Chapter 6: Interest Rates
Comprehensive/Spreadsheet Problem
133
c.
d. The real risk-free rate would be the same for the corporate and treasury bonds. Similarly,
7–year Corporate yield = r* + IP7 + MRP7 + LP + DRP = 7.817%
5%
6%
7%
Interest Rate
Yield Curve
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Chapter 6: Interest Rates
Now we can graph the data in the first 3 columns of the above table to get the Treasury and A-
rated Corporate yield curves:
8%
Interest Rate
Treasury and A-Rated Corporate Yield Curves
Note that if we constructed yield curves for corporate bonds with other ratings, the higher the
f.
(1) The 1-year rate, 1 year from now
(2) The 5-year rate, 5 years from now
(4) The 10-year rate, 20 years from now
Chapter 6: Interest Rates
Integrated Case
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Integrated Case
6-21
Morton Handley & Company
Interest Rate Determination
Maria Juarez is a professional tennis player, and your firm manages her
money. She has asked you to give her information about what determines
the level of various interest rates. Your boss has prepared some questions
for you to consider.
A. What are the four most fundamental factors that affect the cost of
money, or the general level of interest rates, in the economy?
Answer: [Show S6-1 and S6-2 here.] The four most fundamental factors
affecting the cost of money are (1) production opportunities, (2)
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Chapter 6: Interest Rates
B. What is the real risk-free rate of interest (r*) and the nominal risk-
free rate (rRF)? How are these two rates measured?
Answer: [Show S6-3 and S6-4 here.] Keep these equations in mind as we
discuss interest rates. We will define the terms as we go along:
Chapter 6: Interest Rates
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137
C. Define the terms
inflation premium (IP), default risk premium
(DRP), liquidity premium (LP), and maturity risk premium (MRP)
.
Which of these premiums is included in determining the interest
rate on (1) short-term U.S. Treasury securities, (2) long-term U.S.
Treasury securities, (3) short-term corporate securities, and (4)
long-term corporate securities? Explain how the premiums would
vary over time and among the different securities listed.
Answer: [Show S6-5 here.] The inflation premium (IP) is a premium added
to the real risk-free rate of interest to compensate for expected
inflation.
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Chapter 6: Interest Rates
3. The rate on short-term corporate securities is equal to the real
4. The rate for long-term corporate securities also includes a
D. What is the term structure of interest rates? What is a yield
curve?
Answer: [Show S6-6 here. S6-6 shows a recent (April 2014) Treasury yield
Chapter 6: Interest Rates
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139
Yield Curve for April 2014
E. Suppose most investors expect the inflation rate to be 5% next
year, 6% the following year, and 8% thereafter. The real risk-free
rate is 3%. The maturity risk premium is zero for bonds that
mature in 1 year or less and 0.1% for 2-year bonds; then the MRP
increases by 0.1% per year thereafter for 20 years, after which it
is stable. What is the interest rate on 1-, 10-, and 20-year
Treasury bonds? Draw a yield curve with these data. What factors
can explain why this constructed yield curve is upward-sloping?
Answer: [Show S6-7 through S6-12 here.]
Step 1: Find the average expected inflation rate over Years 1 to 20:
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Chapter 6: Interest Rates
Step 2: Find the maturity risk premium in each year:
Step 3: Sum the IPs and MRPs, and add r* = 3%:
The shape of the yield curve depends primarily on two factors: (1)
expectations about future inflation and (2) the relative riskiness of
securities with different maturities.
F. At any given time, how would the yield curve facing a AAA-rated
company compare with the yield curve for U.S. Treasury
securities? At any given time, how would the yield curve facing a
BB-rated company compare with the yield curve for U.S. Treasury
securities? Draw a graph to illustrate your answer.
Chapter 6: Interest Rates
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Answer: [Show S6-13 and S6-14 here.] (Curves for AAA-rated and BB–
rated securities have been added to an illustrative yield curve to
Illustrative Corporate and Treasury Yield Curves
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Chapter 6: Interest Rates
G. What is the pure expectations theory? What does the pure
expectations theory imply about the term structure of interest
rates?
Answer: [Show S6-15 and S6-16 here.] The pure expectations theory
assumes that investors establish bond prices and interest rates
H. Suppose you observe the following term structure for Treasury
securities:
Maturity Yield
1 year 6.0%
2 years 6.2
3 years 6.4
4 years 6.5
5 years 6.5
Assume that the pure expectations theory of the term structure is
correct. (This implies that you can use the yield curve provided to
“back out” the market’s expectations about future interest rates.)
What does the market expect will be the interest rate on 1-year
securities 1 year from now? What does the market expect will be
the interest rate on 3-year securities 2 years from now? Calculate
these yields using geometric averages.
Chapter 6: Interest Rates
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Answer: [Show S6-17 through S6-20 here.] Calculation for r on 1-year
securities one year from now:
I. Describe how macroeconomic factors affect the level of interest
rates. How do these factors explain why interest rates have been
lower in recent years?
Answer: [Show S6-21 here.] Expected inflation, default risk, maturity risk,
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Chapter 6: Interest Rates