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Deciding whether to buy back stock when it's trading at a high valuation is easier said than done in the bank industry. Image source: iStock/Thinkstock.

Being the most profitable big bank in the United States presents U.S. Bancorp (NYSE:USB) with an enviable problem: Its shares trade for upwards of three times tangible book value.

This may not seem like a problem, given that having one of the most highly valued stocks in the bank industry is a testament to U.S. Bancorp's success and a just reward to long-term owners of its shares. But there is a downside to U.S. Bancorp's richly valued stock.

Because banks tend to spend a third or more of their earnings on share buybacks, this means that U.S. Bancorp is repurchasing its stock at a steep premium to its tangible book value.

The issue with stock buybacks

The recent surge in bank stocks has brought this issue to the fore. "I've always had an issue about stock buybacks," said JPMorgan Chase (NYSE:JPM) CEO Jamie Dimon at an industry conference in early December. "If you're forced to buy back stock and the stocks eventually are high, you shouldn't be doing that to your capital.

Warren Buffett has said the same thing, writing in his 2011 letter to shareholders of Berkshire Hathaway (NYSE:BRK-A) (NYSE:BRK-B) that:

Charlie [Munger] and I favor repurchases when two conditions are met: first, a company has ample funds to take care of the operational and liquidity needs of its business; second, its stock is selling at a material discount to the company's intrinsic business value, conservatively calculated.

We have witnessed many bouts of repurchasing that failed our second test. Sometimes, of course, infractions -- even serious ones -- are innocent; many CEOs never stop believing their stock is cheap. In other instances, a less benign conclusion seems warranted. It doesn't suffice to say that repurchases are being made to offset the dilution from stock issuances or simply because a company has excess cash. Continuing shareholders are hurt unless shares are purchased below intrinsic value. The first law of capital allocation -- whether the money is slated for acquisitions or share repurchases -- is that what is smart at one price is dumb at another.

Holding all else equal, a bank that's able to repurchase its stock over a long period of time for 1 times tangible book value can more than double the return of a bank that buys its stock back for 3 times tangible book value.

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Assumes a 14% return on tangible common equity; that earnings are split evenly between buybacks, dividends, and retained earnings; and that dividends are immediately reinvested into shares of common stock. Chart and calculations by author.

The catch-22 of bank buybacks

This seems to make the issue pretty simple: Just like Buffett has done at Berkshire Hathaway -- he says he won't repurchase stock unless it dips below 1.2 times book value -- a bank like U.S. Bancorp seemingly shouldn't be buying back stock at high valuations either.

In the third quarter, U.S. Bancorp spent $660 million repurchasing stock at an average price of $42.53 a share. That equates to 2.2 times tangible book value. Fast forward to today, and its shares are trading for 2.7 times tangible book value. Buying back stock at the current level, in other words, seems like a surefire way to slow the rate at which the Minneapolis-based bank creates shareholder value.

Unfortunately, however, the question of whether to continue doing so at these levels is more complicated than it seems. This is because the two other ways U.S. Bancorp can allocate its earnings have downsides as well.

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Data source: U.S. Bancorp's 3Q16 10-Q, pages 37-40. Chart by author.

No good options

If U.S. Bancorp retained the third or so of its earnings that it uses to buy back stock, then its profitability would suffer. This is because capital is in the denominator of a bank's return on equity, the preferred profitability metric tracked by investors and analysts. As shareholders' equity goes up, profitability goes down.

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A serious consequence of allowing capital to accumulate on U.S. Bancorp's balance sheet is thus the pressure it would exert on it to expand too aggressively, taking on too much risk, in an effort to abate the decline in profitability.

The other alternative is to increase U.S. Bancorp's dividend with the capital that would otherwise be used for buybacks. But there are problems here as well. In the first case, the incremental shareholder value from even over-priced buybacks would no longer accrue to U.S. Bancorp's long-term shareholders. It would be released instead into the proverbial ether, landing as cash in investors' retirement and brokerage accounts.

Moreover, the Federal Reserve, which exercises strict control over big bank capital plans, has made it clear that it favors buybacks over dividends and would prefer that banks pay out no more than 40% of their earnings via dividends. According to the Fed's logic, buybacks can be canceled at any time with little impact on a bank's stability, whereas cutting a bank's dividend can lead depositors to question the bank's solvency, igniting a run on its liquidity.

This leaves a bank such as U.S. Bancorp (as well as JPMorgan Chase for that matter) with two bad options: Temper the rate of value creation by repurchasing stock at a high multiple to tangible book value, or retain the earnings and accept that its return on tangible common equity will suffer. This is the enviable problem that great banks like U.S. Bancorp must navigate.

John Maxfield owns shares of US Bancorp. The Motley Fool owns shares of and recommends Berkshire Hathaway (B shares). Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.