Why are they using the price of the convertible bond and not the par value to calculate the conversion price of the convertible bond?
Because instead of converting the bond, you could sell it.
so i am assuming we always need to use the market convertible price right?
No need to assume it; you know it.
no, because we can use both the par value as well as the market value to calculate the conversion price. That’s why when I tackled the problem, I didn’t use the market value of the bond, but rather the par value. But I think here we are not hoping to convert the bond, but rather play with the mispricing which is why we use the market right?
Do not conflate the conversion price and the conversion value.
The conversion price does, in fact, use the par price/value.
The conversion value uses the market price/value.
The conversion price is used to determine how many shares you get per convertible bond (aka, the conversion ratio). The conversion value is used to determine whether or not to exercise the conversion option.