Present Value and Future Value

The time value of money concepts of present value and future value, like the concepts of compounding and discounting, are two sides of the same coin.

Planning Tools Use this Present Value of Future Payments Table to figure the present value of amounts to be paid in the future. The tables in this tool shows how much $1, to be paid at the end of various periods in the future, is currently worth, with interest at different rates, compounded annually. To use the table, find the vertical column under your interest rate (or cost of capital). Then find the horizontal row corresponding to the number of years it will take to receive the payment. The point at which the column and the row intersect is your present value of $1. You can multiply this value by the number of dollars you expect to receive, in order to find the present value of the amount you expect.

As an example of how the Present Value of Future Payments Table can be used to compute the net present value of a major project, consider the following:

Example Traders, Inc. is considering the acquisition of a new machine. After all the factors are considered (including initial costs, tax savings from depreciation, revenue from additional sales, and taxes on additional revenues), Traders projects the following cash flows from the machine: Cash Flow After Purchase Year 1 ($10,000) Year 2 $ 3,000 Year 3 $ 3,500 Year 4 $ 3,500 Year 5 $ 3,000 Assume that Traders' cost of capital is 9 percent, using the net present value table shows whether the new machine would at least cover its financial costs: Net Present Value After Purchase Year Cash Flow Multiplied by Table Factor Equals Present Value 1 ($10,000) x 1.000000 = ($10,000.00) 2 $ 3,000 x 0.917431 = $2,752.29 3 $ 3,500 x 0.841680 = $2,945.88 4 $ 3,500 x 0.772183 = $2,702.64 5 $ 3,000 x 0.708425 = $2,125.28 Net Present Value = $526.09 Since the net present value of the cash flow is positive, the purchase of the new machine would be at least slightly profitable for Traders.

But what happens if you're planning on receiving a series of $1 payments, to be paid at the end of each period for a specified number of periods into the future, with interest at different rates, compounded annually. In other words, you'll need to know what you should be willing to pay, today, in order to receive a certain series of payments of $1 each.

Planning Tools Use this Annuity Table figure the present value of a series of payments to be made in the future, based on interest at different rates. To use the table, find the vertical column under your interest rate (or cost of capital). Then find the horizontal row corresponding to the number of the last year you will receive the payment. The point at which the column and the row intersect is your present value of a series of $1 payments. You can multiply this value by the number of dollars you expect to receive in each payment, in order to find the present value of the series.

When figuring how the table can be used to compute the Internal Rate of Return (IRR) of a major project, consider the following example.

Example Paul's Pliers, Inc. is considering the purchase of a new computer system that will cost $7,500, but will allow it to save about $2,000 a year in desktop publishing expenses. If you want to use the annuity tables to calculate the IRR of Paul's project, you must first compute the number to look up in the tables. You can do this by dividing the expected net cash outflow (costs) for the project by the expected average annual net cash inflow (savings). In this case, the cost of the project (net cash outflow) is $7,500, and the average annual net cash inflow is $2,000. $7,500 ÷ $2,000 = 3.75 Then, look at the row corresponding to the number of years the project or equipment will be in use (in this case, five). Look across the rows until you find the number that is closest to the result you found (3.75). Then look at the top of the column in which the closest number was found, to see the interest rate that is Paul's IRR (in this case, 10 percent).