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 US Treasury note with three years to maturity has a coupon rate of 3%. The yield to maturity (YTM) of the bond is 7.70%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

$1,051,447.12

$552,009.74

$876,205.93

$744,775.04

Based on your calculations and understanding of semiannual coupon bonds, complete the following statement:

The T-note described in this problem is selling at a

discount or premium

Answer 1

Par Value = $1,000,000

Annual Coupon Rate = 3.00%
Semiannual Coupon Rate = 1.50%
Semiannual Coupon = 1.50% * $1,000,000
Semiannual Coupon = $15,000

Time to Maturity = 3 years
Semiannual Period = 6

Annual YTM = 7.70%
Semiannual YTM = 3.85%

Price of Bond = $15,000 * PVIFA(3.85%, 6) + $1,000,000 * PVIF(3.85%, 6)
Price of Bond = $15,000 * (1 - (1/1.0385)^6) / 0.0385 + $1,000,000 * (1/1.0385)^6
Price of Bond = $876,205.93

Using this information and ignoring the other costs involved, the value of the Treasury note is $876,205.93

Based on your calculations and understanding of semi coupon bonds, complete the following statements:
Assuming that interest rates remain constant, the T-note’s price is expected to increase.
The T-note described is selling at a discount.