I manage a band and want to pay a studio to record them—I have both a business and personal account with funds. How is my equity affected if I pay out of either to the studio?
Basically, any money you put into the business with personal funds is a loan into the business to be paid back. Lets say you put in $10. At the end of the year you profit $100 dollars. That $100 goes back to you as owner, however only $90 of it is considered taxable money since the 10 is just a payback of the loan.
That's the simplified version, assuming you're an LLC or S-Corp. Talk to an accountant to get advice relevant specifically to you.
Personal Funds are loans to the Company or Equity Contributions. This does not change your net income or what is taxable to you as the owner. If the Business nets $100, then you pay tax on $100. You can chose to pay yourself back with the $100 or not.
It sounds like you are renting studio space for your company (which would be a deductible rental expense for the business), and need to pay the invoices using either funds in your business bank account or personal bank account.
If you pay for business expenses using the company funds, the payments are deducted as an expense which reduces the company's net income for the period. Anytime an expense is incurred at the company level, this is a reduction in the overall equity of the company. It doesn't impact your equity account directly. The net amount of income over expenses for the year is closed out to the company's retained earnings, which is a part of the company's total net equity.
If you pay for the studio rental expense with personal funds, the expense is still a business deduction on the company's accounting records. However, because the expense was paid using personal funds, you need to record an additional entry to evidence your contribution for the expense. This can be recorded as either an equity contribution or a loan to the company. For example, the transaction would be recorded on your general ledger as a Debit to rental expense, and a corresponding Credit entry to either "Loans to Owners" (a liability account) or to "Additional Paid in Capital" (an equity account).