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The concept that future cash flows have a lower present value and the set of tools used to discount
future cash flows to their present values are collectively 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 answered 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 certainty 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 flexibility 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 flows are worth than deferred cash
flows. 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. Unfortunately, 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 friendship, 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 your friend is offering you now worth the same as the $100 he borrowed a year
earlier? Actually, no, a $100 cash flow 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 flow 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 PV stands for present value, FV is future value, n is the number of periods in the future that
the future cash flow is paid, and r is the appropriate interest rate or discount rate.
Discounting Cash Flows
Suppose in the brewery example that the appropriate discount rate for translating future values to
present values is 20%. Recall that the brewery project is forecast to generate $2.42 million of cash in
year 1. The present value of that cash flow, as of year 0, is $2,016,667, computed as follows: