2. You can buy or sell a 5.0% coupon $10,000 par U.S. Treasury Note that matures

Question

2. You can buy or sell a 5.0% coupon $10,000 par U.S. Treasury Note that matures in 12.5 years. The first coupon payment pays 6 today, 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 3.000%. (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 ALL coupon payment(s)? (c) What is the present value of ALL principal payment(s)? (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 S1000, would you buy or sell it - and why?

Explanation / Answer

2.

a)

Cash flows associated with this note are:

i) Semi-annual interest payment of $10,000*5%*1/2 = $250. It is ordinary annuity

ii) Face value of bond to be redeemed on maturity = $10,000. It is a single cash flow

b)

Number of semi annual coupon payments = 12.5 years * 2 = 25

Semi-annual yield to maturity = 3%/2 = 1.5% = 0.015

Present value of annuity = Annuity * {1-(1+r)-n}/r

Present value of coupon payments = $250*(1-1.015-25)/0.015 = $5,179.90

c)

Present value of principal payment = $10,000/1.01525 = $6,892.06

d)

Present value of all payments = $5,179.90 + $6,892.06 = $12,071.96

e)

No, you would not sell it because the fair value of bond is $12,071.96 which is more than the offered price.

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