Bond Valuation Problems
3. Interpreting Bond Yields Suppose you buy a 9 percent
coupon, 15-year bond today when it’s first issued. If interest
rates suddenly rise to 15 percent, what happens to the value
of your bond? Why?
Answer: $649.16
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Bond Valuation Problems
5. Bond Yields N&N Co. has 11 percent coupon bonds on the
market with 8 years left to maturity. The bonds make annual
payments. If the bond currently sells for $1,110.70 what is its YTM?
Answer: 9%
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Bond Valuation Problems
6. Coupon rates Merton Enterprises has bonds on the market
making annual payments, with 14 years to maturity, and selling for
$950. At this price, the bonds yield 7.5 percent. What must the
coupon rate be on Merton’s bonds?
Answer: 6.911%
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Bond Valuation Problems
22. Interest Rate Risk Bond J is a 4 percent coupon bond. Bond
K is a 10 percent coupon bond. Both bonds have 10 years to
maturity, make semi-annual payments and have a YTM of 9
percent. If interest rates suddenly rise by 2 percent, what is the
percentage price change of these bonds? What if rates suddenly
fall by 2 percent instead? What does this problem tell you about
the interest rate risk of lower-coupon bonds?
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Bond Valuation Problems
23. Bond Yields BrainDrain Software has 12 percent coupon
bonds on the market with 9 years to maturity. The bonds make
semiannual payments and currently sell for 125.32 percent of par.
What is the current yield on BrainDrain bonds? The YTM? The
effective annual yield?
Answer: CY=9.58%
YTM=8%
EAR=8.16%
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Example. Decomposition of total return
when YTM at the end of a period is same as YTM at the beginning
of the period then
total realized return=YTM at the beginning of the period =
capital gains yield + interest income
for instance:
coupon rate=9% annual coupon N=10 years P=$882.22
P10=882.22= 90 PVIFAk,10 + 1000PVIFk,10
k=11%=YTM at the beginning of the period
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Example. Decomposition of total return
after 1 year if YTM is still 11%
P9= 90 PVIFA11%,9 + 1000PVIF11%,9=$889.26
total realized return=0.798%+10.202% =11% =YTM at the
beginning of the period
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Example. Decomposition of total return
if YTM rises to 13% at the end of the period
P9=$794.73
total realized return=-9.917%+10.202% =0.285%  YTM at the
beginning of the period
Note: To be able to calculate realized return for more than one
period we need to make assumptions about reinvestment rates.
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Bond Valuation Problems
40. Holding Period Yield The YTM on a bond is the interest rate you
earn on your investment if interest rates don’t change. If you actually sell the bond
before it matures, your realized return is known as the holding period yield (HPY).
Suppose you buy a 10 percent coupon bond making annual payments today for
$1,064.18. The bond has 10 years to maturity. What rate of return do you expect
on your investment?
Two years from now, the YTM on your bond has declined by 3 percent, and you
decide to sell. What price will your bond sell for? What is the HPY on your
investment assuming that you reinvest coupons at HPY? Compare this yield to the
YTM when you first bought the bond. Why are they different?
Answer:
1,064.18=100 PVIFA10,k + 1,000 PVIF10,k
YTM=9%
b.
New YTM=9%-3%=6%
$1,248.39=100 PVIFA8,6% + 1,000 PVIF8,6%
1,064.18=100 PVIFA2,HPY + 1,248.39 PVIF2,HPY
HPY=17.361% note this assumes you could reinvest $100 coupon at 17.361%
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