CFA Practice Question

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CFA Practice Question

Assume that three months have elapsed since the last coupon payment date. The ex-coupon price of $250,000 par value of a five-year bond paying an 8% coupon rate in semi-annual payments is $225,990. What is the full price?

A. $230,990
B. $235,990
C. $232,657
Correct Answer: A

The accrued interest is (3/6) x (1/2) x (8%) x $250,000 = $5,000
The full price = $225,990 + $5,000 = $230,990

User Contributed Comments 10

User Comment
danlan Note "three months have elapsed".
george2006 The ex-coupon price is lower than full price or cum-coupon price.

There is no direct relationship between ex-coupon and clean price. They are two different things. Ex-coupon simply means that the buyer are not entitled to the next coupon payment.
Bibhu Ex-Coupon price is lower than full price by accrued interest amount
2014 Ex coupen price do not include Interest in it. So you are required to factor interest in to it to make it cum interest/full interest price/dirty price (all same different names) Like god is one names are different
gill15 Why didnt they just say in the Notes Dirty Price = Clean Price + Accrued Interest....Done then undertsood..
pranubal can you please explain this further, what is the formula for full price
robbiecow @pranubal

AI = t/T * PMT, where PMT is the coupon rate (8%/2) multiplied by the Par Value, or 250,000. t/T is 3/6 because we have 6 in which the coupon "accrues" and we are 3 months in to that period (i.e., 3 months of accrued interest)
AI = (8%/2)*(3/6)*(250,000)

The flat price is actually supplied. The ex-coupon price is the PV of ONLY the par value to an time 0, or time to which you are discounting.
robbiecow Just to clarify the ex coupon bit; this is the agreed to price--which should be the PV of the bond--by the buyer and seller with the knowledge that the investor will not receive the next coupon payment from the bond.
Rsanches The rate is anual compound semianually, right?
So, why do we divide for 3? why we don't compound the rate for month? In my view, this way is not considering the compound.

PV = 225,990
i = 0,6558%(monthly)
N = 3
FV = 230,465.35
Fabulous1 According to the Schweser Notes, the full price is NOT calculated by adding accrued interest to the value on its last payment date but by taking the value on its last payment date and multiplying it (in this case) by (1+YTM)^3/6 in order to account for the increased value due to a shorter time frame until the next coupon payment.
This full value slightly deviates from the value on its last payment date plus accrued interst since accrued interest is not discounted.
But since we dont know how many coupon payments are left we cannot caclulate the YTM for this problem and hence have to take above calculation as a proxy. Correct me if I'm wrong
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