Question

Which of the following bonds would be cheapest to deliver given a T-note futures price of 120.6773? (Assume that all bonds have semiannual coupon payments based on a par value of $100.)

	a.	6.5-year bond with 3.5% coupons and a yield of 2.5%
	b.	9.5-year bond with 5% coupons and a yield of 3.5%
	c.	9-year bond with 3% coupons and a yield of 1.5% explain steps

Answer 1

Price = 120.6773
Par value =100
a) Coupon rate = 3.5%
YTM = 2.5%
Time = 6.5

Coupon = 2.5%* 100/2 = 12.5
Price = Coupon/(1+YTM//2)^2t + Par value /(1 +YTM/2)^2t
Price = 12.5/(1+2.5%//2)^2t + 100 /(1 +2.5%/2)^2t = 105.55

b)

Coupon rate = 5%
YTM = 3.5%
?Time = 9.5

Coupon = 5%* 100/2 = 25
Price = Coupon/(1+YTM//2)^2t + Par value /(1 +YTM/2)^2t
Price = 25/(1+3.5%//2)^2t + 100 /(1 +3.5%/2)^2t = 111.51

c)

Coupon rate = 3%
YTM = 1.5%
?Time = 9

Coupon = 3%* 100/2 = 15
Price = Coupon/(1+YTM//2)^2t + Par value /(1 +YTM/2)^2t
Price = 15/(1+1.5%//2)^2t + 100 /(1 +1.5%/2)^2t = 112.58

First bond would be cheapest to deliver.

Best of Luck. God Bless