Question

Two bonds have par values of $1,000. One is a 5.5%, 20-year bond priced to yield 8.5%. The other is a(n) 7%, 24-year bond priced to yield 5.5%. Which of these two has the lower price? (Assume annual compounding in both cases.) The price, PV, of the 5.5%, 20-year bond is $ . (Round to the nearest cent.) The price, PV, of the 7%, 24-year bond is $ . (Round to the nearest cent.) Which of these two has the lower price? (Select the best answer below.) The 5.5%, 20-year bond has lower price of $716.10. The 7%, 24-year bond has lower price of $716.10. O

Answer 1

Price of bond 1

Price of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)

Interest = 1000 x 5.5% = 55$

YTM% = 8.5% , n = no. of year till maturity = 20 years

PVIFA(YTM%,n) = [1-(1/(1+r)^n / r]

PVIFA(8.5%,20) = [1-(1/(1+8.5%)^20 / 8.5%]

=[1-(1/(1+0.085)^20 / 0.085]

=[1-(1/1.085)^20 / 0.085]

=[1-0.1956/0.085]

=0.8044/0.085

=9.4633

PVIF(8.5%,20) = 1/(1+r)^n

=1/(1+0.085)^20

=1/(1.085)^20

=0.1956

Price of bond = 55 x 9.4633 + 1000 x 0.1956

=520.48 + 195.62

=716.10$

Price of Bond 2

Price of bond = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)

Interest = 1000 x 7% = 70$

YTM% = 5.5% , n = no. of year till maturity = 24 years

PVIFA(YTM%,n) = [1-(1/(1+r)^n / r]

PVIFA(5.5%,24) = [1-(1/(1+5.5%)^24 / 5.5%]

=[1-(1/(1+0.055)^24 / 0.055]

=[1-(1/1.055)^24 / 0.055]

=[1-0.2767/0.055]

=0.7233/0.055

=13.1517

PVIF(5.5%,24) = 1/(1+r)^n

=1/(1+0.055)^24

=1/(1.055)^24

=0.2767

Price of bond = 70 x 13.1517 + 1000 x 0.2767

=920.619 + 276.7

=1197.28$

Ans) The 5.5%,20 year bond has lower price of 716.10$