Question

You can buy or sell a 3.5% 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 (treat this as your discount rate) is 3.000%. (a) What are the cash flows associated with this Note? (b) Which of these cash flows are annuity dues, ordinary annuities, or single cash flows? (c) What is the present value of all payments associated with this Note? (d) If interest rates moved up, what would happen to the value of this 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.)

Answer 1

(a) Coupon on Note = 3.5 % payable semi-annually,

Tenure = 6 years,

Discount Rate = 3 %

Par Value of Note = $ 1000,

∴

Semi-Annul Coupon = 0.035 × 1000 × 0.5 = $ 17.5

(b) The semi-annual coupons are ordinary annuities.

(c) Value of the Note = Sum of the Present Value of Payments

=
`17.5 * (1)/(1.015) * [1 - (1)/(1.015)^(12)}] +(1000)/(1.015)^(12)`

= $ 1027.27

(d) The value of the note is inversely proportional to the relevant discount rate. Therefore, if the discount rate increase the note value will decrease.

(e) To buy a note at $ 1000 if it is primitively worth $ 1027.27 is a lucrative deal.