
Discounting is a technique used to find the value today or "present value" of money paid or received in the future. This value is found using the following formula:
Future dollar amount discount factor = present value
The discount factor depends on the opportunity cost of capital expressed as an interest rate and a time period. Figure A1 illustrates how discount factors are usually displayed. The discount factors are grouped according to the annual interest rate, expressed as the present value of $1.00, and then listed according to the year the amount comes due. The table should be read this way: When a dollar earns 10 percent per year uniformly over time, a dollar received at the end of the second year is equivalent to (worth) about 86 cents today.
Year  Present Value (Today's Value) 

01  $0.9516 
12  0.8611 
23  0.7791 
34  0.7050 
45  0.6379 
To adjust the model's results for the time element, we discount both the positive and negative cash flow forecasts for each period at the company's marginal rate of return to determine their present value. This discounting process makes the forecasts equivalent in time. We can now add the present values of these cash flow forecasts to derive the net present value (NPV). The NPV is a meaningful measure of the economic consequences of an investment decision since it measures all benefits and all costs, including the opportunity cost of capital.
When the NPV of a proposed investment is determined, we are ready to decide whether it should be accepted. This is done by comparing it to the economic consequences of doing nothing or of accepting an alternative. The general rule followed in comparing alternative projects is to choose the course of action that results in the highest NPV.
Figure A2 illustrates the cash flow forecasts and timevalue calculations for a typical proposal to invest in a new project when the alternative is to do nothing, that is, to maintain liquidity rather than invest. A discount rate of 10 percent is assumed as the company's marginal rate.
Year  Benefits  Costs  Cash Flow  PV of $1 @ 10%  Discounted Cash Flow 

0  $ 0  $ (500)  $(500)  1.000  $(500) 
01  425  (200)  225  .952  214 
12  425  (200)  225  .861  194 
23  350  (200)  150  .779  117 
34  250  (200)  50  .705  35 
TOTAL  $1,450  $(1,300)  $ 150  $ 60 NPV 
The proposed project will cost $500 in year 0, and cash operating expenses thereafter will be $200 per year for four years. Assume the cash benefits will be positive but decline over the four years and total $1,450. The cash flow is negative in the year of investment but positive in the succeeding years, and there is a net positive cash flow over the life of the project of $150 before discounting. When the cash flow forecasts are made equivalent in time by multiplying each annual cash flow by the present value of the dollar for each period, the timeadjusted cash flow is determined, and the NPV is found to be $60. The proposed investment is better than doing nothing because all costs are covered, the 10 percent opportunity cost of the corporation's funds is realized, and in addition, the project will yield an additional $60 return.
Figure A2 indicates an NPV of $60. Depending on the cash flow and/or the discount rate, the NPV could be negative or zero. If the NPV were zero, the company would have projected earnings exactly equal to its marginal rate of 10 percent. If there were no alternative projects, and the only alternative were to do nothing, the project with the NPV of zero would be accepted because the company would earn its marginal rate of return. (As explained later, the NPV of zero would yield the discounted cash flow rate of return, that is, 10 percent.) If the NPV were negative because of an inadequate cash flow, assuming the same 10 percent marginal rate required by management, it would mean the project would earn less than 10 percent, and it would be rejected.
A number of evaluation methods are employed in capital budgeting; however, after critical examination of all methods, only the arithmetic developed in this simple model will be used to examine three methods used in evaluating capital budget proposals: (1) cash payback, (2) net present value, and (3) discounted cash flow rate of return (DCFROR)—sometimes referred to as the "internal rate of return."
Cash payback is commonly used by business managers evaluating investment opportunities, but it does not measure rate of return. It measures only the length of time it takes to recover the cash outlay for the investment. It indicates cash at risk. In our model there are costs of $500 committed in year 0. To determine payback, we merely add the unadjusted cash flow for each year and determine how many years it takes to get the outlay back. In the first two years $450 is recovered, and by the end of the third year $600 is recovered. By interpolation we find cash recovery to be approximately 2.3 years. It is obvious that the rational manager does not commit a large sum of money just to recover it. He expects a rate of return commensurate with the risks and his alternative use of his funds in alternative investments (opportunity cost). In our example, the calculation of payback reveals a relatively short exposure of funds and cash flow continuing beyond the payback period. It is interesting information in overall project evaluation, but it is not conclusive. Our model will automatically throw off payback as a byproduct as we calculate the crucial timeadjusted NPV of the investment and DCFROR.
A version of cash payback is the cash bailout method. This approach takes into account not only the annual cash flow as shown in Figure A2 but also the estimated liquidation value of the assets at the end of each year. If the liquidation value of a highly specialized project is zero, then cash payback and cash bailout are the same. But if it is assumed in our example that the liquidation value of the investment at the end of year 1 will be $275, the cash bailout would be one year (cash flow $225 plus liquidation value $275 = $500 original cash commitment).
We consider NPV as described a valid basis for determining the economic consequence of an investment decision. Many business economists use it as their sole criterion for the gonogo decision for investment. We recognize this method as paramount throughout our analysis but prefer using it in conjunction with other measures rather than as the sole criterion.
