Question

A bond of par value 1,000 pays a coupon of 4% p.a. annually for 20 years and the par value is 1,000 (coupon calculated on this number and not on maturity value). Calculate the following: The price of the bond and the current yield/ maturity of the bond is also 4%, if the 1. a. maturity value is: . $1,000 i. $950 b. Explain the answers as to the prices of the bonds as to why they are equal to, greater than or less than the par value in a. I. and a.i. Interest rates rise to 5% calculate the price of the bond in a i, and a. . d. Explain why the price of the bond has changed and the reason for directional move of the price of the bond. If the bond only had a maturity of 5 years and rates rose from 4% to 5%, would the price change be the same, bigger or smaller. Explain. C. e.

Answer 1

a.

The price of the bond is $1000

B7 =PV(B5,B4,B3,B1) в 1 Par Value 2 Coupon rate 3 Coupon Payment 4 Maturity 5 Yield |1000 0.04 I=B2*B1 20 10.04 Price =PV(B5,B4,B3,B1) 7 8

B7 - for =PV(B5,B4,B3,B1) X А В $ 1 Par Value 2 Coupon rate 3 Coupon Payment 4 Maturity 5 Yield 6 7 Price 1,000.00 4% 40.00 20 4% $ -1,000.00

b.

As coupon rate equals discount rate hence the bonds sells at par.

c.

B7 - X V fx =PV(B5,B4,B3,B1) Α. в 1 Par Value 2 Coupon rate 3 Coupon Payment 4. Maturity Yield 1000 0.04 =B2*B1 120 10.05 7 Price =PV(B5,B4,B3,B1)

B7 X V =PV(B5,B4,B3,B1) В 1 Par Value 2 Coupon rate 3 Coupon Payment 4 Maturity 5 Yield 1,000.00 4% 40.00 20 5% 7 Price -875.38

d.

Price of a bond is inversely related to the yield. As yield increased in this case hence the price of the bond decreased. Long term bonds are more volatile for a change in interest rate and hence greater price change will be seen for the bond with maturity of 20 years.