Net present value(NPV), the basics
The net present value, residual value or current valueThe net present value tells you the value of a pending sequence of payments at today's time.
It answers the question, what is the fair price for a contract that still brings certain payments. For example, the
termination of a lease contract before it expires. Or the sale of a security with some disbursements pending. It is thus
the typical question for the secondary market of fund portions.
Comparison net yieldTo determine the value of a sequence of pending payments you need to indicate a comparison net yield, which
could be obtained alternatively with the capital. One could call this comparison net yield or the capital costs if
one needs to borrow the money. This comparison net yield should contain a risk impact, which covers the uncertainty
of the payments that can be received. For example one could take the net yield (approx. 4%) of government
notes as the comparison net yield and add some points for the higher risk. Mostly you will use comparison yields
from 4-10%. Where 4% represents very safe investment and 10% an investment in a business with certain risks.
NPV = Sum of (payments /((1 + comparison yield)powers duration))
NPV= net present value
The formula in a mathematical expression:
Comparison yield: eg. 6% = 0.06
Duration: the time between the purchase date and the date of a payment in years. One year
is thus 1 and one day 1/365 or 1/365.25.
NBW(B, t, r) = Sum B[i]/(1+r)^t[i]
B[i] is the i.th payment amount.
Summary: to obtain the NPV you simply build the sum of all payments whereby the worth of payments, with a maturity
in the future, is reduced as a function of the time and the comparison yield. With a comparison yield from 0% the net present value is
equal to the sum of all still pending payments.
The more detailed article Future and
Present Value of Money is available at
r is the indicated comparison yield.
t[i] is the time between the beginning (e.g. buy) and a date of a payment. The unit of the time can be
arbitrarily selected. However, one must select years as unit for the time to obtain the net yield per year
or per annum (p.a.).
Net present value
Valuation using discounted cash flows (DCF)