Hello, I am working on finishing up a case study about Marriott corporation and cannot understand the reasoning behind my solution. In this case study there is a question which asks for marriotts service divisions unlevered beta by using the companies overall beta. I found the solution, but I am having difficulty in saying why I used a certain method to find the unlevered beta. I used the following method.

Marriotte has three divisions, Restaurant, Lodging, and Contract Services. I know the percent of identifiable assets for each division. I know the unlevered betas (Bu) for the restaurant and lodging division as well as the Bu for the company overall. So I set up this equation and solved for the unknown Bu (contract services Bu=X).

(Percent of assets for restaurant*restaurants Bu)+(Percent of assets for lodging*Lodging Bu)+(Percent of assets for contract services*X)=Marriotts overall Bu.

I have been told this is the best way to solve for the Bu of contract services, but I don't know why. What does percent of identifiable assets have to do with finding beta? Or in this case, Bu.

As you can see here there is not real numbers in this problem, just an explanation as to why I am using this method to find Bu.

Thank you