Question

A 27-year U.S. Treasury bond with a face value of $1,000 pays a coupon of 6.00% (3.000% of face value every six months). The reported yield to maturity is 5.6% (a six-month discount rate of 5.6/2 = 2.8%).

a. What is the present value of the bond?

Present value            $

b. If the yield to maturity changes to 1%, what will be the present value?

Present value            $

c. If the yield to maturity changes to 8%, what will be the present value?

Present value            $

d. If the yield to maturity changes to 15%, what will be the present value?

Present value            $

Answer 1

Face Value of Bond = $1000

Semi-annual coupon payment = $1000*6%*1/2

= $30

No of coupon payments = No of years to maturity*2

= 27 years*2

= 54

a). YTM = 5.6%

Semi-annual YTM = 5.6%/2

= 2.8%

calculating the Price of Bond:-

price = $830.253 + $225.10

Price of Bond = $1055.35

b). YTM = 1%

Semi-annual YTM = 1%/2

= 0.5%

calculating the Price of Bond:-

price = $1416.642 + $763.89

Price of Bond = $2180.53

c). YTM = 8%

Semi-annual YTM = 8%/2

= 4%

calculating the Price of Bond:-

price = $659.79 + $120.28

Price of Bond = $780.07

d). YTM = 15%

Semi-annual YTM = 15%/2

= 7.5%

calculating the Price of Bond:-

price = $391.947 + $20.13

Price of Bond = $412.08