Question

Bob owns $4,000,000 of 4.75% US Treasury Notes that mature on May 15, 2030, and has a yield to maturity of 6%.

a. What is the flat price of the bond today (4/3/2019)?

b. What is the invoice price of the bond?

Answer 1

Invoice price = flat price + accrued interest

This is a semiannual payment bond.

Days between next coupon payment and last coupon payment (T) = 181

Number of days passed since the last payment date (t) = 181-(May 15 - Apr 3) = 181 - 43 = 138

PV of the bond: N = 24 (number of payments left to be made till May 2030); PMT = 4.75%/2*4,000,000 = 95,000; I (same as YTM) = 6%/2 = 3%; FV = 4,000,000, solve for PV.

PV = 3,576,611.45

Full price = PV*(1+r)^(t/T) where r = 4.75%/2 = 2.375%

Full price = 3,576,611.45*(1+2.375%)^(138/181)

= 3,641,194.84

This is the invoice price of the bond.

Accrued interest = (t/T)*PMT = (138/181)*95,000 = 72,430.94

Flat price = full price - accrued interest = 3,641,194.84 - 72,430.94 = 3,568,763.90

Note: There are 2 ways to count the number of days - actual-actual and 30/360. It is not specified which method has to be used in the question.