Chapter 14  Bond Prices and Yields
141
CHAPTER 14: BOND PRICES AND YIELDS
PROBLEM SETS
1.
The bond callable at 105 should sell at a lower price because the call provision is more
valuable to the firm. Therefore, its yield to maturity should be higher.
2.
Zero coupon bonds provide no coupons to be reinvested. Therefore, the investor's proceeds
from the bond are independent of the rate at which coupons could be reinvested (if they
were paid). There is no reinvestment rate uncertainty with zeros.
3.
A bond’s coupon interest payments and principal repayment are not affected by changes
in market rates. Consequently, if market rates increase, bond investors in the secondary
markets are not willing to pay as much for a claim on a given bond’s fixed interest and
principal payments as they would if market rates were lower. This relationship is
apparent from the inverse relationship between interest rates and present value. An
increase in the discount rate (i.e., the market rate) decreases the present value of the
future cash flows.
4.
a.
Effective annual rate for 3month Tbill:
%
0
.
10
100
.
0
1
02412
.
1
1
645
,
97
000
,
100
4
4
=
=
−
=
−
⎟
⎠
⎞
⎜
⎝
⎛
b.
Effective annual interest rate for coupon bond paying 5% semiannually:
(1.05)
2
– 1 = 0.1025 or 10.25%
Therefore the coupon bond has the higher effective annual interest rate.
5.
The effective annual yield on the semiannual coupon bonds is 8.16%. If the annual
coupon bonds are to sell at par they must offer the same yield, which requires an annual
coupon rate of 8.16%.
6.
The bond price will be lower. As time passes, the bond price, which is now above par
value, will approach par.
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Chapter 14  Bond Prices and Yields
142
7.
Yield to maturity
: Using a financial calculator, enter the following:
n = 3; PV =
−
953.10; FV = 1000; PMT = 80; COMP i
This results in: YTM = 9.88%
Realized compound yield
: First, find the future value (FV) of reinvested coupons and
principal:
FV = ($80
×
1.10
×
1.12) + ($80
×
1.12) + $1,080 = $1,268.16
Then find the rate (y
realized
) that makes the FV of the purchase price equal to $1,268.16:
$953.10
×
(1 + y
realized
)
3
= $1,268.16
⇒
y
realized
= 9.99% or approximately 10%
8.
a.
Zero coupon
8% coupon
10% coupon
Current prices
$463.19
$1,000.00
$1,134.20
b.
Price 1 year from now
$500.25
$1,000.00
$1,124.94
Price increase
$37.06
$0.00
−
$9.26
Coupon income
$0.00
$80.00
$100.00
Pretax income
$37.06
$80.00
$90.74
Pretax rate of return
8.00%
8.00%
8.00%
Taxes*
$11.12
$24.00
$28.15
Aftertax income
$25.94
$56.00
$62.59
Aftertax rate of return
5.60%
5.60%
5.52%
c.
Price 1 year from now
$543.93
$1,065.15
$1,195.46
Price increase
$80.74
$65.15
$61.26
Coupon income
$0.00
$80.00
$100.00
Pretax income
$80.74
$145.15
$161.26
Pretax rate of return
17.43%
14.52%
14.22%
Taxes**
$19.86
$37.03
$42.25
Aftertax income
$60.88
$108.12
$119.01
Aftertax rate of return
13.14%
10.81%
10.49%
* In computing taxes, we assume that the 10% coupon bond was issued at par and
that the decrease in price when the bond is sold at year end is treated as a capital
loss and therefore is not treated as an offset to ordinary income.
** In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary
income (see part (b)) and the remainder of the price increase is taxed as a capital
gain.
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 Spring '10
 AttilaOdabaşı
 Interest Rates, Colina bond

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