Time Value of Money
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Money has a time component i.e. money has a time unit identifying when it is received/paid.
The reason is that there is an opportunity cost associated with money in the future; we miss out on the opportunity to invest it today. This cost is determined by the nature of the investment:
If we invest the money in something relatively safe, then the opportunity cost is low
If we invest the money in something relatively risky, then the opportunity cost is high
Opportunity cost is basically the return on investment.
As such, $100 today is worth more than $100 in the future because having $100 today will keep us from missing out on the opportunity to invest it.
Since money has a time unit, we cannot aggregate money across different points in time directly. To do so, we need the following tools:
Timeline
Discount Factor
The timeline is used to represent cash flows (the flow of money in/out) at specific points in time. 0 denotes the current period/timestamp. 1, 2, 3... are future periods/timestamps. denotes the cash flow at timestamp i.
It is important to note that we must never aggregate (add/subtract) cash flows at different timestamps!
Just as we cannot add/subtract different currencies before converting them to a common base using an exchange rate, we also cannot aggregate cash flows at different timestamps without bringing them to a common base first. To do so, we need some sort of exchange rate for time.
The discount factor serves as an exchange rate for time. It is given by:
where:
R is the rate of return offered by investment alternatives in the capital markets of equivalent risk. It is also known as discount rate, hurdle rate or opportunity cost of capital For simplicity, we assume that R is constant over time
t is the number of time periods into the future (t>0) or past (t<0) to move CFs
