Time Value of Money
We now discuss how managers can use present value analysis to properly account for the
timing of many decisions which involve the gap between the time when the benefits of the
project are received.
The timing of many decisions involves a gap between the time when the costs of a project are
borne and the time when the benefits of the project are received. In these instances it is
important to recognize that $1 today is worth more than $1 received in the future.
Managers can use present value analysis to properly account for the receipts and expenditures.
Why is this?
1. Earning potential: Money you have now can be invested to earn interest, making it grow
over time.
2. Inflation: The purchasing power of money tends to decrease over time due to inflation.
The present value (PV) of an amount received in the future is the amount that would have to be
invested today at the prevailing interest rate to generate the given future value.
The present value (PV) of a future value (FV) received n years in the future is
where i is the rate of interest, or the opportunity cost of funds.
The present value of a future payment reflects the difference between the future value (FV) and
the opportunity cost of waiting (OCW): PV=FV -OCW. Intuitively, the higher the interest rate, the
higher the opportunity cost of waiting to receive a future amount and thus the lower the present
value of the future amount. For example, if the interest rate is zero, the opportunity cost of
waiting is zero, and the present value and the future value coincide.
The basic idea of the present value of a future amount can be extended to a series of future
payments. For example, if you are promised FV1 one year in the future, FV2 two years in the
future, and so on for n years, the present value of this sum of future payments is
Formula (Present Value of a Stream). When the interest rate is i, the present value of a stream
of future payments of FV1, FV2, . . . , FVn is
Given the present value of the income stream that arises from a project, one can easily compute
the net present value of the project.
The net present value (NPV) of a project is simply the present value (PV) of the income stream
generated by the project minus the current cost (C0) of the project: NPV=PV-C0.
If the net present value of a project is positive, then the project is profitable because the present
value of the earnings from the project exceeds the current cost of the project. On the other hand,
a manager should reject a project that has a negative net present value, since the cost of such a
project exceeds the present value of the income stream that project generates.
Real-Life Examples
● Loans: Banks charge interest because they're lending you money now, which they could
invest.
● Investments: The potential for your investments to grow over time is based on the time
value of money.
● Retirement savings: The earlier you start saving, the more time your money has to grow.
Example 1: Saving for a Vacation
● Scenario: You want to go on a vacation in one year and need $2,000.
● Option A: Save $2,000 now and put it in a savings account earning 3% interest.
● Option B: Wait a year and save $2,000.
Why is Option A better? Because the money you save now can earn interest for a year, giving you
more than $2,000 for your vacation.
Example 2: Loan Repayment
● Scenario: You borrow $10,000 from a friend and agree to pay them back in one year with
5% interest.
● Calculation: You owe your friend $10,000 + (5% * $10,000) = $10,500 in one year.
Why do you owe more? Because your friend could have invested the $10,000 and earned
interest. To compensate them for this opportunity, you pay them interest.
Example 3: Investment Growth
● Scenario: You invest $1,000 in a stock that increases in value by 10% per year.
● Year 1: $1,000 * 1.10 = $1,100
● Year 2: $1,100 * 1.10 = $1,210
Why does your investment grow? Because the earnings from the first year are reinvested and
also earn a return in the second year. This is called compounding.
