## Why cash flows across time are not comparable

There are three reasons why cash flows across time are not comparable, and a cash flow in the future is worth less than a similar cash flow today:

(1) Individuals prefer present consumption to future consumption. People would have to be offered more in the future to give up present consumption - this is called the real rate of return. The greater the real rate of return, the greater will be the difference in value between a cash flow today and an equal cash flow in the future.

(2) When there is monetary inflation, the value of currency decreases over time. The greater the inflation, the greater the difference in value between a cash flow today and a cash flow in the future.

(3) Any uncertainty (risk) associated with the cash flow in the future reduces the value of the cashflow. The greater the uncertainty associated with the cash flow, the greater will be the difference between receiving the cash flow today and receiving an equal amount in the future.

The process by which future cash flows are adjusted to reflect these factors is called discounting, and the magnitude of these factors is reflected in the discount rate. Thus the present value of a cash flow (CFt) at a point in time 't' in the future, when the discount rate is r, can be written as follows:

Present Value of Cash Flow = CFt

Note that the second term in the brackets

effectively weights the cash flow by when it occurs. The differences in weights across time will depend entirely upon the level of the discount rate. Consequently, when discount rates are high, which could be due to high real rates, high inflation and/or high uncertainty, returns that occur further in the future will be weighted less. Appendix 1 includes a more complete discussion of the mechanics of present value.

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