It is commonly known that the money in hand today is more worth than the money of same amount in future. This idea is based on earning potential. This principle says that the money can earn interest and gradually can grow. Everyone knows the fact that the money deposited in bank account will earn interest. The time value of the money is a priori principle that a fixed amount of the money that is accessible today is more costly than the same amount of near future. This principle can be generalized for the economic resources available by social contract. We can justify these principles for the three main reasons. One is that we always want to have a resource today in our hand rather than in future because there is always a chance of uncertainty attached with future .we are not sure that we have the same amount in near future. And second is that we always prefer that we can use this resource in the meantime i.e. we always think about the opportunity cost. There is a third reason exist especially for the money that is the concept of inflation. Inflation means we will buy little fewer things in future with cash than in today. Inflation has a negative effect on time value of the money. Due to the decline in buying capacity of the money uninvited dollar is of more value than the same money in dollar that will not be in near future. There also exist negative inflation which means that the money value increases in future as compared to today but this concept is absent in modern money market economies for almost a century.
When taken altogether, these factors mean that people mostly require some compensation for delaying in receiving payment. This compensation is called interest. When a person invests his money somewhere, it means that he is delaying the time when they can spend the money and he expect to receive some amount of interest in compensation for this delay.
When we discuss time value of money, the most important thing is the time line concept. Time lines can also be used to determine when there is cash inflows and outflows so that an appropriate financial judgment can be done. Time line series is shown in following figure with five different time periods. This time period may depict years, months, or may be days. We assume it years in our example. The zero represents today. The one represents a year ahead from today. Any time period during the next 365 days will be shown on the time line from the zero to the one tick. One represents that a full year has been completed. Second mark represents that two full years have been finished, and so on.
Discounting
The time value of money is important in estimating projects because, mostly the costs and benefits of a typical project are extended in time.
The process of taking into account the time value of money when estimating a project is called discounting. It includes reducing the value of future the cash flow according to a discount rate.
Appropriate discount rate choice is not an easy task but IR depends upon various factors.
Time value of the money is actually the money potential to grow or increase with the passage of time. For example if someone will give us 200$ today and we will invest it at annual rate of 10%.then at year’s end we can earn 240$ which is more than the amount 200$ received at that point. Time value of money can also be used to calculate the amount of investment to meet a specific future goal. The calculations for the time value of the money derive from the present value of the future cash flow discounted to the present by an equal amount of the time value of the money. Future cash flow is denoted by FV and interest rate is with “i” and present value with PV.
Present values can be represented by different following equations. The solutions may be found by using either the formulas or a financial calculator or a spreadsheet.
These equations are combined for particular uses. For example, bonds can be priced by using these formulas. For example a typical coupon bond has two types of payments: a specific amount at equal intervals similar to an annuity, and at the end of time period a lump-sum amount of capital, that is, a future payment. Combination of two formulas is done to find out the present value of the coupon bond.
The most important thing in time value of the money is the calculation of interest rate for the given time period. To calculate the annuity value, i will be the annual/yearly interest rate. For payment stream in which different payment schedule exist the interest rate must be altered into the relevant periodic interest rate. For instance, a monthly rate for a coupon bond with monthly payments, demands that the interest rate must be divided by 12. . The choice of an appropriate rate is crucial to the practice, as well as use of this inappropriate discount rate will make the result worthless.
Some standard calculations are based on time value of money are followings:
Present Value
It is actually the current value of a future cash flow that is given for a specific rate of return. Future cash flow is discounted at the discount rate .if discount rate is higher than there will be decrees in present value of the future cash flow.
Present Value of an Annuity
It is a series of equal payments that we receive at specific intervals .for example the rental payments .if the payment will occur at the end of the period than the annuity is called ordinary annuity and if the payment will receive at the beginning of each period than this is called annuity due. The formula for present value of annuity is
Present Value of Growing Annuity
It means that each cash flow grows gradually by a factor of (1+g). It is the same formula as of the annuity with only the difference that in this formula a new rate or return g is introduced that is the growth rate. There are two cases for growth rate
When i ≠ g: when interest rate is not equal to the growth rate
When i = g: when interest rate is equal to the growth rate
For the PV of a growing annuity due, we must multiply the above equation by (1 + i).
Present Value of the Perpetuity
It means that the constant and infinite stream of cash flow of the same amount. Following are the formula for perpetuity
Where A means annuity
Future Value
It is the value of cash at a specific date in the future. It is based on the value of that cash in the present. Following is the formula for calculating future value.
Future Value of an Annuity:
The future value of payments (annuity) is calculated by considering that the payments are invested at a given specific rate of interest. Following is the formula of the future value annuity
For the FV of an annuity due, multiply equation by (1+i)
Future Value of a Growing Annuity
FVA formula has following variables, and these are solved for:
When i ≠ g: when interest rate is not equal to the growth rate
When i = g: when interest rate is equal to the growth rate
The above formulas use these variables:
- PV =the value at time=0 (present value)
- FV =the value at time n
- A= value of the same payments at specific time period
- N= the number of periods
- I = interest rate for discounting each period.
- G= growing rate of cash over time period
Conclusion
TVM is an important theory for the perspective of financial management. It can also be used to compare investment alternative decisions and to solve problems that involve loans, mortgages, rentals and annuities.
Historic concept is applied on TVM that a dollar that you have now is more valuable than the hope that you receive a dollar in near future. Money you have now in your hand is value more because you can invest it now in somewhere and can earn interest. In fact you should receive some type of compensation for this previous spending. For example, you have an opportunity to invest your dollar for one year at the rate of 7% and can earn up to $1.07 at the end of following year. You can also interpret this, that the future value of one dollar is $1.06 at 7% interest rate and for a one year period. It also can be described in a way that the present value of the $1.06 that you expect to have in this year is of only $1.
In capital budgeting decision this concept of time value is of very importance. Because this allows the manager to adjust his cash flows with the passage of time. There are some capital budgeting techniques that use the concept of time value of the money. Total cash approach; NPV, PPI and IRR collectively contribute to TMV. For the long term investment purpose decision time value of money is consider very important .when we want to compare the cost of sources of different financing then the time value of money is used to calculate the best and appropriate rate of interest. What will be the appropriate source of finance depends upon the present value of the alternatives. To evaluate the different credit policies and efficiency of the firm in handling the cash, time value of money concept is used.
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References
- Besley, Scott, and Eugene Brigham. Principles of finance. Cengage Learning, 2011.
- Wong, John D. "Time Value of Money." Encyclopedia of Public Administration and Public Policy, Second Edition. 2008. 1923-1930.
