Question

Today is 1 July 2020, William plans to purchase a corporate bond with a coupon rate of j2 = 3.65% 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 = 4.12% p.a. Assume that this corporate bond has a 1.7% 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. 83.636

b. 98.370

c. 85.010

d. 97.835

Answer 1

Calculation of Fair Value of Bond:

Bond price =C/ YTM (1-1/(1+YTM)^Y)+(FV/(1+YTM)^Y)

C = annual coupon, the sum of two semi-annual coupons

FV = face value

M = maturity in years

YTM = yield to maturity

Face Value	100
Date of Issue	01-07-2020
Maturity	At 100
Maturity Date	01.01.2025
	Coupon Rate	Yeild
J2	3.65%	4.12%

Default Chance		1.7% in any 6 months period of tenure
Total Tenure of Bond		54 Months or 4.5 Years
Number of Default probability		9

When Default is @1.7% for 6 months then defaul probability for 4.5 years is 7.65%

Present Value of Bond considering yeild and Coupon rate and time period of 4.5years is 98.10

However Yeild after adjusting risk factor 1.70*2+4.12=7.52

So using Discount factor of 7.52% the present value of Bond is 85010