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:

Value of treasury Note = $876,205.93

Explanation:

The value of the notes is the present value of future cash flow discounted at its YTM of 7.70%.

The value of the Note is the present value of the future cash receipts expected from the it. The value is equal to present values of interest payment and the redemption value (RV).

Value of Notes = PV of interest + PV of RV

The value of Note can be worked out as follows:

Step 1

Calculate the PV of Interest payment

Present value of the interest payment

PV = Interest payment * (1 - (1+r) ^ (-n)) / r

r-Yield to Maturity, n - number of years

Interest payment = 3% * $1,000,000 * 1/2 = $15000.

Semi-annual interest yield = 7.7%/2 = 3.85

PV = 15,000 * (1 - (1.0385) ^ (-3*2) / 0.0385) = 79,017.4892

Step 2

PV of redemption Value

PV of RV = RV * (1+r) ^ (-n)

= 1000,000 * (1.0385) ^ (-3*2)

= 797188.4444

Step 3

Calculate Value of the Notes

=79,017.4892 + 797,188.44

= $876,205.93

Value of treasury Note = $876,205.93