The concept of the time value of money asserts that the value of a dollar today is worth more than the value of a dollar in the future. This is typically because a dollar today can be used now to earn more money in the future. There is also, typically, the possibility of future inflation, which decreases the value of a dollar over time and could lead to a reduction in economic buying power.
At this point, potential effects of inflation can probably best be demonstrated by a couple of examples. The first example is the Ford Mustang. The first Ford Mustang sold in 1964 for $2,368. Today's cheapest Mustang starts at a list price of $25,680. While a significant portion of this increase is due to additional features on newer models, much of the increase is due to the inflation that occurred between 1964 and 2019.
Similar inflation characteristics can be demonstrated with housing prices. After World War II, a typical small home often sold for between $16,000 and $30,000. Many of these same homes today are selling for hundreds of thousands of dollars. Much of the increase is due to the location of the property, but a significant part is also attributed to inflation. The annual inflation rate for the Mustang between 1964 and 2019 was approximately 4.5%. If we assume that the home sold for $16,500 in 1948 and the price of the home in 2019 was about $500,000, that's an annual appreciation rate of almost 5%.
Today's dollar is also more valuable because there is less risk than if the dollar was in a long-term investment, which may or may not yield the expected results. On the other hand, delaying payment from an investment may be beneficial if there is an opportunity to earn interest. The longer payment is delayed, the more available earning potential there is. This can be enticing to businesses and may persuade them to take on the risk of deferment.
Businesses consider the time value of money before making an investment decision. They need to know what the future value is of their investment compared to today's present value and what potential earnings they could see because of delayed payment. These considerations include present and future values.
Before you learn about present and future values, it is important to examine two types of cash flows: lump sums and annuities.
lump sum is a one-time payment or repayment of funds at a particular point in time. A lump sum can be either a present value or future value. For a lump sum, the present value is the value of a given amount today. For example, if you deposited $5,000 into a savings account today at a given rate of interest, say 6%, with the goal of taking it out in exactly three years, the $5,000 today would be a present value-lump sum. Assume for simplicity's sake that the account pays 6% at the end of each year, and it also compounds interest on the interest earned in any earlier years.
In our current example, interest is calculated once a year. However, interest can also be calculated in numerous ways. Some of the most common interest calculations are daily, monthly, quarterly, or annually. One concept important to understand in interest calculations is that of compounding. Compounding is the process of earning interest on previous interest earned, along with the interest earned on the original investment.
Returning to our example, if $5,000 is deposited into a savings account for three years earning 6% interest compounded annually, the amount the $5,000 investment would be worth at the end of three years is $5,955.08 ($5,000 × 1.06 – $5,300 × 1.06 – $5,618 × 1.06 – $5,955.08). The $5,955.08 is the future value of $5,000 invested for three years at 6%. More formally, future value is the amount to which either a single investment or a series of investments will grow over a specified time at a given interest rate or rates. The initial $5,000 investment is the present value. Again, more formally, present value is the current value of a single future investment or a series of investments for a specified time at a given interest rate or rates. Another way to phrase this is to say the $5,000 is the present value of $5,955.08 when the initial amount was invested at 6% for three years. The interest earned over the three-year period would be $955.08, and the remaining $5,000 would be the original deposit of $5,000.
As shown in the example the future value of a lump sum is the value of the given investment at some point in the future. It is also possible to have a series of payments that constitute a series of lump sums. Assume that a business receives the following four cash flows. They constitute a series of lump sums because they are not all the same amount.
| December 31, 2019 | $12,000 |
| December 31, 2020 | 12,000 |
| December 31, 2021 | 11,500 |
| December 31, 2022 | 12,000 |
The company would be receiving a stream of four cash flows that are all lump sums. In some situations, the cash flows that occur each time period are the same amount; in other words, the cash flows are even each period. These types of even cash flows occurring at even intervals, such as once a year, are known as an annuity. The following figure shows an annuity that consists of four payments of $12,000 made at the end of each of four years.
| December 31, 2019 | $12,000 |
| December 31, 2020 | 12,000 |
| December 31, 2021 | 11,500 |
| December 31, 2022 | 12,000 |
| Year | Interest Earned | Investment Balance |
| 0 | $10,000 | |
| 1 | ($10,000 × 10%) $1,000 | 11,000 |
| 2 | (11,000 × 10%) 1,100 | 12,100 |
| 3 | (12,100 × 10%) 1,210 | 13,310 |
| 4 | (13,310 × 10%) 1,100 | 14,641 |
| Total Interest Earned |