June 3 (Reuters) - APM Human Services International said on Monday it would be bought by U.S.-based private equity firm Madison Dearborn Partners (MDP) in a deal valuing the Australian company's equity at A$1.3 billion ($865.2 million).

The Australian employment services firm has been a takeover target since February this year as it battles a labor crunch amid concerns around higher wages and increasing rent, and higher drawn debt balances.

Under the scheme with MDP, APM shareholders will receive A$1.45 in cash per share, representing a premium of about 16% to the stock's last close of A$1.25 on May 30.

Shares in APM, which were halted on May 30, advanced more than 11% by 0038 GMT, while the benchmark S&P/ASX 200 index was up about 1%.

MDP, which is APM's top shareholder with a 29% stake, had offered in April to buy the remaining 71% of the Australian employment services firm it does not own for A$1.40 apiece, slightly below the new offer price.

Before that, APM had rejected a A$1.60 per-share bid from private equity firm CVC, which later won due diligence with a higher A$2 apiece offer. APM, however, walked away from the offer.

The APM board unanimously recommended on Monday that shareholders vote in favor of the scheme with MDP, in the absence of a superior proposal.

APM has been reeling from low client flows in its employment services businesses in Australia and the UK through April and May, with full-year profits now expected around the bottom end of the forecast range.

The company in April forecast an underlying net profit after tax and amortization between A$95 million and A$105 million for fiscal 2024, lower than the A$178.2 million posted last year.

APM expects activity levels seen in the second half of fiscal 2024 would continue into 2025, it said.

Implementation of the scheme is expected to occur before the end of 2024.

($1 = 1.5026 Australian dollars) (Reporting by Roushni Nair in Bengaluru; Editing by Jacqueline Wong and Subhranshu Sahu)