Do companies destroy value when they borrow to pay dividends?

Not inherently. If the company growth rate is greater than the interest rate there is no negative consequence. All good debt is good debt because you earn more from your investments than the cost servicing the debt. Bad debt is the opposite.

Interest rates have been very low for publicly traded companies, historical lows.

If a company's revenue stream is disrupted, and other capital sources are disrupted, then the debt will compound the issue. Dividends would likely have been cut long before then.

Borrowing money and paying out dividends are separate events. Paying out dividends decreases stock price. Whether the dividends "came from" borrowing is somewhat incoherent; money is fungible. So the only question is whether borrowing destroys value, not whether borrowing money when preceding a dividend destroys value.

In an efficient market, When a company borrows money, that does not affect stock price. Total value is increased, but liabilities are increased equally, so equity value remains constant. Responding to a question in the comments: if a company borrows $100m and now owes $110m in principal+interest, isn't their increase in liabilities ($110m) greater than their increase in total assets ($100m)? No, because their increase in total value is 100m of today dollars, and their increase in liabilities is 110m in tomorrow dollars. If the going interest rate is such that they have to pay $10m in interest, that means that the market has said that 110m tomorrow dollars have the same value as 100m today dollars, so their net book value is unchanged (again, this is assuming efficient markets). Interest is compensation for the risk level of the debt. The company loses money in the sense of paying interest, but it does so by offloading some of its risk onto lenders, and this lower risk level increases its value equal to the interest paid. Looked at another way, the company has money now, which it can apply to some current expenditure, and that expenditure will presumably give a return whose expected value is equal to the interest.

Companies borrow money all the time. It is a much easier source of cash, than having it floating around the company all the time. You should in general try to limit capital not in use, which then as a matter of fact also applies to cash. As long as the cash flow is positive, and the yearly result is positive, borrowing to pay dividend shouldn't be an issue at all. Cash - liabilities - obligations - assets - equity - it is all just capital you either have or owe in different grades of liquidity.

In a well balanced system there really is only a miniscule difference between the opportunity cost of having cash around, and the interest cost of borrowing it.

Money is fungible. That means that once my paycheck goes into my pocket, it becomes indistinguishable from the money I picked up off the ground. Often people will treat personal 'windfall' money (especially 'my tax refund', which is just the government paying you back money they over-withheld from you during the year) as money above-and-beyond their regular budget, but once the money has been earned, it is just money - and being responsible with a $500 paycheque and being irresponsible with a $500 tax rebate in the same month just means you were 50% responsible that month.

For a corporation, this remains true with a small caveat - was money borrowed with the express intent to pay the dividend? And why was that decided that way? Assume two cases:

• Assume a company has multiple sources of financing, $10B of assets, and pays $100M of dividends per year. Some years, debt will overall go down, based on repayment structures, and various cash intakes through the years. Some years, debt will go up, based on new cash needs like capital investment, etc.. In a year where debt happened to go up by $1B, if that $100M of dividends remained constant, you could argue that the dividend was 'financed by debt', because with no dividend, the company maybe could have just borrowed $900M instead. But a financially healthy company will have its debt levels fluctuate, and it is largely pointless to tie 'this' financing to 'that' project.

The key here is that some level of debt is actually healthy in most industries. This is because debt is cheaper than equity, in the sense that debtholders might only want a 4% interest payment, but shareholders might expect a total return of 10%, between dividends and value growth of their shares. This remains true until so much debt is taken on that the company actually has insolvency risk, where it might possibly default on debt and have to declare bankruptcy.

• Alternatively, assume a company is similarly positioned, has $10B of assets, and regularly pays $100M of dividends. Assume profit is down one year, cash reserves dry up, and it looks like paying the dividends won't be possible. Management has 2 options to try and keep the dividends constant - sell assets or take on debt. They take on $100M of debt. Now the same thing happens 2 years in a row. Suddenly 5 years later the company has an extra $1B in debt as a cash crunch starts to snowball, and interest rates they are getting become less favourable, and the risk of insolvency rises. In this case, every time they take on debt, their debt to equity ratio continues to rise, and they are ultimately becoming more and more risky from a potential bankruptcy perspective.

So, in cases where the company is not financially healthy to take on more debt, taking on debt to pay dividends, rather than responsibly deferring dividends for that year, could be a sign that management is unable to 'correct the ship' and bring the company back to profitibility.

It is not whether debt 'was used for' dividends [because fungible money means that is not truly a relevant concept], the key question is - can the company afford more debt at all, and is this dividend coming at the cost of insolvency risk? This comes back to your theory that taking debt increases interest costs and therefore might itself destroy value - that is only true if the debt is unaffordable, and otherwise could form part of a healthy mix of debt and equity financing. No single line item on the financial statements tells you whether something is good or bad, the context is relevant to understanding the impact of a particular item.