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

Question

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 $1000, would you buy or sell it - and why?

Explanation / Answer

cash flow is coupon every 6 months (=5%*10000/2=250) and principal (=10000) at the time of maturity

Present value of all coupon payments=250/1.015+250/1.015^2.....250/1.015^25=250/0.015*(1-1/1.015^25)=5179.90

Present value of all principal payments=10000/1.015^25=6892.058

Present value of all payments that is present value of note=5179.90+6892.058=12071.96

If the stranger was willing to sell it for 10000 we will buy it as he is selling at less than fair value of the note

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