Question

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with five years to maturity has a coupon rate of 3%. The yield to maturity (YTM) of the bond is 11.00%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

Answer 1

$698,495

Step-by-step explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond.

As per given data:

Face Value = $1,000,000

Coupon Payment = $1,000,000 x 3% x 6/12 = $15,000 semiannually

YTM = 11.00% annually = 5.50% semiannually

Numbers of period = 5 years x 2 = 10 periods

Formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Placing values in the formula

Price of the Bond = 15,000 x [ ( 1 - ( 1 + 5.5% )^-10 ) / 5.5% ] + [ $1,000,000 / ( 1 + 5.5% )^10 ] = $113,064 + $585,431 = $698,495