cash-flow - TIM 50 Fall 2011 Notes on Cash Flows and Rate...

TIM 50
Fall 2011
Notes on Cash Flows and Rate of Return
Time Value of Money
A cash flow is a series of payments or receipts spaced out in time. The key concept in analyzing
cash flows is that receiving a $1 today is more desirable than receiving a $1 at some point in the
future. How much more desirable $1 today is compared to $1 in the future depends on the
person or firm’s point of view, of course. The person or firm, which we will simply refer to as
the decision maker, quantifies what he or she thinks $1 in the future is worth by deciding what
quantity of money, received today, would be equally desirable.
For example, the decision maker may believe, “I would just as soon get $0.80 today as wait a
year for that dollar.” To formalize the logic, the decision maker defines a discount factor δ and in
our example sets it equal to 0.80. It’s important to remember that this is the decision maker’s
personal discount factor, and other people’s discount factors might be different. (For example,
someone else might value $1 one year from now as much as $0.90 today and pick a discount
factor of 0.90.)
If someone asked our decision maker to value $5 one year in the future, he or she would multiply
$5 times the discount factor δ =0.80 , yielding $4. Often it is helpful to visualize the cash flow on
a timeline. For example, a cash flow where $5 is received one year from now might be drawn as:
Time
$5
0
1 2
The horizontal axis is in units of years. It is common convention to label the current year as “0.”
Because the decision maker’s discount factor δ is 0.80, the above cash flow is exactly as
desirable as the cash flow below:
Time
0
1 2
δ× $5 = $4

Net Present Value
The same approach can be used to compute how desirable it would be to receive $1 two years
from now.
In the figure below, we multiply the $1 in year 2 by δ to determine that it would be equally
desirable to receive $0.80 a year earlier, and in this case a year earlier would be year 1. Then we
multiply $0.80 by the discount factor delta to determine that is equally desirable to receive $0.64,
a year earlier, which would be year 0. This calculation is equivalent to taking original amount
$1, and multiplying it by δ 2 . Thus it is equally desirable to receive $1.00 in two years as it is to
receive $0.64 today. What we have computed is what is called a Net Present Value (NPV) . The
net present value of a cash flow is a quantity of money, which if received today, would be
equally desirable as the cash flow. So the cash flow of receiving $1 in year 2, has an NPV of δ 2 =
$0.64. Note that the answer depends on the value of our discount factor δ .