3·You can buy or sell a 4.125% coupon $1,000 par U.S. Treasury Note that matures

Question

3·You can buy or sell a 4.125% coupon $1,000 par U.S. Treasury Note that matures in 6 years. The first coupon payment pays 6 months from now, and the Note pays coupons semi-annually until maturity. It also pays par on maturity. The Yield to Maturity of the Note right now is 4.000% (a) What are the cash flows associated with this Note? Clearly identify which of these cash flows are annuity dues, ordinary annuities, or single cash flows. (b) What is the present value of the coupon payments? (c) What is the present value of the principal payment? (d) What is the present value of all payments associated with this Note, and thus the Note? (e) If a stranger was willing to buy or sell you the bond for $1000, would you buy or sell it - and why? (Hint: assume no altruism here.)

Explanation / Answer

a) The cash flows associated with the note are: The maturity value of the note of $1000, which is a single cash flow and The semiannual coupon payments of $1000*4.125%/2 = 20.625 which is an ordinary annuity, with 6*2 = 12 periods. b) PV of coupon payments = 20.625*(1.02^12-1)/(0.02*1.02^12) = $         218.12 [The formula used is the one for finding PV of an ordinary annuity] c) PV of principal payment = 1000/1.02^12 = $         788.49 d) PV of all payments associated with the note = 218.12+788.49 = $      1,006.61 e) As the value of the bond of $1006.61 is more than the price offered by the stranger, I would buy the bond.

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