Which of the following answer is the correct formula to calculate the price of a fixed rate bond (Expiring in 2 years, Yearly coupon rate 3%) given the following informations about the interest rates: interest rate swap 2 years: 3%, spread 1%.

a. 3/(1 + 2%) + 103 / ((1 + 4%)^2)

b. 3/((1+4%)^2)+100/((1 + 4%)^2)

c. 103 / (1 + 3% + 1%)^2

d. 3/(1 + 3%) + ( 3 + 100)/((1 + 4%)^2)

Answer:

In the given question,

Yearly coupon payment is 3%. Therefore,

Coupon Payment to be received each year for 2 years = Par Value * Coupon Rate

=100*3%

= 3

Further maurity value of 100 to be received at the end of year 2.

Interest rate swap 2 years: 3%, spread 1%

Bond Value = Coupon Payment/(1+r%)¹ + (Coupon Payment + Maturity Value)/(1+r%)²

Here,

Option 1 is incorrect, because even though it considers both cash flows i.e. Coupon Payment of 3 at the end of year 1 and Coupon Payment+ Maturity Value (3+100=103) at the end of year 2 but it discounts year 1 coupon payment with incorrect rate of 2% which is not given.

Option 2 is incorrect because it does not consider discounted value of Coupon Payment of 3 at the end of year 1 in calculation.

Option 3 also does not consider discounted value of Coupon Payment of 3 at the end of year 1 in calculation and therefore incorrect.

Option 4 is correct because it correctly discounts Coupon Payment at the end of year 1 by 3% interest rate and Coupon Payment+ Maturity Value (3+100=103) at the end of year 2 with interest rate of 4% i.e. 3%, spread 1%