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5-17
t Price of Bond C Price of Bond Z
0 $1,012.79 $ 693.04
1 1,010.02 759.57
5-18 r = r* + IP + MRP + DRP + LP.
r* = 0.02.
5-19 First, note that we will use the equation rt = 3% + IPt + MRPt. We have the data needed
to find the IPs:
IP5 =
5
4% + 4% + 4% + 5% + 8%
=
5
25%
= 5%.
Now we can solve for the MRPs, and find the difference:
Answers and Solutions: 5 - 1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
5-20 Basic relevant equations:
rt = r* + IPt + DRPt + MRPt + LPt.
But here IP is the only premium, so rt = r* + IPt.
IPt = Avg. inflation = (I1 + I2 + ...)/N.
r3 = r* + IP3 = 2% + IP3 = 7%, so
We also know that It = Constant after t = 1.
We can set up this table:
r* I Avg. I = IPtr = r* + IPt
5-21 a. The bonds now have an 8-year, or a 16-semiannual period, maturity, and their value is
calculated as follows:
Calculator solution: Input N = 16, I/YR = 3, PMT = 50, FV = 1000,
b. Calculator solution: Change inputs from Part a to I/YR = 6, PV = ?
Answers and Solutions: 5 - 2
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
5-22 a. Find the YTM as follows:
b.Find the YTC, if called in Year 5 as follows:
c. The bonds are selling at a premium which indicates that interest rates have fallen since
d. Similarly from above, YTC can be found, if called in each subsequent year.
If called in Year 6:
If called in Year 7:
If called in Year 8:
If called in Year 9:
According to these calculations, the latest investors might expect a call of the bonds is in
Answers and Solutions: 5 - 3
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website, in whole or in part.
5-23 a. Real
Years to Risk-Free
Maturity Rate (r*) IP** MRP rT = r* + IP + MRP
1 2% 7.00% 0.2% 9.20%
2 2 6.00 0.4 8.40
**The computation of the inflation premium is as follows:
Expected Average
Year Inflation Expected Inflation
1 7% 7.00%
2 5 6.00
For example, the calculation for 3 years is as follows:
5.00%. =
3
3% + 5% + 7%
Answers and Solutions: 5 - 4
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
For a strong company such as ExxonMobil, the default risk premium is virtually zero
for short-term bonds. However, as time to maturity increases, the probability of
c. LILCO bonds would have significantly more default risk than either Treasury
securities or Exxon bonds, and the risk of default would increase over time due to
Answers and Solutions: 5 - 5
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
SOLUTION TO SPREADSHEET PROBLEM
5-24 The detailed solution for the problem is in the file Ch05 P24 Build a Model
Solution.xlsx and is available on the instructor’s side of the textbook’s web site.
Answers and Solutions: 5 - 6
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Answers and Solutions: 5 - 7
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
MINI CASE
Sam Strother and Shawna Tibbs are vice-presidents of Mutual of Seattle Insurance
Company and co-directors of the company's pension fund management division. A major
new client, the Northwestern Municipal Alliance, has requested that Mutual of Seattle
present an investment seminar to the mayors of the represented cities, and Strother and
Tibbs, who will make the actual presentation, have asked you to help them by answering
the following questions. Because the Boeing Company operates in one of the league's cities,
you are to work Boeing into the presentation.
a. What are the key features of a bond?
Answer:
1. Par or face value. We generally assume a $1,000 par value, but par can be
2. Coupon rate. The dollar coupon is the "rent" on the money borrowed, which is
generally the par value of the bond. The coupon rate is the annual interest
5. Default risk is inherent in all bonds except treasury bonds--will the issuer have the
Answers and Solutions: 5 - 8
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
b. What are call provisions and sinking fund provisions? Do these provisions make
bonds more or less risky?
Answer: A call provision is a provision in a bond contract that gives the issuing corporation the
right to redeem the bonds under specified terms prior to the normal maturity date.
A sinking fund provision is a provision in a bond contract that requires the issuer
The call privilege is valuable to the firm but potentially detrimental to the
investor, especially if the bonds were issued in a period when interest rates were
Although sinking funds are designed to protect bondholders by ensuring that an
issue is retired in an orderly fashion, it must be recognized that sinking funds will at
Answers and Solutions: 5 - 9
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
c. How is the value of any asset whose value is based on expected future cash flows
determined?
Answer: 0 1 2 3 n
| | | | |
CF1 CF2 CF3 CFN
PV CF1
PV CF2
The value of an asset is merely the present value of its expected future cash flows:
.
)
r + (1
CF
=
)
r + (1
CF
+ . . . +
)
r + (1
CF
+
)
r + (1
CF
+
)
r + (1
CF
= PV = VALUE t
t
N
1 =t
N
N
3
3
2
2
1
1
If the cash flows have widely varying risk, or if the yield curve is not horizontal,
which signifies that interest rates are expected to change over the life of the cash
flows, it would be logical for each period's cash flow to have a different discount rate.
However, it is very difficult to make such adjustments; hence it is common practice to
use a single discount rate for all cash flows.
The discount rate is the opportunity cost of capital; that is, it is the rate of return that
could be obtained on alternative investments of similar risk. For a bond, the discount
rate is rd.
Answers and Solutions: 5 - 10
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
d. How is the value of a bond determined? What is the value of a 10-year, $1,000
par value bond with a 10 percent annual coupon if its required rate of return is
10 percent?
Answer: A bond has a specific cash flow pattern consisting of a stream of constant interest
payments plus the return of par at maturity. The annual coupon payment is the cash
flow: pmt = (coupon rate) (par value) = 0.1($1,000) = $100.
For a 10-year, 10 percent annual coupon bond, the bond's value is found as
follows:
82.64
.
.
.
Expressed as an equation, we have:
$1,000. = $385.54 + $38.55 + . . . + $90.91 =
)r + (1
$1,000
+
)r + (1
$100
+ . . . +
)r + (1
$100
=
V
d
10
d
10
d
1
B
The bond consists of a 10-year, 10% annuity of $100 per year plus a $1,000 lump
sum payment at t = 10:
The mathematics of bond valuation is programmed into financial calculators which
Answers and Solutions: 5 - 11
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website, in whole or in part.
