Present value calculations are an essential part of almost every industry. I see projects every day whose economic basis depend on knowing the present value of a stream of cash flow. Unfortunately most of the time projects are justified simply on the basis of having money in the budget and choosing the next project in the priority list.
A single payment
The present value, in today’s dollars, of one single future payment is:
P = (1 + i)-n
Where:
P = Value in today’s dollars
i = interest rate (%)
n = number of compounding periods
The common notation to express this calculation is P = (P/F, i%, n). For example, if I was trying to communicate that a project will receive a $1,000 income in 2 years time, with a discount o 8%, I would write (P/F, 8%, 2) = $961.17.
Multiple payments
If there is more than one payment, as inevitably all projects have, it’s the same calculation but many times over. There are two variations on this, the uniform series and the uniform gradient.
Uniform Series
This is a series of payments of the same size and spacing. The notation is:
P = (P/A, i%, n)
The present value calculation is:
$$P = \frac{(1 + i)^n – 1}{i(1 + i)^n}$$
Uniform Gradient
This is a series of payments that are changing at a uniform rate. The notation is:
P = (P/G, i%, n)
The present value calculation is:
$$P = \frac{(1 + i)^n – 1}{i^2(1 + i)^n} – \frac{n}{i(1 + i)^n}$$
