A bond has the following terms: Principle amount $1000 Semi--annual interest $50

ID: 2659551 • Letter: A

Question

A bond has the following terms:

Principle amount $1000

Semi--annual interest $50

Maturity 20 years

a. what is the bonds price if comparable debt yields12%?

b. what would be the price if comparable debt yields 12% and the bond matures after 5 years?

c. what are the current yields and yields to maturity in a. and b. ?

d. what would be the bonds price in a. and b. if interest rates declined to 8%?

e. what are the current yields and yield to maturity in d.? what two generalizations may be drawn from the above price changes?

a) bonds price if comparable debt yields12%,

here n=2*20 =40(as semi annual) and yield for semi annual =12%

= 50/(1.06)+50/(1.06)^2+--------+50/(1.06)^40 +1000/(1.06)^40

=$849.54

b)price if comparable debt yields 12% and the bond matures after 5 years =

=50/(1.06)+50/(1.06)^2++++++50(1.06)^10 +1000/(1.06)^10

=$926.4

c) As current yield = coupon per year/bond price yield to maturity =yield per year

for part a) current yield = 50*2/(849.54) =11.77% and yield to maturity = 12%

similarly for part b)current yield = 2*50/926.4 and yield to maturity = 12%

d)
if interest rates declined to 8%

part a) price = 50/(1.04)+50/(1.04)^2+--------+50/(1.04)^40 +1000/(1.04)^40

=$1,197.93

for part b) price =50/(1.04)+50/(1.04)^2++++++50/(1.04)^10 +1000/(1.04)^10

=$1081.11

e) current yield in d) of part a = 50*2/1197.93 = 8.35%

of part b) =50*2/1081.11 =9.25%

As we see in part d) when Yield declined from 12% to 8% , price has increased in both cases

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