Question

Suppose a trader purchases a bond between coupon periods. The days between the settlement date and the next coupon period is 45. There are 90 days in the coupon period. Suppose that the bond purchased has a coupon rate of 8.0% and there are four quarterly coupon payments remaining. Face value is $100.

a) What is the dirty price of this bond if a 5.6% discount rate is used (assume that 5.6% is compounded quarterly)?

b) What is the accrued interest for this bond?

c) What is the clean price?

Answer 1

Value of the bond on last Coupon date:

Still there are four quarterly coupons are remaining

Let us find out the value of the coupon on the last received coupon date

We know that the value of the bond on that date = Present value of future cash inflows

Coupon Amount = $ 100*8% /4 = $ 2

No.of Coupon Payments per year = 4

Discount rate per year = 5.6%

Discount rate per Quarter = 5.6%/4 = 1.4%

Value of the Bond = $ 20 * PVAF ( 1.4%,4) + $ 100*PVF( 1.4%,4)

= $ 2*3.8638+ $ 100*0.9459

= $ 7.7276+$ 94.59

= $ 102.3176

Hence clean price of a bond is $ 102.3176

a) Value of the bond on the Valuation date ( Dirty Price)[ After 45 days from clean price]

= $ 102.3176( 1+i/400)^4n Where n= No.of years

= $ 102.3176(1+5.6/400)^4*45/360

= $ 102.3176( 1.014)^0.5

= $ 102.3176*1.006976

= $103.0313

Hence Dirty Price of a bond is $ 103.0313

b) Accrued intrest for 45 days = $ 100*8%*45/360 = $ 1

c) Hence Clean price on valuation date = Dirty Price - Accrued intrest

= $ 103.0313-( $ 100*8%*45/360)

= $103.0313--1

= $ 102.0313

Hence Clean price of a bond is $ 102.0313.