Question

A $2,500 14% six-year bond with annual coupons is bought to yield 6%annually. The price is $3,600. Find its clean and dirty values at the end ofthe first quarter of the third year after issue, by the theoretical method.

NO EXCELL ONLY FORMULAS THANK U

Answer 1

Value of a bond as on the date of payment is the same as the Present Value (PV) of the future benefits.

However if the bond is valued in between the payment dates, there is a accured interest factor that comes to play. THis is because, the holder of the bond has additionally held the bond for a specific period(from the last payment date tilll today).

Hence, it has 2 parts: Flat price and accrued interest

where t = time passed since last payment to the settlement date

T = Time between two payment dates

is also called dirty price

is also known as clean price

On simplification, we get:

i.e. multiplying a fator (1+r)^(t/T) with the PV will give us full price.

Also, Accured Interest (AI) = PMT * t/T

In our case,

t/T = 1/4 = 0.25

PMT = 350

AI = 350 * 0.25 = $87.5

Note here that PV of the bond is not equal to

To compute PV,

FV = 2500

n = 8yr

pmt = $350

r= 6%

Substituting, we get PV = 3741.958

= $3796.8669

= 3796.8669 - 87.5 = $3709.3669

Hence, dirty price = $3796.8669

clean price = $3709.3669