Question

Problem 1 : Suppose you buy a 3-year US Treasury bond with a face value of $1,000. It pays three annual coupons at a rate of 2.50% exactly 1, 2, and 3 years from the day you purchase it. (a) Assume that when you purchase the bond, its yield to maturity equals 3%. What is its value on the day of purchase? (b) Is this bond issued at par, a discount, or premium? (c) Next assume the moment after you purchased the bond market rates change and the yield to maturity has increased to 3.5%. Does the value of the bond increase or decrease? (d) Next assume it is one year later and you have just received the first coupon. Assume the yield to maturity has remained at 3.5%. You want to sell the bond. What is the value of the bond at that moment.

Answer 1

a

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(2.5*1000/100)/(1 + 3/100)^k]     +   1000/(1 + 3/100)^3

k=1

Bond Price = 985.86

b

Discount bond as price is less than par value

c

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(2.5*1000/100)/(1 + 3.5/100)^k]     +   1000/(1 + 3.5/100)^3

k=1

Bond Price = 971.98

Price decreased

d

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =2

Bond Price =∑ [(2.5*1000/100)/(1 + 3.5/100)^k]     +   1000/(1 + 3.5/100)^2

k=1

Bond Price = 981