I sometimes find these pricing issues to be comical. OK, I'm coming from a position of not needing to chase work, so I'm feeling secure. So here's my view on this scenario.
As an individual businessman, you know the standards you work to. You know how much effort, investment, technology and knowledge it has taken you to achieve this position. You have put a value on your services. You are now putting yourself in a position whereby you may be prepared to lower the value of your service in order to make a sale (ie you want to achieve the largest return possible, but are prepared to lower your price to obtain the work).
For me, with my set up, this type of work is very demanding. Soiling levels are higher than normal. Gum is a time consuming issue. The hours worked are usually unsociable. Extra labour and costs are frequently required to complete the work within the timeframe. You will frequently be spending the following day in bed. So, with all these extra demands, I would be tempted to charge a premium rather than discount. I would sell firstly on quality. That's imperative. Also quote a lower price for following up with a planned maintenance program. With your initial clean, you may need to move downwards a little on price, but not too much. For everthing you give, you want something in return. For example, you could work the unsociable hours without charging a premium. Ditto the extra labour costs for completion within a limited time frame. You may offer X% discount for payment in 7 days or upon completion. Maybe a little too if the floor is cleared of all furnishings etc. But to offer a lower price in order to win on price is, for me, a no no. That is not the way to build a sustainable business or attract the type of customers I want.
Safe and happy cleaning

Ken