KKR & Co LP has added a small sweetener to its bid for Australia's Pepper Group, caving to a demand from the non-bank lender's biggest shareholder and bringing the deal value to A$682 million ($543 million).

With the new offer, which sent Pepper's shares surging, the U.S. buyout firm gains a slice of Australia's A$1.7 trillion mortgage market while investors will be able to cash in at a 42 percent premium to its IPO price two years earlier.

KKR announced a special dividend of 10 cents per share while the investment company Perpetual Investments, which has a 14.7% stake in Pepper Group, emphasized that it has been a decent investment.

Keeping its strategic investments, in July KKR acquired WeMD health group for $2.8 billion.