Question

Today is 1 July 2020, William plans to purchase a corporate bond with a coupon rate of j2 = 2.18% 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 = 3.99% p.a. Assume that this corporate bond has a 2.3% 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. 73.706

b. 75.856

c. 92.971

d. 92.407

Answer 1

No of semiannual Coupon payments = 9

half yearly Coupon = $100 * 2.18%/2 = $1.09

Half yearly YTM = 3.99%/2 =0.01995

Now, Expected value of 1st coupon = (1-0.023)*1.09 = $0.977*1.09

Expected value of 2nd coupon = (1-0.023)^2*1.09 = $0.977^2*1.09

and so on

Expected value of 9th coupon = (1-0.023)^9*1.09 = $0.977^9*1.09

Expected value of principal repayment = (1-0.023)^9*100 = $0.977^9*100

So, value of the bond today

=0.977*1.09/1.01995 +0.977^2*1.09/1.01995^2+.....+0.977^9*1.09/1.01995^9 + 0.977^9*100/1.01995^9

=0.977*1.09/1.01995* (1-(0.977/1.01995)^9)/(1-0.977/1.01995) + 0.977^9*100/1.01995^9

=$75.85571

or $75.856 (option b)