Clean Dirty Bond Price

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Libre27

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CFA Volume 5 Reading 67 Question 9A:
Suppose that a bond is purchased between coupon periods. Days between settelment date and next coupon period are 115. There are 183 days in the coupon period. Suppose the bond purchased has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining.
What is the dirty price for this bond if a 5.6% discount rate is used?
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I keep getting 107.756 even when I calculate the PV of the cash flows the same way CFA did it in the solutions, yet they have 108.8676. What am I missing here? Am I somehow not including the accrued interest correctly?
Thank you for any help.
 
Hi there:
The reason why you are getting the question wrong is the following.
To calculate the full price (the price that the bond purchaser is paying), you must discount the payments using the the time remaining for the next coupon AT THE TIME OF PURCHASE.
We know the following:
115 days until next payment in a 183 day period so: 115/183 = 0.628 is the first coupon payment interest earned for the recent bond purchaser.
Period 1: 0.628
Period 2: 1+0.628
Period 3: 2+0.628
and so on…
Therefore:
PV = 3.7/((1+0.56/2)^0.628) + 3.7/((1+0.56/2)^1.628) + …… (3.7+100)/((1.056/2)^(10-1+0.628))
This gives you the correct answer.
(There is no quick way I have found to do this in the calculator. Note the calculator assumes you purchase the bond with 1 full period to the next coupon payment).
Hopes this helps,
Ali
 
Describe your method. I get
29.38 + 79.49 = 108.87.
The ‘powers’ in the PV calculation should be .6284, 1.6284, …, 9.6284. The coupons are 3.7, and use a discount rate of 2.8 (semi annual).
 
You can simplify the calculation by calculating the PV of the bond at the next coupon payment then discounting it back by 0.628 periods
Calculate the PV of the bond at the next coupon payment
I/Y = 2.8 = 5.6/2; N = 9; PMT = 3.7; FV = 100
CPT -> PV = -107.07
Add back in the first coupon payment to get the PV of the bond including the next coupon payment on the date the payment is made
107.07 + 3.7 = 110.77
Discount that back by 0.628 periods
110.77/ (1.028^0.628)
= 108.86
 
Thanks for the help. This clears it up for me.
 
I realize the question has been answered … yet. If you have BA-II Plus, this approach might be easier. This is assuming bond matures on 12/31/1995 when settlement date is 3/9/1991 (you can choose year/date as per you convenience as long as the 115 days thing is factored in)
2nd Bond
(V) SDT (V) CPN (V) RDT (V) RV (V) ACT (leave as is)
(V) 2/Y (set as reqd)
(V) YLD (V) PRI (CPT) —-> 107.48985
(V) AI ——> 1.39006
 
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