When you know the cost of equity with no gearing and you want to calculate what it will be with gearing (or vice versa).
You can always calculate by gearing or ungearing the beta using the asset beta formula. But if you aren’t given the beta than it is a little bit faster to use the MM2 formula (rather than have to calculate the beta yourself first and then use the asset beta formula).
From memory it has only been useful one time in the exam 🙂