Determining the "Cost" of One Additional Housemate

[Kevin Fritz]

Hey everybody,  

Thank you for taking the time to read this post.  I am trying to determine our real cost of having one extra person live in our household.  
Below is an overview of our unusual housing situation, followed by the goal/problem we are trying to solve.

Situation:

My wife and I own our primary residence in Sonoma County, CA.  We have offered a bedroom and bathroom in our home to an old friend as she works on getting established.  She wants to contribute monetarily, and doesn't want to "cost" us anything by living here.  

Goal:

Determine the "Break-even" cost of having one additional adult (and dog) live in our home.  We do not want to turn a profit. 

We can easily determine the additional cost of electricity, gas, water usage, and consumables (paper towels, laundry detergent, cleaning products, etc.).  We are looking for insight regarding calculating depreciation/wear/repair costs of common use items (refrigerator, freezer, W/D, gas fireplace, A/C, furnace, oven, stove, dishwasher, water heater, water softener, etc.).  Does anybody know a rule-of-thumb for this sort of cost, or the acceleration of wear with additional use?

I know this is an unusual case.  She is insistent on costing us nothing, and we are insistent on helping without monetary profit.  We are looking to provide her with an accurate estimation of her "consumption" while living here.

We appreciate your time, and thank you for your help!

Kevin (and Maddy)