Shares of Honeywell rose as much as 4 percent after hours following news that Dan Loeb's Third Point had added to its stake in the company.

The hedge fund disclosed its stake in Honeywell in its first-quarter investor letter. As of Dec 31, Third Point owned 1.4 million shares of Honeywell, according to its quarterly filing.

The firm has substantially added to the Honeywell stake it reported at the end of last year, a person familiar with the fund told CNBC. Honeywell is a top-five holding of Third Point's now, the person said.

In the investor letter, Third Point said Honeywell's stock is trading "at a substantial discount to its industry peer group. Third Point believes that a separation of the aerospace unit via a spin off transaction would result in a sustained increase in shareholder value in excess of $20 billion."

In a statement, Honeywell said it "strives to keep an open dialogue with all of its shareholders. We are focused on enhancing shareholder value and will continue to evaluate all ideas that have the potential to help us achieve this goal."

Honeywell's aerospace segment is its largest in terms of revenues and represented just under 40 percent of the company's total annual sales of $39.3 billion in 2016. But operating margins for the aerospace segment were lower last year and it is expected to experience a second year of falling revenue in 2017.

The aerospace business has faced headwinds from an industry-wide slump in the business jet market as well as weakness in the defense and space markets. The commercial side of the business suffered a 13 percent slide in sales last year, while the defense and space portion was down by 7 percent.

That said, Honeywell has been helped by sales of Lockheed Martin's F-35 Joint Strike Fighter, a stealth aircraft with power thermal management systems built by Honeywell. Also, ongoing overhaul and repair of some legacy planes such as the B-52 operated by the U.S. military brings added revenue since the company provides aircraft instruments and aircraft accessories to support and sustain critical weapon systems.

Honeywell's new CEO, Darius Adamczyk, took the reins at the Morris Plains, New Jersey-based company on March 31 and has indicated one of his priorities will be to accelerate organic growth within the company, which has four different business segments: aerospace, home and building technologies, performance materials and technologies, and safety and productivity solutions.

One of its fastest growing areas is the home automation market, where it makes everything from high-tech thermostats to alarm systems controlled by smartphones. It also sells advanced lighting technology, including control systems and actual LED lights.

At Honeywell's analyst day event last month, Adamczyk also indicated he would focus on expanding margins, more aggressive capital deployment, and "transforming the company from an industrial company to a software industrial company."

"Spinning off aerospace would transform Honeywell into an industrial growth company with a focus on automation and productivity," Third Point said in its investor letter. The activist investor group said similar companies today enjoy a price-earnings multiple of 23 times, or roughly 30 percent premium to Honeywell's forward multiple.

Added Third Point, "A more focused Honeywell should match or exceed the multiples of its peer group, especially if management delivers on its commitment to return to free cash flow conversion in excess of 100 percent by 2018."

Historically, Honeywell has done more acquisitions than business divestitures. The company, however, last year year did spin off its $1.3 billion resins and chemicals business into a standalone, publicly-traded entity known as AdvanSix. It also sold the government services unit in the aerospace segment to KBR, an engineering and construction firm.

Honeywell said in its statement Thursday that its "management and board regularly conduct portfolio assessments and have a demonstrated track record of effective portfolio realignment and capital deployment actions."

The company added, "Regarding the Third Point investment thesis, we intend to take the time necessary to ensure a comprehensive, informed and objective review of the potential separation of the aerospace business."

In after-hours trading, Honeywell stock was up $6.12, or 4.7 percent, to $136.