Time Value of Money, or simply TVM, refers to the fact that money has a value in time due to its earning power. The concept is such that a dollar today is worth more than one in the future merely because it can be invested and grow. Present Value (PV) and Future Value (FV) money that might accrue is a necessary part of financial planning, investment analysis, and decision-making. This paper will be written to give the basics of TVM calculations along with examples in PV and FV.
What does Time Value of Money (TVM) mean?
The time value of money refers to that money existing currently having more values than similar money at later dates because it can earn more. It forms the base for many monetary decisions such as saving, investing, and borrowing. TVM calculation provides a basis on which people can calculate present or future values of cash flows to make wise decisions.
The Building Blocks of TVM
To calculate and understand Time Value of Money appropriately, you must first learn what the building blocks are:
Present Value (PV)
The amount of money you expect to be received or invested in the future.
Future Value (FV)
Amount of money an investment will grow into at a predetermined interest rate over time.
Interest Rate (i)
Rate at which money grows per period; also known as discount rate.
Number of Periods (n)
Number of years, months, etc. over which the money is invested or borrowed for.
Payment (PMT)
In annuity calculations, multiple payments are used that have been made over a period but in single PV or FV calculations the above values are not used.
Compounding Future Value (FV)
Future Value let you compute the value of a sum of money at some later date, assuming some interest rate. The FV formula is as follows:
FV = PV times (1 + i)^n
Where:
– ( PV ) = Present Value
– ( i ) = Interest Rate per period
– ( n ) = Number of periods
Understanding the Present Value and Future Value Calculation Example
Example Calculation of Future Value:
Suppose you had invested 1000 dollars at an interest rate of 5% or i = 0.05 for 3 years (n = 3).
FV = 1000 × (1 + 0.05)^3 = 1000 × 1.157625 = 1157.63
After 3 years the investment will become $1157.63
The present value is the worth of current money sum for future amount at appropriate rate of return. The formula for PV is represented as follows:
PV = FV/(1 + i)^n
Where,
– ( FV ) = Future Value
– ( i ) = Interest Rate per period
– ( n ) = Number of periods
Compute Present Value:
Assume you want to determine the present value of $1,000 (FV) you will receive in 3 years where an interest rate is 5% or i = 0.05.
PV = 1000/(1 + 0.05)^3 = 1000/1.157625 = 863.84
In 3 years, $1,000 received at a 5% interest rate is equivalent to $863.84 at present.
Applications of TVM
Time Value of Money is applied in many financial applications, examples include:
Investment Decisions
Find out whether an amount invested today will yield the given amount tomorrow.
Loan and Mortgage Payments
Calculate the current value of a series of payments that are to be made at some future date.
Retirement Planning
Find out how much must be invested in the present so that the amount meets some financial requirements at a specified future date.
Business Valuation
It discounts the future cash flows of a business to find its current value.
Other Key TVM Formulas
More complex formulas are required, like the Present Value of an Annuity or Future Value of an Annuity. Here is a brief look at these formulas:
FVA = PMT × [(1 + i)^n – 1]÷ i]
PVA = PMT × [1 – (1 + i)^- n] ÷ i]
Conclusion
The art of understanding TVM and calculating Present Value and Future Value is vitally important for making the correct financial decisions.
Whether it is savings for retirement, planning to invest in something, or loans, all these calculations will help in determining the value of money after crossing a certain period of time.
Thus, the application of principles of TVM will enable you to come up with better financial plans that optimize growth possibilities and minimize costs.