Annuities and the Time Value of Money

According to Warren Fees in his book Accounting (2002), an annuity can be thought of as any recurring series of payments. For example, a life insurance policy may make a series of annual payments to the beneficiary. Those payments would be referred to as an annuity. The** Present Value of an Annuity** is the value of a stream of expected or promised future payments that have been discounted to a single equivalent value today.

The concept of the Time Value of Money (TVM) takes into account both default risk and inflation risk. If there are risks involved in an investment, these risks can be reflected through the use of a risk premium. The risk premium required can be found by comparing the investment with the rate of return involving an investment with essentially no risk such as an investment in a U.S. Savings Bond or a Treasury Bill. Thus it is possible to take account of uncertainty involved in various investments.

Mr. Fees explains that the TVM concept recognizes that an amount of cash invested today will have the potential to earn income and therefore will increase in value over time. Therefore, a dollar received today is worth more than a dollar in the future because the dollar received today can earn interest up until the time the future dollar is received.

Mr. Fees also writes that the benefit of money received and invested today is increased by the phenomenon of compound interest.

Compounding is the process by which interest is earned on interest. When a principal amount is invested, interest is earned on the principal during the first period. In the second period or year, interest is earned on the original principal plus the interest earned in the first period. Compounding increases the original investment more quickly when the rates of return are higher, or as a result of more frequent interest re-investment. Compound interest is a type of interest calculation in which interest is calculated on both the principal and the interest previously earned or accrued. For compounding to occur, interest earned is not withdrawn or automatically paid out to the investor/depositor. Instead, interest is added to the principal. In contrast, simple interest is interest paid only on the original investment meaning no interest is paid on the interest accrued. The process of calculating the future value of an investment requires and involves compounding.

There is a related concept called an opportunity cost. An opportunity cost is slightly counter-intuitive. An opportunity cost describes the cost of something in terms of an unrelated opportunity that is forgone. A simple example might involve the options to deposit $20,000 into a savings account, or to spend the same $20,000 to purchase a new car. If the decision maker deposits the $20,000 in the bank, the opportunity cost is the new car. If the decision maker purchases the car, the opportunity cost is the decision to forgo a $20,000 deposit in addition to all of the interest that money would earn in the bank.

The present value (PV) formula is used to discount future money streams from investments. This process of discounting converts future amounts to their equivalent present day value. Present value analysis is necessary because investors’ time horizon extends beyond the current period. Investment decisions that have multi-period cash flow implications must be compared and contrasted in some rational manner before the investment is made.

If an investor knows the right of return and they expect to earn on an investment they can answer the question: How long will it take to double my money based on this rate of return using the Rule of 72? Using the Rule of 72, one needs only to divide 72 by the investor’s expected rate of return to arrive at the number of years it will take to double the original investment. For example, if an investor can earn 10 percent on an investment, using the Rule of 72 investor would know take 7.2 years [72 divided by 10] to double the investment. An investor earning a rate of return and 15 percent would double that investment in 4.8 years using this calculation: [72 divided by 15 = 4.8] (Fees 2002).