A company raises $100 of debt to buy equipment. Walk me through the three statements at the time of purchase.

At the time of purchase, nothing changes on the income statement. Raising debt isn't revenue, and buying equipment isn't an expense. It's a capital expenditure, so it goes on the balance sheet as an asset. On the cash flow statement, raising the debt is a $100 inflow in cash flow from financing. Buying the equipment is a $100 outflow in cash flow from investing. So cash goes up and then back down. Both items sit outside cash flow from operations, which doesn't change, so the net change in cash is zero. On the balance sheet, PP&E is up by $100 on the assets side and cash is unchanged. Debt is up by $100 on the liabilities side. Equity doesn't change, so both sides are up by $100 and it balances. The company is bigger by $100 on each side, but shareholders are no better or worse off.

At the time of purchase, nothing changes on the income statement. Raising debt isn't revenue, and buying equipment isn't an expense. It's a capital expenditure, so it goes on the balance sheet as an asset. There's no interest or depreciation yet either, because no time has passed. On the cash flow statement, raising the debt is a $100 inflow in cash flow from financing. Buying the equipment is a $100 outflow in cash flow from investing. So cash goes up and then back down. Both items sit outside cash flow from operations, which doesn't change, so the net change in cash is zero. On the balance sheet, PP&E is up by $100 on the assets side and cash is unchanged. Debt is up by $100 on the liabilities side. Equity doesn't change, so both sides are up by $100 and it balances. The company is bigger by $100 on each side, but shareholders are no better or worse off. That's only at the time of purchase. Later on, the income statement does change. Say after one year, with 10% interest and a ten-year useful life, there's $10 of interest and $10 of depreciation, so pre-tax income is down by $20. At a 25% tax rate, net income is down by $15. On the cash flow statement for that year, I add back the $10 of depreciation, so cash is down by $5, assuming no principal is repaid. On the balance sheet, cash is down $5 and PP&E is down $10, so assets are down $15, which matches the $15 drop in retained earnings.