Question

a) Consider the following, a AAA rated Treasury bond with a face value of $1000, maturing in 20 years and paying 14.00 per cent per annum coupons semi-annually. If current market yields for this type of security are 12.00 per cent per annum, what price would you pay for the instrument?

b) What will happen to the price of the bond if yields adjust
from

12.00 to 10.00 percent per annum?

c) Consider now the bonds noted above in (a) and (b). What
generalisation emerges from the examples concerning the response of
prices of bond market instruments when there is a change in
yields?

d) What implications do the coupon size and term to maturity have
for the duration or interest rate sensitivity of a Bond?

Answer #1

Answer a) Face value $1000, N= 20, Coupon rate= 14%, Yield= 12%

for Semi annual bond we take n= 40, Coupon rate = 14/2=7%, Yield= 12/2= 6%

Price= 70(present value annuity factor @ 6% for 40terms) + 1000(present value factor @ 6% for 40th term)

= 70(15.0462) + 1000(0.0972) = $1150.434

b) Price of bond if yield is 10%

70(present value annuity factor @ 5% for 40terms) + 1000(present value factor @ 5% for 40th term)

= 70(17.15) + 1000(0.1420) = $1342.5

c) There is an inverse relation between yield and bond price, hence if the yield decreases, we get a higher bond value

d) The larger the coupon, the shorter the duration number becomes

Johnson and Johnson (JNJ), rated AAA by S&P, issues an
8-year $1000 par value bond that
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priced at $1096.59.
At the same time Valero Corporation (rated BBB by S&P)
issues a similar bond with same
maturity, par value, and coupon rate and frequency. The BBB-AAA
spread is 90 basis points.
Find the bond price of Valero Corporation.
[Hint: First find the semi-annual yield of the JNJ bond. Then
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Consider a 2-year bond with a principal of $100 that provides
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(a) What is the duration of this bond?
(b) Suppose the yield on this bond decreases by 0.1%.
Calculate the new bond price exactly.
Estimate the new bond price approximately using duration.

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If the market yield rises by 1%, how much change will there be in
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Ray Co.’s bonds, maturing in 3 years, pay 8 percent interest on
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Consider a 2-year Treasury bond with a face value of $100 and
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0.5 3.0%
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1.5 3.6%
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1.
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Face value of $1000,
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12 years to maturity.
The bond is callable after 7 years with the call price of
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If the market interest rate is 4.27% in 7 years when the bond
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