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

Settlement Date = 1 July 2020

Coupon rate = 2.18%

Face Value = 100

Since its semi-annual coupon, coupon = coupon rate * face value/2 = 2.18% * 100/2 = 1.09

Maturity Date = 1 January 2025

Yield rate, r = 3.99%

Since this is a corporate bond, day count convention = 30/360

Probability of default, P = 2.3%

Probability of No default for the first 6 months = 1-P = 1-2.3% = 97.7000%

Probability of No default for the second 6 months = (1-P)² = (1-2.3%)² = 95.4529%

Probability of No default for the third 6 months = (1-P)³ = (1-2.3%)³ = 93.2575%

And so on. The no default probability has been calculated for each period in the spreadsheet.

Discount factor for each period is calculated using the formula

Discount Factor, DF = 1/(1+r/n)^(n*t)

Where n is the number of compounding per year.

Here, n = 2

Bond Price is calculated using the formula

Where, T is the total number of cash flows

CF_i is the cash flow for period i

DF_i is the discount factor for period i

PND_i is the probability of no default for period i

The calculations are shown below

Purchase price of the bond = 75.856