I will ask the following non-rhetorical question first: what is the need for re-branding in the first place if the “brand equity” is immense?
Vital information may be missing here that can be collected via the following sub-questions:
- Are we dealing with a new product by the brand OR new customers OR new markets?
- Your brand equity is immense and superior, but is it “negative” or positive” for your new positioning?
- Is it needed for the repositioning to a new customer segment that is willing to pay for “cheaper” more generic products than “branded ones”?
I believe the core of your question lies in the word “simultaneously”. And I think that in doing both simultaneously, the risk is higher and indeed closer to a suicide (if it fails). Why? That is too much change at once! Besides, to which one will you attribute a possible failure and how much time, effort and cost will such inquiry entail before you can reverse damage?
You may want to re-position first, benefiting form the superior brand name you have and the value derived thereof and see the result. Second, if you want to offer a different price-category, you may want to re-brand and see the effects of such action, better to pilot it and research it thoroughly first.
In many cases, considering an “endorsed identity” is much safer, one that derives trustworthiness, value, quality and recognition from the mother brand but offers “almost-the-same-for-less”. One that you can “easily” (=with minimal damage incurred) withdraw from without “self-killing” your mother brand.