Future Value and Present Value

Finance is centered around the growth of money. Understanding future value and present value is relatively simple, but it is also imperative to understand most financial dealings.

The One-period Case: Future Value

When computing the future value of an amount of cash we have today, we simply multiply the amount of cash today by the interest rate plus 1:

FV = C0 * (1 + r)
Where r is the interest rate,
C0 is the cash flow today, at time 0, (this is the same as the Present Value) and
FV is the Future Value, the value of C0 in the next period.

Example:
Question: If we have $1000 today and we invest it for one year (one period) at 5% interest, then how much money will we have in one year?
FV = C0 * (1 + r) FV = $1000 * (1 + 5%)
FV = $1050
Answer: $1050

This is easy enough. We can break the equation into two parts: the amount of money we begin with plus the amount of interest that will accrue by the end of the period. In the example, we begin with $1000. We accrue interest of $50 ($50 = $1000 * 5%). Add the two together to get the total Future Value of our money in one year (one period).
Future Value = $1000 + ($1000 * 5%)
= $1000 * (1 + 5%)
= $1000 * (1 + .05)
=$1050

The One-period Case: Present Value

Now let's compute the Present Value of a future amount of money. Present Value is the current value of money that we expect to receive in the future. To obtain the Present Value, we use a discount rate to discount the Future Value of money. The discount rate is usually equal to some interest rate. In finance, the Weighted Average Cost of Capital (WACC) is often what's used for the discount rate (there will be another article about this later on).

PV = C1 / (1 + r)
Where r is the discount rate,
PV is the Present Value, and
C1 is the cash flow at period 1 (the Future Value at period 1).

Example:
Question: If we will receive $1000 in one year (one period), and our appropriate discount rate is 5%, then how much is it worth to us now?
PV = C1 / (1 + r)
PV = $1000 / (1 + .05)
PV = $952.38
Answer: $952.38


Multi-Period Future Value and Present Value

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