BOB just sold $4 million face value of 4.75% US Treasury Notes that mature on May...

BOB just sold $4 million face value of 4.75% US Treasury Notes that mature on May 15, 2030, and has a yield to maturity of 5%. SHOW YOUR WORK STEP BY STEP FOR CREDIT!

a. What is the flat price of the bond today (4/1/2020)?

b. What is the invoice price of the bond?

Solutions

Expert Solution

Assumptions:

1) Coupons are paid once every year on May 15.

2) 4/1/20 is taken as 1st April, 2020.

Period	Discounting Factor [1/(1.05^period)]	Discounting Factor Annuity (Sum of discounting factor & all previous discounting factors)
1	0.952380952	0.952380952
2	0.907029478	1.859410431
3	0.863837599	2.723248029
4	0.822702475	3.545950504
5	0.783526166	4.329476671
6	0.746215397	5.075692067
7	0.71068133	5.786373397
8	0.676839362	6.463212759
9	0.644608916	7.107821676
10	0.613913254	7.721734929
11	0.584679289	8.306414218

Flat Price(i.e. Price as on May 15 2019) = PV of All Coupons + PV of Maturity Value = [Coupon*Annuity Factor] + [Maturity Value*Discounting Factor] = [4000000*4.75%*8.3064] + [4000000*0.58468] = 1578216 + 2338720 = $3916936

Invoice Price = Flat Price - Accrued Interest till April 1, 2020 = 3916936 + (4000000*4.75%*10.5/12) = 3916936 + 166250 = $4083186

jeff jeffy answered 1 year ago

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