Question

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.)

Answer 1

a) Identification of cash flows :-

Payment at the end of	Amount of cash flow	Type of cash flow
6 month	$20.625	ordinary annuity
1 year	$20.625	ordinary annuity
1.5 year	$20.625	ordinary annuity
2 year	$20.625	ordinary annuity
2.5 year	$20.625	ordinary annuity
3 year	$20.625	ordinary annuity
3.5 year	$20.625	ordinary annuity
4 year	$20.625	ordinary annuity
4.5 year	$20.625	ordinary annuity
5 year	$20.625	ordinary annuity
5.5 year	$20.625	ordinary annuity
6 year	$20.625	ordinary annuity
6year	$1000	single cash flow

Note1:- Ordinary annuity is the amount of equal payments made at the regular interval at the end of the periods. Since all the interest will be paid at the end of half year or end of year, hence all the payments will be ordinary annuity.

Note2:- Annuity dues means series of payments at the regular interval made at the beginning of the period. Since all payments are made at the end of so there are no annuity due payments.

b) Present value of coupon payments

            =Semi annual interest *PVIFA(RR,N)

Where RR= Half yearly YTM = 4%*1/2= 2%

N= Total number of coupon payments = 6*2 = 12

Semiannual interest = $20.625

Now,

PV of coupon payment= $20.625*PVIFA(2% ,12)

                                    =$20.625*10.575341

                                    =$218.1164

Hence the present value of coupon payment = $218.12

c) Present value of the principal payment

                        =Maturity value/(1+RR)^N

                                =$1000/(1+2%)¹²

                        =$1000/1.268242

                        =$788.49

Hence the present value of principal payment = $788.49

d) present value of all payments associated with this Note or the Note

            =PV of coupon payment +PV of principal payment

            =$218.12+$788.49

            =$1,006.61

e) Since the fair price of bond is $1,006.61, hence if the stranger is willing to sell that bond for $1000, we should buy it.

Please feel free to ask if you have any query in the comment section.