Present Value and Discounting
What is Present Value?
It is the current value of a future cash flow(s), discounted at an
appropriate discount factor (or interest rate).
This follows the same
principle as compounding.
Alternatively:What will we need today, invested at that same rate, to
give us an amount equal to the future cash flow?
Recall that FV = P(V)(1+r)
; let’s do some simple algebra, then
PV = FV/(1+r)
where r is the discount rate for t periods of time
in the future
Let’s look at a single period example:
An antique auto dealer can buy a “mint condition” 1928 Bugatti auto
He is certain
that he can resell the car in one year for
He also has the opportunity to make a well-collateralized
loan to an acquaintance for one year at 12% (assume essentially no
What should he do?
Before solving this problem, let’s introduce the concept of
Opportunity cost is simply the best alternative
financial opportunity that exists, at the same risk level as the one
In the auto example, it is the 12% certain, that
he can earn on the loan.
Therefore, the appropriate discount rate is
PV = $70,000/(1+0.12) = $62,500 vs. the $60,000 that he must pay for
the car today.
If he made the loan, then his PV (at 12%, of course) is
(If he makes the loan to his acquaintance, he will receive in
one year $67,200 – his $60,000 plus the 12% interest, or $7200.
$67,200/1.12) = $60,000.)