We all intuitively feel that receiving Rs 100 today is better than receiving Rs 100 after sometime. The principles ofpresent value explain how much better it is to receive that 100 today than receiving after a year by enabling us to calculate the value of Rs 100 receivable (say) after one in today’s rupees. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications. It is useful in decision-making ranging from simple personal decisions – buying a house, saving for a child’s education and estimating income in retirement, to more complex corporate financial decisions – picking projects in which to invest as well as deciding the right financing mix for these projects.
Time Lines and Notation
Dealing with cash flows that are at different points in time is made easier using a time line that shows both the timing and the amount of each cash flow in a stream. Thus, a cash flow stream of Rs100 at the end of each of the next 4 years can be depicted on a time line like the one depicted in Figure 1.
In the figure, 0 refers to right now. A cash flow that occurs at time 0 is therefore already in present value terms and does not need to be adjusted for time value. A distinction must be made here between a period of time and a point in time. The portion of the time line between 0 and 1 refers to period 1, which, in this example, is the first year. The cash flow that occurs at the point in time “1” refers to the cash flow that occurs at the end of period 1. Finally, the discount rate, which is 10% in this example, is specified for each period on the time line and may be different for each period. Had the cash flows been at the beginning of each year instead of at the end of each year, the time line would have been redrawn as it appears in Figure 2.
Note that in present value terms, a cash flow that occurs at the beginning of year 2 is the equivalent of a cash flow that occurs at the end of year 1.
Cash flows can be either positive or negative; positive cash flows are called cash inflows and negative cash flows are called cash outflows. We will follow the following notations in this lesson:
|CFt||Cash flow at the end of time t|
|A||Annuity, constant cash flow for several periods|
|g||Expected growth rate in cash flows|
|n||Number of years over which cash flows are received or paid|
The Intuitive Basis for Present Value
There are three reasons why a cash flow in the future is worth less than a similar cash flow today.
(1) We all prefer present consumption to future consumption and, therefore, need to be offered more in the future to give up present consumption. If the preference for current consumption is strong, individuals will have to be offered much more in terms of future consumption to give up current consumption. Conversely, when the preference for current consumption is weaker, individuals will settle for less in terms of future consumption.
(2) During inflation, the value of currency decreases over time. The greater the inflation, the greater will be the difference in value between a cash flow today and the same cash flow in the future. Suppose inflation is 10%. It means prices are going up by 10% a year. What I could buy with Rs 100 today will cost me Rs 110 after one year. If inflation were the only consideration, Rs 110 receivable after one year would be equal to Rs 100 today or 100 is the PV of a positive cash flow of 110 after one year.
(3) A promised cash flow might not be delivered for a number of reasons: the promisor (one who makes the promise) might default on the payment, the promisee (to whom the promise is made) might not be around to receive payment; or some other contingency might intervene to prevent the promised payment or to reduce it. Any uncertainty (risk) associated with the cash flow in the future reduces the present value of the cash flow.
The process by which future cash flows are worked upon to get present values, (reflecting the factors enumerated above), is called discounting, and the magnitude of these factors is reflected in the discount rate. The discount rate incorporates all of the above mentioned factors. In fact, the discount rate can be viewed as a composite of the expected real return (reflecting consumption preferences in the aggregate over the investing population), the expected inflation rate (to capture the deterioration in the purchasing power of the cash flow) and the uncertainty associated with the cash flow.