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Principles of Finance 6e Chapter 5
Besley/Brigham
5-1
CHAPTER 5
ANSWERS
5-1 The return associated with any investment is based on the change in the investor’s wealth. Any
5-2 a. Regional mortgage rate differentials do exist, depending on supply/demand conditions in
the different regions. However, relatively high rates in one region would attract capital from
other regions, and the end result would be a differential that was just sufficient to cover the
5-3 Short-term rates are more volatile because (1) the Federal Reserve operates mainly in the
5-4 A significant increase in productivity would raise the rate of return on producers' investments,
5-5 a. The immediate effect on the yield curve would be to lower interest rates in the short-term
end of the market, because the Fed deals primarily in that market segment. However,
5-6 Treasury bonds, along with all other bonds, are available to investors as an alternative
investment to common stocks. An increase in the return on Treasury bonds would increase the
5-7 The open market operations of the Federal Reserve are carried out by buying and selling
Chapter 5 Principles of Finance 6e
5-2
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
deposits in the banking system, and hence it affects the money supply. If the Fed wants to lower
interest rates, it would increase the money supply by purchasing government securities, and
vice versa.
5-8 When an interest rate change occurs, the value of a financial asset changes in an opposite
direction—that is, when the rate increases, the value decreases, and vice versa. This is a
5-9 If investors are convinced that interest rates will increase in the future, they will not want to “lock
5-10 Reinvestment rate risk has a greater impact on short-term investments than long-term
investments. For any investment, an investor has the opportunity to reinvest the funds that are
───────────────────────────────────────────────────────
SOLUTIONS
5-1
%1.57571.0
500,10$
000,6$
500,10$
)000,1($4)500,10$500,12($
HPY ===
+−
=
over the four-year period
000,1$
)20($50
5-3 a.
1,000[($45 $50) 8($0.50)] $1
Return 0.02 2.0%
1,000($50) $50
− + −
= = =− =−
Year 2 1,000[($45 $45) 4($0.50)] $2
1,000($45) $45
5-3
5-4 a. rRF1 = 5%, and
.5%7 =
2
2) Yearin r( + %5
=
rRF
2RF
Solving for rRF in Year 2, we obtain
rRF in Year 2 = (7.5% x 2) - 5% = 10%.
b. For riskless bonds under the expectations theory, the interest rate for a bond of any
maturity is rRF = r* + average inflation over n years. If r* = 3%, we can solve for IPn:
Year 1: rRF1 = 3% + Infl1 = 5%;
Infl1 = Year 1 expected inflation = 5% - 3% = 2%.
5-5 r* = 4%; MRP = 0%; rRF1 = 11%; rRF2 = 13%
RF1 RF RF
RF2
r +( r in Year 2) 11% + (r in Year 2)
r = 13% =
22
Chapter 5 Principles of Finance 6e
5-4
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
The average interest rate during the two-year period differs from the one-year interest rate
expected for Year 2 because of the inflation rates reflected in the two interest rates. The
inflation rate reflected in the interest rate on any security is the average rate of inflation
expected over the security's life.
5-6 Basic relevant equations:
rt = r* + IPt + DRPt + MRPt + LPt.
But here IP is the only premium, so rt = r* + IPt.
IPt = Avg. inflation = (Infl1 + Infl2 + … + Infln)/n
We can set up this table:
r* I Average I = IPt r = r* + IPt
1 2% 3% 3%/1 = 3% 5%
5-7 rRF = 2.2% in Year 1; IP1 = rRF – r* = 2.2% - 2.0% = 0.2% = Infl1
rRF averages 3.0% for two years. Thus, rRF in Year 2 is:
5-8 Because the only difference between Bond A and Bond B is the term to maturity, the difference
in the yields of these two bonds must be the result of their MRPs. Thus,
Principles of Finance 6e Chapter 5
Besley/Brigham
5-5
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
MRP = (8% - 7.5%)/5 = 0.1% per year
If the yields for Bond A and Bond B are deflated by the MRPs, then the interest rate on the risky
bonds is 7 percent:
Bond A yield = 8.0% = rRF + MRP + DRP = (5.5% + DRP) + 0.1%(10) = (5.5% + DRP) + 1.0%.
Deflating the yield on Bond A by MRP = 1.0%, gives 7.0% = 5.5% + DRP.
Thus, DRP = 7.0% - 5.5% = 1.5%
Bond B yield = 7.5% = rRF + MRP + DRP = (5.5% + DRP) + 0.1%(5) = (5.5% + DRP) + 0.5%.
Deflating the yield on Bond B by MRP = 0.5%, gives 7.0% = 5.5% + DRP.
Thus, DRP = 7.0% - 5.5% = 1.5%
5-9 We know the following:
r3-year bond = 6%
Year Annual Rate
2018 5%
2019 4
2020 3
5-10 We know the following:
r4-year bond = 2.5%
Year Annual Rate
2019 4.5%
5-11 Maturity Yield
1 year 5.0%
2 years 5.5
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-6
Year Rate in Year t
1 5.0%
In one year, the bond that matures in one year will mature (die), and the other bonds will have
one less year to maturity. Given the one-year interest rates computed above, the yields on the
three remaining bonds will be:
Original Maturity Maturity after 1 Year New Yield
1 year Matured --
Following the same logic for the next two years, we have:
Original Maturity Maturity after 2 Years New Yield
1 year Matured --
Original Maturity Maturity after 3 Year New Yield
1 year Matured --
5-12 Maturity Yield
5 years 3.1%
6 years 2.9
5-7
5-13 a. Real
Years to Risk-Free
Maturity Rate (r*) IP** MRP rT = r* + IP + MRP
1 2% 7.0% 0.2% 9.2%
2 2 6.0 0.4 8.4
**The computation of the inflation premium is as follows:
Expected Average
Year Inflation Expected Inflation
1 7% 7.0%
2 5 6.0 = (7 + 5)/2
Thus, the yield curve would be as follows:
b. The interest rate on the IBM bonds has the same components as the Treasury
securities, except that the IBM bonds have default risk, so a default risk premium must
be included. Therefore,
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
0
2
4
6
8
10
12
14
16
18
20
Years to maturity
Yield
(%)
T-Bonds
IBM
LILCO
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-8
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
For a strong company such as IBM, the default risk premium is virtually zero for
short-term bonds. However, as time to maturity increases, the probability of default,
although still small, is sufficient to warrant a default premium. Thus, the yield risk curve
for the IBM bonds will rise above the yield curve for the Treasury securities. In the graph,
the default risk premium was assumed to be 1.2 percentage points on the 20-year IBM
bonds. The return should equal 6.3% + 1.2% = 7.5%.
c. LILCO bonds would have significantly more default risk than either Treasury securities or
5-14 a. - c.
Arithmetic
1-Year Average Maturity Estimated
Expected Expected Risk Interest
Year Inflation Inflation r* Premium Rates
1 3% 3.0% 3% 0.0% 6.0%
2 5 4.0 3 0.2 7.2
3 4 4.0 3 0.4 7.4
e. Yield curve:
5-15 a. MRP for 10-year T-bond = 6.5% - 3.5% = 3.0%
5.0
5.5
8.5
9.0
0
2
4
6
8
10
12
14
16
18
20
Principles of Finance 6e Chapter 5
Besley/Brigham
5-9
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
MRP per year = 3.0%/10 = 0.3%
b. DRPNextel = 7.5% - (rRF + MRP) = 7.5% - [3.5 + 0.3%(6)] = 2.2%
c. r* = 3.5% – IP = 3.5% - 2.0% = 1.5%
5-16 a. Dollar return = $120
Yield = $120/$1,080 = 0.1111 = 11.11%
5-17 Term Rate
6 months 0.17%
1 year 0.26
The yield curve is as follows:
5-18 a. The average rate of inflation for the 5-year period is calculated as:
Yield (%)
Maturity
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-10
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
b. r5-yr = r* + IPAvg. = 2% + 4.8% = 6.8%.
c. Here is the general situation:
Arithmetic
One-Year Average Maturity Estimated
Expected Expected Risk Interest
Year Inflation Inflation r* Premium Rates
1 4% 4.00% 2% 0.1% 6.10%
2 5 4.50 2 0.2 6.70
3 7 5.33 2 0.3 7.63
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
0 2 4 6 8 10 12 14 16 18 20
Years to Maturity
Yield (%)
d. The “normal” yield curve is upward sloping because, in “normal” times, inflation is not
e. If inflation rates are expected to be constant, then the expectations theory holds that the yield
Principles of Finance 6e Chapter 5
Besley/Brigham
If maturity risk premiums were added to the yield curve in part e above, then the yield curve would be
more nearly normal—that is, the long-term end of the curve would be raised.
5-19 Integrative Problem
a. The dollar return is the amount in dollars that an investor would be paid if an investment is
liquidated at a particular period. For example, If you buy a stock for $40 today, you are paid
a $5 dividend during the year, and you sell the stock for $50 at the end of the year, the total
Return (Yield) = Dollar return
Original investment value
b. Total dollar return = ($240 - $250) + $25 = $15
c. The interest rate is the price paid for borrowed capital, while the return on equity capital
comes in the form of dividends plus capital gains. The return that investors require on
capital depends on (1) production opportunities, (2) time preferences for consumption, (3)
risk, and (4) inflation.
Pure expectations yield curve
Maturity risk
premium
Actual yield curve
Years to Maturity
Yield (%)
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-12
Risk, in a money and capital market context, refers to the chance that a loan will not be
repaid as promised—the higher the perceived default risk, the higher the required rate of
return.
d. Keep these equations in mind as we discuss interest rates. We will define the terms as we
go along:
r = r* + IP + DRP + LP + MRP.
rRF = r* + IP.
e. The inflation premium (IP) is a premium added to the real risk-free rate of interest to
compensate for expected inflation.
The default risk premium (DRP) is a premium based on the probability that the issuer will
default on the loan, and it is measured by the difference between the interest rate on a U.S.
Treasury bond and a corporate bond of equal maturity and marketability.
Principles of Finance 6e Chapter 5
Besley/Brigham
5-13
f. The term structure of interest rates is the relationship between interest rates, or yields, and
the maturities of securities. When this relationship is graphed, the resulting curve is called a
yield curve. The yield curve normally slopes upward, indicating that short-term interest
rates are lower than long-term interest rates.
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Years to Maturity
Yield
g. The market segmentation theory states that each borrower and lender has a preferred
maturity, and that the slope of the yield curve depends on the supply of and demand for
funds in the long-term market relative to the situation in the short-term market.
U.S. Treasuries
Microsoft
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-14
h. Step 1: find the average expected inflation rate over years 1 to 20:
Year 1: IP = 1.0%
Step 2: Find the maturity premium in each year:
Year 1: MRP = 0.0%
The yield curve is based directly on, hence is consistent with, at least two of the theories:
(1) expectation and (2) liquidity preferences. It contains a maturity risk premium, which is
Years to Maturity
Interest
(%)
0
2
4
6
8
10
1 6 11 16
5-20 Computer-Related Problem
a.
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
1
2.50%
8.00%
0.10%
10.60%
2
2.50%
7.00%
0.20%
9.70%
3
2.50%
6.00%
0.30%
8.80%
4
2.50%
5.25%
0.40%
8.15%
5
2.50%
5.20%
0.50%
8.20%
10
2.50%
4.10%
1.00%
7.60%
20
2.50%
3.55%
2.00%
8.05%
30
2.50%
3.37%
2.00%
7.87%
b. The yield curve is downward sloping, which suggests that the demand for short-term funds is
c. After one year has passed:
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
0
1
2.50%
6.00%
0.10%
8.60%
2
2.50%
5.00%
0.20%
7.70%
3
2.50%
4.33%
0.30%
7.13%
4
2.50%
4.50%
0.40%
7.40%
Chapter 5 Principles of Finance 6e
Besley/Brigham
5-16
9
2.50%
3.67%
0.90%
7.07%
19
2.50%
3.32%
1.90%
7.72%
29
2.50%
3.21%
2.00%
7.71%
After two years have passed:
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
-1
0
1
2.50%
4.00%
0.10%
6.60%
2
2.50%
3.50%
0.20%
6.20%
3
2.50%
4.00%
0.30%
6.80%
8
2.50%
3.38%
0.80%
6.68%
18
2.50%
3.17%
1.80%
7.47%
28
2.50%
3.11%
2.00%
7.61%
After three years have passed:
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
-2
-1
0
1
2.50%
3.00%
0.10%
5.60%
2
2.50%
4.00%
0.20%
6.70%
7
2.50%
3.29%
0.70%
6.49%
17
2.50%
3.12%
1.70%
7.32%
27
2.50%
3.07%
2.00%
7.57%
After four years have passed:
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
-3
-2
-1
0
1
2.50%
5.00%
0.10%
7.60%
6
2.50%
3.33%
0.60%
6.43%
16
2.50%
3.13%
1.60%
7.23%
Principles of Finance 6e Chapter 5
Besley/Brigham
5-17
26
2.50%
3.08%
2.00%
7.58%
After five years have passed:
Years to
Real risk-free
Inflation
Maturity Risk
Treasury
Maturity
rate (r*)
Premium (IP)
Premium (MRP)
Yield
-4
-3
-2
-1
0
5
2.50%
3.00%
0.50%
6.00%
15
2.50%
3.00%
1.50%
7.00%
25
2.50%
3.00%
2.00%
7.50%
d. Yields on AAA-rated bonds and B-rated bonds:
Years to
Maturity
Real Risk-
Free Rate
Inflation
Premium (IP)
Maturity Risk
Premium
(MRP)
Treasury
Yield
AAA
Rating
DRP
AAA-
Rated
Bond
Yield
B-
Rating
DRP
B-Rated
Bond
Yield
1
2.50%
8.00%
0.10%
10.60%
1.50%
12.10%
4.00%
14.60%
2
2.50%
7.00%
0.20%
9.70%
1.53%
11.23%
4.08%
13.78%
3
2.50%
6.00%
0.30%
8.80%
1.56%
10.36%
4.16%
12.96%
4
2.50%
5.25%
0.40%
8.15%
1.59%
9.74%
4.24%
12.39%
5
2.50%
5.20%
0.50%
8.20%
1.62%
9.82%
4.33%
12.53%
10
2.50%
4.10%
1.00%
7.60%
1.79%
9.39%
4.78%
12.38%
20
2.50%
3.55%
2.00%
8.05%
2.19%
10.24%
5.83%
13.88%
30
2.50%
3.37%
2.00%
7.87%
2.66%
10.53%
7.10%
14.97%
ETHICAL DILEMMA
Unadvertised Special: Is It a “Shark”?
Ethical dilemma:
Skip Stephens is trying to decide whether it would be wise to consolidate his debt by borrowing funds
from Syndicated Lending, a firm that he doesn’t know much about. Syndicated is an Internet lender that
doesn’t post much information about the costs of the loans it offers. Some of the additional information
Skip has gathered from various sources suggests the Syndicated might use such unethical practices as
“bait and switch” to attract customers.
5-18
Discussion questions:
• Is there an ethical problem? If so, what is it?
In this case, the ethical situation would be the manner in which Syndicated conducts business.
• What are the implications if Skip borrows from Syndicated?
This is a tough question. Skip might end up paying much more for his debt if he borrows from
• Should Skip borrow from Syndicated?
Before he makes a decision, Skip should dig deeper to determine (estimate) the cost of borrowing
References:
The following articles might be assigned for background material:
James R. Hagerty, “Mortgage Brokers: Friends or Foes?” The Wall Street Journal Online, May 24, 2007.
