# Managerial Economics/Cash Flow

The basics of cash flow can be summed up by the concept of time value of money. This concept is the idea that having money now is better than money in the future, since you can spend it or put it to use. As a result you should be compensated for the time you do not have the use of your money. To make equivalent the differences in time we use a flip sided principle knows as discounting (bringing future cash flows to the present) or income (taking present values to the future). The rate of change required to make cash flows equivalent over time periods is known as the discount rate (both i d and r are common variables for the discount rate, although i is usually reserved for inflation). This rate can change with time or for different people. Imagine how high your discount rate would be if you had won a large cash prize in a radio contest, but had to phone the station within a minute and had no quarters.

The time that cash flows are discounted to sets a frame of reference for series of cash flows. This time is usually known as t0 pronounced "t not." While any frame of reference can be chosen the most common reference time is now. In retirement problems the frame of reference can be the date of retirement.

The basic cash flow equation is FV=PV*(1+r)^t, where FV is the future value (time at some future time), PV is the present value (value at t0, r is the discount (interest) rate, and t is the time between the future value and present value. The units of time do not matter, but must be the same as the period rate in which r is quoted. Both are usually in annual terms.

An example of this is the future value of \$100 in one year with a discount rate of 5%. To solve this problem you would evaluate the following statement:

```FV=\$100*(1+0.05)^1
FV=\$100*1.05
FV=\$105
```

See that was pretty easy wasn't it. All of finance can be summed up with variants of that basic formula.

According to this principle, if a decision affects costs and revenues in long-run, all those costs and revenues must be discounted to present values before valid comparison of alternatives is possible. This is essential because a rupee worth of money at a future date is not worth a rupee today. Money actually has time value. Discounting can be defined as a process used to transform future dollars into an equivalent number of present dollars. For instance, \$1 invested today at 10% interest is equivalent to \$1.10 next year.