The myth* is as follows, and it perpetrated in particular by bankers:
"Companies (especially banks) like financing their activities with loans rather than with share capital, because the cost of share capital is higher."
i. Nonsense. There are ten million worthy articles, books and theses about the ideal mix of loans and shareholders' funds (share capital, retained profits) and the short answer is that a business, any business, exists to make a profit and then we have to invent rules as to how these profits are to be shared out.
ii. Once wages, expenses and taxes have been paid, the remaining profit goes to the "owners", be they sole traders, partners, members, shareholders or bondholders, these are just legal-contractual arrangements to say how profits will be split up and do not really affect the actual profits made by the actual business.
iii. Let's ignore borrowing from banks for the time being as this is negligible anyway and such lending to business as exists usually relates to land and buildings.
iv. With a sole trader, partnership, a building society or a co-operative, there usually isn't any split (in economic terms) between "owners' funds" and "loans from owners", the split only exists with companies limited by shares.
v. Now, some people like to play safe and prefer investing in corporate bonds because they are lower risk and lower return; other people like investing in shares because they are higher risk and higher return, so it makes sense for a business to tap both sources, but overall it all averages out. If there are more bonds, then they become riskier and demand higher returns, and with higher leverage, the shares also become riskier and demand higher returns, but they are fighting over the same pot and the size of the pot doesn't change.
Really, it is a principal-agent problem
vi. Senior managers of quoted companies are often paid according to how well the share price** is doing and not according to how well the underlying business is doing, so for them it makes sense to gamble and gear up by borrowing to fund expansion rather than using retained profits, or borrowing money to finance share buy backs etc. If the gamble fails, they gain or lose little, if it pays off, they get a disproportionate share.
vii. In particular, senior bankers (for whom share-price related bonuses are de rigeur) are wailing that higher capital requirements mean that their "cost of capital" increases. But the "cost of capital" is merely the sum total of profits paid out to its owners (shareholders and bondholders) and while at any point in time the payments/reward to £1 shareholders' funds is higher than the payments/reward to £1 of borrowing/bonds, shifting from bonds to shares does not increase the total "cost of capital".
How can it? "cost of capital" just means "profits" which are largely unaffected by these shenanigins i.e. if the business/bank uses more shareholders' funds, then the amount is pays bondholders goes down (in absolute terms and as a % of bonds outstanding) and the amount it pays shareholders goes up in absolute terms and down as a % of shareholders' funds. The total income and the total profits stay the same. It's like somebody complaining that his wages will go down if he gives his wife more housekeeping money. It's like a sole trader complaining about his own drawings from the business, or an owner-manager complaining that his salary is too high or his dividends are too high.
viii. So what these senior bankers really mean is that higher capital requirements mean that their bonuses would go down, is all.
* For further debunking of this and similar EM's particular to the banking sector, see this article in The Economist.
** The share price is in turn a nigh meaningless figure, being calculated on the basis of two consensus wild guesses - future profits and the appropriate discount rate. Future profits are unearned income in the literal sense that they have not been earned yet, and there is all sorts of other manipulation going on and people have to try and guess how successful any business or industry will be at lobbying for tax breaks, subsidies, regulations etc.
