Discounting
Discounting is nothing more than the flip side of compounding!
The time value of money is a two-way street. You start with the premise that a dollar you get today is worth more than a dollar you'll get at some point down the road, because you can invest today's dollar and earn interest on it starting today. (And add to that the thought that inflation hasn't had a chance to erode today's dollar yet.)
Conversely, a future dollar is worth less in today's terms, so you "discount" it to get its present value. "Discounting" is a way of expressing the loss of interest income and/or erosion by inflation that you suffer by not getting that dollar until some point in the future. You can determine the discount rate by using a financial calculator or by using good old-fashioned standard tables.
Here's a table that shows how much $1, 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 (your 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.
| Net Present Value of a Dollar |
| Year |
9.0% |
9.5% |
10.0% |
10.5% |
| 1 |
$0.917431 |
$0.913242 |
$0.909091 |
$0.904977 |
| 2 |
$0.841680 |
$0.834011 |
$0.826446 |
$0.818984 |
| 3 |
$0.772183 |
$0.761654 |
$0.751315 |
$0.741162 |
| 4 |
$0.708425 |
$0.695574 |
$0.683013 |
$0.670735 |
| 5 |
$0.649931 |
$0.635228 |
$0.620921 |
$0.607000 |
| 6 |
$0.596267 |
$0.580117 |
$0.564474 |
$0.549321 |
| 7 |
$0.547034 |
$0.529787 |
$0.513158 |
$0.497123 |
| 8 |
$0.501866 |
$0.483824 |
$0.466507 |
$0.449885 |
| 9 |
$0.460428 |
$0.441848 |
$0.424098 |
$0.407136 |
| 10 |
$0.422411 |
$0.403514 |
$0.385543 |
$0.368449 |
| 11 |
$0.387533 |
$0.368506 |
$0.350494 |
$0.333438 |
| 12 |
$0.355535 |
$0.336535 |
$0.318631 |
$0.301754 |
For example, suppose you are designing a building for a big client who wants you to agree to wait for payment of your fees until the building is built and rented out. Let's say he needs five years for this, and let's also say you think you could be earning 10 percent interest on your money if you got your fees upfront. Go to the 10-percent column and slide down to the 5-year row. . .and be dismayed to learn that your today's dollar will only be worth 62 cents in 5 years (or $00.620921 to be precise).
And here's an example of how the table can be used to compute the net present value of a major project by discounting the cash flow. Let's say you're 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), you project 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 your cost of capital is 9 percent, 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 |
Table Factor |
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 |
| NPV = $526.09 |
Since the net present value of the discounted cash flow is positive, the purchase of the new machine looks like it might be a good decision.
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