300 Planning and Forecasting
The concept that future cash f lows have a lower present value and the set
of tools used to discount future cash f lows to their present values are collec-
tively known as “time value of money” (TVOM) analysis. I have always thought
this to be a misnomer; the name should be the “money value of time.” But
there is no use bucking the trend, so we will adopt the standard nomenclature.
You probably already have an intuitive grasp of the fundamentals of
TVOM analysis, as your likely answer to the following question illustrates:
Would you rather have $100 today or $100 next year? Why?
The answer to this question is the essence of TVOM. You no doubt an-
swered that you would rather have the money today. Money today is worth
more than money to be delivered in the future. Even if there were perfect cer-
tainty that the future money would be received, we prefer to have money in
hand today. There are many reasons for this. Having money in hand allows
greater f lexibility for planning. You might choose to spend it before the future
money would be delivered. If you choose not to spend the money during the
course of the year, you can earn interest on it by investing it. Understanding
TVOM allows you to quantify exactly how much more early cash f lows are
worth than deferred cash f lows. An example will illuminate the concept.
Suppose you and a friend have dinner together in a restaurant. You order
an inexpensive sandwich. Your friend orders a large steak, a bottle of wine, and
several desserts. The bill arrives and your friend’s share is $100. Unfortu-
nately, your friend forgot his wallet and asks to borrow the $100 from you. You
agree and pay. A year passes before your friend remembers to pay you back the
money. “Here is the $100,” he finally says one day. Such events test a friend-
ship, especially if you had to carry a $100 balance on your credit card over the
course of the year on which interest accrued at a rate of 18%. Is the $100 that
your friend is offering you now worth the same as the $100 that he borrowed a
year earlier? Actually, no; a $100 cash f low today is not worth $100 next year.
The same nominal amount has different values depending on when it is paid. If
the interest rate is 18%, a $100 cash f low today is worth $118 next year and is
worth $139.24 the year after because of compound interest. The present value
of $118 to be received next year is exactly $100 today. Your friend should pay
you $118 if he borrowed $100 from you a year earlier.
The formula for converting a future value to a present value is:
where PVstands for present value, FVis future value, nis the number of peri-
ods in the future that the future cash f low is paid, and ris the appropriate in-
terest rate or discount rate.
Discounting Cash Flows
Suppose in the brewery example that the appropriate discount rate for translat-
ing future values to present values was 20%. Recall that the brewery project
PV FV
r= n
()^1 +