Big oil companies like ExxonMobil, (XOM 0.23%) Chevron (CVX 1.04%), and Royal Dutch Shell (RDS.B) have a problem: They are struggling to grow. Exxon, for example, is bringing more projects onstream during 2014 than it has ever done before, but this is not going to be enough. 

Too big to grow
According to some sources, ExxonMobil is facing a decline rate of roughly 200,000 to 300,000 barrels a day. The company is having to buy or find oil production equivalent to one Hess Corp per annum just to break even; that's nearly $30 billion per annum.

Chevron is also struggling to drive growth. The company has nearly 100 projects coming onstream through the end of the decade -- 25 of these projects have a price tag of over $1 billion.

Originally, these projects were supposed to underpin Chevron's production growth through 2017. The company's output was forecast to hit 3.3 million barrels of oil equivalent by 2017, up from 2.6 million at present. However, this forecast has already been revised downwards to 3.1 million barrels as future uncertainties, project delays, asset sales, and a slowdown within the U.S. gas market all take their toll on Chevron's forecasts.

Hopefully, Chevron will not hit further headwinds that push forecasts even lower.

The problem is not just limited to Chevron and ExxonMobil. Shell's production has remained constant at 1.2 million barrels per day for the last three years. That said, the company is planning to ramp up production by around 600,000 barrels of oil equivalent per day through to 2017, just like Chevron. Once again, though, it is likely that Shell's growth will slow after this expansion.

So how do these oil majors grow? They return cash to investors.

Throwing out cash
Realistically, cash returns are the only way these oil majors are going to be able to drive earnings-per-share growth over the longer term and keep shareholders happy. Essentially, the investment case for big oil comes down to the question of who has the deepest pockets to fund the best share repurchase programs and dividends.

Unfortunately, this is where Shell falls down. While the company does offer an attractive dividend yield that currently stands at around 4.2%, the company's stock buybacks are only enough to offset the script dividend payment.

Both Chevron and ExxonMobil offer attractive cash returns, and high single-digit effective yields.

During 2013, Exxon returned a total of $11 billion to investors by the way of dividends and $16 billion in the way of share repurchases. Based on the fact that the company had 4.5 billion shares in issue at the end of 2012, that's a per-share cash return of $6, or an effective yield of 6.7% if you brought the shares at the beginning of 2013.

Meanwhile, Chevron returned a total of $7.5 billion to investors by the way of dividends and $4.5 billion in the way of share repurchases. Based on the fact that the company had 1.95 billion shares in issue at the end of 2012, that's a per-share cash return of $6.2, or an effective yield of 5.6% if you brought the shares at the beginning of 2013.

With these figures in mind, it would appear that Exxon is the better choice for investors as the company is retuning more cash and has a higher effective dividend yield.

Foolish summary 
Big oil's problem is the fact that these companies are struggling to expand production and drive growth. In order to appease investors, big oil is buying back stock and dishing out dividends. When it comes to the question of which company has the deepest pockets to fund these payouts, it would seem that ExxonMobil is in the best position. During 2013, Exxon returned cash to investors equivalent to a yield of 6.7%, a return better than almost any of the company's peers.