Time Value of Money
Time Value of Money
To make itself as valuable as possible to stock holders; an enterprise must choose the best combination of decisions on investment, financing and dividends. In any economy in which firms have the time preference, the time value of money is an important concept. Stockholders will pay more for an investment that promises returns over years 1 to 5 than they will pay for an investment that promises identical returns for years 6 through 10. Essentially one must determine if future benefits are sufficiently large to justify current outlays. The development of mathematical tools of the time value of money is important as the first step towards making capital allocating decisions (Malawi, 2008).
Financial Applications of Time Value of Money
The time value of money is essentially saying that today’s dollar is worth more than if I would get the same amount at a later date. Whenever one decides to allocate capital, make purchases of new plant and equipment or introduce a new product one must determine if the projected future benefits are sufficiently large to justify the current outlay.
The concept discussed above has many applications for a given interest rate calculating the future value of an amount compounded over a period of years, present value of an amount discounted over a period of years, future value of annuity, present value of annuity and how mortgage amortization is calculated.
Applications include retirement plan choices, capital investment strategies such as buy versus lease decisions and personal choices concerning annuities to name a few. The choices concerning retirement and how to save are relatively simple and can be evaluated using two of the time value concepts and equations. When an amount of money is invested over a number of years, the interest earned can be dealt with in two ways: simple interest, where the interest earned is NOT added back to the principal amount invested; or compound interest, interest paid on an investment is added to the principle and as a result, interest is earned on interest. Compounding is the arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied (Malawi, 2008).
The following are the variables used in the mathematical modeling of time value of money:
FV = Future value
PV = Present value
A = Annuity Value
i = Interest rate
n = Number of periods
As an example, what is better, investing a $100 per month or investing $1200 once a year for the next 20 years at an interest rate of 5%? Using the future value of annuity relationship, FVa = A *[ ], one finds that saving on a monthly basis gains us ($41,009-$39,679) $1,330.0 after 20 years.
Table 1, Example of annuity earnings for $1,000.0 (Block & Hirt, ch9 p242)
Even better would be to invest the whole amount up front as "an asset with interest compounded annually: = Original Investment x (1+interest rate)^number of years" ...