Chapter 5 Solutions

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CHAPTER 5 BOND VALUATION AND
ANALYSIS
1.
a) Par value - also referred to as face value or maturity value is the amount the
bondholder receives in addition to any interest payments when the bond
matures.
b) Yield to maturity - is the rate of return on a bond. Calculated by finding the
interest rate which makes the price of the bond equal to the present value of
the future cash flows. Sometimes referred to as the internal rate of return on a
bond.
c) Zero-coupon bond - a bond which makes no explicit interest payments, rather
interest is realized as the difference between the price paid for the bond and
the bond's par value. Sometimes referred to as a pure discount bond.
d) Yield curve - is a graph of the time to maturity and the yield to maturity for
bonds which have the same risk.
e) Coupon interest rate - is the percentage of a bond's par value which is paid as
interest.
2.
a) Based upon the expectations theory, short term interest rates are expected to
rise in the future.
According to the liquidity theory, the upward slope may be due to the
premium investor's desire to hold longer term bonds.
According to the market segmentation theory, there exist separate markets for
different maturity bonds and so the yield curve tells us nothing about the
relationship between long and short term interest rates.
b) Whether you buy long or short term bonds depends on whether you agree with
the yield curve or not. There are three possible cases:
Case I:
Agree with the shape of the yield curve.
- Then by the expectations hypothesis, you will receive the same
average return whether you buy long or short term bonds.
Case II:
-
Believe rates will rise faster than yield curve predicts.
In this case, you can earn a higher average return by purchasing
short term securities and rolling them over when they mature.
Case III:
-
Believe rates will rise at a slower rate than the yield curve predicts.
In this case, you will average a higher return by purchasing long
term bonds and locking into a higher coupon rate.
3. To evaluate this bond, we need to calculate the theoretical price of the bond, P,
and compare it to the current market price.
PB 

IP
IP
IP
MV



2
3
(1  i ) (1  i ) (1  i ) (1  i )3
120
120
120
1, 000



2
3
(1  .10) (1  .10) (1  .10) (1  .10)3
 $1, 049.74
In this case, the bond is overpriced but only by $.26. If the $.26 is not due to a
rounding error, the bond should not be purchased.
4. Yield to maturity is the interest rate r, which makes price of bond equal to the
present value of the future cash f1ows.
953 
90
90


(1  r ) (1  r )2
solve by trial and error
Try 10%

90
1, 000

5
(1  r ) (1  r )5

90

(1  .10)

90
1, 000

5
(1  .10) (1  .10)5
 962.19
Try 11%
90


(1.11)

90
1, 000

 925.64
5
(1.11) (1.11)5
Yield to maturity is between 10 and 11 percent.
To get the exact value, we need to interpolate between 10% and 11% as follows:
x
962.19  953

1 962.19  925.64
x  .2514
YTM  10.25%
5.
a) Bond A
PA 
10, 000
 $6, 499.31
(1.09)5
Bond B
PB 
900

(1.09)

900
10, 000

 $10, 000
5
(1.09) (1.09)5
b) Need duration concept which is covered in Chapter 20.
DURA  5 years
 90   90   90   90   90 
1
  2
  3
  4
  5

1.10   1.102   1.103   1.104   1.105 

DURB 
1, 000

81.82  148.76  202.85  245.88  3,384.02
1, 000
 4.06 years
P
100   DUR  i
P
For Bond A
%P  5  3%  15%
For Bond B
%P  4.06  3%  12.18%
6. Call risk is the risk the bondholder faces that the bond will be called (redeemed
early) by the issuer. If the bond is callable and if it is likely that the bond will be
called, the appropriate yield is the yield to call. The yield to call will be lower than
the promised yield.
7. After-tax return on corporate bond is
9% (1 – .28) – 6.48%
So, corporate bond is preferred to tax free bond.
8. Revenue bonds are bonds issued by state and local governments to finance
projects such as bridges and toll roads. Revenues from these projects are used to
pay interest and principal.
General obligation bonds are municipal bonds which are backed by the full taxing
power of the issuing government.
Because general obligation bonds are backed by the full taxing power of the
issuing government, they are less risky than revenue bonds and should have a
lower yield to maturity than revenue bonds.
9. Bond prices and interest rates have an inverse relationship. The reason for this is
that interest payments on bonds are fixed for the life of the bond. As market
interest rates rise, previously issued bonds -will be less desirable because currently
issued bonds of the same risk will pay higher interest, and, therefore, the price of
previously issued bonds will fall as market interest rates rise.
10. Because the current price of the bond is greater than the par value plus one
year's interest, the bond is likely to be called and the appropriate yield is the
yield to call. Need to know call price, since it is not given assume Pc = $11,500
PC  PO
11,500  11, 000
900 
nC
5

PC  PO
11,500  11, 000
2
2
C
AYC 
 .0888 or 8.9%
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