Discounting

Discounting is simply 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.

Financial Calculators This calculator works just like a pocket calculator. And this more advanced calculator computes present value, future value, payments, and/or number of periods.

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. The table illustrates how much difference a 1.5 percent difference in rate can make.

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.

Planning Tools A table showing a broad range of interest rates is available in this Annuity Table.

The following examples illustrates the importance of understanding the time value of money.

Example You are designing a building for a major client. The client wants you to agree to wait five years to be paid--until the building is built and rented out. You could be earning 10 percent interest on your money, if you got your fees upfront. To determine the true cost of waiting, go to the 10-percent column in the table above and slide down to the 5-year row. You will be dismayed to learn that your today's dollar will only be worth 62 cents in 5 years (or $00.620921 to be precise). Armed with this knowledge, you can either refuse to delay receipt of your fees or increase your fees to offset the impact of the delay.

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.

Example You're considering acquiring 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 nine 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 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 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.