Let's assume that the company's fiscal year ends Dec. 31. This is important because we will assume no depreciation the first year.
A purchase of equipment is considered a capital expenditure (CapEx) which doesn’t impact net income. And since we are also assuming no depreciation, there is no impact to net income and no impact to the income statement.
There is no change to net income so nothing changes in cash flow from operations. The $100 increase in CapEx means there is a $100 use of cash in cash flow from investing activities. There is no change in cash flow from financing since this is a cash purchase so the net effect is a use of cash of $100.
Cash (asset) is down $100 and PP&E (asset) up $100 so no net change to the left side of the balance sheet and no change to the right side. We are balanced.
Here we will assume straight line depreciation over 5 years and a 40% tax rate.
We have $20 of depreciation, which results in a $12 reduction to net income.
Net income is down $12 and depreciation up $20. No change to cash flow from investing or financing activities. Net effect is cash up $8.
Cash (asset) is up $8 and PP&E (asset) is down $20, so the left side of the balance sheet is down $12. Retained earnings (shareholders' equity) is down $12 and we are balanced.