Hi,
I am hoping to get some clarification regarding a business strategy. 
My SaaS start-up (stealth mode) is developing software for a specific industrial application. One of the big companies in the field who offers generic software feels that our focused software will be a nice add-on to theirs to provide value for their customers, who are a sizeable subset (15%) of our target market.
They are asking us to integrate our software as an addon to their main software but without our startup's name for this specific subset of customers.
At my previous employer, I had collaboration with this big company, and they are aware of our potential and the capabilities of the software. 
We initially planned to sell our software as subscription @ $ XX to general customer base. Now, they want to sell it to their customers without our name.  My question is what premium do we charge this big company? The premium is not for using our name and developing our brand with customers but at the same time, we get access to a good number of users. I do not want to quote a high premium so it may not be worth to them.
Here is what I had in mind when it comes to discussion:
 If we sell the software to individual customer, I get $ XX and some branding. As I am foregoing the branding and still giving you the value. Can we have a licensing deal for a lumpsum money and pricing for each subscription @ $XX (may be a small discount?)? This lumpsum will help us accelerate our product development. If the big company were to develop this add-on by themselves it will take more time and money than this lumpsum amount. In this case, it will be a win-win. Is this a good strategy?
 As I am not experienced, I would like to hear your thoughts and experiences.
Since our startup is in stealth mode and the discussions with big company is not yet public, I am sorry that I was not able to divulge more details regarding the exact application and more background. 
Thanks in advance,