Page 475 - Introduction to Business

CHAPTER 13 Financial Management of the Firm and Investment Management 449

interest rate would be only 5 percent, which is known as the riskless rate of interest. riskless rate of interest The interest
The risky interest rate is 10 percent, as it is made up of the sum of the riskless rate of rate charged by lenders in the case that
the borrower has no default risk
interest and the default premium (5 5 percent).
We can restate the above loan agreement between lender and borrower in a
different way. The bank is making an investment of $100 that will earn an
expected profit of $10 after one year. The rate of return on this investment is
Rate of return profit/investment cost rate of return The ratio of profit on an
investment to the cost of the investment
In our example the rate of return is the rate of interest, or 10 percent ($10
profit/$100 investment). This required rate of return by the bank on the loan is due
to the time preference for consumption, expected inflation, and default risk. The
future value of the $100 investment or loan is $110. Alternatively, the present future value The value of a dollar in the
value of the future $110 principal and interest is $100. We can write these concepts future, which is less than its value today
in equation form. present value The value today of money
to be received in the future
Present value nominal interest rate future value
In our example, that is

$100 0.10 $110
or
Present value future value/discount rate
$100 $110/(1 0.10)

Notice that the nominal interest rate is referred to as the discount rate when discount rate Any rate used in present
it is used to convert future values back to present values. You can now see that value calculations to convert money
from its future value to its present value
interest rates connect present values to future values of money, and vice versa.
Exhibit 13.3 summarizes different terms for and components of the nominal
interest rate.
For more details about the time value of money, including mathematical equa-
tions, see the box “The Time Value of Money: How Money Grows.” Exhibit 13.4 (on
p. 450) shows how $100 invested today and earning 10 percent each year will grow
in value over 20 years. The value of money grows at an increasing rate over time.
Compound interest causes money to grow faster than a simple linear rate. Com- compound interest Interest that is
pound interest is interest earned on previous interest paid. This makes it attractive earned on previous interest, also known
as the force of interest
for banks, individuals, and others to invest money for longer periods of time than
one year. The longer money is invested, the more it grows.

reality Do you save some of your money for the future? Would you save more
CH ECK if the interest rate earned on your savings were very high?

EXHIBIT 13.3
Nominal = riskless interest rate + default risk
interest rate premium What’s in an Interest Rate?

Other Names: Components: The risk of not
• Stated Real interest rate + expected inflation rate being paid back
interest rate
• Interest rate
• Discount rate Time preferences Rising prices of
• Rate of return for consumption goods and services

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