Because this area of valuation is critical, it has been refined quite a bit. We need to start with some definitions in order to keep straight how everything interacts and how this valuation happens.
- Annuity - A set of fixed payments that happen over a period of time (loan, lease, etc.)
- Present Value (PV) - The present value of future cash
- Future Value (FV) - The future value of present cash
- Discount rate - a rate used to find the present value of future cash
- Net Present Value (NPV) - the difference between what something costs, and what it provides when discounted to PV
- Discounted Cash Flow (DCF) Analysis - calculating cashflows and determining if their NPV > 0
Why do we care about discounting money to present values? Because projects and investments do not instantaneously finish and mature; They do so over different periods of time. Because of this, we must adjust them for the time value of money.
Here are the most important formulas used when dealing with PV, FV, and annuities.
PV / FV Formula
Ordinary annuity formulas
r = the interest rate / 100 (6.5% = .065)n = the number of periods (months, years, etc.)
c = total payment
Annuity PV/FV = total principal
In practice, people generally use something like Excel rather than the formulas to compute these values. Excel does have these built in and labels the functions pv, fv, and pmt.
The discount rate, used as the rate (r) parameter in the preceding formulas, can be arbitrarily set to some required rate. The most commonly used discount rate is the cost of capital, specifically the Weighted Average Cost of Capital (WACC). The WACC is made up of the weighted cost of debt and equity or in other words, what currently satisfies debtors and shareholders.
These formulas can be used to put money at different times on the same playing field and allows for true comparison. The annuity formulas are also useful for everyday calculations such as mortgage payments.
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