COGS for Construction Contractor

Let's break these apart a bit:

"They supply everything, however often times he has to purchase additional materials for various reasons."

If that is materials to be consumed on the job, that is COGS and can be job tracked, as directly for that job, if that also matters. If that is, for instance, he is getting low on Caulking and needs to pick some up while en route, that is just Supplies expense.

"Sometimes it’s tools he’ll use later on other jobs."

Tools are Never COGS. Saws, for instance, are either Fixed assets or his own Equipment expense. COGS would be Saw Blades that get used on the job; if they last 2-5 years, that is also not COGS. That is Supplies expense.

"So my question is on the additional and unexpected supplies and materials he uses to install on job does that go to COGS or expenses and does the tools book as inventory?"

He is not Buying tools to sell them as a retailer, so nothing here is Inventory.

"Sometimes he eats the cost of materials"

Yes, you Always see this as Gross COGS. "Eats" just means, there is no direct offsetting Income from this; his Contract Price Point is supposed to cover the incidental and direct costs, the costs for operations, overhead, operating the vehicle, etc.

"or bills it back to store he has contract with."

Which then makes an Income flow, as gross revenue. But a Contract con be "cost inclusive" like a Bid Price. I would not charge you for individual supplies if we agreed to a Fixed Bid Contract.