Question

Bonds often pay a coupon twice a year. For the valuation of bonds that make semiannual payments, the number of periods doubles, whereas the amount of cash flow decreases by half. Using the values of cash flows and number of periods, the valuation model is adjusted accordingly. Assume that a $1,000,000 par value, semiannual coupon U.S. Treasury note with three 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

Value of the Treasury note is $800,178.78

Step-by-step explanation:

The price of bond can be calculated by discounting all the future cash flows associated with that bond

We will use the following formula to calculate the value of the Treasury note.

Value of Treasury note = C x ( 1 - ( 1 + r )^-n / r ) + ( F / ( 1 + r )^n )

Where

From the given statement in the question, it is concluded that the coupon payment is made twice a year.

F = Face Value = $1,000 ,000

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

n = number of periods = 3 years x 12 / 6 = 6 peiods

r = Yield to maturity = 11% x 6/12 = 5.5%

Placing values in the formula

Value of Treasury note = $15,000 x ( 1 - ( 1 + 5.5% )^-6 / 5.5% ) + ( $1,000 / ( 1 + 5.5% )^6 )

Value of Treasury note = $74,932.95 + $725,245.83

Value of Treasury note = $800,178.78