R19.P1.T3.Hull-Chapter 6- Conversion Factor

[gargi.adhikari]

In reference to R19.P1.T3.Hull-Chapter 6, Pg 86- Conversion Factor:-
Price (at Last Coupon) = $ 109.43-- is this a given parameter or we calculated this ?
Full Price = $ 111.06 -- is this a given parameter or we calculated this ?
What formula did we use for PV here =?
How is the Years(since last coupon)= 2.5 years ...? since last Coupon Dt was = 1/1/13 and Next Coupon was = 7/1/13.....?

Can someone please elaborate the calculations on this page or at least point me to the relevant sheet in the Learning Spreadsheet...?

 

[bpdulog]

To get to $109.43, you can use the TVM calculations on your calculator. However, since coupons are paid semi-annually you need to make sure:

-If time to maturity is expressed in years, multiply by 2 (N=5)
-Enter yield divided by 2 (2%)
-Enter coupon divided by 2 ($4 per $100 par value)


After, to get to the $111.06 you take the $109.43 and future value it by the yield times the 1-remaining maturity, as you circled above: $109.43*1.02^.75=$111.0674; .75=(180-45)/180

Then you can subtract the AI of $3=$4*((180-45)/180) to get $108.06

 

[David Harper CFA FRM]

Thank you @bpdulog, well done!

@gargi.adhikari I realize there is a typo (sorry), you are correct about the 2.5 years: bond should mature in 7/1/2015 (not 7/1/2016). Here is a spreasheet that shows the calculations if we assume the bond matures in 7/1/2015: http://trtl.bz/Hull-Ch6-ai-example i.e.,

The full (dirty) price at the last coupon date (i.e., 1/1/2013) = -PV(4%/2, 2.5*2, 100*8%/2, 100) = $109.43 which implies a full price at settlement of $109.43*(1+4%)^(135/180) = $111.06--which is equal to the discounted cash flow price--such that the clean price on settlement = $108.06 = $111.06 - 3.00. Sorry for the confusion, but awesome catch on your part. Thank you!

Also, here is a worked problem with helpful comments at https://forum.bionicturtle.com/threads/l1-t3-170-clean-versus-dirty-bond-prices.4561/

 

[gargi.adhikari]

@David Harper CFA FRM @bpdulog Thank you both for the above