Mini Case: 4 – 34
j. Define the nominal risk-free rate (rRF). What security can be used as an estimate
of rRF?
Answer: The real risk-free rate, r*, is the rate that would exist on default-free securities in the
absence of inflation:
k. Describe a way to estimate the inflation premium (IP) for a T-Year bond.
Answer: Treasury Inflation-Protected Securities (TIPS) are indexed to inflation. The IP for a
particular length maturity can be approximated as the difference between the yield on
Mini Case: 4 – 35
l. What is a bond spread and how is it related to the default risk premium? How
are bond ratings related to default risk? What factors affect a company’s bond
rating?
Answer: A “bond spread” is often calculated as the difference between a corporate bond’s
yield and a Treasury security’s yield of the same maturity. Therefore:
2. Provisions in the bond contract:
A. Secured vs. Unsecured debt
3. Other factors:
Mini Case: 4 – 36
m. What is interest rate (or price) risk? Which bond has more interest rate risk, an
annual payment 1-year bond or a 10-year bond? Why?
Answer: Interest rate risk, which is often just called price risk, is the risk that a bond will lose
value as the result of an increase in interest rates. Earlier, we developed the following
values for a 10 percent, annual coupon bond:
Maturity
rd 1-Year Change 10-Year Change
Interest Rate Price Risk for 10 Percent Coupon
Bonds with Different Maturities
Bond Val ue
($)
1,800
Mini Case: 4 – 37
n. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-
year bond or a 10-year bond?
Answer: Investment rate risk is defined as the risk that cash flows (interest plus principal
repayments) will have to be reinvested in the future at rates lower than today’s rate.
To illustrate, suppose you just won the lottery and now have $500,000. You plan to
o. How are interest rate risk and reinvestment rate risk related to the maturity risk
premium?
Answer: Long-term bonds have high interest rate risk but low reinvestment rate risk. Short-
Mini Case: 4 – 38
p. What is the term structure of interest rates? What is a yield curve?
Answer: The term structure of interest rates is the relationship between interest rates, or
yields, and maturities of securities. When this relationship is graphed, the resulting
curve is called a yield curve.
Mini Case: 4 – 39
q. Briefly describe bankruptcy law. If this firm were to default on the bonds,
would the company be immediately liquidated? Would the bondholders be
assured of receiving all of their promised payments?
Answer: When a business becomes insolvent, it does not have enough cash to meet scheduled
interest and principal payments. A decision must then be made whether to dissolve
the firm through liquidation or to permit it to reorganize and thus stay alive.
The decision to force a firm to liquidate or to permit it to reorganize depends on
If the firm is deemed to be too far gone to be saved, it will be liquidated and the
priority of claims would be as follows:
1. Secured creditors.
If the firm’s assets are worth more “alive” than “dead,” the company would be
reorganized. Its bondholders, however, would expect to take a “hit.” Thus, they
Web Solutions: 4 – 40
Web Appendix 4A
A Closer Look at Zero Coupon Bonds
Answers to Questions
4A-1 No, not all original issue discount bonds have zero coupons. Zero coupon bonds are just
4A-2 Shortly after corporations began to issue zeros, investment bankers figured out a way to
create zeros from U.S. Treasury bonds, which at the time were issued only in coupon
form. In 1983, Salomon Brothers bought $1 billion of 12%, 30-year Treasuries. Each
bond had 60 coupons worth $60 each, which represented the interest payments due every
4A-3 Treasury zeros are not protected from interest rate (price) risk, because the principal is
totally susceptible to interest rate movements. You can see this by changing interest rates
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Solutions to Problems
4A-1
Year 0 1 2 3 4
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Accrued valuet = Accrued valuet – 1(1.09).
Interest = Accrued valuet – Accrued valuet – 1.
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4A-2 0 1 2 3 4
Accrued value 708.43 772.19 841.69 917.44 1,000.00
Accrued valuet = Accrued valuet – 1(1.09).
Interest = Accrued valuet – Accrued valuet – 1.
4A-3
Using a financial calculator, enter the following data: N = 5; I/YR = 10; PMT = 0; FV =
6000000; and then solve for PV = $3,725,527.94.
4A-4 Step 1: Find out what was paid for the bond:
PV = $1,000/(1.068)7 = $630.959.
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4A-5 First find the yields on one-year and two-year zero coupon bonds, so you can find the
implied rate on a one-year bond, one year from now. Then use this implied rate to find its
price.
1-Year:
Therefore, if the implied rate = X, then:
Now find the price of a 1-year zero, 1 year from now:
Using a financial calculator, enter the following data: N = 1; I/YR = 7.5; PMT = 0; FV =
1000; and then solve for PV = -$930.23.
4A-6 0 10 50
-87.2037 1,000
Step 1: Using a financial calculator, we find the PV of the zeros at Time 0 by entering the
following data:
N = 50; I/YR = 5; PMT = 0; FV = 1000; and then solve for PV = $87.2037.
Web Solutions: 4 – 44
Web Appendix 4D
The Pure Expectations Theory and Estimation of Forward
Rates
Solutions to Problems
4D-1 r
T1 = 5%; 1rT1 = 6%; rT2 = ?
4D-2 Let X equal the yield on 2-year securities 4 years from now:
4D-3 a. (1.045)2 = (1.03)(1 + X)
1.092/1.03 = 1 + X
X = 6%.
b. For riskless bonds under the expectations theory, the interest rate for a bond of any
maturity is
rN = r* + average inflation over N years. If r* = 1%, we can solve for IPN:
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4D-4 r
* = 2%; MRP = 0%; r1 = 5%; r2 = 7%; X = ?
X represents the one-year rate on a bond one year from now (Year 2).