Stepping up its share repurchase authorization is the right move for American International Group (NYSE:AIG) to create immediate value for shareholders. As long as AIG's market price remains below its book value, share buybacks make a heck of a lot of sense, driving book value per share growth, and, ultimately, AIG's share price.

And by recently announcing that it is going to step up its share repurchases to the tune of $2 billion thanks to the recent ILFC sale which should further support AIG's book value growth and share price.

A pretty great deal
Not too long ago, American International Group tried to sell 81% of its aircraft leasing unit ILFC to an investor consortium including P3 Investments and Taiwan's Fubon Group, but the deal ultimately fell through as the consortium struggled to come up with the financing for the deal. American International Group eventually sold its aircraft leasing business to AerCap Holdings N.V. (NYSE:AER) for $5.4 billion at the end of last year.

While many analysts were skeptical about whether AIG would be able to sell ILFC at all, the insurance company actually negotiated quite a neat deal for AIG shareholders: As part of the purchase agreement, American International Group was getting paid $3 billion in cash and received about 97.6 million in newly issued AerCap shares, valued at approximately $2.5 billion dollars and gave American International Group an approximately 46% stake in AerCap.

Since AerCap's shares kept soaring after the deal, American International Group now sits on book value gains of around $2.3 billion, giving the insurance company more firepower to deploy capital for share repurchases.

The clearly positive, but unexpected, deal outcome now allows American International Group to materially upsize its existing share repurchase authorization and deliver value to shareholder via additional share repurchases.

Fueling growth with buybacks
Last week, American International Group announced that its board of directors had authorized additional share repurchases in the amount of $2.0 billion. This comes after the insurance company heavily repurchased its own shares in the first five month of 2014. In the first quarter of 2014 alone, American International Group spent approximately $867 million on share buybacks and another $418 million since the end of the first quarter.

Share buybacks are an essential part of American International Group's capital management strategy, and share repurchases at market prices below book value are accretive and actually spur book value growth.

Since American International Group still trades at a 25% discount to book value five years after the financial crisis, accretive share repurchases are clearly the right strategy to create value for shareholders.

Since the end of 2012 American International Group has grown its book value by approximately 8%. With an additional batch of share repurchases below book value and continued earnings growth, American International Group's book value per share is set to experience another boost in the coming quarters and years.

Source: American International Group, UBS Global Financial Services Conference Presentation

With an increasingly better earnings outlook and additional funds available for share repurchases from the AerCap deal, AIG's book value is likely to grow strongly over the next couple of years.