = A[1/(1+k)]n
Where,
PV = Present Value of the Cash flow
A = Cash flow under consideration
K = interest rate
N = duration after which the cash flow under consideration is expected to be received.
Calculating the present value of a stream of cash flows: The present value of a stream of cash flows is the aggregate of current discounted values of each particular cash flow of the stream.
The general formula for the present value of a steam of cash flows is: PV = A[(1+k)n - 1/k(1+k)n]
Where,
PV = Present value of the stream of cash flows
A = Periodic cash flows
K = interest rate
N = duration of the annuity or the stream
- Rule of 72 - If one wished to know in how many years one would double his money given a particular rate of interest then he/she can use the rule of 72. According to this rule, ones money would double at a compounded rate of interest in approximately 72/I years (I being the interest rate).
If the interest rate were 6% then money would double in about 12 (72/6) years.
- Rule of 69 - The above rule of 72 is an approximation. If one does not mind doing a slight bit of more calculation to find out a more appropriate result then he/she can use the rule of 69. According to this rule, ones money would double at a compounded rate of interest in approximately 0.35+69/I years.
If the interest rate were 10% then the doubling period is 7.25 (0.35+69/I) years.
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