I am the owner of a single-member LLC and am taxed as a pass through entity. At the beginning of the year is a pass through entity’s cash balance always considered $0 with respect to a balance sheet? How can a pass through entity maintain savings from a previous year’s profit? Hypothetically, if I pay a bill for the company on Jan 1 (i.e. before any profit is made) is this considered an additional capital investment?
How can a pass through entity maintain savings from a previous year’s profit?
This is the concept of retained earnings. A corporation can pay out after tax profits to shareholders or retain them for future use, but they are taxed in either case. Same goes for you as a sole proprietor, you'll pay income tax and self-employment tax on the profits whether they are retained or not.
If so inclined, the sole proprietor would track money he contributed to the business initially and retained earnings in an Owner's Capital account, and track payments out from the business in an Owner's Draw account.
Since the distinction has no tax implication, many don't bother.
No. You're confusing the functions of the Balance Sheet and the P&L.
Your P&L starts the year at zero, because it's an accumulation of credits and debits over the year.
Your Balance Sheet starts the year exactly where the last year ended, because it is a snapshot of where your assets and liabilities stand at a given point in time.
(Also though, given that you are taxed as a pass-through and presuming you're talking about US tax laws, the Balance Sheet is not very relevant to your tax situation. Schedule C only cares about line items on your P&L.)