Answers and Solutions: 5 – 11
5-16
Price at 8%
Price at 7%
Pctge. change
10-year, 10% annual coupon
$1,134.20
$1,210.71
6.75%
10-year zero
463.19
508.35
9.75
5-year zero
680.58
712.99
4.76
30-year zero
99.38
131.37
32.19
$100 perpetuity
1,250.00
1,428.57
14.29
5-17
t
Price of Bond C
Price of Bond Z
0
$1,012.79
$ 693.04
1
1,010.02
759.57
2
1,006.98
832.49
3
1,003.65
912.41
4
1,000.00
1,000.00
5-18 r = r* + IP + MRP + DRP + LP.
r* = 0.02.
r = 0.02 + 0.035 + 0.003 = 0.058 = 5.8%.
5-19 First, note that we will use the equation rt = 3% + IPt + MRPt. We have the data needed
to find the IPs:
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5-20 Basic relevant equations:
rt = r* + IPt + DRPt + MRPt + LPt.
r3 = r* + IP3 = 2% + IP3 = 7%, so
IP3 = 7% – 2% = 5%.
2 2 I (3% + I)/2 = IP2
3 2 I (3% + I + I)/3 = IP3 r3 = 7%, so IP3 = 7% – 2% = 5%.
5-21 a. The bonds now have an 8-year, or a 16-semiannual period, maturity, and their value
is calculated as follows:
c. The price of the bond will decline toward $1,000, hitting $1,000 (plus accrued
interest) at the maturity date 8 years (16 six-month periods) hence.
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5-22 a. Find the YTM as follows:
N = 10, PV = –1200, PMT = 110, FV = 1000
I/YR = YTM = 8.02%.
present level, investors would expect to earn the yield to call. (Note that the YTC is less
than the YTM.)
d. Similarly from above, YTC can be found, if called in each subsequent year.
N = 7, PV = –1200, PMT = 110, FV = 1070
I/YR = YTC = 7.95%.
If called in Year 8:
According to these calculations, the latest investors might expect a call of the bonds is in
Year 7. This is the last year that the expected YTC will be less than the expected YTM.
At this time, the firm still finds an advantage to calling the bonds, rather than seeing them
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%
**The computation of the inflation premium is as follows:
Expected Average
Year Inflation Expected Inflation
1 7% 7.00%
For example, the calculation for 3 years is as follows:
5.00%. =
3
3% + 5% + 7%
Thus, the yield curve would be as follows:
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 ExxonMobil bonds will rise above the yield curve for the
Treasury securities. In the graph, the default risk premium was assumed to be 1.0
points on the 20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.
Answers and Solutions: 5 – 17
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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.
Mini Case: 5 – 18
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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?
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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.
The call provision generally states that the company must pay the bondholders an
amount greater than the par value if they are called. The additional sum, which is
called a call premium, is typically set equal to one year’s interest if the bonds are
called during the first year, and the premium declines at a constant rate of INT/n each
year thereafter.
A sinking fund provision is a provision in a bond contract that requires the issuer
to retire a portion of the bond issue each year. A sinking fund provision facilitates the
orderly retirement of the bond issue.
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
cyclically high. Therefore, bonds with a call provision are riskier than those without
a call provision. Accordingly, the interest rate on a new issue of callable bonds will
exceed that on a new issue of noncallable bonds.
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
times work to the detriment of bondholders. On balance, however, bonds that provide
for a sinking fund are regarded as being safer than those without such a provision, so
at the time they are issued sinking fund bonds have lower coupon rates than otherwise
similar bonds without sinking funds.
Mini Case: 5 – 20
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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.