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Problem 1 : Suppose you buy a 3-year US Treasury bond with a face value of...

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Finance

Problem 1 : Suppose you buy a 3-year US Treasury bond with aface value of $1,000. It pays three annual coupons at a rate of2.50% exactly 1, 2, and 3 years from the day you purchase it. (a)Assume that when you purchase the bond, its yield to maturityequals 3%. What is its value on the day of purchase? (b) Is thisbond issued at par, a discount, or premium? (c) Next assume themoment after you purchased the bond market rates change and theyield to maturity has increased to 3.5%. Does the value of the bondincrease or decrease? (d) Next assume it is one year later and youhave just received the first coupon. Assume the yield to maturityhas remained at 3.5%. You want to sell the bond. What is the valueof the bond at that moment.

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4.3 Ratings (949 Votes)

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

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