Time Value of Money

People continually face important financial decisions that require an understanding of the time value of money. Should we buy or lease car? How much and how soon do we need to save for our children's education? What size house can we afford? Should we refinance our home mortgage? How much must we save in order to retire comfortably? The answer to these question are often complicated, and they depend on a number of factors, such as housing and education costs, interest rates, inflation, expected family income, and stock market returns.
In case Mr. Jones, who earns $85,000, retires in 2000, expects to live for another 20 years after retirement, and needs 80 percent of her pre-retirement income, she would require $68,000 during 2000. However, if inflation amounts to 5 percent per year, her income requirement would increase to $110,765 in 10 years and to $180,424 in 20 years. If inflation were 7 percent, her year 20 requirement would jump to $263,139! How much wealth would Ms. Jones need at retirement to maintain her standard of living, and how much would she have had to save during each working year to accumulate that wealth?
The answer depends on a number of factors, including the rate she could earn on saving, the inflation rate, and when her saving program began. Also the answer would depend on how much she will get from her corporate retirement plan, if she has.
For this above sample cases, we have to understanding the concept of the time value of money. It will help us a lot too, to calculate another personal financial planning.

Future Value
A dollar in hand today is worth more than a dollar in the future because, if you had it now, you could invest it, earn interest, and end up with more than one dollar in the future. Future value (FVs) is the amount to which a cash flow or series of cash flow will grow over a given period of time when compounded at a given interest rate.
Suppose you deposit $100 in a bank that pays 5 percent interest each year. How much would you have at the end of five years?

Equation 1:
FVn = PV (1+i)n
Where
FVn = future value or ending amount, of your account at the end of n years.
PV = present value, or beginning amount, in your account.
i = interest rate the bank pays on the account per year
n = number of periods involved in the analysis.

Spreadsheet solution
You could find the FV by clicking the function wizard, then financial, then scrolling down to FV, and then clicking OK to bring up the FV dialog box. Then enter 0.05 for Rate, 5 for Nper, 0 or leave blank for Pmt because there are no periodic payment, -100 for PV, and 0 or leave blank for type to indicate that payment occur at the end of the period. Then, when you click OK, you get the future value, $127.63

Present Value
The present value of a cash flow due n years in the future is the amount which, if it were on hand today, would grow to equal the future amount. So the present value (PV) is the value today of a future cash flow or series of cash flows. Since $100 would grow to $127.63 in five years at a 5 percent interest rate, $100 is the percent value 0f $127.63 due in five years when the opportunity cost rate is 5 percent.

Equation 2:
PV = FVn / (1+i)n

Spreadsheet Solution
In Excel, click the function wizard, indicate that you want a Financial function, scroll down, and double click PV. Then, in the dialog box, enter 0.05 for Rate, 5 for Nper, 0 for Pmt (because there are annual payments), -127.63 for FV,and 0 (or leave blank) for type because the cash flow occurs at the end of the year. Then press OK to get the answer, PV=$100.00.

Source: Eugene F. Brigham, Joel F. Houston, Fundamentals of Financial Management, Harcourt, Inc, 2001.