CFAI text V4 P112: Example 10 why, different, equation, example

Dapper425

How come the answer indicates the new bond market value = dollar duration of old bond / DOLLAR DURATION of new bond * 100? Yet the equation above example 10 (on the same page) indicates the new bond market value = dollar duration of old bond / DURATION of new bond * 100. Can anyone tell the why it’s different?

needhelp1700

thanks, this is very helpful! sometimes the wordings are little bit confusing…

leadcfa

The fixed-income readings are vague and sometime can be misleading ! I spent very much time but still some questions remained.

Nishant1

So, to say “dollar duration of 4.5 per bond” is the same as to say “duration of 4.5”?
Sorry to beat to death, but I re-read the passage 3 times & your response and it hasn’t sunk in yet.

ShooterMcCFA

I am sorry again that I made mistakes again because I am in a hurry.
Please double check if I am right in deriving the formula as follows.
DD(N)pb = D(N) x MV(N)pb x 0.01 = D(N) = DD(N)pb/ [MV(N)pb x 0.01]
= D(N) = [DD(N)pb/ [MV(N)pb] x 100 = [DD(N)pb x 100]/ [MV(N)pb]
= MV(N) = [DD(O) / D(N)] x 100 = [DD(O) x 100] / {[DD(N)pb x 100]/ [MV(N)pb]}
= [DD(O) / DD(N)pb] x MV(N)pb
PV(N)
= MV(N) x [PV(N)pb / MV(N)pb] = {[DD(O) / DD(N)pb] x MV(N)pb} x [PV(N)pb / MV(N)pb]
= [DD(O) / DD(N)pb] x PV(N)pb
In this example DD(O) = 220,000 DD(N)pb=5x90x0.01=4.5 PV(N)pb = 100
= PV(N) = (220.000/4.5) x 100 = 4.899M
PV(N) : Total par value of new bond
PV(N)pb : par value per new bond
It is simplified in the example while actually it is complicated !