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Chapter 3
Interest Rates and Rates of Return
Brief Chapter Summary and Learning Objectives
3.1 The Interest Rate, Present Value, and Future Value (pages 50–58)
Explain how the interest rate links present value with future value.
People value funds in the future less than they do funds in the present, so funds that will be
received in the future need to be discounted to determine their present value.
3.2 Debt Instruments and Their Prices (pages 58–62)
Distinguish among different debt instruments and understand how their prices are determined.
Debt instruments take different forms because lenders and borrowers have different needs. There
are four basic categories of debt instruments: simple loans, discount bonds, coupon bonds, and
fixed-payment loans.
3.3 Bond Prices and Yield to Maturity (pages 62–67)
Explain the relationship between the yield to maturity on a bond and its price.
The yield to maturity equates the present value of the payments from an asset with the asset’s
price today.
3.4 The Inverse Relationship between Bond Prices and Bond Yields (pages 67–73)
Understand the inverse relationship between bond prices and bond yields.
The reasoning behind the inverse relationship between bond prices and yields to maturity is that
if interest rates rise, existing bonds issued when interest rates were lower become less desirable
to investors and the prices of those bonds will fall.
3.5 Interest Rates and Rates of Return (pages 73–75)
Explain the difference between interest rates and rates of return.
The rate of return is the return on a security as a percentage of the initial price. The rate of return
includes capital gains as well as interest payments.
3.6 Nominal Interest Rates Versus Real Interest Rates (pages 75–78)
Explain the difference between nominal interest rates and real interest rates.
The real interest rate is the nominal interest rate adjusted for inflation.
Key Terms
Capital Gain An increase in the market price of
an asset.
Capital Loss A decrease in the market price of
an asset.
Debt instruments (also known as credit market
Compounding The process of earning interest on
interest as savings accumulate over time.
Coupon bond A debt instrument that requires
multiple payments of interest on a regular basis,
such as semiannually or annually, and a payment of
the face value at maturity.
instruments or fixed-income assets) Methods
of financing debt, including simple loans,
discount bonds, coupon bonds, and fixed
payment loans.
Deflation A sustained decline in the price level.
Discount bond A debt instrument in which the
borrower repays the amount of the loan in a
single payment at maturity but receives less than
the face value of the bond initially.
Discounting The process of finding the present
value of funds that will be received in the future.
Equity A claim to part ownership of a firm;
common stock issued by a corporation.
Financial arbitrage The process of buying and
selling securities to profit from price changes
over a brief period of time.
Fixed-payment loan A debt instrument that
requires the borrower to make regular periodic
payments of principal and interest to the lender.
Future value The value at some future time of
an investment made today.
Interest-rate risk The risk that the price of a
financial asset will fluctuate in response to
changes in market interest rates.
Nominal interest rate An interest rate that is not
adjusted for changes in purchasing power.
Present value The value today of funds that will
be received in the future.
Rate of return, R The return on a security as a
percentage of the initial price; for a bond during a
holding period of one year, the coupon payment
plus the change in the price of a bond divided by
the initial price.
Real interest rate An interest rate that is adjusted
for changes in the purchasing power.
Return The total earnings from a security; for a
bond, during a holding period of one year, the
coupon payment plus the change in the price of
the bond.
Simple loan A debt instrument in which the
borrower receives from the lender an amount
called the principal and agrees to repay the lender
the principal plus interest on a specific date when
the loan matures.
Time value of money The way that the value of a
payment changes depending on when the payment
is received.
Yield to maturity The interest rate that
makes the present value of the payments from
an asset equal to the asset’s price today.
Chapter Outline
Teaching Tips
This chapter may be the most important in the book. Interest rates can be mysterious to some students.
Students who fail at the beginning of the semester to understand the basics of calculating interest rates
experience considerable difficulty understanding the subsequent material. So carefully going over this
material should pay large dividends later in the semester.
The concept of present value is fundamental to interest rate calculations, but many students find it
difficult to grasp when first presented. Working through several examples—such as those presented in the
text—can be a worthwhile use of class time. You may want to direct students’ attention to Table 3.1 on
page 56 of the text. This table summarizes the relationship between present value, time to maturity, and
the interest rate. Students also often have difficulty grasping the difference between the yield to maturity
and the rate of return on a financial asset for a given holding period (one year, in the examples in the text).
Several important points made later in the text turn on this distinction.
Students often find the interpretation of the bond price and bond yield listings to be one of the more
interesting and useful exercises in the course. So, it may be worth spending time on the material
discussed in the Making the Connection that begins on page 71 of the chapter. Finally, the distinction
between nominal and real interest rates is also worth stressing. A worthwhile class discussion can be
centered on the question of how to decide whether a nominal interest rate of, say, 10% is high or low.
Will Investors Lose Their Shirts in the Market for Treasury Bonds?
Teaching Tips
You can use the chapter opener, “Will Investors Lose Their Shirts in the Market for Treasury
Bonds?” during class to show how changing interest rates affect the price of bonds. Begin by
stating that a person purchased a bond that pays 2% interest per year for $1,000. Suppose that new
bonds now pay an interest rate of 6%. Ask students how much interest they would receive each
year if they held the original bond to maturity. Next, ask students whether they would be willing
to sell their bond for $1,000 and use the $1,000 to purchase a new bond yielding 6% interest.
Follow up by asking whether someone would be willing to purchase their bond for $1,000. If not,
would any of your students be willing to accept less than $1,000? Have students explain the
reasoning behind their answer. Discuss what would happen to the price of a bond as a result of
higher interest rates. Also, discuss how an increase in interest rates affects existing bondholders.
3.1 The Interest Rate, Present Value, and Future Value (pages 50–58)
Learning Objective: Explain how the interest rate links present value with future value.
A. Why Do Lenders Charge Interest on Loans?
Interest on loans compensates lenders for inflation, default risk, and the opportunity cost of
waiting to spend money.
B. Most Financial Transactions Involve Payments in the Future
Most loans involve future payments to pay off the loan. Interest rates are an important factor in
comparing different financial transactions.
C. Compounding and Discounting
Economists refer to the process of earning interest on interest as savings accumulate over time as
compounding. Funds in the future are worth less than funds in the present, so funds in the
future have to be reduced, or discounted, to find their present value. Funds in the future are
worth less than funds in the present because: (1) Dollars in the future will usually buy less than
dollars can today; (2) Dollars that are promised to be paid in the future may not actually be
received; and (3) There is an opportunity cost in waiting to receive a payment because you
cannot get the benefits of the goods and services you could have bought if you had the money
today.
D. Discounting and the Prices of Financial Assets
By adding up the present values of all the payments, we have the dollar amount that a buyer
will pay for the asset; in other words, we have determined the asset’s price.
3.2 Debt Instruments and Their Prices (pages 58–62) 3.3
Learning Objective: Distinguish among different debt instruments and understand how their prices
are determined.
A. Loans, Bonds, and the Timing of Payments
Debt instruments include (1) loans granted by banks and (2) bonds issued by corporations and
governments. Debt instruments take different forms because lenders and borrowers have
different needs. There are four basic categories of debt instruments:
1. Simple loans: The borrower receives from the lender an amount of funds called the
principal and agrees to repay the lender the principal plus interest on a specific date when
the loan matures.
2. Discount bonds: The borrower pays the lender an amount called the face value at
maturity
but receives less than the face value initially. The interest paid on the loan is the
difference between the amount repaid and the amount borrowed.
3. Coupon bonds: The borrower makes interest payments to the lender in the form of
coupons at regular intervals, typically semi-annually or annually, and repays the face
value at maturity.
4. Fixed-payment loans: The borrower makes periodic payments to the lender. The
payments are of equal amounts and include both interest and principal.
3.3 Bond Prices and Yield to Maturty (pages 62-67)
Learning Objective: Explain the relationship between the yield to maturity on a bond and
its price.
A. Bond Prices
The price of a coupon bond is the present value of all future payments including coupons and its
face value.
B. Yield to Maturity
The yield to maturity equates the present value of the payments from an asset with the asset’s price
today. Calculating yields to maturity for alternative investments allows savers to compare any type
of debt instrument.
C. Yields to Maturity on Other Debt Instruments
For both simple loans and discount bonds, the yield to maturity is the interest rate that makes the
lender indifferent between having the amount of the loan today or the final payment at maturity.
Calculating the yield to maturity for a fixed-payment loan is similar to calculating the yield to
maturity for a coupon bond. The yield-to-maturity is the interest rate that ensures that the amount
of the loan today equals the present value of the loan payments.
Teachings Tips
Refer students to Solved Problem 3.3 on page 66, which provides a nice summary of how to solve
for the yield to maturity for the different types of debt instruments.
3.4 The Inverse Relationship between Bond Prices and Bond Yields (pages 67-73)
Learning Objective: Understand the inverse relationship between bond prices and bond yields.
A. What Happens to Bond Prices When Interest Rates Change?
Because the coupon is fixed once a bond is issued, a change in market interest rates affects the
present
value of future payments and therefore affects the price of a bond. Higher market interest rates
reduce
the price of existing bonds, while lower market interest rates increases the price of existing bonds.
B. Bond Prices and Yields to Maturity Move in Opposite Directions
If the yield to maturity increases, then the present values of the coupon payments and the face
value payment must decline, causing the price of the bond to decline. The economic reasoning
behind the inverse relationship between bond prices and yields to maturity is that if interest
rates rise, existing bonds issued when interest rates were lower become less desirable to
investors and the prices of those bonds fall.
C. Secondary Markets, Arbitrage, and the Law of One Price
If yields to maturity on comparable securities differ, traders on secondary markets will engage
in financial arbitrage, the process of buying and selling securities to profit from price changes
over a brief period of time. Prices of securities adjust very rapidly—often within seconds—to
eliminate arbitrage profits because of the very large number of traders participating in financial
markets and the speed of electronic trading. This description of how prices of financial securities
adjust is an example of a general economic principle called the law of one price, which states
that identical products should sell for the same price everywhere.
Teaching Tips
Making the Connection: How to Follow the Bond Market: Reading the Bond Table on pages 71–73 helps
students learn how to obtain and interpret real-world information about bonds instead of just
understanding theoretical concepts. A brief discussion of bid and ask prices can reinforce how bond prices
are determined by the interaction of buyers and sellers in the bond market.
3.5 Interest Rates and Rates of Return (pages 73–75)
Learning Objective: Explain the difference between interest rates and rates of return.
A. A General Equation for the Rate of Return on a Bond
The rate of return is the return on a security as a percentage of the initial price; for a bond, the
coupon payment plus the change in the price of a bond divided by the initial price. In general,
the rate of return is the current yield (coupon divided by the initial price) plus the rate of capital
gain.
B. Interest-Rate Risk and Maturity
Economists refer to the risk that the price of a financial asset will fluctuate in response to
changes in market interest rates as interest-rate risk. Bonds with fewer years to maturity will be
less affected by a change in market interest rates than would bonds with more years to maturity.
Teaching Tips
Consider a three-year coupon bond that sells for $1,000 with an initial coupon rate of 5%. Solve for the
price of the bond (present value), assuming the yield to maturity is equal to the coupon rate (answer is
$1,000). Now have students determine the new price if the interest rate rises to 6%. Have students note
how much the bond price changes (new price is $973.27). Next, consider what happens to the price if one
year passes (new price is $981.67). Point out to students that the three-year coupon bond now behaves as
a two-year bond. Also, the price of the bond doesn’t decline as much as it did when it was a three-year
bond (example of interest-rate risk). This example shows how the interest-rate risk on bonds rises as the
time-to-maturity increases.
3.6 Nominal Interest Rates versus Real Interest Rates (pages 75–78)
Learning Objective: Explain the difference between nominal interest rates and real interest rates.
A nominal interest rate is an interest rate that is unadjusted for changes in purchasing power. The
real interest rate is the interest rate adjusted for changes in purchasing power. Because lenders and
borrowers don’t know what the actual real interest rate will be during the period of a loan, they
must make saving or investing decisions on the basis of what they expect the real interest rate to be.
The expected real interest rate is the nominal interest rate minus the expected inflation rate.
