Question

3. (20 points) You can buy or sell a 3.0 % coupon $1,000 par U.S. Treasury Note that matures in 30 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 4.0%.

(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?

Answer 1

(a)

The cash flows are the semiannual coupon payments, and the par value payable at maturity.

Semiannual coupon payment = par value * coupon rate / 2 = $1000 * 3% / 2 = $15

Par value payable at maturity = $1000

(b)

The semiannual coupon payments are ordinary annuities because they are a stream of fixed cash flows occurring at the end of each semiannual period.

The par value payable at maturity is a single cash flow because it is a single payment at maturity.

(c)

Present value of its cash flows is calculated using PV function in Excel :

rate = 4%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 30 * 2 (30 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 3% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $826.20

A1 fc =PV(4%/2,30*2,1000*3%/2,1000) D E F G B C 1 ($826.20)

(d)

If interest rates moved up, the value of this Note would decrease. This is because the present value of its cash flows would be lower. According to the time value of money concepts, the present value is lower if the discount rate is higher.

(e)

I would sell it because the value of the bond is only $826.20. Hence, I would make a profit by buying the bond in the market for $826.20 and selling it to the stranger for $1000.