# Time value of money.

Time Value of Money

Last month we discussed the analysis of capital investments using methods which compared the rate of return or the payback period for various assets. Neither of these methods considers the time value of money or the concept of present value. They are useful in evaluating investments which have relatively short lives. However, in some cases an investment may cover a longer period of time and the time value of money may become an important consideration when determining the worth of that investment.

The basic concept of the time value of money is that cash received at a later is not equal to the same amount of cash which is presently on hand. The cash on hand has earning power and can be invested for growth. A basic example takes the amount of \$20,000 invested at \$12%. At the end of a year, that \$20,000 is worth \$22,400 (the original \$20,000 plus the \$2,400 earned in interest). The \$20,000 held today can be referred to as the present value of \$22,400 which will be received a year from today.

Let's use this concept to calculate the present value of the cash flows from an investment. We can do this by using what is referred to as the "discounted cash flow" method or the "net present value" method. As an illustration of this method, take an instance where you anticipate receiving \$20,000 one year from now and the appropriate rate of interest is 12%. The present value amount is \$17,857, calculated by dividing \$20,000 by 1.12. If you had to wait two years for the \$20,000, the present vlaue is \$15,944 (\$17,857 divided by 1.12). Obviously, to do a series of divisions based on the number of years involved would be cumbersome and tables have been set up which can readily be used. We can now consider a more complex situation. We'll continue to use a rate of return of 12%. The actual rate of return in any given situation would depend on a number of factors such as the cost of obtaining funds for the project, the desired rate of return and the profitability of the company. In our example, a manufacturing company is considering purchasing new equipment at a cost of \$420,000. The company would like to recover this cash outlay during the first five years of the equipment's use. They anticipate an annual cash flow as shown in Table 1. Using the 12% rate of return, we can see if the present value of the anticipated cash flow is equal to or greater than the expense.

As can be seen in Table 1, the present value of the anticipated cash flow not only covers the cost of the equipment, but also provides more than the minimum rate of return. If there are alternative proposals to be considered and the expenditure is the same in each case, the alternative which gives the largest excess of present value over the amount to be invested is the best choice.

When the amount to be invested in equipment varies from proposal to proposal, the various alternatives can be ranked using a present value index. This index is computed by dividing the present value of the total net cash flow by the amount to be invested. In this example, the calculation is as follows: Present Value Index = \$425,270/\$420,000=1.01

Let's look at an example (Table 2) where a decision has to be made among three different alternatives. For each situation we can assume that we have already calculated the total present value of the net cash flow and we know the amount to be invested, so we can go ahead and compute the excess present value and the present value index.

The results of the calculations in Table 2 show that Alternative B gives us the largest excess of cash over the amount invested. However, Alternative C shows a better present value index which means that for each dollar invested, the return is better. It should also be noted that C requires the smallest outlay of cash. The company must then look at alternative uses for the \$70,000 not expended under this proposal.

As stated at the beginning of this column, it is sometimes necessary to consider the time value of money when making investment decisions. The method shown in Table 2 does just that. However, it does have some disadvantages. The most obvious being that it is fairly complicated and does take some work. However with present day computers and software, that chore is made easier. A more important disadvantage is the assumption that the rate of return will be the same from year to year. Because of constantly changing economic conditions, this assumption is probably not valid. The length of time over which the calculations are made and the economic climate must always be considered before making any final investment decisions. [Tables 1 to 2 Omitted]
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