Question

s Click here to read the eflook: Bond Valuation Click here to read the eBook: Bond Yelds INTEREST RATE SENSITIVITY Each bond had a par value of $1,000 and an 9% yield to day, Immediately after the investor purchased them, interest rates fell, and each then had a new nvestor pnhased the "olowing 5 bond, YTM of 5%, the numbers What is the percentage change in price for eech bond ater the decline in interest rates?7 Fillis the Hulowing table Round your ansmers to the nearest cent or to two decimal places. Enter slil amourts as postive Pree 5% Percentage Oange 10-year, 10% annual coupon 10-year zere S year nere 30-year zene $100 perpetuity

Answer 1

Answer:

Given

Face Value F=$1000

Bond price P=F*c*(1-(1+r)^-N)/r + F/(1+r)^N

Where

c= coupon rate

r= yield to maturity

N=maturity years

For 10 years 10% coupon bond

when r=9%

Price P1=1000*10%(1-(1+9%)^-10)/9% + 1000/(1+9%)^10

P1=$1064.18

when r=5%

Price P2=1000*10%(1-(1+5%)^-10)/5% + 1000/(11386+5%)^10

P2=$1386.09

Change in Price =(P2-P1)/P1=(1386.09-1064.18)/1064.18=30.25%

For 10 years 0% coupon bond

when r=9%

Price P1= 1000/(1+9%)^10

P1=$422.41

when r=5%

Price P2= 1000/(11386+5%)^10

P2=$613.91

Change in Price =(P2-P1)/P1=(613.91-422.41)/422.41=45.34%

For 5 years 0% coupon bond

when r=9%

Price P1= 1000/(1+9%)^5

P1=$649.93

when r=5%

Price P2= 1000/(11386+5%)^5

P2=$783.53

Change in Price =(P2-P1)/P1=(783.53-649.93)/649.93=20.56%

For 30 years 0% coupon bond

when r=9%

Price P1= 1000/(1+9%)^30

P1=$75.37

when r=5%

Price P2= 1000/(11386+5%)^30

P2=$231.38

Change in Price =(P2-P1)/P1=(231.38-75.37)/75.37=206.98%

For perpetual bond

Price = C/r

C=coupon payment =100

for r=9%

Price P1=100/9% =$1111.11

for r=5%

Price P1=100/5% =$2000

So change in price of bond = (2000-1111.11)/1111.11=80%