I run a digital design business and I have to take on an additional designer to handle an increased workload from my main client. The client  is willing to pay for the added design resource plus a markup for my project management time (I will be designing and managing) but I'm not sure how to add this fee or what it should be . The idea is that the client will be able to scale and take on more business with our help, and it will also allow me to scale my business in the process. 

I estimate I will spend about 25% of my time managing the other designer, the rest of my time designing. So, do I add 25%? And do I add it onto MY rate or the total of my rate + designer rate? I'm not sure what the correct formula would be.

The additional designer rate = $30ph and my rate = $50ph.

I've mostly been a one man band until now so it would be good to get some experienced guidance on this.