Question

Suppose you purchase a 30-year, SEK 10,000 par value, zero-coupon bond with a yield to maturity (YTM) of 4.4%. You hold the bond for 9 years before selling it.

(a) What is the price of the bond when you buy it?

Answer: The price of the bond is SEK . (round to full SEK)

(b) If the bond’s yield to maturity drops by 1% when you sell it, what is the internal rate of return of your investment?

Answer: If YTM drops by one percent when you sell the bond, IRR is %. (round to one decimal)

(c) If the bond’s yield to maturity drops by 2% when you sell it, what is the internal rate of return of your investment?

Answer: If YTM drops by two percent when you sell the bond, IRR is %. (round to one decimal)

(d) If the bond’s yield to maturity increases by 1% when you sell it, what is the internal rate of return of your investment?

Answer: If YTM increases by one percent when you sell the bond, IRR is %. (round to one decimal)

Answer 1

Given

Face value F=$10000

Period N=30 years

YTM =4.4%

Coupon =0

A)

Price of bond=F/(1+YTM)^N=10000/(1+4.4%)^30=$2747.80

B)

If YTM decrease by 1% when I sell it than

New YTMN =4.4%-1%=3.4%

Bond price after 9 years =F/(1+YTMN)^(N-9)=10000/(1+3.4%)^21=$4955.29

Let r be the IRR so

2747.80=4955.29/(1+r)^9

r=6.77%

C)

If YTM decrease by 2% when I sell it than

New YTMN =4.4%-2%=2.4%

Bond price after 9 years =F/(1+YTMN)^(N-9)=10000/(1+2.4%)^21=$6077.16

Let r be the IRR so

2747.80=6017.16/(1+r)^9

r=9.22%

D)

If YTM Increase by 1% when I sell it than

New YTMN =4.4%+1%=5.4%

Bond price after 9 years =F/(1+YTMN)^(N-9)=10000/(1+5.4%)^21=$3313.96

Let r be the IRR so

2747.80=3313.96/(1+r)^9

r=2.10%