Question

Today is 1 July 2020, William plans to purchase a corporate bond with a coupon rate of j₂ = 2.19% p.a. and face value of 100. This corporate bond matures at par. The maturity date is 1 January 2025. The yield rate is assumed to be j₂ = 3.62% p.a. Assume that this corporate bond has a 7.1% chance of default in any six-month period during the term of the bond. Assume also that, if default occurs, William will receive no further payments at all. Calculate the purchase price for 1 unit of this corporate bond. Round your answer to three decimal places.

Select one:

a. 46.866

b. 50.266

c. 95.139

d. 93.470

Answer 1

a. 46.866

No. of Coupon payments = 4.5 x 2 = 9

Half yearly Coupon = $100 * 2.19%/2 = $1.095

Half yearly YTM = 3.62%/2 = 1.81%

Expected value of 1st coupon = (1-0.071)*1.095 = $0.929*1.095

Expected value of 2nd coupon = (1-0.071)^2*1.095 = $0.929^2*1.095

Expected value of 9th coupon = (1-0.071)^9*1.095 = $0.929^9*1.095

Expected value of principal repayment = (1-0.071)^9*100 = $0.929^9*100

Value of the bond today = 0.293*1.095/1.0181* (1-(0.929/1.0181)^9)/(1-0.929/1.0181) + 0.929^9*100/1.0181^9
= 46.866