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Have you noticed that you always give up something when you make choices? In every financial decision, you sacrifice something to obtain something else that you consider more desirable. For example, you might forgo current buying to invest funds for future purchases or long-term financial security. Or you might gain the use of an expensive item now by making credit payments from future earnings. These opportunity costs may be viewed in terms of both personal and financial resources (see Exhibit 1-7).
PERSONAL OPPORTUNITY COSTSAn important personal opportunity cost involves time that when used for one activity cannot be used for other activities. Time used for studying, working, or shopping will not be available for other uses. The allocation of time should be viewed like any decision: Select your use of time to meet your needs, achieve your goals, and satisfy personal values. Other personal opportunity costs relate to health. Poor eating habits, lack of sleep, or avoiding exercise can result in illness, time away from school or work, increased health care costs, and reduced financial security. Like financial resources, your personal resources (time, energy, health, abilities, knowledge) require careful management. FINANCIAL OPPORTUNITY COSTSYou are constantly making choices among various financial decisions. In making those choices, you must consider the time value of moneyIncreases in an amount of money as a result of interest earned, the increases in an amount of money as a result of interest earned. Saving or investing a dollar instead of spending it today results in a future amount greater than a dollar. Every time you spend, save, invest, or borrow money, you should consider the time value of that money as an opportunity cost. Spending money from your savings account means lost interest earnings; however, what you buy with that money may have a higher priority than those earnings. Borrowing to make a purchase involves the opportunity cost of paying interest on the loan, but your current needs may make this trade-off worthwhile. The opportunity cost of the time value of money is also present in these financial decisions:
INTEREST CALCULATIONS Three amounts are required to calculate the time value of money for savings in the form of interest earned:
These three items are multiplied to obtain the amount of interest. Simple interest is calculated as follows:
For example, $500 on deposit at 6 percent for six months would earn $15 ($500 × 0.06 × 6/12, or 1/2 year). You can calculate the increased value of your money from interest earned in two ways: You can calculate the total amount that will be available later (future value), or you can determine the current value of an amount desired in the future (present value).
FUTURE VALUE OF A SINGLE AMOUNT Deposited money earns interest that will increase over time. Future valueThe amount to which current savings will increase based on a certain interest rate and a certain time period; also referred to as compounding. is the amount to which current savings will increase based on a certain interest rate and a certain time period. For example, $100 deposited in a 6 percent account for one year will grow to $106. This amount is computed as follows:
The same process could be continued for a second, third, and fourth year, but the computations would be time consuming. Future value tables simplify the process (see Exhibit 1-8). To use a future value table, multiply the amount deposited by the factor for the desired interest rate and time period. For example, $650 at 8 percent for 10 years would have a future value of $1,403.35 ($650 × 2.159). The future value of an amount will always be greater than the original amount. As Exhibit 1-8A shows, all the future value factors are larger than 1.
Note: See the appendix at the end of this chapter for more complete future value and present value tables. Future value computations may be referred to as compounding, since interest is earned on previously earned interest. Compounding allows the future value of a deposit to grow faster than it would if interest were paid only on the original deposit. The sooner you make deposits, the greater the future value will be. Depositing $1,000 in a 5 percent account at age 40 will give you $3,387 at age 65. However, making the $1,000 deposit at age 25 would result in an account balance of $7,040 at age 65.
FUTURE VALUE OF A SERIES OF DEPOSITS Quite often, savers and investors make regular deposits. An annuity is a series of equal deposits or payments. To determine the future value of equal yearly savings deposits, use Exhibit 1-8B. For this table to be used, the deposits must earn a constant interest rate. If you deposit $50 a year at 7 percent for six years, starting at the end of the first year, you will have $357.65 at the end of that time ($50 × 7.153). The Financial Planning Calculations box on page 21 presents examples of using future value to achieve financial goals. PRESENT VALUE OF A SINGLE AMOUNT Another aspect of the time value of money involves determining the current value of an amount desired in the future. Present valueThe current value for a future amount based on a certain interest rate and a certain time period; also referred to as discounting is the current value for a future amount based on a certain interest rate and a certain time period. Present value computations, also called discounting, allow you to determine how much to deposit now to obtain a desired total in the future. Present value tables (Exhibit 1-8C) can be used to make the computations. If you want $1,000 five years from now and you earn 5 percent on your savings, you need to deposit $784 ($1,000 × 0.784).
The present value of the amount you want in the future will always be less than the future value, since all of the factors in Exhibit 1-8C are less than 1 and interest earned will increase the present value amount to the desired future amount. PRESENT VALUE OF A SERIES OF DEPOSITS You can also use present value computations to determine how much you need to deposit so that you can take a certain amount out of the account for a desired number of years. For example, if you want to take $400 out of an investment account each year for nine years and your money is earning an annual rate of 8 percent, you can see from Exhibit 1-8D that you would need to make a current deposit of $2,498.80 ($400 × 6.247). The formulas for calculating future and present values, as well as tables covering a wider range of interest rates and time periods, are presented in the appendix at the end of the chapter. Computer programs for calculating time value of money are also available.
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