Help Modeling Out a Statistics Scenario to Prove Statement

[LCM9001]

Context: I'm a salesperson that works for a company that has a product that helps to increase Influenced Hires, a company would want to hire more Influenced Hires because they have a 27% higher promotion rate than Non-Influenced Hires.

Based on the assumption that employees that are promoted are highly engaged employees, and studies show that highly engaged employees produce 21% more profit, I want to illustrate to clients the potential positive financial impact increasing their percentage of Influenced Hires could have on Revenue by investing in my company's product.

Some assumptions & inputs:
- Company made 55 hires in the past year, if relevant/necessary we can assume the company will make 55 hires in each of the next 3-5 years (if longer timeline is helpful to proving statement that's fine)
- Company had a 35% Influenced Hire Rate in the past year
- Median Salary at company is $100,000
- Organizational Value of each Employee is 2x their annual salary, meaning each employee is expected to generate $200,000 in Revenue
- Profit margin stays constant year over year meaning the 21% more in profit mentioned earlier can be applied to revenue
- Average promotion rate in the US is 10%
- Influenced Hires have a 27% higher promotion rate than Non-Influenced Hires
- Employees promoted are highly engaged & highly engaged employees produce 21% more profit

I've been running into issues doing the math and it showing that despite a 27% higher promotion rate, the expected number of promotions for Non-Influenced Hires comes out to be higher than the expected number of promotions for Influenced Hires.

I think that might be because I'm using the 35% Influenced Hire Rate when in order to support my claim, I'd need to be using a 50:50 split, but math is really not my strong suit so need confirmation if using a 50:50 split is ideal or not.

It could also have something to do with using too short of a timeline?

What would be the best way to model this out to support my claim?