CHAPTER 14: BOND PRICES AND YIELDS
CHAPTER 14: BOND PRICES AND YIELDS
PROBLEM SETS
1. a. Catastrophe bond—A bond that allows the issuer to transfer “catastrophe risk”
from the firm to the capital markets. Investors in these bonds receive a
compensation for taking on the risk in the form of higher coupon rates. In the
c. Zero-coupon bond—A bond that makes no coupon payments. Investors receive
h. Equipment obligation bond—A collateralized bond for which the collateral is
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CHAPTER 14: BOND PRICES AND YIELDS
2. The bond callable at 105 should sell at a lower price because the call provision is
3. Zero coupon bonds provide no coupons to be reinvested. Therefore, the investor’s
4. 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
5. Annual coupon rate: 4.80% $48 Coupon payments
Current yield:
$48 4.95%
$970
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6. a. Effective annual rate for 3-month T-bill:
%0.10100.0102412.11
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.
7. The effective annual yield on the semiannual coupon bonds is 8.16%. If the
9. Yield to maturity: Using a financial calculator, enter the following:
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CHAPTER 14: BOND PRICES AND YIELDS
Realized compound yield: First, find the future value (FV) of reinvested coupons
and principal:
10.
a. Zero coupon 8% coupon 10% coupon
c. Price increase $ 37.06 $ 0.00 − $ 9.26
d. Taxes* =37.06.3 =80.3 =(-9.26) .2+100.3
$ 11.12 $ 24.00 $ 28.15
* 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
11. a. On a financial calculator, enter the following:
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CHAPTER 14: BOND PRICES AND YIELDS
You will find that the yield to maturity on a semiannual basis is 4.26%. This implies
b. Since the bond is selling at par, the yield to maturity on a semiannual basis is
c. Keeping other inputs unchanged but setting PV = –1050, we find a bond
12. Since the bond payments are now made annually instead of semiannually, the
bond equivalent yield to maturity is the same as the effective annual yield to
maturity. [On a financial calculator, n = 20; FV = 1000; PV = –price; PMT = 80]
The resulting yields for the three bonds are:
Bond Price Bond Equivalent Yield =
Effective Annual Yield
The yields computed in this case are lower than the yields calculated with
semiannual payments. All else equal, bonds with annual payments are less
13.
Price
Maturity
(years)
Bond Equivalent
YTM
$400.00 20.00 4.688%
500.00 20.00 3.526
14. a. The bond pays $50 every 6 months. The current price is:
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CHAPTER 14: BOND PRICES AND YIELDS
If the market interest rate remains 4% per half year, price six months from now is:
b. Rate of return
$50 ($1,044.52 $1,052.42) $50 $7.90 4.0%
$1,052.42 $1,052.42
+ – –
= = =
15. The reported bond price is: $1,001.250
However, 15 days have passed since the last semiannual coupon was paid, so:
16. If the yield to maturity is greater than the current yield, then the bond offers the
prospect of price appreciation as it approaches its maturity date. Therefore, the
bond must be selling below par value.
17. The coupon rate is less than 9%. If coupon divided by price equals 9%, and
18. a. On a financial calculator, enter the following:
b. On a financial calculator, enter the following:
c. Longer maturity bonds appear to be more sensitive to changes in interest rates
19. The price schedule is as follows:
Remaining Constant Yield Value
Imputed Interest
(increase in constant
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CHAPTER 14: BOND PRICES AND YIELDS
Year Maturity (T). $1,000/(1.08)Tyield value)
0 (now)
20 years
$214.55
20. The bond is issued at a price of $800. Therefore, its yield to maturity is: 6.8245%
21. a. The bond sells for $1,124.72 based on the 3.5% yield to maturity.
b. If the call price were $1,050, we would set FV = 1,050 and redo part (a)
c. Yield to call is 3.031% semiannually, 6.062% annually.
22. The stated yield to maturity, based on promised payments, equals 16.075%.
Based on expected reduced coupon payments of $70 annually, the expected
23. The bond is selling at par value. Its yield to maturity equals the coupon rate, 10%. If
Therefore, realized compound yield to maturity is a function of r, as shown in the
following table:
rTotal proceeds Realized YTM = – 1
8% $1,208
– 1 = 0.0991 = 9.91%
CHAPTER 14: BOND PRICES AND YIELDS
24. April 15 is midway through the semiannual coupon period. Therefore, the invoice
25. Factors that might make the ABC debt more attractive to investors, therefore
justifying a lower coupon rate and yield to maturity, are:
i. The ABC debt is a larger issue and therefore may sell with greater liquidity.
ii. An option to extend the term from 10 years to 20 years is favorable if interest
iii. In the event of trouble, the ABC debt is a more senior claim. It has more
iv. The call feature on the XYZ bonds makes the ABC bonds relatively more
v. The XYZ bond has a sinking fund requiring XYZ to retire part of the issue each
26. A. If an investor believes the firm’s credit prospects are poor in the near term and
wishes to capitalize on this, the investor should buy a credit default swap.
Although a short sale of a bond could accomplish the same objective, liquidity is
27. a. When credit risk increases, credit default swaps increase in value because the
28. a. An increase in the firm’s times interest-earned ratio decreases the default risk
b. An increase in the issuing firm’s debt-equity ratio increases the default risk of
c. An increase in the issuing firm’s quick ratio increases short-run liquidity,
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CHAPTER 14: BOND PRICES AND YIELDS
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