The stock, which closed up 2.7 per cent at $7.19 last night, has fallen about 15 per cent over the past year while the S&P/NZX 50 has gained more than 7 per cent.
A full break-up of Fletcher - with regional businesses, such as its Australian operations, split into stand-alone entities - should be given serious consideration, First NZ said.
Its $8.65 share valuation is based on an enterprise valuation of the business of $7.71 billion and net debt of $1.74 billion. The valuation is made up of $4.7 billion for New Zealand, $1.77 billion for Australia and $1.24 billion for the rest-of-the-world operations. Based on its assessment, the company is under-valued by up to $1.2 billion, the report said.
Devon Funds Management portfolio manager Nick Dravitzki said it was no secret Fletcher had struggled with its businesses outside NZ.
"If you could demerge and get reasonable prices for the Australian businesses in particular ... that would be seen as a potentially sensible thing to do," Dravitzki said. "Clearly the issue with [Fletcher] is it's this mix of an integrated, high-margin domestic New Zealand business with this array of businesses particularly in Australia that have no particularly logical reason to be together."
He said the company was already making moves to reorganise and enhance the value of its poorly performing Australian businesses.
Last week it announced it had received regulatory approval for the sale of Rocla Quarry Products in Australia to Hanson Construction for a post-tax profit of $85 million, which will be booked in the 2016 financial year.
Richard Stubbs, of Auckland fund manager Castle Point, said the scale and integration of Fletcher's New Zealand business made it the most valuable part of the company.
"If the less-integrated international parts of the business can be sold at a decent price it would not be a bad strategy."
Milford Asset Management executive director Brian Gaynor said further rationalisation of Fletcher's portfolio businesses could be expected over the next six to 12 months.
"I think the sale of some of those non-performing, non-New Zealand assets would be viewed positively as long as they get a reasonable price."
But Fletcher chief executive Mark Adamson said that while he believed the firm's shares were undervalued, a full break-up of the business wasn't being considered.
The reorganisation into five divisions and the Higgins buy would help add to the valuation, he said.
"There's a lot of juice still left in the Fletcher Building assets."
- additional reporting BusinessDesk