Present value factor definition

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What is the Present Value Factor?

The present value (PV) factor is used to derive the present value of a receipt of cash on a future date. The concept of the present value factor is based on the time value of money - that is, money received now is worth more than money received in the future, since money received now can be reinvested in an alternative investment to earn additional cash. The PV factor is greater for cash receipts scheduled for the near future, and smaller for receipts that are not expected until a later date. The factor is always a number less than one. The formula for calculating the present value factor is:

P = (1 / (1 + r)n)

Where:

P = The present value factor
r = The interest rate
n = The number of periods over which payments are made

The present value factor is typically stated in a present value table that shows a number of present value factors in relation to a grid of interest rates and time periods. A sample table that shows the present value factor for a standard set of time periods and interest rates appears in the following table.

Present Value of 1 Table

n 1% 2% 3% 4% 5% 6% 8% 10% 12%
1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9259 0.9091 0.8929
2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8573 0.8265 0.7972
3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.7938 0.7513 0.7118
4 0.9610 0.9239 0.8885 0.8548 0.8227 0.7921 0.7350 0.6830 0.6355
5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.6806 0.6209 0.5674
6 0.9421 0.8880 0.8375 0.7903 0.7462 0.7050 0.6302 0.5645 0.5066
7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.5835 0.5132 0.4524
8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5403 0.4665 0.4039
9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5003 0.4241 0.3606
10 0.9053 0.8204 0.7441 0.6756 0.6139 0.5584 0.4632 0.3855 0.3220
11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4289 0.3505 0.2875
12 0.8875 0.7885 0.7014 0.6246 0.5568 0.4970 0.3971 0.3186 0.2567
13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.3677 0.2897 0.2292
14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3405 0.2633 0.2046
15 0.8614 0.7430 0.6419 0.5553 0.4810 0.4173 0.3152 0.2394 0.1827
16 0.8528 0.7285 0.6232 0.5339 0.4581 0.3937 0.2919 0.2176 0.1631
17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.2703 0.1978 0.1456
18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2503 0.1799 0.1300
19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2317 0.1635 0.1161
20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2146 0.1486 0.1037
21 0.8114 0.6598 0.5376 0.4388 0.3589 0.2942 0.1987 0.1351 0.0926
22 0.8034 0.6468 0.5219 0.4220 0.3419 0.2775 0.1839 0.1229 0.0826
23 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.1703 0.1119 0.0738
24 0.7876 0.6217 0.4919 0.3901 0.3101 0.2470 0.1577 0.1015 0.0659
25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1460 0.0923 0.0588

For a greater degree of precision for values between those stated in such a table, use the formula shown above within an electronic spreadsheet.

The only situation in which the present value factor does not apply is when the interest rate at which funds could otherwise be invested is zero.

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Example of the Present Value Factor

ABC International has received an offer to be paid $100,000 in one year, or $95,000 now. ABC's cost of capital is 8%. When the 8% interest rate is factored into the present value equation, the present value factor is 0.9259. When the present value factor is multiplied by the $100,000 to be paid in one year, it equates to being paid $92,590 right now. Since the offer of being paid $95,000 is greater than the present value to ABC of the later payment, ABC should accept the immediate payment of $95,000.

Financial Analysis with the Present Value Factor

The present value factor is a major concern in capital budgeting, where proposed projects are being ranked based on their net present values. If a proposed project is expected to experience cash flows over a long period of time, or only starting several years in the future, then it will be assigned an unfavorable present value factor, resulting in a low net present value. This is especially the case when interest rates are high, since this drives down the net present value of the project. Conversely, projects generating immediate cash flows, and especially when interest rates are low, will have a more favorable net present value, making them more likely to be selected over projects with delayed cash flows.