Formula for par value of a bond

[sfad]

To find the par value of a bonds we can use:
Par value = market value of bond / par value per $ notional.
Can someone please explain the logic of this formula?

 

[S2000magician]

What study session / reading is this?

 

[cpk123]

This stems from the value of a bond being stated as a % of the Par value.
So a 96 bond means its Par Value = 100, and its value is $96 per $100 of Par.
Given that Market Value / Par Value per notional = Par Value.

 

[sfad]

This is reading 23, example 10 of the CFAI text. We want to maintain portfolio duration in changing portfolio holdings.
The new bond market value = (dollar duration old bond / duration of new bond) x 100.
Which in this example = (220,000 / 5) x 100
= 4,400,000
The bond is trading at $90 per $100 par, so par = market value / par value per notional.
= 4,400,000 / 0.9
I now understand why par = market / par value per notional, but what is the explanation of new bond market value = (dollar duration old bond / duration of new bond) x 100