Hi,
in bond valuation section there are a couple of formulas used to calculate the full price.
For yield calculation the formula PVfull = AI + Pf flat is highlighted.
However, in duration section another formula is brought in: PV full = (PMT / (1+r)^1 + PMT + FV / (1+r)n * (1+r)^t/T
Please help to explain the difference between these 2 and why is the second formula used with no explanation in the CFA study book.
Many thanks
The present value of any cash producing asset is the summation of all the the discounted future cash flows.
The first equation is the dirty-price method, which takes into account accrued interest on the bond, this affects only the first payment (AI).
Don’t have an idea what the second equations means.
In addition to what Mr Smart said, the dirty price of the bond is the price that an investor will actually pay to acquire the bond (must pay accrued interest to current bondholder for the time they held the bond between the last coupon date and the selling date).
Hi Kaia,
The first formula tells us when bond is in between its coupon payment date then its full price has to part accrued interest and flat price.
Let say you will recieve coupon payment semiannually on 15th May and 15th Nov . Let assume in between you want to sell your bond and by the time you find a buyer and settled the bond on 27th June. Being the owner of the bond till 27th June you have earned the interest amount between last coupon date 15th May and settlement day 27th June (42 days). So the buyer has to give you that amount of interest which is a part of coupon payment =42/180* PMT.
For second formula you are discounting the future PMT for the reminder of coupon period ie 1-t/T , 2-t/T and so on.
In mathematics the expression (1+r)^(1-t/T) can be rewrite as (1+r)^1 /( 1+r)^t/T