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 $3,000,000 par value, semiannual coupon U.S. Treasury note with five years to maturity (YTM) has a coupon rate of 4%. The yield to maturity of the bond is 7.40%. Using this information and ignoring the other costs involved, the value of the Treasury note is   .

Answer 1

Value of the Treasury Note

The Value of the Treasury Note is the present value of the coupon payments plus the present value of the par value

Par Value = $30,00,000

Semi-annual Coupon Amount = $60,000 [$30,00,000 x 4% x ½]

Semi-annual Yield to Maturity = 2% [4% x ½]

Maturity Period = 10 Years [5 Years x 2]

Value of the Treasury Note = Present Value of the Coupon Payments + Present Value of the Par Value

= $60,000[PVIFA 2%, 10 Years] + $30,00,000[PVIF 2%, 10 Years]

= [$60,000 x 8.23340] + [$30,00,000 x 0.69536]

= $494,004 + $20,86,093

= $25,80,097

“Therefore, the Value of the Treasury Note would be $25,80,097”