Question

Today is 1 July 2020, William plans to purchase a corporate bond with a coupon rate of j₂ = 4.41% 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 = 3.87% p.a. Assume that this corporate bond has a 5.7% 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. 101.182

b. 60.639

c. 63.344

d. 103.130

Answer 1

No of Coupon payments = 9

half yearly Coupon = $100 * 4.41%/2 = $2.205

Half yearly YTM = 3.87%/2 =0.01935

Now, Expected value of 1st coupon = (1-0.057)*2.205 = $0.943*2.205

Expected value of 2nd coupon = (1-0.057)^2*2.205 = $0.943^2*2.205

and so on

Expected value of 9th coupon = (1-0.057)^9*2.205 = $0.943^9*2.205

Expected value of principal repayment = (1-0.057)^9*100 = $0.943^9*100

So, value of the bond today

=0.943*2.205/1.01935 +0.943^2*2.205/1.01935^2+.....+0.943^9*2.205/1.01935^9 + 0.943^9*100/1.01935^9

=0.943*2.205/1.01935* (1-(0.943/1.01935)^9)/(1-0.943/1.01935) + 0.943^9*100/1.01935^9

=$63.343687

or $63.344 (option c)